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GLIMPSES OF A

NEW

PARADIGM

K.V.K. NEHRU

Reflections and Comments

Glimpses of a New Paradigm

How do We Meet the New Age Ushered in by the Reciprocal System?

Subversive Reflections on the Practice of Physics

Dialogue with D. B. Larson: Part I

Dialogue with D. B. Larson: Part II

Scientific Correspondence

Particle Physics

Lifetimes of C-Atom Decays

Lifetime of C-Argon, the Muon

Internal Ionization and Secondary Mass

The Lifetime of the Neutron

Relative Abundance of the Elements

The Inter-regional Ratio

The Nature of Scalar Motion

Electric Ionization

The Law of Conservation of Direction

Is Ferromagnetism a Co-magnetic Phenomenon?

Theoretical Evaluation of Planck‘s Constant

Superconductivity: A Time Region Phenomenon

On the Nature of Rotation and Birotation

The Photon as Birotation

Birotation and the Doubts of Thomas

Wave Mechanics in the Light of the Reciprocal System

―Quantum Mechanics‖ as the Mechanics of the Time Region

‗Non-Locality‘ in the Reciprocal System

Some Thoughts on Spin

High Energy Physics and the Reciprocal System

Astrophysics

Gravitational Deflection of Light Beam in the Reciprocal System

New Light on the Gravitational Deflection of Radiation Path

Gravitational Redshift according to the Reciprocal System

The Gravitational Limit and the Hubble‘s Law

Precession of the Planetary Perihelia due to Co-ordinate Time

Glimpses into the Structure of the Sun, Part I

Glimpses into the Structure of the Sun, Part II

Distribution of the Masses of Protostars in Globular Clusters

Intrinsic Variables, Supernovae and the Thermal Limit

The Quasar Paradox?

Radio Component Separation in Quasars

Another Look at the Pulsar Phenomemon

The Cosmic Background Radiation: Origin and Temperature

The Large-scale Structure of the Physical Universe

GLIMPSES OF A NEW PARADIGM

For centuries mankind has held implicitly the view that we live in a universe of matter

contained in space and time. All scientific theories hitherto have been built on this

paradigm. Now Dewey B. Larson introduces the new paradigm that motion is the basic

and sole constituent of the physical universe, and space-time is the content—not the

container—of the universe. We review in this article some of the highlights of his theory,

the Reciprocal System, which he develops from the new paradigm.

Introduction

The objective of this article is to introduce the physical theory being called The

Reciprocal System. Its originator, Dewey Larson, starting from two Postulates as

regarding the nature of the basic constituents of the physical universe and the

mathematics applicable thereto, builds a cogent theoretical structure that lays claim to

being a general theory. As it is impossible to outline the whole theory in the short space

of an article, an attempt has been made to present only those salient features that do not

require lengthy explanation and have a broad-enough scope to enable the interested

reader to appreciate its potentialities. More esoteric features of the theory have been

intentionally omitted from this preliminary treatment. They are, of course, available in

the published works of Larson[1-7].

The Conceptual Roadblock

The view that the physical universe is made up of basic units of matter, embedded in a

framework of space and time, has been held by the common man and the

scientist/philosopher for over the entire period of recorded history. Every new century

has brought new and revolutionary ideas about the Universe that shook and changed our

earlier views, but the concept of matter contained in a space-time background has

remained unquestioned. Larson finds that it is this concept—which we shall call the

concept of the universe of matter—that stood in the way of development of a truly

general physical theory, one that explains all domains of physical facts—from the atomic

to the astronomical—from the same set of fundamental premises. He has carried out the

needed review of the concepts of space and time and finds that the introduction of the

new paradigm, that the fundamental and the sole constituent of the physical universe is

motion, leads us to an understanding of all the physical phenomena, and makes possible

the construction of the long-sought after general theory.

To be sure, there have been earlier thinkers who attempted to build a general theory based

on motion as the fundamental constituent. Larson points out that the lack of success in all

earlier attempts was due to the fact that these thinkers failed to realize the crucial point

that in a universe based on motion (which is a relation of space and time), space and time

cannot have independent existence (or definition), that they cannot be regarded as a

background (or ‗container‘) for themselves. No matter what conceptual reforms these

thinkers introduced into physical theory they all alike continued to subscribe to the

container view of space and time and as a result blocked themselves from true progress.

Space, Time and Progression

The first of the two fundamental Postulates of the Reciprocal System from which Larson

derives every aspect of the physical universe is

―The physical universe is composed entirely of one component, motion, existing in three

dimensions, in discrete units, and with two reciprocal aspects, space and time.‖

Larson considers speed, which is the relation of space and time, s/t, as the measure of

motion and points out that a unit of speed is the minimum quantity that can exist in the

universe of motion, since fractional units are not permitted by the Postulate of his theory.

Since one unit of speed is the minimum quantity admissible, both space and time have to

be quantized: unit speed must therefore be the ratio of a unit of space to a unit of time,

each of which is the minimum possible quantity. Certain corollaries follow.

Corollary (1)

Firstly, we see that space and time are reciprocally related to speed: that doubling the

space with constant time, for example, has the same effect on speed as halving the time at

constant space. As a recognition of the far-reaching significance this reciprocal relation

holds for the explanation of all the physical facts, Larson names his theoretical structure

The Reciprocal System of theory.

Corollary (2)

At the unit level, not only is one unit of space like all other units of space, but a unit of

space is equivalent to a unit of time. Larson postulates a total uniformity in the properties

of space and of time, except for the fact that they are reciprocal aspects of motion. Thus

he concludes that time, like space, is three-dimensional, and that space, like time,

progresses.

At this juncture it may be pointed out that in order to understand (or evaluate) the new

ideas engendered by the new paradigm, namely that the physical universe is a universe

composed of units of motion (speed), it is necessary to view them in their new context.

On the other hand, the most frequent mistake committed by the novice is to view the new

concepts from the habitual viewpoint of the previous paradigm, that the universe is a

universe of matter, embedded in a framework of space and time. Such an attempt leads

one, often, to seemingly absurd, impossible or incredulous conclusions. To avoid slipping

back involuntarily into the old and inadmissible frame of mind while evaluating the

Reciprocal System theory is one of the most difficult tasks that a critic has to constantly

accomplish .

Now it is important to recognize that there is absolutely nothing space-like in the three

dimensions of time: they are entirely temporal parameters. The common belief that time

is one-dimensional is an unwarranted conclusion drawn from the fact that time enters our

experience as a scalar quantity. The real reason why time appears as a scalar quantity in

the equations of motion lies in the fact that no matter how many dimensions of time may

exist, they have nothing to do with directions in space.

The idea that space progresses in the same manner as time might look more weird than

the idea of multi-dimensional time. Our immediate experience is that of stationary space.

But history has repeatedly shown that our immediate experience of space has always

proved to be a bad guide in understanding the true nature of the universe. We first

thought that the earth is flat. Then we made the mistake of thinking our earth to be the

center of the universe and ended up in the maze of epicycles. Larson draws our attention

to the fact that the increased scope of our scientific observations has brought us to the

point where too many epicycles have once again been accumulated in the field of science

in the form of unresolved old questions, fresh new puzzles and ever-increasing

complexity of physical theory. He questions whether our anthropocentric view of space is

not once again the culprit that is barring progress.

He points out that our experience of space as stationary is valid only locally (that is, in

the context of a gravitationally-bound system). The true nature of space is to progress, to

expand ceaselessly outward. Wherever gravitation (an inward motion) becomes

negligible, weakened by distance, the inherent progression of space becomes apparent.

The observed recession of the distant galactic systems stems directly from this space

progression, not from any hypothetical ‗big bang.‘ In fact, the observed Hubble‘s law is

derivable from the postulates of the Reciprocal System.

Since a universe of motion cannot exist without the existence of motion, the most

primitive condition of the universe is the steady progression of space coupled with the

progression of time: in other words, a motion at unit speed. Beginners usually encounter

here the difficulty of imagining the existence of motion without it being the motion of

anything. But a little reflection should show that in a universe of motion the most

fundamental constituent is motion, and all ‗things‘ are derivatives of motion. Since every

space unit is like every other space unit, and every unit of time is like every other unit of

time, such a condition appears to our view as a featureless uniformity in which nothing is

happening and constitutes the null background. Thus unit speed, and not zero speed, turns

out to be nature‘s starting point. Larson refers to this background space-time progression

as the ‗natural reference frame,‘ and identifies the unit speed with the speed of light, c.

Emergence of Physical Phenomena

By virtue of the fact that either the space unit or the time unit could progress inward,

rather than outward as they do in the case of the space-time progression, speeds other

than unity become possible. Larson points out that it is these deviations (or

‗displacements‘) from the unit speed that constitute observable phenomena, namely,

radiation, gravitation, electricity, magnetism and all the rest. These are autonomous,

independent motions in contra-distinction to the ever-present background progression.

This gives rise to two possibilities. Suppose k number of reversals occur in the space

component, and suppose the unit speed of space-time progression contains n space units

per n time units (n/n = 1). Such a situation produces less than unit speeds, (n-k)/n. Since

such a motion detaches itself from the space-time progression in its spatial aspect, we

find it to be a motion in space. The second possibility is that the reversals occur in the

time component of the motion. This results in greater than unit speeds, n/(n-k). In this

second case it is the time component which gets detached from the background

progression and we note that it constitutes what might be termed a motion in time (not

‗time travel‘). This is the reason why unit speed (c, the speed of light) is the upper limit

for motion in space. It does not mean, as concluded in Relativity, that speeds greater than

c are impossible in the physical universe: it only means that such speeds do not manifest

in our conventional, stationary reference frame of three-dimensional space as

displacements in space. These greater-than-unit speeds (namely, the motion in time) can

be represented truly only in a ‗stationary‘ reference frame of three-dimensional time.

Our state of knowledge thus far has disposed us to assume tacitly that motion means

motion in space; the possibility of motion in time has never been imagined, much less

investigated. While such motion cannot be truly represented in the conventional, spatial

reference frame, it has nevertheless some observable features by virtue of the inverse

relationship between space and time. For example, in a supernova explosion, if sufficient

energy is available, Larson points out that some of the constituent matter of the star gets

propelled to greater-than-unit speeds. The less-than-unit speed component manifests itself

as a cloud expanding in space. On the other hand, the greater-than-unit speed component

manifests itself as a cloud expanding in time (since it is a motion in time). In view of the

reciprocal relation between space and time referred to above, this expansion in time

manifests itself to us as contraction in space and we observe this component as a

superdense and compact star. Thus we have the red giant/white dwarf combination so

frequently found as supernova product.

Larson‘s theoretical investigations show that the same concept of motion in time can

explain every other type of superdense astronomical phenomena, not just the white

dwarfs. He shows that as age advances, the central regions of massive galaxies keep on

accumulating motion in time (since greater than unit speeds do not involve movement in

space, this matter does not leak out). When enough energy accumulates, it results in a

stupendous explosion in which the central part(s) of a galaxy gets ejected and is found as

a superdense star system, which, of course, is observed as a quasar. All the strange and

unconventional characteristics of quasars—like their high density, large redshift,

stupendous luminosity, jet-structure, peculiar radiation structure, evolution—can be

deduced from the theory.

We have seen that the null condition of the universe of motion is unit speed and that a

‗displacement‘ from this condition takes the form of either less than unit speed (s/t) or

greater than unit speed (the latter being equivalent to less than unit inverse speed, t/s).

Larson identifies this displaced speed with radiation, and the speed displacement with its

frequency. While the photon gets detached from the background space-time progression

in the dimension of its oscillation, it does not have any independent motion in the

dimension of space perpendicular to the dimension in which the vibratory motion occurs.

Thus the photon is permanently situated in the space unit of the space-time progression in

which it is created. But from the context of the stationary spatial reference frame any

location of the space-time progression appears to progress outward (away) at unit speed.

Thus, while actually the photon is stationary in the natural reference frame, ostensibly it

appears to move away at unit speed. Incidentally we might note that, when in a single

process a photon pair happens to be created, while the individual photons seemingly

appear to fly off in space in opposite directions, they continue to be connected in time.

This results in a correlation between them that is not representable in three-dimensional

space (the EPR paradox).

Once photons are available, the possibility of a compound motion appears wherein the

photon could be subjected to a rotational displacement in two dimensions (covering all

the three dimensions of space). Larson identifies such units of compound motion with the

atoms of matter. Because of the two facts that the maximum possible speed is unity and

that the background space-time progression is already taking place at that speed in the

outward (away from each other) direction, all autonomous (independent) motions

(speeds) have to take place in the inward (toward each other) direction only. Thus the

units of rotational displacement start moving in the inward direction, reversing the pattern

of space-time progression. Larson identifies this inward motion with gravitation. We now

see that there is no propagation involved in gravitation, nor it can be screened off: it is the

inherent motion of each atom toward every other atom—in fact, toward every other

location of the space-time progression, whether or not occupied by an atom. The non-

existence of propagation time and the seeming action-at-a-distance, both owe their origin

to the above fact.

Theoretical analysis reveals that elements with atomic numbers 1 through 117 can all

exist in young matter. In old matter, however, elements with the higher atomic numbers

become subject to radioactive decay, by a process identified by Larson.

The Regions of the Physical Universe

An interesting fact that needs special mention is that the rotational displacement that

constitutes the atoms could be either of the less-than-unit-speed type or the greater-than-

unit-speed type. In either case gravitation acts inward (in opposition to the outward

progression of space-time). But in the case of the former type of atoms, since less-than-

unit speeds produce motion in space, gravitation acts inward in space, resulting in the

formation of aggregates in the three-dimensional spatial reference frame. Larson calls this

portion of the universe the material sector. On the other hand, the atoms constituted of

greater-than-unit speeds manifest motion in time. The resulting gravitation acts inward in

time, and produces aggregates in the three-dimensional temporal reference frame. Larson

refers to this matter as cosmic matter, their inward motion in time cosmic gravitation, and

this portion of the physical universe the cosmic sector. We therefore discover another half

of the physical universe where all the phenomena pertaining to our sector are duplicated,

but with the roles of space and time interchanged. Even though cosmic matter occurs as

ubiquitously and abundantly as ordinary matter we do not encounter it readily. Firstly, the

atoms of the cosmic stars and galaxies are aggregated in three-dimensional time but are

randomly distributed in space, so that we see a cosmic star not as a spatial aggregate, but

atom by atom. Secondly, while the cosmic gravitation moves the cosmic atoms inward in

time, our own matter progresses outward in time. Thus, even the chance of encounters of

atoms with cosmic atoms do not last for more than one natural unit of time (about one-

seventh of a femtosecond).

Larson identifies all the exotic particles that abound in the high-energy environment of

the particle accelerators with the ‗cosmic atoms,‘ with some additional features acquired

under the artificial environment.

A further fact of interest is that while the radiation emitted by the stars of our sector is at

a high temperature, that emitted by the cosmic stars would be at a high inverse

temperature, that is, at a low temperature. Since radiation moves at unit speed, unit speed

being the border between both the sectors of the universe, it is observable from both the

sectors, in whichever sector it originates. Therefore, the radiation emitted by the cosmic

stars, as it comes from a region not localized in space, is received in the material sector

(that is, the three-dimensional spatial reference frame) with an absolutely uniform and

isotropic distribution. We observe this as the low-temperature, cosmic background

radiation. In the Reciprocal System, we find no necessity to reconcile the absolute

isotropy of this background radiation with the clumpiness of the spatial distribution of the

material aggregates.

The Grand Cycle of the Universe

We have already mentioned that quasars are the high (greater than unit) speed explosion

products of aged galaxies. When gravitation in space is attenuated by distance (time) and

becomes negligible, the quasar as a whole shifts from the region of less than unit speed

(conventional spatial reference frame) to the region of greater than unit speed (the three-

dimensional temporal reference frame). Gravitation ceases to act in space and starts

acting in time. This leaves the outward progression of space-time without check (as there

is no inward progression of gravitation in space) and the constituents of the quasar start

flying out in space at unit speed. Eventually the quasar ceases to exist as a spatial

aggregate and disappears altogether from the material sector. In other words, the atoms of

the erstwhile quasar emerge into the three-dimensional temporal reference frame of the

cosmic sector at totally random locations (in time).

The corollary is that similar set of events occurs in the cosmic sector—cosmic atoms

aggregate in three-dimensional time forming cosmic stars and galaxies, parts of which

explode on attaining a size limit and eject cosmic quasars, which eventually exit the

cosmic sector and end up entering the material sector. Since they come from a region not

localized in space, these incoming cosmic atoms would be uniformly and isotropically

distributed throughout the three-dimensional space. Since the transfer occurs at the unit

speed we ought to observe these particles at unit or near-unit speed. These, of course, are

the observed cosmic ray primaries.

The Reciprocal System traces out in detail how these cosmic atoms, being greater-than-

unit-speed structures in a less-than-unit-speed environment, promptly decay, ejecting

speed (energy) and ‗cosmic mass‘ (that is, inverse mass), finally ending up as the most

primitive atomic structures of the material sector, namely, hydrogen. Then the entire

cycle of aggregation in space and eventual ejection begins. In the long run, as much

matter comes from the cosmic sector as it leaves the material sector. Thus the dual sector

universe as a whole is in equilibrium and steady state, while each sector continues to

expand in space or in time as the case may be. There is no necessity to assume the

singularity of a ‗big bang‘ nor to breaking of any conservation laws as in ‗continual

creation.‘

The Solid State

Because of the fact that the minimum space that can occur in physical action is one

natural unit of space (the quantum of space), if two atoms are made to approach each

other they cannot come any nearer than one unit of space. However, by virtue of the

reciprocal relation between space and time, these atoms can accomplish the equivalent of

moving inward in space by actually moving outward in time. This they promptly do until

a force (motion) equilibrium is achieved, giving rise to the solid state of matter. Since

less than one unit of space does not exist, within the unit of space all motion could be in

time only. The inside of unit space is therefore referred to as the time region by Larson.

The space-time progression always acts away from unity. In the outside region away

from unity is also away from zero (outward). But in the inside region away from unity is

towards zero. Therefore the space-time progression is inward in the time region. Since

gravitation always opposes space-time progression, it acts outward in the time region

(repulsion). Further, while the space-time progression is constant at unit value,

gravitation attenuates with distance. The two motions (forces) therefore reach a stable

equilibrium at some distance in the time region and produce the configuration of solid

state. Larson finds that a single theory of cohesion explains all kinds of bonds. Basing on

purely theoretical computations he is able to accurately calculate the various solid state

properties of hundreds of elements and compounds.

New Light on Quantum Phenomena

Since in the time region only motion in time can truly exist, the appropriate reference

frame that ought to be adopted for the description of the phenomena is the three-

dimensional temporal reference frame, and not the conventional, spatial reference frame.

The origin of the conventional reference frame is at zero speed, whereas the origin of the

temporal reference frame is at zero inverse speed, which is tantamount to infinite speed in

the context of the conventional spatial frame, and consequently a location pertaining to

the temporal reference frame is found not to be localized in the conventional reference

frame. This is the origin of the nonlocality characteristic so perplexing in quantum

theory. This reciprocal (inverse) relation between these two types of reference frames

also explains why a localizable particle in the context of a temporal reference frame

needs to be regarded as an endless repetition, namely, as a wave, in the context of the

spatial reference frame. Thus the Reciprocal System throws new light on the concepts of

quantum theory. As the time region is a region of motion in time, it requires the adoption

of a temporal reference frame for the description of particle phenomena. But, being

irrevocably wedded to the spatial reference frame of the material sector, we are unable to

accomplish this. However, we are able to accomplish the equivalent of adopting the

temporal reference frame by resorting to the expedient of adopting the wave picture in the

place of the particle picture.

This insight resolves the problem of the wave-particle duality. It further clarifies that the

question of adopting the wave picture arises only on entering the time region, the region

inside the unit of space. To associate a wave with every gross object is unwarranted.

There are yet unforeseen insights brought to light by the Reciprocal System. In the

outside region, that is, in the context of the three-dimensional spatial reference frame,

speed (s/t) is directional (vectorial). However, in the time region, that is, in the context of

three-dimensional temporal reference frame inverse speed (t/s) is the quantity that is

‗directional‘ while speed appears scalar. But it must be cautioned that this ‗direction‘

pertains to the realm of three-dimensional time and has nothing to do with direction in

space. Thus inverse speed, though it could be ‗directional‘ in time, is not a vector. In the

universe of motion all physical quantities can be reduced to space-time terms. Larson, in

a major overhaul of the dimensions of various physical quantities, arrives at the

conclusion that the dimensions of energy are those of inverse speed, namely, t/s.

Consequently, energy needs to be represented by complex numbers in the time region and

negative energy states are as natural in the time region as negative speeds (velocities) are

in the spatial reference frame.

Conclusion

We have endeavoured to sketch out some of the important contributions of the Reciprocal

System to the understanding of the physical universe starting from a new paradigm—the

concept of a universe of motion, in place of the current one of a universe of matter

embedded in a framework of space and time. The examples cited here are expected to

convey the broad-enough scope of the theoretical system and establish that a prima facie

case exists for a general theory. It is only fair to record that some of the more esoteric

aspects of the theory, such as multi-dimensional motion, the scalar region of the universe,

etc., have had to be omitted entirely for pedagogical reasons and hence interesting

questions concerning two large and important fields, namely, of electricity and

magnetism, could not be considered in this article. Mention must also be made of the fact

that Larson finds the basic constituent of the universe according to the new paradigm,

namely, motion, to be scalar motion. Even though the existence of this kind of motion has

been recognized, it has played a very minor and insignificant role in physical theory

hitherto. So, Larson carries out a full-scale investigation of the properties and possibilities

of scalar motion and discovers that this type of motion plays a central role in the drama of

the physical phenomena. He finds, for example, that some of the unexplained physical

facts are really the unfamiliar features of certain types of scalar motion. In this

preliminary article we have refrained, for practical reasons, from dwelling on this

important contribution of the Reciprocal System.

Surely one might question the rationale of omitting some of these important contributions

of the theory when at the same time emphasizing its all out nature. The real reason is—as

has been hinted at the outset—no matter how simple and logical the new conclusions are

from the viewpoint of the new paradigm, since one is habituated to the old paradigm,

some of them might look unimaginable or utterly unscientific. Having invested one‘s

entire professional career in the existing paradigm, one‘s mind does not take kindly to the

prospect of a basic paradigm change. The first few contacts are the most difficult ones as

Kuhn points out. One would not be inclined even to pay attention to the new conclusions,

much less evaluate them on their own merit.

References

1. Larson, D.B., The Case Against the Nuclear Atom, (North Pacific Publishers,

Portland, OR, USA, 1963)

2. Larson, D.B., Beyond Newton, (North Pacific Publishers, Portland, OR, USA,

1964)

3. Larson, D.B., New Light on Space and Time, (North Pacific Publishers, Portland,

OR, USA, 1965)

4. Larson, D.B., Nothing But Motion, (North Pacific Publishers, Portland, OR, USA,

1979)

5. Larson, D.B., Basic Properties of Matter, (ISUS, Salt Lake City, UT, USA, 1979)

6. Larson, D.B., The Neglected Facts of Science, (North Pacific Publishers, Portland,

OR, USA, 1982)

7. Larson, D.B., The Universe of Motion, (North Pacific Publishers, Portland, OR,

USA, 1984)

HOW DO WE MEET THE NEW AGE

USHERED IN BY THE RECIPROCAL SYSTEM ?

The student of the Reciprocal System is often beset with a peculiar difficulty, the nature

of which he does not recognize readily. The result is that he does not even suspect that his

progress is being blocked by this difficulty. I have writen several times referring to this

but find that it is by no means easy for the student to realize the point I am endeavoring to

show. For instance, in a recent communication, circulated by Maurice Gilroy (Re:

Message 17 of Conference 01 mailed 8/19/93), we find Robert Tucek asking: ―What

observations correspond to a basic rotation of natural units?‖ (Please see the short note on

STP at the end. ) The context of his questioning was, of course, about the possibility of

rotation as a primary motion as against linear translation. A little later he emphasizes,

―Rotational motion, by definition, requires an object!‖

The prevailing view in the ISUS seems to be that while linear motion can exist without

any object, rotation is not possible without an object. We wish to show that this view is

not applicable in the context of the universe of motion postulated by the Reciprocal

System. Larson has repeatedly pointed out to us that the most basic component of the

universe of motion is motion, not matter or any other ‗object.‘ On the other hand, the

most basic component of the universe of matter is matter: motion being regarded as

something added on to these primary units, namely, matter. Let us highlight these:

Concept of the Universe of Motion:

Motion or space/time: the content of this universe; primary component

Concept of the Universe of Matter:

Matter: the content of this universe; primary component

Space/time: the background or container

Motion: something that could be acquired by objects, like matter.

Therefore, referring to the primary units of motion, in the context of the universe of

motion, when we speak of rotational motion, we do not mean the rotational motion of an

object, for the simple fact that there is no ‗object‘ logically prior to the primary motion.

The term ‗primary component‘ implies logical priority. In fact, the expression ‗rotation of

natural units,‘ used by Tucek, as also by so many other students, is positively misleading:

as though the natural units are first existing and then are given a rotation. The truth is that

when we speak of a rotational space unit (as against linear space unit) we do not mean

―the rotation of the space unit;‖ rather, we mean ―the rotation that is the space unit.‖

Our preoccupation with the Cartesian (rectangular) co-ordinate frame has some biasing

inf luence. Turning, instead, to the polar co-ordinates, r and q, we find that the linear and

rotational space are on an equal footing. A scalar parameter has only magnitude and no

direction in space. Examples are wages (dollars/hr) or production (units/min) etc. Though

speed (cm/sec)—in contrast to velocity—is taken to be scalar, it is not scalar in the

absolute sense of the previous examples (in the sense that dollars or numbers have no

relation whatsoever to direction in space). This is because distance between two points,

say, A and B, does have an intrinsic direction, namely, AB or BA (which wage or

production does not have). ‗Scalar speed‘ merely means that this intrinsic direction is not

oriented in any direction of the reference system. That is to say that there is no specific

relation between this intrinsic direction and the conventional reference frame. Thus we

use the word ‗scalar‘ either in a strong (or absolute) sense or in a weak sense. Wage is an

absolute scalar in that it does not have an intrinsic direction, whereas speed has a

potential direction in space that could be actualized in the context of a spatial reference

frame.

In exactly the same manner a scalar speed could be rotational (radians/sec) instead of

linear (cm/sec). Rotation also has an intrinsic direction, namely, the axis of rotation. Our

pre-occupation with rectangular reference frames might make us think that the direction

germane to rotation is the ever-changing direction of the radius. But this is not correct.

The intrinsic direction of rotation is that of its axis (adopting the righthand screw

convention). The problem is that we are not used to think of rotation without imagining a

rotating object. Even if we are careful enough not to picture any gross physical object, we

cannot help imagining a conceptual object, a sphere or disk of space, and see it rotate.

The catch here is that we are still envisioning ‗the rotation of the disk,‘ instead of ‗the

rotation that is the disk,‘ and so are back in the trap! But the truth is that in the case of

rotational speed, d /dt, there is no radius, r, involved. In the case of translational speed

we can imagine dr/dt without any connection or reference to !

One useful excercise that might help us overcome this difficulty is first to imagine a

rotating disk and then to visualize the disk to be shrinking progressively, such that we are

ultimately left with only rotation (radians per sec). Having realized that the intrinsic

direction of rotation is its axis, and not the changing direction of the radius, we see that

rotation could be as much a scalar quantity as translation is, so long as the intrinsic

direction, in either case, is not oriented in any specific direction of the conventional

reference frame.

Tucek‘s assertion, which is a statement of the difficulty that is common to many other

students, that ‗Rotational motion, by definition, requires an object,‘ is true only in the

context of the concept of the universe of matter, not in the context of the concept of the

universe of motion. In the context of the universe of motion, primary motion—whether

translational or rotational—by definition, does not require an object. This is the

implication of the expression ‗basic component of the universe.‘ This demonstrates that it

is by no means easy to dislodge our moorings to the concept of the universe of matter.

We—our generation—are born and bred in the context of this concept. So even though

we are repeatedly cautioned we continually keep slipping back into the old view point.

When I talk of the primacy of motion—either linear or rotational—as when saying:

―Rotation is possible prior to the existence of ‗things‘ or ‗objects,‘...‖ and if someone

finds that either it is

a. absurd,

b. illogical, or

c. impossible,

then it does not establish that I am wrong. It only indicates that either one of us is wrong.

Therefore it becomes necessary to examine whether one has, by dint of inveterate habit,

slipped back to the view point of the universe of matter. Our thinking is guided by the

language, and the present grammatical patterns are thoroughly conditioned by the

viewpoint of the universe of matter. Great caution must be excercised in using ellipsis,

metaphor or other figures of speech in our discourse. Tedious repetition of long

expressions may have to be resorted to so as to avoid misguiding, or evoking semantic

responses incongruous to the new view point.

For the conventional scientists of our generation (let us call them Group A) there is no

difficulty: they are wedded to the viewpoint of the universe of matter from the beginning

to the end. For the scientists of the future generation (Group B) there is no difficulty

either: from birth they would be raised in the context of the viewpoint of the universe of

motion, and the viewpoint of the universe of matter would only be a matter of historical

interest. The difficulty is only for those of our generation (Group C) who, while having

been bred in the viewoint of the universe of matter, are promoting the study of the

Reciprocal System that requires the new viewoint, namely, that of the universe of motion.

We keep slipping back to the conventional viewoint. And trying to study the universe of

motion from the background of the concept of the universe of matter leads to absurd

results. While persons of Groups A and B might be intelligent, those of Group C have not

only to be intelligent in the conventional way, they must be intelligent in a different way

too. This latter involves an ability to perceive whether, down the line, one has

involuntarily reverted to the viewoint of the universe of matter. ‗Illogical,‘ ‗absurd,‘

‗non-sensical‘and ‗impossible‘ are some of the watchwords that should alert us to this.

Surreptitious pride in one‘s intellectual superiority is the first stumbling block. An

attitude of cocksureness and finality is the second impediment. The tendency to take the

unfamiliar for the inadmissible is the third. Reliance on majority opinion is the fourth.

In the chain of deduction from the Fundamental Postulates, far down the line, work is not

so difficult. So some of us might have published ‗learned‘ papers or literature on the

Reciprocal System. The true difficulty is nearer the Fundamental Postulates, most at the

first step, in deducing the primary motions. This is where the clash between the viewpoint

of the universe of motion that needs to be adopted and the viewpoint of the universe of

matter to which we keep slipping back (unconsciously) has the most deleterious effects.

Advocating censorship has good intentions. But implementing it is tricky: we might be

unwittingly jeopardizing the very cause which we are professing to promote. We, in our

eagerness to reject all that is alien to the Reciprocal System, might commit the mistake of

rejecting all that is alien.

In the recent ISUS Newsletter (ISUS News, V(1), Spring 1993, pp. 5-8) I have discussed

point by point how the President was misguided in his ruling. However, I know that truth

cannot be forced, it must dawn on oneself. Only he who has been able to extricate himself

from thinking in terms of the inadmissible viewpoint of the universe of matter and is

constantly on vigil to see if he has slipped back to this view point, either in his own study

or in criticizing others‘ work, is the right person to censor. The prevailing correspondence

clearly shows that not one of us is equal to the task.

The Space-Time Progression

The question is often raised that if rotational motion is as primary as linear motion, what

is the observable effect, in the case of rotation, which corresponds to the outward

progression of space-time (STP) in the case of linear motion.

The natural reference system manifests in the conventional reference frame as a one-

dimensional scalar outward progression. Let a length AB grow to ABl in x (natural) units

of time, such that BBl = x units of space. We make the following observations:

Observation I: Since the STP is scalar, it is independent of (i) any direction and (ii) any

reference point of the conventional reference frame.

Observation II: The effect of the non-dependence on direction is to distribute the

progression into spherical symmetry.

Observation III: The effect of the non-dependence on reference point is to distribute the

increase in length, namely, the x units of space, uniformly throughout the original length

AB. That is, it is not the case that a length BBl is added to the end of the original length

AB at B, but additional linear space emerges between every two adjacent points

(locations) on AB. Suppose M was the midpoint of AB. After x units of time it occupies

location Ml such that it is still the midpoint of ABl . It is extremely important to

distinguish this type of increase of length from an increase that is merely appended to the

end of an existing length. Both the ubiquity of the STP and the ‗action-at-a-distance‘ of

gravitation stem from this non-dependence of scalar motion on reference point.

The same state of affairs holds good in the case of rotational motion too, but first we must

note the following correspondences between translational and rotational motions:

i. Length is measured between two points, one of which is a reference point. Angle

is measured between two directions, one of which is a reference direction.

ii. The scalar speed cm/sec has an intrinsic direction that may be oriented in any

direction of the conventional reference frame. The scalar speed radians/sec has an

intrinsic direction that may be oriented in any direction of the conventional

reference frame.

Now we are ready to make three observations in the case of rotation as we did in the case

of translation above. Let /POQ be an angle f, such that O is the origin, OQ the reference

direction and OP another direction. In y units of time let f increase by y units of angle.

Observation I: Since the rotational counterpart of the STP is scalar, it is independent of (i)

any rotational direction and (ii) any reference direction of the conventional reference

frame.

Observation II: The effect of the non-dependence on rotational direction is to distribute

the rotation into spherical symmetry.

Observation III: The effect of the non-dependence on reference direction is to distribute

the increase in angle, namely, the y units of angle, uniformly throughout the original

angle /POQ. That is, it is not the case that an angle y is added to the end of the original

angle /POQ at OP, but additional angular space emerges between every two adjacent

directions in /POQ

It is extremely important to distinguish this type of increase of angle from an increase

that is merely appended to the end of an existing angle. Now a complication arises that

the conventional reference frame cannot accommodate more than 2 radians of angle (or

4 steradians of solid angle). Therefore, in the case of the former type of increase, as

soon as this limit is reached, no further observable effect manifests. Thus the rotational

counterpart of the linear STP is seen as no (or zero) rotation. On the other hand, since no

such limitation exists for accomodating linear space we observe an unlimited outward

progression in the linear case.

SUBVERSIVE REFLECTIONS

ON THE PRACTICE OF PHYSICS

―The transition from a paradigm in crisis to a new one is far from a cumulative process.

Rather it is a reconstruction of the field from new fundamentals.‖

—Thomas S. Kuhn, The Structure of Scientific Revolutions, pp. 84-85

In the article High Energy Physics and the Reciprocal System¹ we indicated that high

energy physics is a field approaching a crisis, and therefore the Reciprocal System,

originated by Dewey B. Larson, has greater chances of getting a hearing since it offers a

truly general theoretical framework resolving long-standing problems. We believe that

the dawning of a new century is particularly propitious for new ideas—as it always has

been—and the Reciprocal System, with its new paradigm of scalar motion as the sole

content of the physical universe, has much to contribute. The need of the times is a good

number of interface articles that could bring the knowledge of the Reciprocal System to

the orthodoxy, or at least to the iconoclastic thinkers in its ranks.

The title of this article is adopted from that of an article² written by A. J. Leggett in the

Indian journal of Current Science. I shall quote extensively from this article, giving the

page numbers in parentheses. Prof. Leggett is well known in the field of condensed

matter physics. He advances in the above article forceful arguments against the

reductionist viewpoint in science. Reductionism implies that the behavior of macroscopic

systems is in principle entirely determined by the behavior of their microscopic

constituents. Leggett is not alone in drawing attention to the limitations of reductionism.

Since the pioneering work of the celebrated thermodynamicist and Nobel laureate, Ilya

Prigogine, there has been a growing awareness of the limited applicability of the

reductionist viewpoint in the fields of physics and life sciences.

Epistemology of Reductionism

Leggett observes that the reductionist argument goes like this: ―We have analyzed the

properties of macroscopic bodies in terms of those of atoms and molecules; these systems

in turn behave as they do because of the properties of the electrons and nuclei; the

behavior of the nuclei is determined by that of their constituent nucleons; and now we

trace the properties of the nucleon itself to that of its constituent quarks. What could be

more obvious than that the behavior at each level is determined by that of the constituents

at the next level below?‖ (p. 787).

He then tracks down that ―our experience of ‗understanding how things work‘ starts with

mechanical devices made by other human beings, and that the most natural way of

achieving such an understanding is precisely to take the device apart into its constituent

parts, since these are what the maker started with. Does this experience subconsciously

color our perception of what constitutes an ‗explanation‘ of natural phenomena as well as

of human artifacts?‖ (p. 787)

He questions that would it be really obvious ―that the behavior of complex bodies is

entirely determined by that of their constituents‖ (p. 792) were it not for this

subconscious conditioning about what constitutes ‗explanation.‘ ―Reductionism is

probably as deeply ingrained in the thinking of most of us as any single element in the

whole of our scientific world view.‖(p. 792)

Who Put Reductionism in Nature?

Let us inquire, says Leggett, what most of the contemporary experimentalists and

theorists in the field of high energy physics are involved in.

―Most high-energy experimentalists are engaged in a single enterprise which,

conceptually if not technically, has a very simple structure. Namely, they accelerate

particle A and particle B so as to hit one another, and watch where they and/or particles

C, D, E emerge, and with what energy and (sometimes) spin. In particular, the

experiment is designed so that, as nearly as possible, the incoming beams are each

described by quantum-mechanical pure states of definite momentum; and while the

theory certainly predicts that, in certain cases at least, the outgoing states are not simple

classical ‗mixtures‘ of products of plane wave states, but have built into them subtle

quantum correlations of the type which are important in Bell‘s theorem, the whole setup

is designed precisely so that such subtleties can be neglected.‖ (p. 787)

Now when the particle physicists claim that experiments show that Nature is actually

simpler at higher energies, might it not be due, Leggett wonders, at least partly ―to the

fact that we have chosen to ask her only questions, which by their very construction allow

no subtlety in the answers?‖ (p. 787)

Referring to the theoretical front he says: ―A few years ago, at least, there were high

hopes (I am not clear how far those at the forefront of the field now share them) that in

the ‗super-string‘ picture the constraints imposed by the need for self-consistency would

be so severe that they would uniquely determine the parameters of the theory, including

as outputs not only the masses and coupling constants of the known elementary particles

but even the ‗true‘ dimensionality of space-time.‖ (p. 788)

He then raises the genuine epistemological quandary: ―Can mathematics—a subject

which is usually taken to be concerned with analytic truth—really put constraints on how

Nature can behave?‖ (p. 788)

The Whole is the Sum of the Parts—Or is it?

Leggett now surveys the evidence for and against reductionism in science. He points out:

―So long as one is dealing with those phenomena, and only those, where we believe that

the predictions of quantum mechanics are well approximated by those of classical

physics, then the evidence for the reductionist point of view is very strong, and moreover

there is absolutely no a priori, internal reason to challenge it.

―For example, in a typical ‗macroscopic quantum effect‘ in the conventional sense, such

as the Josephson effect, what we are actually seeing is the effect of a macroscopically

large number of Cooper pairs behaving in identical fashion; the observed supercurrent is

simply the sum of the supercurrents carried by the individual pairs of electrons. Similarly,

in laser diffraction, we are simply seeing the coherent sum of the behavior of many

individual photons. So long as we are dealing with the summed effects—even the

summed quantum effects—of a large number of small groups, there seems no reason to

doubt a reductionist approach.‖ (p. 793)

He continues: ―It is only when we come to intrinsically quantum phenomena that we have

a problem. First the positive evidence in favor of reductionism in this regime is much less

strong than it looks at first sight and secondly, there are indications, which are intrinsic to

the quantum formalism itself, that the reductionistic program not only might, but must

eventually fail.

―Let us start with the phenomenon usually known as the Aharonov-Bohm effect. In this,

the current flowing through a region of metal which encloses a hole turns out to be

affected by the magnetic flux through the hole, even though the magnetic field vanishes

everywhere within the metal itself. In other words, the electrons carrying the current are

sensitive to the conditions in a region which they never enter, but only enclose with their

paths! This already demonstrates that quantum mechanics forces us to give up some of

our classical notions about the ‗locality‘ of physical effects.‖ (p. 793)

As the next example he considers Bell‘s theorem and the related experiments: ―given that

we make our normal assumptions about local causality in the sense of special relativity

theory, and about the statistical properties of ensembles being determined entirely by the

initial conditions, then what Bell‘s theorem and the associated experiments show is that

even though two regions of the universe may be spatially separated and physically

noninteracting, we nevertheless cannot ascribe to each of them individual properties; any

‗realization‘ of properties takes place only at the level of the combined system.‖(p. 793)

What Bell‘s theorem experiments have shown us is that, in the context of reductionism

which implies that ‗the behavior of macroscopic systems is entirely determined by that of

their atomic-level constituents,‘ we are not justified in assuming that the concept of

‗constituent‘ is necessarily associated with spatially localized region. So Leggett

exclaims that ―the Bell's theorem experiments are a death-knell for reductionism.‖ (p.

793)

The Quantum Measurement Paradox

There is one more feature of the current quantum mechanics world view to which Leggett

draws attention, which gives us reason to doubt the validity of reductionism—the

quantum measurement paradox.

―Consider an ensemble of systems which can go from some initial to some final state by

either of two paths B and C. At the microlevel, we believe that despite the fact that

‗measurement‘ of the path followed by any individual system will always show that it

followed either B or C, the quantum formalism must nevertheless be interpreted as in

some sense saying that if no measurement was made, it simply is not the case that one

(unknown) possibility out of B and C was realized; rather, both possibilities are in some

sense represented in the correct description. as a matter of experimental fact, the

properties of our actual ensemble are not identical to those which we would obtain from a

combination of the two ensembles obtained by allowing only B and only C respectively;

i.e., we verify, experimentally, the phenomenon of interference between the two paths. So

it seems that the quantum formalism in some sense either ascribes ‗reality‘ to both the

possibilities B and C, or ascribes it to neither.‖ (p. 794)

"At the macrolevel the formalism of quantum mechanics remains exactly the same; but

there is now no direct experimental evidence against the hypothesis that one of the

possibilities B or C has been realized in each particular case.

―We have here a case in which we have two maps of reality—the quantum-mechanical

map which we apply to atomic phenomena, and the ‗'common-sense,‘ classical map

which we use for the macroscopic, everyday world. The problem is that they claim in

principle to describe the same level of reality—the world of counters, cats etc.—and yet

no one has succeeded in showing that they are compatible.‖ (p. 795)

Now, Leggett‘s penetrating insight into this enigma, which first fastened our attention

onto his article, was the realization that ―under appropriate circumstances if we

extrapolate [the quantum] formalism up from the microlevel to the macrolevel, there is

no point at which any natural discontinuity occurs.‖ (p. 794) [my emphasis]

He is unequivocal in his conclusion: ―My own belief is that the quantum measurement

paradox can have no solution within our current reductionist world-view.‖ (p. 795) He

opines that the quantum field theory is only a half-way house, sure to be supplanted by ―a

radically new picture of physical reality whose nature we cannot at present even guess.‖

(p. 795) He adds: ―I for one intend to use my best efforts to hasten that day.‖

Enter the Reciprocal System

The Reciprocal System, with its new paradigm that (scalar) motion is the sole constituent

of the physical universe, resolves all the difficulties. Larson‘s finding that space and time

are discrete in nature and quantized answers the crucial question raised by Leggett above,

that ―there is no point at which any natural discontinuity occurs.‖ Such a natural

discontinuity does occur at the boundary of the natural unit of space. We have explained

in detail in a previous article how at the boundary between the time region (the region

inside unit space) and the familiar³ three-dimensional spatial region a discontinuity

occurs, and how the apparent directions of the forces applicable (the gravitation and the

space-time progression) change from outward to inward and vice versa. We have shown

that this gives rise to the solid, liquid and the gaseous states.

Larson‘s discovery that space and time are reciprocally related had been a crucially

important finding. This led to the discovery of the existence of coordinate time analogous

to the familiar coordinate space. We have shown³ that the phenomenon of spatial non-

locality arises due to the switching from the spatial reference frame to the temporal

reference frame on entering the time region. This makes for the equal possibility of all the

alternative paths, at the microlevel. At the macrolevel, however, this is not the case since

the interaction is no longer in the time region but is in the conventional spatial frame. We

have further explained the concept of temporal non-locality which is responsible for

producing the statistical pattern out of the independent microlevel events of an ensemble.

Larson pointed out the fact that correlated particles—like in the EPR experiment—

maintain contiguity either in space (if separated in time) or in time (if separated in space).

We also note that in the Reciprocal System there are two kinds of time: the coordinate

time and the clock time. These are respectively the reversible time, t, which occurs in the

equations of classical physics and quantum mechanics, and the irreversible time, T,

which is relevant to living processes and consciousness. This distinction arises naturally

and logically in the Reciprocal System, whereas in the world view of the current science,

as Prigogine finds, it is to be introduced as an ad hoc necessity. Analogous to coordinate

time and clock time we also find that there are two kinds of space: the familiar coordinate

space and what Larson terms clock space. The latter manifests itself to us as an

irreversible and continual expansion, as is evidenced in the recession of the distant

galaxies. In the Reciprocal System there is no need for the purely ad hoc assumption of

the ‗Big Bang‘ to account for the galactic recession!

The Reciprocal System repudiates reductionism at the very outset. Larson finds the atom

to be a unit of compound motion and without parts. The so-called sub-atomic particles

turn out to be incomplete atoms and without parts. In the Reciprocal System there is no

need for quarks and gluons, not even for nucleons. We can identify the cosmic ray decay

particles and the exotic particles generated in the accelerators to be the transient

apparitions of the atoms of the conjugate sector of the physical universe, which Larson

refers to as the cosmic sector.¹ The cosmic sector is a complete duplicate of our material

sector with the roles of space and time interchanged.

Larson was able to explain the characteristics peculiar to biological systems by the

possibility of conjoining the structural units pertaining to the cosmic sector with the

material structures. Remember that the structural units of the cosmic sector are not

aggregates in space. Rather, they are aggregates in time, and hence their control on the

cells, for example, appears totally nonlocal. This makes it possible for the logical

inclusion of self-organization and creativity among other things.

All these insights about the quantum phenomena which the Reciprocal System is able to

provide acquire even greater significance when we realize that its creator, Dewey Larson,

had never explicitly thought out these aspects when he originally developed the theory. A

perusal of his early correspondence with other students even reveals that he looked upon

these quantum-mechanical phenomena, like the tunneling, with hesitation. (This,

however, does not mean to underestimate his genius: he was so pre-occupied with the

overall development of the theory so as to establish its generality, accuracy and cogency

that he hardly ever had the time to go into the quantum subtleties. He used to do all his

typing work himself, and imagine that his typewriter didn't even have the '+' key: he used

to type '-', then backstep and overtype '/'.) Be that as it may, the actual fact is that the

logical development of the Reciprocal System of theory comes up to match with the

requirements to be satisfied by the ‗new picture of physical reality‘ we are looking for,

and whose nature could not even be guessed by the scientists. The next question,

therefore, is since such a theory did appear now, whether or not we can see the truth of

this!

References

1. Nehru, K. V. K., ―High Energy Physics and the Reciprocal System,‖ Reciprocity,

Volume XXVI, No. 2, Summer, 1997.

2. Leggett, A. J., ―As a Martian might see us: Subversive reflections on the practice

of physics,‖ Current Science, Volume 67, No. 11, 10 December 1994, pp. 785-

795

3. Nehru, K. V. K.,―‗Non-locality‘ in the Reciprocal System,‖ Reciprocity, Volume

XXVI, No. 1, Spring 1997, pp. 7-14

DIALOGUE WITH DEWEY B. LARSON, PART I

Reproduced below are comments on D. B. Larson‘s Nothing But Motion (NBM) and New

Light on Space and Time (NLST) interspersed with responses by the author. The

correspondence from which this dialogue is excerpted took place c. 1980.

1. KVK: p. 156, 13th line from bottom, NLST: Instead of the words ―basic vibrating

unit‖ it must be ―rotational base.‖

p. 123, 10th line from bottom, NBM: in ―However, the rotational

displacement...,‖ the word ―rotational‖ should be replaced by ―vibrational.‖

DBL: You are right on both of these items. I have expressed the first one in the

correct manner on page 140 NBM.

2. KVK: There is a difference in the notations used for representing the rotations of

atoms (e.g.: 2–1–0, p. 236, NLST) and of the sub-atomic particles (e.g.: 1–0–(1)).

In the former the numbers represent double natural units whereas in the latter they

represent single natural units. This divergence is a source of confusion as no

attempt was made to clarify it, and both modes of notation were used at the same

places, as in p. 236, NLST.

DBL: I gave a brief explanation on page 231 NLST, but this book is, as I said in

the preface, a ―bird‘s eye view,‖ and I could not go into much detail on anything.

There is a more extended explanation on page 140 NBM, including setting up a

new system of notation to avoid the difficulty that you point out. I do not believe

it advisable to try to use the same notation for both atoms and sub-atomic

particles, as this would lead to complications in the development of the theory.

3. KVK: p. 170, last but one para, NLST: It is not clear how a proton, M 1–1–(1),

can acquire a positive electric charge (see p. 145, NBM). From what has been

explained in the para cited above and elsewhere, as its electric rotational

displacement is space-like, the proton can only acquire a negative electric

charge—like the electron.

DBL: An electric charge is a one-dimensional rotational vibration. In order to be

stable and identifiable as a separate entity it must oppose the rotation with which

it is associated, but this does not have to be the rotation in the electric dimension.

The charge can oppose the rotation in one of the magnetic dimensions. Since the

magnetic rotation is always positive in the material sector, this means that all

material elements can take positive electric charges under appropriate conditions.

In fact, at high temperatures, such as those in the stars, all elements are positively

charged.

4. KVK: On p. 155-6, NLST, the apparent reduction in the velocity of light in a

material medium is attributed to the additional space involved due to the

rotational space-like displacements included in the structure of most atoms of

matter. On this score, the apparent velocity of light in a material medium with

only positive rotational displacements should be greater than c!

DBL: I am not quite clear as to the point of your comment. I will say, however,

that ordinary matter is a time structure; that is, one in which n units of time are

associated with each unit of space (as we see the situation in the context of the

conventional fixed system of reference). When the photon passes through this

matter, the total time involved in the motion is increased by the addition of the

time component of this matter. The photon speed, the ratio of space to time,

therefore decreases. Conversely, in the cosmic sector, where matter is a space

structure, the speed of light is increased in passing through cosmic matter.

5. KVK: Speaking of the progression of the photon in the free dimension it is

remarked that ―...the combination of a vibratory motion and a linear motion

perpendicular to the line of vibration results in a path which has the form of a sine

curve.‖ (p. 51, NBM) In the case of HF radiation, the space component of the

vibration progresses unidirectionally while it is the time component that oscillates

back and forth. As such ―the linear motion perpendicular to the line of vibration‖

referred to above cannot be the scalar progression of the space component of the

general space-time progression. Is the sine curve form, then, taken to be

pertaining to the three-dimensional time?

DBL: The frequency of the radiation is irrelevant. In either case, HF or LF, the

progression of the natural reference system in the dimension of the vibration is

neutralized by the reversals. This permits a progression to take place in a

perpendicular dimension. The scalar motion (progression) in this second

dimension is totally independent of that in the first, as scalar quantities cannot be

combined vectorially.

[KVK: Apparently, my question was not clear here. What I meant was: a

progressing sine wave has two components— (i) the oscillation in the lateral

dimension and (ii) the uniform forward progression. Now my point is, that both

these components must be of the same nature—either spatial or temporal. Thus, if

the oscillation component is in time, the progression component in the

perpendicular dimension to be compounded with this has to be in time also; and

the sine wave must be envisaged as occurring in three-dimensional time and not

in three-dimensional space.]

6. KVK: Explaining the effect of adding rotation to the vibrational units of a photon,

it is said that the ―remaining vibrational units of the originat photon continue as a

photon of lower displacement‖ (p. 123, 3rd para, NBM). But it is not clear how

the detachment of one of the vibrational units (which are anyway discrete) reduce

the displacement of the original photon.

DBL: The units that I am talking about here are units of displacement—that is,

units of speed. (See explanation of the use of the term ―displacement‖ on pages

119-121 NBM.) When one unit is detached to join the rotational motion, the

photon continues on its way with one less unit of speed (a lower frequency).

7. KVK: The liquid state is the result of vanishing of the force of cohesion in one

dimension (and the gaseous state in three dimensions). However, whether the

vanishing of the cohesion in two dimensions results in any specificalty observable

distinction is not made clear. Is it to be equated to the vapor state?

DBL: Probably. I had not covered this subject fully twenty years ago when I

interrupted my research work in order to start publication of my results, and I

have not been able to get back to it since. My conclusions in this area are

therefore somewhat tentative.

8. KVK: p. 173, top para, NLST: Not only this—if the hypothesis of the tendency of

atoms to assume a stabler structure like that of inert gases by gaining an electron

is true, should not the atoms, say, of chlorine, tend to transform to those of argon,

if placed in an environment of negative electrons, by absorbing single electrons?

DBL: It looks that way to me, too, but I suppose we will have to let the supporters

of conventional theory answer this question.

9. KVK.: p. 50, bottom para, NBM: It is not clear why do the inward/outward scalar

reversals result in vectorial direction reversal in only one dimension? Why they

do not produce a three- or two-dimensional vibrating unit?

DBL: We are dealing with a scalar motion, and the only latitude that we have, at

this stage of the step-by-step development, is to change from + to - and vice versa.

This does not necessarily preclude introducing additional dimensions of motion

later in the development, but multi-dimensional scalar motion has some

unfamiliar features. I intend to discuss this type of motion at considerable length

in Volume II.

10. KVK: p. 195-6, NLST: In view of the dimensional differences in the origin of

electrical, magnetic and gravitational forces which are actually motions of the

same general nature, it is shown that the force exerted by an electric charge on an

uncharged mass is only 1/c² as great as the force on an object with a charge of

comparable magnitude. However, no mention is made of the force exerted by the

electric charge on a magnetic charge, which, though it must be less than the force

of an electric charge on electric charge, must, nonetheless, be greater than the

force exerted by electric charge on uncharged mass. Hence this must be within the

possibillty of detection, like the weak force exerted by a magnetic charge

(referred to in the para cited) on a (magnetically uncharged) mass unit.

DBL: I have not arrived at a firm conclusion on this point as yet. It had occurred

to me, and I have given it some consideration. So far, I am inclined to believe that

it will be ruled out by the directional orientation of the electric and magnetic

forces.

11. KVK: Within the gravitational limit of a material aggregate there is net inward

scalar motion. As such, what would happen to a photon emitted from the object,

within the gravitational timit? As the photon has no independent motion but is

only carried away by the general space-time progression and since the net motion

now is inward , how can we account for the velocity, c, of the photon and its

eventual emergence from the domain of the gravitational limit?

I think, the argument that the above net inward motion within the gravitational

limit belongs only to the material aggregate and does affect the photon is not

valid. Even if such an argument is proferred, it raises another difficulty: how to

account for the bending of light rays in a gravitational field gradient.

DBL:

Diagram (a) shows how the photon motion P and gravitation G, without any

modifying influences, would look relative to the natural reference system. The

photon is motionless, while gravitation has an inward speed 1+x. Diagram (b)

shows the same situation relative to the conventional fixed reference system. Now

the photon has an outward speed 1, while the inward gravitational speed has been

reduced to x. Diagram (c) shows the usual situation encountered in practice. The

gravitational speed x has been modified slightly by random motion, and now has a

magnitude y, still very small compared to 1. A photon emitted from the

gravitating object moves outward from that object at unit speed.

12. KVK: The massless sub-atomic particles do not have net time-like displacement

in three dimensions like the atoms. As such why are they not carried away by the

general space-time progression, since inward gravitational motion is not present

to counteract the outward scalar progression? Doubtless, they differ from the

photons thus carried away by the space-time progression in having additionally

rotational displacements. But so long as the net rotational displacement is in less

than three dimensions, the space-time progression should carry it off in the free

dimension. Perhaps this could be the reason that this class of sub-atomic particles

is not observed (p.142, NBM).It is put forward that the uncharged electron, for

example, cannot move through space as its net displacement is space-like and the

relation of space to space is not motion. However, since the one unit of two-

dimensional rotation is balanced by the unit of negative vibration, and the net

space-like rotation is only in the electric dimension, is there no dimension

effectively free so that the scalar space-time progression applies in that

dimension?

DBL: These massless particles undoubtedly move at the speed of light, as you

suggest. Our inability to observe them is not due to their speed, but to the fact

that, except in the case of the neutrino, we have not, thus far, identified processes

in which they take part. Experience with the neutrino suggests that some of the

effects of the other massless particles may also be detectable if we look in the

right places.

13. KVK: Instead of a RV¹ displacement being added to an existing rotational

displacement as in the case of atoms, is it possible to have a rotational vibration

(of opposite space-time character) directly added to the linear vibrating unit that is

a photon? For example, a negative electric charge, RV¹-, can be imposed on a

photon, LV¹+?

DBL: No. A charge is a rotational vibration. As such, it can only exist as a

modifier of a rotation. Otherwise there would be nothing to constrain it into the

rotational path, and it would revert to the status of a linear vibration.

14. KVK.: Chapter 13, NLST: The discussion does not bring out some important

aspects of the difference in the characteristics of electric and magnetic charges

compared to those of gravitation.

Firstly: Like electric charges repel each other and unlike charges attract. In order

to explain this should it be taken that the scalar effect of the charge is both inward

and outward in space-time at the same time?

Secondly: The gravitational force, unlike that due to charges, cannot be screened

off (p. 60, line 3, NBM) because gravitational motion is inward scalar motion

with respect to the general structure of space-time. Now if, the motion which

gives rise to the electric or magnetic forces is a motion of the same general nature

as that of gravitation, being the motion of the individual atom or particle with

respect to the general structure of space-time (p. 186, NLST), it is difficult to see

how these forces can be screened off as is possible actually.

As regards the first point the following line of explanation may be considered.

The negative electric charge, being a time-like RV displacement, must have an

attendant scalar translational motion in space (just like the gravitational motion of

a positive rotation). Like the positive rotation, it may appear that this RV

displacement should therefore involve a scalar inward motion in space. However,

―...because of its vibrational character each unit of this charge is only half as

effective as a unit of unidirectional rotation.‖ (p. 190, NLST) Consequently, this

accompanying scalar translational motion is midway between the general outward

space-time progression and the inward scalar translational motion of a rotational

unit. Thus it appears as a scalar outward motion in space from the point of view of

the gravitationally-bound stationary reference system. This manifests as mutual

repulsion between the negative electric charges.

On the other hand, the rotational vibration that is a positive electric charge, is a

space-like RV displacement. Hence it involves a scalar translational effect similar

to that of a unidirectional rotation that is space-like (motion in time). But the

scalar translational motion of space-like rotational displacement units (i.e.,

rotation in time) is the gravitation in time. As such the space-like RV

displacement too involves a scalar inward motion in time. Once again, as in the

previous case, because of the fact that the vibrational rotation is onty half as

effective as a unidirectional rotation, this attendent scalar inward motion in time

of a positive electric charge falls midway between the general outward space-time

progression and the inward gravitational motion in time. Now, in order to

understand how this appears from the point of view of the stationary spatial

reference system, we must recall that in the context of such a reference system,

the progression of the time component is the same as that in the natural reference

system. Consequently, the scalar translational motioh of the positive electric

charge is apparent as inward in time. This manifests itself to us as mutual

repulsion of the positive charges, since the inward scalar motion in time is

tantamount to outward scalar motion in space.

Finally, the relationship of negative to positive electric charges is that of scalar

outward motion in space to scalar inward motion in time and manifests to us as

mutual attraction of the positive and negative electric charges.

Regarding the possibility of screening off the electrical charge effects: once we

see them as basically scalar motions of the individual charges, screening becomes

impossible, like in the case of gravitation. The following interpretation may be

relevant. The screening is a balancing of the inward (or outward, as the case may

be) scalar motion by a vectorial motion (i.e., ―co-ordinate‖ as versus ―clock‖

motion) in the dimension (or dimensions) concerned, by the screening object.

This characteristic of the screen, the generation of motion oppositely directed to

that of the scalar translational effect of the charge is not unlike the process of

acquisition of gravitational charges due to captured charged neutrinos.

As given, since ―... the natural unit equivalent of a magnetic (2-dimensional)

displacement n is 4n² ...,‖ i.e., (2n)² , the natural unit equivalent of a magnetic

displacement unit of 1 is 2² = 4, and in equivalent electric units is 4/2 = 2 (in view

of the double units we are working with). On the other hand, the natural unit

equivalent of the magnetic displacement unit of 1 is ( 2)²= 2 and in equivalent

electric units is 2/2 = l. Thus, it does not seem to matter, at unit level, whether we

consider the first unit of magnetic displacement as 1 or 1, only the latter is

actually relevant, since this alone gives us the correct atomic number sequence.

This important point is not brought out in the discussion and the whole issue is

glossed over with nothing more than one sentence, ―At the unit level dimensional

differences have no numerical effect, i.e., 1³ = 1² = 1.‖ (p. 128, NBM).

Indeed, the role of unity, as a natural datum, is of far-reaching significance. The

requirement of the first effective unit of the 2-dimensional displacement being 1

instead of 1 can be seen to be arising out of the following. The first unit of

displacement, from the rotational base, has a unique and distinguishing

characteristic in that it marks the emergence of ―something physical compared to

the prevenient nothingness.‖ Inasmuch as this is so, the difference between the

first unit and the rest is not only one of degree—but something else besides. The

addition of the first displacement unit involves a transit from the region inside the

unit displacement to that outside. Hence the dictum that ―... all of the physical

phenomena of the inside region ... are ... second power expressions of the

corresponding quantities of the outside region‖ (p. 155, NBM) applies here.

Consequently, the 1 unit displacement, when looked at from the viewpoint of

physical manifestation—i.e., from the ―somethings‖ side of the unit boundary as

against the ―nothings‖ side—is to be regarded as 1.

It must be noted that the setting up of units and measurement procedures from the

standpoint of the natural reference system, in terms of speed displacements results

in the relation between the algebra of displacements and the algebra of the

conventional speed units being exponential in nature. This is to say that the

addition of displacements is equivalent to the multiplication of the corresponding

speeds.

Suppose we define the speed displacement d, of a speed v, as d = 1g c - 1g v,

since it is a deviation from the unit speed, c; all speeds like 1/n give positive

displacements, lg n, while speeds like n give negative displacements, -1g n, and

unit speed c gives zero displacement, 1g 1. Though this definition does not

exactly tie in with the treatment in the book, it nonetheless serves to demonstrate

the general exponential nature of the relationship mentioned above. It also

illustrates how the addition of a motion of (n-1) positive displacement units to

another of (n-1) negative displacement units produces zero displacement (p. 121,

NBM), since in dealing with the corresponding speeds we need to multiply the

speed n (represented by (n-1) negative displacement units) by speed 1/n ((n-1)

positive displacement units) to obtain the unit speed (zero displacement).

DBL: Your criticism of the lack of coverage of electricity and magnetism is valid,

but here again you should bear in mind that a ―bird‘s eye view‖ does not see

everything. I will give you a much broader view of these subjects in Volume II of

the new edition.

As brought out in Volume I (particularly in Chapter 18), linear motion is limited

to two full units, from +1 to -1, as seen in our fixed reference system. In terms of

the natural reference system both +1 and -1 are zero, the + zero and the - zero, we

may say, if we look at the situation from the standpoint of what is happening in

the region between the two. The motion of an electric charge is always outward,

but the motion of a positive charge is outward from the positive zero, while that of

a negative charge is outward from the negative zero. Two positive charges move

away from each other, as shown in the upper tine of the diagram below. Two

negative charges also move outward away from each other, as shown in the lower

line. But a positive charge and a negative charge move toward each other, as

indicated by the middle line, even though they are both moving outward from

their respective zero points.

Screening is simply a matter of mathematics. A+B is always greater than A, but

A-B can take any value. Since all gravitational motion is in the same direction, the

effect of introducing matter between objects X and Y is to increase the original

gravitational motion A to A+B. But since the motion of charges can take either

direction, the introduction of matter between charges X and Y may have a

resultant A-B.

15. KVK: Regarding the lifetimes of the cosmic decay particles (Ch. 15, NBM) the

following points may be considered. The spatial extension of the cosmic atom is

the analog of the lifetime of the atom in the material sector. As such the lifetimes

of the decaying c-atoms must bear a relation to their spatial extensions before the

decay.

The correlation of lifetimes with the dimensions shown in p. 192, (NBM), can be

arrived at by tying together some loose ends as below (with appropriate

interchange of the words ―space‖ and ―time‖):

i. The limiting spatial extension of the incoming atom in each dimension is

one natural unit (i.e., s in conventional units). Thus the extension space

involved in two dimensions becomes s², and in three dimensions, s³.

ii. The temporal equivalent of this spatial extension s is s/c.

iii. ―..If the motion is one-dimensional, all of the effects can be transmitted. If

it is two-dimensional, the fraction transmitted ... is 1/c of the total ... The

transmitted fraction is only 1/c² in the case of three-dimensional rotation.‖

(p. 185, NLST)

iv. ―...The time region speed, and all quantities derived therefrom, which

means all of the physical phenomena of the inside region ... are ...second

power expressions of the corresponding quantities of the outside region.‖

(p. 155, NBM)

The Table below shows the result of applying these criteria (i) to (iv) above to the

various dimensional motion.

Criterion No. Number of Dimensions

1 2 3

i s s² s³

ii s/c s²/c s³/c

iii (s/c) (s²/c)(1/c) (s³/c)(1/c²)

iv (s/c)½

[(s²/c)(1/c)]½ [(s³/c)(1/c²)]

½

Result in secs. 1.233148 × 10-8 1.520655 ×10-16 1.875193 × 10-24

On the other hand, if the extension space involved in the two- and three-

dimensional cases is respectively /4s² and /6s³ (based on statistical circular and

spherical symmetry in co-ordinate space) instead of s² and s³, we have the

calculated values of the lifetimes in the two- and three-dimensional cases as

respectively 1.347645×10-16 and 1.356892×10-24 seconds.

DBL: You may have something here. I do not have time to make a full evaluation

of your proposal now. In fact, I have a general policy of not making a quick

decision on any new idea, whether it is my own or comes from someone else. But

it appears to me that this may be the kind of a thing that I was looking for

(unsuccessfully) at the time I wrote Chapter 15. I suggest that you prepare a paper

on this subject and send it to Professor Meyer for publication in Reciprocity, so

that the NSA members can take a look at it.

16. KVK: The general space-time progression of our universe is an outward scalar

progression. How is this to be distinguished from one with both space and time

progressing inward? The universe of motion with both space and time progressing

outward is indistinguishable from that with both space and time progressing

inward. In addition, both these cases are indistinguishable from a third case where

for one unit both space and time progress outward and in the next unit both of

them progress inward, alternately. It is not clear how this indistinguishability is

built into the conceptual framework of the theory. Moreover, how (or whether)

our consciousness has come to regard it as an outward progression is not evident.

DBL: The existence of a physical universe is possible only if gravitation is

inward, so that the originally widely dispersed units of matter move closer

together and eventually reach positions in which they can interact. This means

that the arbitrary fixed reference system that we set up on the basis of such

interactions is moving inward relative to the natural reference system. The

apparent progression of the natural reference system is therefore outward.

17. KVK: ―...deviations from unit speed ... are accomplished by means of reversals of

the direction of the progression of either space or time.‖ (p. 75, NBM) What about

the case of conjoint reversals of both space and time, like: -s/+t , +s/-t , -s/+t.... .

etc.? That is, for one unit space progresses inward while time progresses outward.

In the next unit space progresses outward and time progresses inward. Such a

basic motion has a speed of -1 that is unvarying and must be both an independent

and a stable motion. Can we identify the above ―coupled-vibration‖ with any

physical entity? The above may even result in rotation. At any rate, the motion is

similar to the inward translational aspect of the material gravitation.

DBL: A speed of unity, 1/1, is no motion at all relative to the natural system. We

cannot distinguish between no motion in space and no motion in time.

[KVK: But reply does not answer the point I raised here. I was asking whether

this ―coupled vibration,‖ with speed of -1 like the gravitational motion, could be

realized in some physical entity?]

18. KVK: I find that the following concepts are not explained adequately, with the

result the reader (who is being exposed the first time) is left with many nagging

why and hows:

a. the inter-regional ratio (p 154, NBM)

b. secondary mass (p. 161, NBM)

c. electric mass and mass of electric charge (p. 163, NBM)

d. secondary neutral valence

DBL: I am not sure just what you have in mind here. Are you merely suggesting

that I should explain these points more fully in later publications? (in which case,

I thank you for the suggestion), or do you have some questions that you want

answered? (in which case I would like to have something more specific).

19. KVK: p. 100, NBM: Continuing the line of argument (in the text), if we substitute

an object with a speed less than c for each of the photons, instead of for only one

(as suggested in the last-but-one para), we arrive at the true relative v speed of the

two objects as (v1+v2)/(v1+v2) = 1 always. Thus the true relative speed always

turns out to be unity for any objects—not necessarily only for photons.

DBL: The time component of speed always includes the time of the progression

(clock time), regardless of whether the moving objects are, like the photons,

moving at the unit speed of the progression, or at some different rate. Thus the

denominator is always 1 ± v, never v alone.

[KVK: Does the answer here mean that the relative speed of two objects with

speeds v1 and v2 (in natural units) is given by (v1+v2)/(1+v1+v2) since the total time

involved would be (1+v1+v2)?]

20. KVK.: 128-9, NBM: It is not clear why the relation that ―...a magnetic

displacement n is equivalent to 2n² electric displacement units‖ does not hold

good for n=1. For n=1, the equivalent electric disptacement works out to be 2, by

this formula. However, in the development of the series of elements, the magnetic

displacement 1 is counted as an equivalent electric displacement of 1 unit and not

2. There is definitely a hiatus in the reasoning here, an examination of which may

lead to some important insight and clarify, among others, the case of half units

represented in M ½-½-0, for example.

Under these circumstances, it is not difficult to see that halving the displacement

unit amounts to taking the square-root of the corresponding speed and does not

involve any half unit of speed (i.e., if d = 1g n, then ½d = ½1g n = 1g n). For

particles below the unit level, as in the case of sub-atomic particles, this gives rise

to the unique possibility of positing ½ unit displacement (141, NBM) because of

the idempotent nature of unity (i.e., 1= 1), without involving anything less than

unit speed.

DBL: I don‘t believe that I get the point of your argument on this item. So far as I

can see, we are applying the same relation all the way through the series of

elements. The sequence of magnetic additions is this:

Rotation Net speed Electric Equiv.

Rotational base (2) 1-0-0 0-0-0 0

Effective zero (unity) 1-1-0 1-0-0 0 } n=1

Helium 2-1-0 1-1-0 2

Neon 2-2-0 2-1-0 10 } n=2

Argon 3-2-0 2-2-0 18

21. We start with a rotational base for each of the two rotating systems of the atom,

with net speed zero in all dimensions. Then we add one magnetic rotational unit

to bring the effective speed to unity, the natural zero level. (The language that I

used in the book may have been somewhat misleading, although I did say

specifically that the purpose of this first magnetic unit is to bring the scalar speed

to zero on the natural basis.) Since this non-effective unit uses up one of the n = 1

spots, there is only 2x 1² group of elements, and a 2 x 2² group follows, as shown

in the tabulation.

22. KVK: p. 154, NBM: The inter-regional ratio is calculated on the basis that ―for

each of the 128 possible rotational positions there is an additional 2/9 vibrational

position...‖ The ratio is thus found to be 128(1+2/9) = 156.44. However, in the

case of sub-atomic particies, which are single rotating systems, only one, and not

two, of the possible nine vibrational positions are occupied. Thus the inter-

regional ratio must be 128(1+1/9) = 142.22 and not 156.44.

DBL: You are correct. The 142.22 ratio must be substituted for 156.44 in the

appropriate applications. I said this on page 163 NBM.

This completes the items that I received from Professor Meyer. I have tried to be

responsive to the questions that you have asked, but it cannot be expected that all

of my answers will be satisfactory. So I want to assure you that I will be glad to

discuss any of them at more length if there are issues that you want to raise. It is

apparent from your comments that you have gained a good deal of insight into the

structure of the theory already, and I would like to help clear away any obstacles

that still remain in the way of a full understanding.

It has become quite clear since publication of Nothing But Motion that the

scientific community in general has very little comprehension of the scalar type of

motion that plays such a large part in my theoretical development, although scalar

motion is not something that is peculiar to my theoretical system. It is something

that exists as one of the phenomena of the physical universe, and any physical

theory should be prepared to deal with it. Since it is a very important factor in my

theoretical structure, and so generally neglected in current practice, I am planning

on including an extended discussion of this type of motion in Volume II. I put a

part of this discussion into a memorandum that I used at the recent NSA

conference at Huntsville, Alabama. I believe that this should be of some interest

to you, and I am therefore enclosing a copy.

DIALOGUE WITH DEWEY B. LARSON, PART II

Below are reproduced further comments on D. B. Larson‘s Nothing But Motion (NBM)

and on Quasars & Pulsars (QP), interspersed with responses by the author. The

correspondence from which this dialogue is excerpted took place c. 1980.

1. KVK: Ref. p.46, para 2, QP: If the n mass-units of a material aggregate are

dispersed in time, no observer can encounter all of them at the same time. For

example, all of the atoms in an object may not manifest at the same time because

of the differences in their coordinate time, even if they are at the same stage of the

progression.

DBL: Two atoms are in contact when they are within the equilibrium distance in

either space or time, regardless of how far apart they may be in the other. They

have to be at the same stage of the progression to make contact in space, but this

has nothing to do with time. It is a result of the fact that even though two objects

may be at the same point in the reference system, they are not at the same location

in space unless they are also at the same stage of the progression.

2. KVK: Ref. p. 48, para 2, QP: This example of the two cardboard disks gives rise

to two possibilities, which are polar opposites as far as the mutual direction of the

coupled rotations are concerned. For a given direction of rotation of disk A, disk

B could be posited either as rotating in the clockwise sense or in the

counterclockwise sense. Do these dual possibilities in the model refer to any

analogously distinguishable categories of the double rotating system of the atoms?

DBL: I have not considered this issue previously, and I do not want to express any

firm conclusions without more extended consideration, but from my findings in

the fields of electricity and magnetism, I would tentatively conclude that reversal

of the direction of rotation would reverse the scalar direction. The resulting

motion would be incompatible with the atomic structure.

3. KVK: Ref. p. 98, line 7, QP: Should not the word ‗active‘ be replaced by the word

‗inactive‘?

DBL: No. Beyond the unit level (the speed of light) motion takes place in two

scalar dimensions.

4. KVK: Ref. p.98, lines 13-16, QP: Firstly, it is not clear how ‗only one dimension

of the explosion speed is coincident with the normal recession.‘ For instance the

recession itself is not limited only to our line-of-sight. Secondly, it is not clear

how the excess redshift and the recession redshift are to be connected, or why the

former is proportional to the square root of the latter.

DBL: These items are also connected with the concept of scalar dimensions. I am

enclosing copies of two pages of the introduction to Volume II of the new edition

of the ―Structure‖, which should help to explain what I mean here. Motion at

speeds beyond the unit level involves both a space magnitude and a time

magnitude. It is therefore a two-dimensional scalar motion, only one dimension of

which can be parallel to the dimension of the reference system.

5. KVK: p.154, line 18, NBM: Should it not read: ―...the ratio of the total magnitude

of motion to the transmitted effect‖ rather than the converse?

DBL: Yes.

6. KVK: p.154, lines 8-7 from bottom, NBM: The possible vibrational positions for

the two-dimensional basic rotation do not seem to me to be nine, in view of the

fact that the respective orientations of the initial vibrating units of both rotating

systems are not independent of each other, after the formation of the double

rotating system. It can be seen that the number of possible orientations for the

vibrational displacement of one of the rotating systems of the atom is three.

However, referring back to the two-disk analogy (p. 48, QP), the number of

possible orientations for the initial vibration of the second rotating system is only

two, because one of the three dimensions is already occupied by the first and there

is no superimposition. As such, the total number of vibrational possibilities is six,

of which one is occupied. Thus the inter-regional ratio must be 128(1 + 1/6)

=149.33.

DBL: I cannot agree with your conclusions here: There are nine different

combinations irrespective of geometrical considerations.

7. KVK: p.163, NBM: In the calculation of the unit of electric mass, why is the 1/9

vibrational factor relevant, since what we are concerned with is the electric

rotation.

DBL: The 1/9 factor applies to the distribution in space. The same factor applies

to both the distribution of the electric rotation and the distribution of the possible

positions of the vibrational units, but this does not mean that there is any

connection between the two.

8. KVK: p.6, para 3, Advance Printing of the first 11 chapters of Volume II: What is

orientation? What is meant by the rotational force acting only during a portion of

unit progression?

DBL: I use the word ―orientation‖ in the sense defined in the dictionary; that is,

position with respect to the environment. I suggest that you review the discussion

of orientation in the references listed under that heading in the index of NBM,

page 291.

9. KVK: The basic scalar reversals that make possible speeds other than unity are

fundamental in the Theory. As such, a thorough understanding of their nature is

important.

The givenness of the 1/1 unidirectional scalar progression is understandable.

However, how the reversal of the scalar direction of the progression is

accomplished in nature is not explained. In the existing pattern of thinking one

posits a cause for a systematic variation of a state of affairs. Inasmuch as these

reversals are systematic and not random (in order to produce a speed other than

unity) it is not clear what sustains them. Why should the reversals occur at all

since the ‗peace‘ of the unidirectional progression has a greater probability? They

stand merely as a logical necessity for the subsequent development of the theory.

DBL: Aristotle and his contemporaries insisted that continuity of position is the

only condition that can be maintained without the application of some external

influence. One of the essential steps toward a theory of motion was a recognition

of the tact that a continuous uniform change of position is just as fundamental,

and just as permanent, as a continuity of position. The essential. feature is the

continuity. What is needed now is recognition of the fact that the same

considerations apply to direction. A continuous uniform change of direction is just

as fundamental, and just as probable a condition, as a continuous direction. A

motion with a continuous uniform change of direction is, of course, a simple

harmonic motion. There is no more need for anything to sustain a simple

harmonic motion than a unidirectional motion.

10. KVK: What is the nature of the connection between the scalar reversals and the

vectorial directional reversals associated with them? In the case of a vibration that

is a photon, since the vectorial reversal occurs at the end of each unit, it is not

always in phase with the scalar reversal. Obviously the two (the scalar and the

associated vectorial) directional reversals are connected: but as this connection is

not explained, one wonders how the vectorial reversal ‗knows‘ when to be in

phase with the scalar reversal and when not to be, in order to produce a regular

oscillation pattern.

DBL: The further changes in the pattern of reversals that, as you say, produce

speeds other than unity, are mathematical possibilities. Each corresponds to a

particular displacement magnitude (a particular number of units of energy in the

phenomena of ordinary life). This displacement (or energy) content is what

maintains the constant reversal pattern. The pattern cannot change unless energy

is added or withdrawn.

11. KVK: The way the reversals are explained to be occurring, they can give rise to

odd frequencies in a straightforward manner. However, the even frequencies are

pictured to be accomplished by the systematic compounding of odd frequencies.

Thus, for example, frequency 4 is obtained by the averaging of the multiple units

of 5 and 3 that occur alternately. But if it is so possible to accomplish frequency 4

by way of compounding of 5 and 3, [(5+3)/2 = 4], why is it not possible to obtain

non-integral frequencies, such as 4.33 for example, by the compounding of

multiple units thus: (5+5+3)/3 = 4.33 etc.? Do we have to take recourse to an ad

hoc constraint to avoid this?

DBL: In view of the systematic relation between number and probability (see item

No. 13 below), the only place where two numbers are equally probable is the

midpoint between successive numbers. In this situation (and no other), probability

usually dictates an equal distribution between the two. In a situation such as that

we are now considering, this distribution must be exactly equal in order to

produce a regular pattern.

12. KVK: In the notation a-b-c of the atomic rotations, ‗a‘ stands for the principal

magnetic rotation and ‗b‘ for the sub-ordinate magnetic rotation. The principal

magnetic rotation is said to be effective in two dimensions while the subordinate

magnetic rotation in one dimension (p.128, NBM). How is this so? as both of

them are two-dimensional rotations, each must be effective in two dimensions.

D B.L.: Two independent rotations of a disk (a one-dimensional rotation of a line)

would produce two spheres, but a rotation of two inter-penetrated disks produces

a spheroid, either an oblate spheroid with a volume proportional to a²b, or a

prolate spheroid with a volume proportional to ab² .

13. KVK: Ref. p.48, para 3, QP: ―...as a general principle low numbers are more

probable than higher numbers...‖ Why should this be so? To be sure, this ‗general

principle‘ is not incorporated in the Fundamental Postulates.

DBL: You can demonstrate this with the standard coin tossing experiment. You

will get two successive heads very often, three much less frequently, four still less

often and so on. The same principle applies throughout the universe.

14. KVK: The electric charge is a one-dimensional rotational vibration, and is

normally a modification of the existing one-dimensional rotation in the electric

dimension. But the exception is the proton which is M 1-1-(1). In this case, if the

electric charge is to be a modification of the rotation in the electric dimension it

would be a negative charge, as in the case of an electron M 0-0-(1), since the

rotation in the electric dimension is negative. As such, it is taken that this electric

charge is a modification of the two-dimensional positive rotation (in the magnetic

dimension). Consequently it will be a positive electric charge as we want.

But why does this positive electric charge, which is one-dimensional, take

precedence over a magnetic charge, which should more naturally be the

appendage to the basic two-dimensional rotation in M 1-1-(1)? Compare with the

case of the neutrino M ½-½-(1) which easily acquires a magnetic charge (on its 1

unit two-dimensional rotation) rather than an electric charge.

DBL: A charge opposes the rotation to which it is applied under ordinary

circumstances, and in the particles (single rotating systems) the units are equal in

size. Thus a negative charge added to the proton, M 1-1-( l ), would increase its

net total displacement to 2. As noted in NBM, it appears that two-unit single

rotations are unstable, and tend to decay back to simpler components, unless they

are able to acquire the second rotating system that is required for converting to

mass 1 hydrogen. A second point in this connection is that a magnetic charge is

not acquired easily. On the contrary, the evidence indicates (although the reason is

still unknown) that acquisition of such a charge by a neutrino is a very rare event.

Concentrations of charged neutrinos are produced only by an enormous number

of interactions with matter over vast periods of time.

15. KVK: While a neutrino M ½-½-(1) can easily acquire a magnetic charge, why

does it not happen to a massless neutron M ½-½-0? (Of course, if it thus gets

magnetically charged, its potential mass becomes actual.)

DBL: A positive magnetic charge added to either the neutrino or the massless

neutron cancels the positive rotational displacement. The effective displacement

of the charged neutrino is equal to that of the uncharged electron, and it acts like

the electron. The effective displacement of a charged massless neutron would be

that of the rotational base, zero, and there would be no effects that could be

observed.

16. KVK: Why is the photon M 1-1-(1), having net rotational displacement in three

dimensions and a mass of one atomic weight unit, not observed in the uncharged

state, when theory does not preclude this?

DBL: The answer to this question is still in doubt. It may be that there are too

many neutrinos in the environment. As indicated in NBM, page 215, an

uncharged proton and a neutrino can combine to form the mass one hydrogen

isotope. It is possible that the uncharged proton never gets a chance to stay around

long enough to be observed.

17. KVK: p. 52, lines 14.-15, QP: ―The atomic number of any ... element is equal to

its equivalent electric time displacement less two units.‖ Take for instance the

case of He: 2-1-0. After accounting for one two-dimensional unit counteracting

the opposite displacement of the basic photon we are left with a net displacement

of 1-1-0. This must naturally yield an electric equivalent of (2×1²) + (2×1²) = 4

displacement units. What is the reason for specifying that one of these two (2×1²)

units is not to be counted?

DBL: As you say, the helium atom has net displacements 1-1-0. If we eliminate

one magnetic unit, we have the combination 1-0-0 (or 1-1-0 in the regular atomic

notation). This is not an atom because it does not have enough effective

displacement to form a double system. It is a base for the atomic rotation in the

same way that the rotational base, M 0-0-0, is for rotation in general. We might

call it an atom of zero atomic number. Thus there is only one 2×1² group of

elements.

18. KVK: Is not the inward translational effect of the scalar rotation (gravity)

proportional to the number of rotational displacement units? If yes, since the

maximum number of unidirectional three-dimensional displacement units is 8,

how to justify the number of units of the inward motion when it exceeds 8, as is

the case of elements with atomic number greater than 8?

DBL: Gravitation is not a unidirectional motion. It is a rotationally distributed

scalar motion. See the memorandum on scalar motion that I sent to you.

19. K.V..K. Ref. p. 98, para 2, QP: The ‗units of motion‘ referred to here are

displacement units, aren‘t they? Why do these 7 units get distributed only

between two dimensions? Why not between the three dimensions? Since the

direction in time taken by the ultrahigh speed unit has no relation to the direction

in space, probability principles require equal distribution among the three

dimensions of space.

DBL: Motion in the region above unit speed takes place in two scalar dimensions

because of the second unit status of this region. All that this means is that it takes

two numerical magnitudes to define the motion, rather than the one that is

sufficient for any motion below unit speed. It has nothing to do with the

dimensions of the spatial reference system.

20. KVK: Then again, the connection between the recession redshift and the quasar

redshift is not clearly explained. The recession redshift depends on the particular

moment at which the explosion happens to take place. As such it should not bear a

strict logical relation to the explosion redshift, since the time of occurrence of the

explosion is determined by various local conditions and not strictly by its distance

from us.

DBL: The difficulty that you mention with respect to the relation between the

redshifts is merely a matter of the time required to transmit information. If an

explosion occurs at a distance x from our location, the corresponding distance in

the explosion dimension is 3.5 x½. This is the actual separation between us and

the quasar in this dimension. But we see the explosion at spatial distance x, and

we cannot get the quasar distance information instantaneously; that is, the quasar

cannot appear to jump directly from x to 3.5 x½ What happens is that this

information comes to us as fast as it can. The quasar appears to move at the speed

of light in the explosion dimension until it reaches the 3.5 x½ distance, after which

it recedes normally. The time required to make this adjustment is very short, and

it is propable that we have never observed a quasar in the adjustment period.

21. KVK: Ref. p. 108-9, QP: Does the same gravitation oppose normal recession

as well as the explosion? Or is it the portion left after countering the recession

that is available to oppose the explosion? On p.109, lines 1-2, what is meant by

the dimension of recession and the dimension of quasar motion? Does it mean that

since 1 unit recession is already present in one dimension of the three dimensions,

the explosion motion takes the remaining two?

DBL: Yes, gravitation opposes each motion independently. In application to

scalar motion, I am using the term ―dimension‖ in the mathematical sense. An n-

dimensional scalar motion is one that requires n separate numbers to define it. The

example given in my dictionary is this: ―a²b²c is a term of five dimensions‖. Only

one of these scalar dimensions of motion can be represented in the conventional

spatial reference system. Any number of motions of an object that can be

represented in the system can be combined vectorially into a one-dimensional

resultant, and the magnitude of the resultant can be expressed by one number.

What the reference aystem does is to subdivide the one dimension of motion into

components by relating it to three dimensions of space. The two dimensions of

motion above unit speed are scalar dimensions, and they are not vector quantities.

22. KVK: Ref, p.123, lines 10-11, QP: But when the speed is changing should not one

take the integral of v·dt as the distance and not simply v·t?

D.B.L.: I see no advantage in so doing. What we are interested in is the average

speed.

23. 23. KVK: p.60, para 3, QP: This phenomenon of positive ionization resulting

from high temperature must be observable experimentally. It would then

constitute an element of validition of the theory.

DBL: This is the ionization that the physiciats and the astronomers talk about.

They attribute it to the loss of successive electrons from the atomic structure as

the temperature increases. My finding is that units of vibrational motion are

added. This is, of course, a deduction from basic principles, but it is worth noting

that it produces a more logical result. An increase in the energy content of the

environment ought to result in processes that gain energy from the environment,

rather than processes that lose energy to the environment.

24. KVK: Ref. p.66, para 2, QP: Here is another venue for observational verification.

During the past millions of years of the age of our planet, the local level of

magnetic ionization must have increased. Can we devise experiments to measure

this and then to correlate this change with (i) the change of isotopic proportions in

the earth‘s crust and (ii) the shift of the radioactive stability limit of the heavy

elements that took place during this period? Also we may verify this correlation

by comparing with systems of matter under a different ambient magnetic

ionization level, as on distant planets.

DBL: The question as to when the magnetic ionization level on earth stepped up

to the present level , which is almost certainly one unit, is not definitely indicated

by the information now available. There are reasons to believe, however, that this

change antedated the formation of the Solar System.

25. KVK: The half-lives of electron and proton are estimated to be about 2x1021 years

and 1027 years respectively. Could the chance encounters with the c-atoms

(moving inward in time) be the cause for these spontaneous decays of electrons

and protons?

DBL: I doubt if these estimates have any real meaning.

26. KVK: The process of the transition of a quasar from our time-space region to the

space-time region of the cosmic sector looks to me analogous to the process of the

transition of the solid state (of matter) from the time region to the gaseous state of

the time-space region.

It is stated that the overcoming of cohesion in one dimension results in the liquid

state and the vanishing of cohesion in three dimensions results in the gaseous

state. While this is true, there is also an intermediate case of the vanishing of

cohesion in two dimensions. My suggestion is that this constitutes the vapor state.

The liquid state ends with the overcoming of cohesion in two dimensions.

Let us take a look at the analogy I was mentioning. Please refer to the Fig. 4, p.68,

QP. For the ‗scalar inversion‘ (by which I mean the transition from the time-space

region to the space-time region) to happen, what is necessary is not unit speed in

all the three dimensions (Fig.4c), but only unit speed in each of the two inactive

dimensions. Since the conversion of unit speed to zero speed in time in the

inactive dimensions (Fig.4d), is a normal, down-hill process in the cosmic sector,

this addition of unit speed in the two inactive dimensions is sufficient to bring the

situation of Fig.4a eventually to that of Fig.4d, and execute the complete scalar

inversion. (Of course, the sub-luminal speed represented by T in Fig.4d, in the

active dimension results in a distortion in the stationary three-dimensional

temporal reference frame of the cosmic sector, showing up as motion in

‗equivalent time‘).

Now the point I want to make is that, in exactly the same way, in our analogy,

what ends the liquid state is the emancipation from cohesion in two dimensions

only, and not in three. Availability of additional thermal energy, however,

converts the vapor to gas by overcoming cohesion in the third dimension too.

Further—please see bottom para, p.75, QP: here I am inclined to consider the

structure of a cluster or galaxy of stars to be more analogous to that of a solid at

high temperature, rather than a liquid as you suggest. The suggestion is perhaps

based on the apparent fluid nature of the structure. But, insofar as the stars occupy

equilibrium positions (under inward gravity and outward progresion) they are

analogous to the solid molecules which too occupy equilibrium positions (under

outward gravity and inward progression), The apparent fluidity in the galactic

instance is due to the different nature of the equilibrium.

Now my sketch below indicates the step by step analogy between the two

processes I was mentioning—one involving transition from the time region to the

time-space region, and the other from the time-space region to the space-time

region. The numbers in the blocks indicate the number of dimensions of motion

pertaining to that particular region in which it is shown. The ‗material rays‘shown

in the c-sector are the analogs of the cosmic rays of our sector.

D. B.L.: The idea of the vapor state having cohesion in only one dimension is an

attractive one, and I gave it considerable attention 30 or 40 years ago when I was

working on liquid and gas properties, I ran into quite a few problems in

developing the idea, mainly because of the coexistence of the liquid and vapor

states over such a wide range of temperatures, and I never reached any firm

conclusions. I discontinued work in this area about 1960 when I decided to reduce

my research activities and spend more time on writing about what I had already

found out.

Your ideas as to the transition from the material to the cosmic sector are on the

right track, although the situation as I find it is more complicated. You may be

interested in comparing your diagram with the following one, taken from the

manuscript of what will probably be my next book:

27. 27. K,V.K.: Why can‘t there be electrical charged neutrons and massless neutrons,

M+ ½-½-(1) , M

-½-½-(1) and M

+ ½-½-0?

DBL: I presume it is because the charge, being a rotational vibration—half of full

rotation—must modify a full rotational unit, but it cannot extend over two

dimensions, as a two-dimensional unit can, and in the cases that you mention

there is no full unit for it to modify.

28. KVK: It is still not clear what the origin of the secondary mass is: what is meant

by ‗the initial level‘ and ‗its motion in the time region‘ (NBM, p.161)?

DBL: The primary mass is a measure of motion that is defined as a relation of

units of space to units of time. But since the equilibrium positions of the atoms of

ordinary matter are inside unit space, some additional effects of their motions take

place within the space units, and a portion of these internal effects is transmitted

to the external region. These are relations of units of equivalent space to units of

time. It seemed to me that the easiest way to grasp what is happening here would

be to regard it as analogous to firing a gun from a moving vehicle. In order to

arrive at the speed of the projectile, we have to take into account the initial level

of speed, the speed of the vehicle, as well as the speed imparted by the explosive

charge.

29. KVK: In view of the discrete unit postulate, the gravitational speed cannot be

greater than 2 inward units. Now suppose there is an atom with Z = 50: does its

atomic weight 100 give rise to 100 units of inward speed, that is, gravity? If not,

how does the magnitude of the inward translational effect (gravity) of an element

with Z = 50 differ from that of an atom with, say, Z = 30? How to account for this

gravitational speed greater than 2 net units? .

DBL: the total gravitational speed of each mass unit is always two units (one net

inward unit). The effect of aggregation of the mass units is to increase the

distribution of this total speed toward the location of the aggregate.

30. K,V,K,: The entire heart of the quasar theory was explained in just one paragraph

(QP, p. 98, top para). The total separation between zero speed in space and zero

speed in (3-dimensional) time is taken to be 8 units. But in your diagram A

(Reciprocity, VIII (4), p. 25) you show only a total of 6 units.

DBL: For this purpose you naed to distinguish between the dimensions of space

(or time) and the dimensions of motion (what I have called scalar dimensions). As

I pointed out in the manuscript of The Neglected Facts of Science (Chapter 2),

only one dimension of motion can be represented m the conventional spatial

reference system. The magnitude of this one dimension of motion is resolved into

three sub-magnitudes by the introduction of directions in space. Thus a one-

dimensional scalar motion is three-dimensional in space.

From zero speed to zero energy in one scalar dimension is two equivalent units of

speed (or energy). The total number of units from the absolute zero of speed to the

absolute zero energy (three scalar dimensions) as thus six units. But each two-unit

component of this total (each dimension) is subject to resolution into three

dimensions of space. This means that there are eight equivalent one-dimensional

spatial units when the one scalar dimension of motion is distributed three-

dimensionally. Only one of these can be represented in the spatial reference

system, but the magnitudes of the motion in time (equivalent space) can be

deteated by the Doppler shifts. However, all relations in which the spatial

equivalent of time is substituted for actual space are two-dimensional (see NBM,

page 155). Consequently, the seven remaining equivalent space units are divided

(usually equally) beween the dimension that is coincident with the dimension of

the reference system and the dimension in which the Doppler shift is

unobservable.

31. KVK: Moreover, is this 8-unit separation in terms of speed units or in terms of

speed displacement units? (since, if the displacement is n, the speed is 1/n+1 or

n+1/1).

DBL: In these instances we are dealing with speed units. Displacement applies

only to those phenomena, in which the effective quantities are the increments

above unity.

32. KVK: See: ―.. the seven units are therefore divided equally between the two

spatial dimensions that are now active.― (p.98, top para, QP). What is meant by

‗active‘ here? Are you referring to the two spatial directions (p. 97, second para,

QP ) in which there can‗t be a translational movement since translation is already

taking place in one direction of the 3-dimensional space due to the recession. To

be specific, let us imagine the x-y-z Cartesian system to locate the quasar. If

translation due to the recession happens to be in the z-direction, the object cannot

have a spatial speed in the x and y directions. If this is so, your words quoted

above seem to mean to me that the 7-unit equivalent of the 1-unit quasar motion

in time is divided between the x and y directions of space. Is this what you wanted

to convey? But in the next sentence you say ―The component of the explosion

speed in the recession dimension is thus 3·50‖. Here your words seem to mean

that this 3·5 units show up in the z-direction of space, in which the recession

speed is manifesting in the coordinate system. Further, a few lines below you

mention, ―...only one dimension of the explosion speed is coincident with the

normal recession...‖ Does not the explosion speed belong to a second scalar

dimension, altogether different from the dimension in which the recession is

taking place? How does one dimension of the explosion speed coincide with the

recession? If the explosion speed is a two-dimensional scalar motion, why can‘t

both these scalar dimensions be other than the dimension of recession, in which

case no dimension of the explosion speed coincides with the normal recession.

That is, suppose a, b, c are the magnitudes of the scalar motions in the three scalar

dimensions and let a represent the recession. If, then b and c pertain to the

explosion motion, none of the dimensions of the explosion motion coincides with

the recession dimension. How then the square-root of zr arises is not clear.

DBL: The recession takes place in all three scalar dimensions. It follows that one

of these three dimensions is coincident with one of the two dimensions of motion

in equivalent space. The total magnitude of the motion in this effective dimension

is the sum of the recession, z and the effective portion of the motion in equivalent

space, 3 · 5 z½.

You should not try to visualize these motions in terms of the spatial reference

system (the x-y-z Cartesian system to which you refer), because neither the low

speed motion in the second and third scalar dimenaions, nor any of the high speed

(above unity) motions can be represented in that system. In dealing with these

motions we have to deal entirely with magnitudes. When we talk about

dimensions in connection with them, it is only in the mathematical sense, in

which an n-dimensional quantity is one that requires n scalar magnitudes to define

it. These dimensions are not the dimensions of the spatial reference system. Since

the quantities with which we are dealing are the same in all cases—that is, units of

motion—any one magnitude outside the reference system can be added to the

magnitude represented in that system. We can then say that the dimension of such

a magnitude is coincident with (or parallel to) the dimension of the motion in the

reference system, meaning merely that the quantities are additive. No more than

one magnitude (dimension) of such outside motion can be coincident in this

manner.

33. KVK: In the calculation of the interregional ratio, how does the factor 8 in 4x4x8

= 128 arise? If we take that the possible number of orientations of the electric

displacement as only 8, how to accomodate the greater than 8 displacements in

the electric dimension of atoms like 3-3-9 or 4-4-12 etc.?

DBL: The value 12 in 4-4-12 is not a displacement; it is a specific rotation. See

page 11, Basic Properties of Matter.

34. KVK: See Reciprocity, VIII (4), p.25: in diagram A we have, as I have already

remarked, 6 displacement units only—not the 8 units between the positive and

negative zero points. The natural datum is shown 3 displacement units away from

the zero datum. Does ‗zero datum‘ mean the stationary reference frame?

See p.26, top line: ―...no effective motion in two of the three dimensions ..‖ Do

you mean the dimensions of motion or the dimensions of 3-dimensional space? In

the next line you mention that gravitational motion ―is an inward motion at unit

speed: the kind of a unit in which line (1) of diagram A is expressed.‖ But line ( l

) is expressed in speed displacement units. So by the words ―gravity is inward

motion at unit speed displacement‖ we find the gravitational speed as 1/(1+1)=½

and not 1. (Moreover, is the gravitational speed of a unit with atomic No. Z equal

to 2Z speed displacement units?)

DBL: The comments in Vol. VIII, No. 4, of Reciprocity were a report of

reflections on an extemporaneous discussion at the Salt Lake conference of some

points that had not been given any extended consideration previously. The

conclusions expressed therein were necessarily tentative. More mature

consideration indicates that they are not complete, and not as well expressed as

they could be. You will find a much better discussion of the subject in Chapter 6,

NFS. Diagram C in this chapter replaces Diagram A in the Reciprocity article, and

Diagram D shows the general relations of the various speed ranges.

35. KVK: See NBM, p.100, lines 4-6: Independent motion at speed 1/n involves a

change of position in 3-dimensional time amounting to 1/n units. Now see the

third para, same page. The forward motion of a photon with unit speed is not an

independent motion. Only its motion in the dimension of oscillation is an

independent motion. As such, how is it that its forward motion (which is

fictitious, being only the result of viewing it from our stationary reference system)

involves coordinate time, which is utized to explain the phenomenon of the

constancy of the speed of light?

DBL: I am not sure that I understand your point here, but I think that it has to do

with my use of the term ―independent‖, so let me say two things: (1) I am calling

any motion other than the outward progression of the natural reference system

independent, and (2) the only way in which an independent motion can originate

is by means of reversals of scalar direction. Such an oscillating motion is

―independent‖ in my terminology, even though it has components that coincide

with the normal outward progression.

36. KVK: When you talk of the possibility of the net speed being 1 - (1/n) , where n is

the number of energy units, do you mean that they are natural units of energy?

Why is it that energy is taken as space displacement? What is the significance of

the minus sign in line (2) of diagram A (Reciprocity, op. cit.)? From line (4) we

see that energy magnitudes greater than 4/1 are not possible. What does this

mean? What is the equivalent, in ergs, of this 4/1 units of energy?

DBL: (a) Yes. See page 118, NFS. ( b) Because it is inverse speed; that is, n units

of space per unit of time, whereas speed, which we define in terms of the region

below the speed of light (unity), is one unit of space per n units of time. (c) When

we express the deviation from unity in units, we have to distinguish between the

direct units and the inverse units in some way. This is one of the ways in which it

can be done. (d) I did not mean to imply that it is possible to attain 4 units of

energy, I was merely showing the equivalents. Further study, the results of which

are described in Chapter 6, NFS indicates that neither speed nor energy can

exceed 2 net units. (e) I have not considered this question at length. Just offhand, I

would say that what we are dealing with is one natural unit of energy; that is, unit

mass times the square of unit speed, or 1.49 x 10³ ergs.

37. KVK: Suppose in some case the spatial speed is v cm/sec. (less than light speed,

c). What is its corresponding unit in terms of speed displacement? Since v/c =

1/(n+1); n, the number of displacement units = (c/v)-1? And from lines (3) and (4)

of diagram A, is a speed v/c equivalent to an energy c/v?

DBL: We can use any appropriate system of measurement, but it is helpful to

adapt the system to the particular situation with which we are dealing. In the case

of the atomic rotational combinations, it is advantageous to deal with

displacements from the natural datum, unity, so that we can express positive and

negative magnitudes in commensurate units, and there is no conventional usage

that stands in the way of doing this. In dealing with translational motion, on the

other hand, we want to examine the effect of successive additions of speed units

beginning at zero speed. Measuring from zero in this case is not only convenient

for our purpose, but also conforms with the conventional usage. This is why I

have substituted Diagram C, NFS, for Diagram A in the Reciprocity article. I

would recommend that you pay no attention to displacement (measurement from

unity) in dealing with translational motion, and express everything in terms of

speed (measured from zero speed), or energy (measured from zero energy).

38. KVK: What is the distinction and relation between (a) the positive zero and the

negative zero (NBM, p.153, para 3) on the one hand, and (b) the zero level of the

stationary spatial reference system (QP, p,58, line 6) and the zero motion in time

(QP, p.68, line, 10) on the other?

Also compare QP, p.97, bottom para and NBM, p.154, top para. These

expositions in connection with the possiblity of 8 units, give the impression as

though ―positive zero‖ means the same thing as ―zero speed in space‖. But I

understand that

―positive zero‖ is the speed 1/ l, whereas

―zero speed in space‖ is 0/1. Further,

―negative zero‖ is .. .. -1/1 or 1/(-1), and

―zero speed in time‖ is 1/0.

DBL: The positive zero (NBM 153), the zero level of the spatial reference system

(QP 58), and zero motion in space are synonymous. Likewmise the negative zero,

and zero motion in time (QP 68) are synonymous. The latter would be the zero

level of a thre-dimensional temporal reference system. As I explain on page 119,

NBM, I measure speed displacement (usually abbreviated as ―displacement‖)

from unity as a datum level. But I measure speed from the mathematical zero in

the usual manner. Just how many units there are between the positive (spatial)

zero and negative (temporal) zero depends on the dimensional situation. If we are

dealing with the full three scalar dimensions, there are six units between the

absolute zero of space and the absolute zero of time. If we are dealing with only

one scalar dimension, there are two linear units between the two zeros. But we

can resolve this one scalar dimension into three dimensions of space, and then

there are eight units (of a different kind) between the two zero points.

39. KVK: I could follow that speeds in the range 1-x pertain to the 3-dimensional

space region, and the speeds in the range 2-x belong to the space-time region (the

3-dimensional temporal reference frame because of the second unit status. How is

it that the speeds of the range 3-x belong back to the time-space region of the 3-

dimensional spatial reference frame?

DBL: What you need here is an understanding of the circumstances under which

time acts as ―equivalent space‖. The second unit of motion, from one unit of

speed to two units, is motion in time, as indicated in Diagram B, NFS. But since

there are six units between the absolute spatial zero and the absolute temporal

zero, a two-unit speed is still spatial as a whole. It follows that the motion in time

in the second dimension has to act as a modifier of the spatial motion rather than

as an actual motion in time. This is the same kind of a situation that we encounter

in the atomic rotations. The negative electric rotation of certain atoms is a motion

in time (speed n/1), but it does not convert the material atom to a cosmic atom,

because the atomic rotation as a whole is still positive. The effect of the motion in

time is therefore to modify the motion in space to the extent of its spatial

equivalent. The motion in the time region, below unit space, is similar. It is a

motion in the spatial equivalent of time, rather than in actual time. The motion

therefore remains within the spatial reference system, rather than moving away

from it and becoming unobservable, as a motion in actual time would do.

Addition of a third translational unit of speed does not revert back to the same

status as the first unit. The motion in equivalent space continues in the dimension

shown in Diagram B, but a motion in actual space is added in a second scalar

dimension.

40. KVK: What happens to the inverse thermal motion of a cosmic atom during

‗scalar inversion‘ (that is, entry from the cosmic sector into the material sector).

Since thermal motion in our sector is a linear vibratory space displacement, the

inverse thermal motion of the sector should be a linear vibratory time

displacement. As such, how does this linear vibratory time displacement dissipate

or show up in our environment?

DBL: Radiation frequency is a speed; that is, cycles per second 1/t, is actualy

units of space per second, s/t.The effective unit of wavelength is about 10-³cm.

Radiation at shorter wavelengths is motion at speeds above unity (displacement in

space). This includes the near infrared, the optical region, and the ultraviolet—

that is, the bulk of the thermal radiation—as well as x-rays and gamma rays. The

inverse thermal radiation occupies a similar range on the long wavelength side of

10-³ cm: the far infrared and the radio range. These are speeds below unity

(displacement in time). Astronomical radio emitters are usually also strong

sources of infrared radiation (inverse thermal).

41. KVK: The frequency of the H.F. radiation is greater than one, say, n/1. This

means that there are n space units associated with 1 time unit. This means that it is

the time component that is alternating between inward and outward directions.

Now if it is the space unit that is so alternating (as in the L.F. radiation), this

appears as an oscillation in space from the point of view of the stationary 3-

dimensional reference frame. But if the alternating unit is time unit, how do we

(from the stationary reference frame) see it, still as a vibration in space, or as a

vibration in time? Please note that I am not asking about the forward movement of

the photon in the perpendicular dimension at all. I am asking about the motion in

the dimension of oscillation.

DBL: In all cases we see one space unit in the reference system, and we have to

measure the time on a clock, There is no way in which we can distinguish

observationally between a space-time ratio of 1/n and one of n/l. If we want to

know the frequency corresponding to unit speed, we have to calculate it.

42. KVK: Have the following been worked out in the context of the RS: (a) The

relative cosmic abundances of the elements; (b) nuclear isomerism—origin and

explanation; (c) radiation emitted due to the electron spin changing direction, for

example, the 21 cm. radiation from hydrogen. How does ‗spin‘ fit in our theory?

(d) explanation of the origin and the characteristics of the cosmic background

radiation (NBM, p,175).

DBL: (a) This has not been studied, so far as I know. (b) I do not know of any

studies made on these items either, (c) The electron does ―spin‖; that is, it rotates,

but I doubt if the accepted explanation of the origin of the radiation is correct. (d)

This is undoubtedly the radiation from the cosmic sector. We have the

explanation for the origin and for the principal characteristic—the isotropy and

the intensity (which we can explain approximately). I do not believe that it is

worth while trying to go any farther at this stage of the theoretical development.

43. KVK: Gravitation is a rotationally distributed motion, its direction being

redetermined after the end of each (natural) unit of time, since it is inward. In the

long run, this results in its being distributed in all directions of 3-dimensional

space, by probability. But suppose there is the intervention of an external element,

which introduces a preferred direction—such as by rapid spinning—does the

gravitational motion get directed in the direction of the spin axis in space more

often than in the other directions, producing in the long run, ‗directed gravity‘?

Does the spinning of an object produce space displacement?

DBL: According to my findings, gravitation is a continous, uniform, rotationally

distributed scalar motion at unit net inward speed, and cannot be anything

different. An external force cannot change the inherent characteristics of this

motion. It simply imparts a vectorial motion to the gravitational combination of

motions.

44. KVK: What is the difference between the inner and the outer gravitational limits

(QP, p.166)? At the outer gravitational limit, the gravitational motion due to the

entire mass aggregate becomes unity and beyond it becomes zero as fractional

units do not exist. But what happens at the inner gravitational limit, where the

inward motion due to gravity equals the outward motion of the progression? Here

too, since the outward motion due to the pregression is unity, is not the inward

motion due to the gravitation also one unit, if both these are to be equal?

DBL: At the gravitational limit the inward motion of an agregate of m units of

mass is m units. The outward motion is likewise m units, and the net speed is

zero. Beyond this limit the gravitational motion decreases with the distance, and

has the value m-x. When m-x = 1, any further increase in the distance drops the

gravitational motion to zero, as there are no fractional units. As can be seen from

the foregoing, the outward motion at speeds less than unity, such as the galactic

recession, is purely a phenomenon of aggregates. In the case of a single isolated

unit of mass, the gravitational motion would drop to zero at the gravitational limit;

that is, the two limits would coincide.

45. KVK: If gravitational effect decreases as 1/d², how does one obtain the linear

relation of Hubble‗s distance vs. speed?

DBL: The inverse square relation applies where the distribution is three-

dimensional. Beyond the gravitational limit (unit gravitational speed) the

distribution is two-dimensional.

46. LIFETIMES OF C-ATOM DECAYS

47. The phenomenon of the entry of c-matter into the material sector or the analogous

entry of matter into the cosmic sector, involving the passage from space-time

domain to time-space domain, may be called ―scalar inversion‖ to emphasize the

nature of the alteration of the reference frame. Scalar inversion involves two

things: firstly, a transformation of motion in time (or space) to motion in space (or

time), through the unit speed boundary, in all the three dimensions. Secondly, the

emergence of a c-atom, for example, into the material sector can take place only

from inside a single unit, since the three dimensions of time have nothing in

common with the three dimensions of space—both having not more than a point

contact, as it were (p. 154, Nothing But Motion—hereinafter NBM).

48. Therefore, in following up the calculation of various quantities across the

boundary in scalar inversion, from the cosmic sector to the material sector, for

example, consideration must be given to: (i) the loss of dimensional ―information‖

during the alteration of the viewpoint from the temporal reference frame to the

spatial reference frame and (ii) the space equivalent of time occurring within a

single unit.

49. As a result of the first point above, it is known that the full influence of spatial (or

temporal) effects does not get transmitted across the boundary except when it

involves only one dimension. On the other hand, only a fraction 1/c in the case of

two-dimensional effects, and a fraction 1/c² in the case of three-dimensional

effects gets transmitted. (See p. 185, New Light on Space and Time—hereinafter

NLST). I will refer to this as criterion No. II in the sequel.

50. Regarding the second point above, namely, concerning the relation between

quanttties within the outside single unit, ―...The time region speed, and all

quantities derived therefrom, which means all of the physical phenomena of the

inside region...are . . second power expressions of the corresponding quantities of

the outside region.‖ (p. 155, NBM) I will refer to this as criterion No. IV. In order

to find the lifetimes of the cosmic atoms in the material environment it is

necessary to apply both the above criteria.

51. The first step in deriving the lifetimes is to recognize that, in view of the scalar

inversion, the spatiat extension of the c-atom, being the analog of the lifetime in

material sector, bears a relationship to the latter. As such we start with the

consideration of the spatial extension of the incoming c-atom. Now, scalar

inversion is not possible with anything more than one unit in each dimension.

Depending on the number of dimensions of the motion eventually acquired during

the inversion process, the amount of space involve~ in the one, two and three-

dimensional cases is respectively s, s² and s³ (where s is the unit space expressed

in the c.g.s. system). Let us refer to this as criterion No. I.

52. The remaining criterion, No. III, necessary for our calcula- tion is the recognition

of the fact that the temporal equivalent of a spatial extension s across the

inversion boundary is s/c (where c, the unit speed, is expressed in the c.g.s.

system). The result of apptying the above four criteria to the one, two and three-

dimensional situations is given in the following table.

Criterion No. Number of Dimensions

1 2 3

i s s² s³

ii s/c s²/c s³/c

iii (s/c) (s²/c)(1/c) (s³/c)(1/c²)

iv (s/c)½

[(s²/c)(1/c)]½ [(s³/c)(1/c²)]

½

Result in secs. 1.233148 × 10-8 1.520655 ×10-16 1.875193 × 10-24

53. The same result could have been obtained more simply though showing less

details of the underlying process by directly noting that the clock-time involved in

the one, two and three-dimensional cases of the decay is t, t² and t³ respectively

(where t0 is the unit time expressed in the c.g.s. system). The measured values of

the lifetimes could then be obtained by applying the criterion No. IV, as t½, (t²)½

and (t³)½ respectively.

54. Further, in the calculations above if the extension space involved is taken as p/4s²

and p/6s³ respectively in the two and three-dimensional cases, based on

symmetrical probability, instead of s² and s³ , we have the computed values of the

lifetimes in the respective situations as 1.348 × 10-16 and 1.357 × 10-24 secs.

55. The acquisition of gravitational charges by the incoming c-atoms has an effect on

the above lifetimes which can be evaluated in the following manner. In view of

the scalar inversion, it must be noted that the gravitational charge of the material

sector, being a two-dimensional rotational vibratory time displacement, is foreign

to the space-time character of the basic rotational displacement of the c-atom. In

the analogous case of a material atom, for example, a gravitational charge of the

cosmic sector is tantamount to a magnetic charge in the material environment.

Consequently the calculation of the influence of a rotational vibration of

spacetime direction opposite to that of the basic rotation, on various quantities

requires the consideration of the appropriate interregional ratio.

56. For exampte, ―...the motion that costitutes the charge is on the far side of another

regional boundary—another unit level—and is subject to ... inter-regional

transmission factors.‖ (p. 163, NBM). Further, ―... inter-regional ratio ... accounts

for the small ‗size‘ of atoms. According to the theory ..., there can be no physical

distance less than one natural unit ... but ... the measured inter-atomic distance is

reduced by the inter-regional ratio, and this measured value is therefore in the

neighborhood of 10-8 cm‖ (p. 154-5, NBM). In exactly the same manner, the

acquisition of a gravitational charge by the c-atom, in view of the interregional

ratio, has the effect of shortening the measured lifetime by a factor of 1/156.44.

(While it is clear that the inter-regional ratio operates here, I am not certain that its

vaiue is 156.44 in this case.)

57. An atom is a double rotating system. The rotational vibration that is a

gravitational charge establishes a coupling with one of these two rotational

systems. In the case of an acquisition af one more gravitational charge, the second

rotational vibratory displacement acquired acts on the second rotational system of

the c-atom rather than adding to the previous system already modified by the first

gravitational charge. As such, the computation of the lifetime in this case involves

the application of the inter-regional ratio once more. Thus the measured lifetime

in the case of two gravitational charges acquired is shortened by a factor of

1/(156.44)² The lifetimes, with or without the gravitational charges, in the one,

two and three-dimensional situations are, therefore, as follows:

Dimensions Charges Lifetime (sec.)

1 0

1.233148 ×10-8

1 1

0.788234 ×10-10

2 0

1.520655 ×10-16

2 2

0.621313 ×10-20

3 0

1.875193 ×10-24

LIFETIME OF C-ARGON, THE MUON

Larson states that the apparent lifetime of c-argon is the sum of its own proper lifetime

and the time required for the conversion of the c-krypton rotations to massless neutrons

[1]. This conversion of the cosmic type rotation, namely (3)-(3)-0 of c-Kr to the material

type rotation, M ½-½-0 of the massless neutron, involves two distinct steps: firstly, there

is the ―scalar inversion‖ resulting in the change of scalar direction, from the standpoint of

the temporal zero (the initial level of negative rotation) to that of the spatial zero (the

initial level of positive rotation), converting the (3)-(3)-0 rotations to the 1-1-0 rotation

(along with the concomitant conversion of the rotational base). Secondly, there is the

―splitting‖ phenomenon, which results in two single rotating systems of the massless

neutrons, M ½-½-0, from the double rotating system of the above 1-1-0 rotation. Thus,

the apparent lifetime of c-Ar comprises three components:

i. the proper decay time of the c-Ar,

ii. the inversion time, and

iii. the splitting time.

The Decay Time: The proper lifetime of the c-Ar, d , in the material environment is the

one-dimensional lifetime, t1D, which has been evaluated [2] as 1.233148 * 10-8 sec. Thus,

d = t1D sec. (1)

t1D is also the unit of time that is relevant in the computation of the inversion and splitting

times.

The Inversion Time: It must be recalled that the two sectors of the physical universe—

the material and the cosmic—are distinguished by the nature of the reference frames to

which each belongs. The time-space region of our sector is reckoned from the standpoint

of the stationary spatial frame of reference, while the space-time region of the cosmic

sector is reckoned from the standpoint of the stationary temporal reference frame. The

one-dimensional lifetime, t was evaluated from a consideration of the kinetics of the entry

from the space-time region to the time-space region.

However, in the inversion of the rotational units of the cosmic type to those of the

material type, there is an additional factor to be taken into consideration. This is because,

while the evanescent manifestation of a decaying c-atom in the material sector is

analogous to the temporary sojourn of an alien visitor on a tourist visa, the scalar

inversion amounts to nothing less than a complete naturalization. The c-atom exists

inside one natural unit of time, the ―space region‖ of the space-time sector, whereas the

material atom (or particle) exists inside one natural unit of space, the ―time region‖ of the

time-space sector. Consequently, the inversion of the c-atom involves the crossing of the

unit time boundary as well as the unit space boundary. But since our observations and

measurements are carried out in the time-space region, outside the unit space (time

region), the additional factor we need to consider is that arising out of the crossing of the

unit time boundary only.

The total number of possible directions—the quantization of orientation, we may say—in

the time region that the scalar effect of the rotation can take is calculated by Larson [3] to

be 156.44. Therefore, in the absence of any preferential direction, the probability, p, that

the scalar inversion takes place in a unit of time (i.e., t1D.) would be 1/156.44.

But this number, 156.44, is specifically applicable to the time region motion only in

relation to our spatial zero point of view, or the analogous case of the space region

motion in relation to the temporal zero point of view. As already mentioned, the inversion

of the negative rotations (3)-(3)-0 to the positive rotations 1-1-0 is tantamount to

switching the viewpoint from the negative zero to the positive zero. Although this entails

no change from the natural standpoint, it amounts to a shifting of 8 displacement units

from the standpoint of our stationary reference system [4]. In view of this 8-unit

separation between the positive and negative zero points, the total number of positive

orientations in the space region, namely 156.44 as reckoned from the negative zero

standpoint, becomes 8 * 156.44, when reckoned from the positive zero standpoint.

Consequently, the probability of inversion, p, becomes 1/(8 * 156.44).

Over and above these, there is a numerical amplification arising out of the fact that x

units measured from zero speed in time are equivalent to 8-x units measured from zero

speed in space. Thus, one unit of motion in time ― . . . the smallest amount that can exist,

is equivalent to seven units measured from the spatial zero. . .‖[5]. Remembering that,

whereas the previous factor 8 applies on the other side of the unit time boundary and

therefore increases the total possibilities (i.e., reduces p), the factor 7 magnifies the

motion on this side of the boundary and increases p. Thus we arrive at the value of the

probability p as 7/(8 * 156.44).

Since p is the probability that the inversion takes place in unit time, the mean time,

required for the completion of the inversion event is 1/p. That is,

i = 8 * (156.44/7) *t1D sec. (2)

The Splitting Time: The splitting of the double rotating system 1-1-0 (three dimensions)

into two of the two-dimensional rotations M ½-½-0 (four dimensions in all), involves one

unit of time modified by the 4/3 dimensional factor, that is, 4/3 t1D. Here it may be argued

that since after the inversion from (3)-(3)-0 to 1-1-0 the motion has already crossed the

unit speed boundary and arrived in the material sector proper, the time unit relevant is no

longer the one-dimensional lifetime, t1D (which is applicable during the transition only),

but the natural unit of time, tnat . However, why this is not correct will be apparent in a

moment.

It must be realized that the 1-1-0 combination is inherently unstable from the probability

considerations [6], whereas the massless neutron, M ½-½-0, is a stable structure. Insofar

as the scalar inversion from (3)-(3)-0 leads to the improbable pattern 1-1-0, the splitting

time, s, is negative. This is the same thing as saying, in common parlance, that a more

probable condition is realized earlier than a less probable one. This clarifies the reason

why t1D and not tnat is the pertinent time unit in the splitting. The time computation

concerning any event after the 1-1-0 event requires consideration of t as the proper time

unit since the event 1-1-0 marks the end of the inversion. But the M ½-½-0 event is

before the 1-1-0 event and thus the relevant time unit is still t1D. Thus,

s = -4/3 t1D sec. (3)

Finally, from the relations (1) (2) and (3) above, we have the apparent lifetime of c-argon

as

= d + i + s

= [1 + (8 * 156.44/7) - 4/3] * 1.233148 * 10-8

= 2.2007 * 10-6 sec.

References

1. Larson, Dewey B., Nothing But Motion (North Pacific Publishers: Portland, OR,

1979), pp. 195-196.

2. Nehru, K.V.K., Lifetimes of c-Atom Decays, Reciprocity XI. 1 (1981), p. 34.

3. Larson, Nothing But Motion, p. 34.

4. Ibid., p. 153

5. Larson, Quasars and Pulsars (North Pacific Publishers, 1971), pp. 97-8.

6. Larson, Nothing But Motion, p. 142.

INTERNAL IONIZATION

AND SECONDARY MASS

In the Reciprocal System the motion that is identified as the electric charge is a one-

dimensional rotational vibration (RV¹) that modifies a basic rotation (R), which is also

normally one-dimensional. Similarly, the motion that is identified as the magnetic charge

is a two-dimesional rotational vibration (RV²), modifying the basic two-dimensional

rotation (R²).

In order to clearly bring out the principles on which the manifestation of the mass effect

of the charges, called the secondary mass, is based, a comparison of the cases of the

electron, the positron and the proton is drawn up in Table 1 below. We will use the

following notation adopted by Larson:

p - primary mass

m - magnetic mass

E - electric mass (3 dim.)

e - electric mass (2 dim.) = (2/3)E

C - mass due to normal electric charge (3 dim.)

c - (2/3)C (2 dim.)

and further introduce

S - space displacement

and T - time displacement

TABLE I. Comparison of the Electrically Charged Subatomic Particles

Particle Notation Space-time direction

of the charge Mass composititon

Charged electron M- 0-0-(1) T e - c

charged positron M+ 0-0-1 S e - c

charged proton M+ 1-1-(1) S p+m+2e+C

The conclusions that could be drawn from an examination of Table I, regarding the sign

of the secondary mass increment, are summarized in Table II. The negative electric

charge is a one-dimensional RV with time displacement and the positive electric charge

is a one-dimensional RV with space displacement. From Table I it is clear that the mass

increment due to the charge is positive if the displacement of both the one-dimensional

RV and the one-dimensional R are of the same space-time direction (cases (3) and (4),

Table II). On the other hand, the secondary mass increment is negative if the

displacement of the one-dimensional RV and the one-dimensional R are respectively of

opposite space-time directions (cases (1) and (2)).

TABLE II. The One-dimensional Rotational Vibration

Rotational

base Nature of charge

Space-time

direction Algebraic sign of the

secondary mass

increment RV¹ R¹

case (1) negative T S -

case (2) positive S T -

case (3) positive S S +

case (4) negative T T +

case (5) positive S T -(-) = +

- M - material base and C - cosmic base

Case (5) deals with the direction of the mass contribution by an electric charge acquired

by a rotation on the cosmic rotational base rather than on the normal, material rotational

base. In this case too, the sign of the mass increment follows the same rule as above, but

since the basic motion is on the opposite side of a regional boundary, the direction of the

effect is reversed. Thus the mass increment (in the material sector) due to a positive

charge acquired by a one-dimensional rotational time displacement on a cosmic rotational

base is positive.

Internal Ionization

Because of the ever-present environmental thermal vibrations, the subatomic as well as

the intermediate particles always get electrically charged. They may remain in the

uncharged condition only at low temperatures or when the effective displacement in the

magnetic dimension is of the ―´ - ´‖ type. This is the reason why the electrons and the

protons are always found in the charged state, and the neutrinos and the massless

neutrons in the electrically uncharged state.

In the case of the intermediate particles, the two rotating systems take on a unit of electric

charge each. But these two charges happen to be of opposite space-time directions

because the charge on one of the rotating system forces an equal and opposite charge on

the second system in order to have an internal equilibrium. This phenomenon can be seen

to be akin to the acquisition of a gravitational charge by an atom in order to equilibrate

the magnetic charge of the neutrino captured by it, except for the difference in the

number of dimensions of the charged motion. We will call this process ‗internal

ionization‘ because it pertains only to the mutual equilibrium of the two rotating systems

of a single particle (or atom). Normally it is to be expected that a positive and a negative

charge neutralize each other. But the continual thermal pumping from the environment

sustains the internal ionization.

The Intermediate Particles

We will now consider the secondary mass situations in the case of the two intermediate

particles, namely the mass-one hydrogen and the compound neutron. Though the net

charge due to the internal ionization is always zero, we will find that the mass effect of

these two charges does show up in the case of the intermediate particles.

The H¹ system is usually denoted as

M 1-1-(1)

] ————

M ½-½-(1]

with the mass composition of p+m+3e, giving a mass of 1.00812815 [1]. As explained

above, a condition of greater probability in the local environment would be that when

both rotating systems acquire an electric charge. The charge on the proton-type rotation

can be either positive or negative as both a rotation with time displacement and a rotation

with space displacement are available to act as a base for it. But the M-neutrino-type

rotation can take on only a negative charge—like the M-electron—since this is solely

determined by the space-time direction of the rotational displacement in the electric

dimension (the ―´-´‖ effective displacement in the case of the electron, in the magnetic

dimensions, being of no help to act as a base for the one-dimensional RV). Thus the more

probable, internally ionized state of H¹ can be designated as

M+ 1-1-(1)

] ————

M- ½-½-(1]

The magnitude of the secondary mass contributed by the positive charge on the proton-

type rotation is C because it is distributed over three effective dimension,while that be the

neutrino-type rotation is only c, in view of the dimensional character of this rotation

(namely, the ―´-´‖ efective rotation). Further, it can be seen that the mass increment due

to the charge on the proton-type rotation is positive, as it belongs to the case (3) (Table

II), whereas that due to the charge on the neutrino-type rotation is negative as it belongs

to case (1). Therefore, the mass composition of the internally ionized H¹ should be

p+m+3e+C-c. Adopting the values listed by Larson [2], this gives a mass value of

1.00814313, which compares more favorably with the observed value of 1.008142, than

the value 1.00812815 given by Larson [1].

The second particle in the intermediate class is the compound neutron

M 1-1-(1)

] ————

C (½)-(½)-1

with the mass composition of p+m+3e+E, giving a mass value of 1.00899621. In this

case, the charge that the c-neutrino-type rotation can take on is positive since the

displacement in the electric dimension—which decides the charge type, rather than the

―´-´‖ displacement in the magnetic dimensions—is a space displacement. Thus the

internally ionized compound neutron is to be designated

M- 1-1-(1)

] ————

C+ (½)-(½)-1

Once again the mass contribution from the charge on the proton-type rotation is C while

that from the neutrino-type rotation is c, the former being negative (belonging to case (1),

Table II) and the latter positive (case (5)). Thus the mass composition becomes

p+m+3e+E-C+c. The calculated mass is 1.00898123. This is nearer to the observed value

of 1.008982 than the value 1.00899621 given by Larson [1].

The Atoms

The ease with which electric charges are acquired by the rotational systems in the local

environment, producing the internal ioinization, also clarifies an important aspect

concerning the (external) ionization of the atoms. The total number of positive charge

units that an atom possibly can acquire equals Z, where Z is atomic number. In the

Reciprocal System the atomic number is the net total equivalent electric displacement.

And the units of electric displacement in the atomic structures is defined as the equivalent

of two natural one-dimensional displacement units [3]. Consequently, the net

displacement of an atom of atomic number Z, in terms of the natural units is 2Z.

An examination of the motional structure of the subatomic particles shows that (1) the

unit of electric charge that these particles can acquire is the minimum that is possible and

is, therefore, the unit of one-dimensional RV in general, and (ii) inasmuch as a charge is a

modification of the basic rotation, the number of unit charges a rotation can take on is

only one per natural unit (of rotational displacement). As such, the total number of

electric charges an atom can aquire comes out to be 2Z according to the Reciprocal

System, in glaring contradiction to the known facts.

The reason why the fully ionized atom cannot ecquire more than Z number of charges,

however, is a follows. We have seen that, in the local environment, a rotating system

easily acquires a RV (i.e., an electric charge), and that in a rotational structure, if there

are two rotating systems, the charges on each of them are mutually of opposite space-

time directions in order that they be in internal equilibrium. As such, each of the two

rotating system of an atom acquires Z number of electric charges: one system carrying Z

positive charges and the other Z negative charges. This leaves the atom itself electrically

neutral.

There is no net contribution to the secondary mass either, since the mass effects of these

to sets of charges mutually cancel out (belonging to cases (2) and (4) (Table II)

respectively. It may be noted that in the case of the intermediate particles, even though

the charges effects of the positive and the negative electric charges acquired respectively

by the two rotating systems likewise cancel out, the mass effects of these charges do not

cancel out, as their numerical magnitudes are different, being C and c.

Now it can be seen that the ionization of a neutral atom consists in supplying additional

one-dimensional RV space displacements, which successively cancel out the Z negative

charges existing in one of its rotating systems. The net secondary mass increment due to

the (external) ionization of the atom can be computed from a knowledge of the degree of

ionization and the algebraic sign of the increment (Table II).

Secondary Mass Effects of Two-dimensional Charges

Table III below shows the effect of the space-time direction of two-dimensional charges

of the algebraic sign of the secondary mass contributed by them.

TABLE III. The Two-dimensional Rotational Vibration

Rotational

base

Nature

of charges Space-time

direction

RV² R²

Algebraic sign

of the secondary

mass increment

M magnetic S T -

M gravitational T T +

It can be seen that the general rule is the same as in the case of the one-dimensional RV:

the mass increment due to the gravitational charge is positive, since the gravitational

charge—which is a two-dimensional RV—and the basic two-dimensional rotation are

both time displacements. One the other hand, the mass effect of a magnetic charge—

which is a two-dimensional RV with space displacement—should be negative [4].

The motion that constitutes the magnetic charge is on the far side of another regional

boundary and is subject to two successive interregional transmission factors. In the case

of the electric charges (which is a one-dimensional RV), the mass of unit charge is the

reciprocal of the product of two interregional ratios [5]. Since the magnetic charge is a

two-dimensional RV, the interregional ratio pertaining to the charge region becomes

(156.44)² (see fig. 1b). Thus the secondary mass arising out of the magnetic charge

amounts to

- 1/156.44² x 1/156.44 = - 2.6117 x 10-7 = - 243.19 eV

The situation, however in the case of the two-dimensional RV with time displacement,

the gravitational charge, is altogether different. The third region, in which the motion of

this charge take place, turns out to be toward ‗our side‘ of the time region rather than the

far-side and therefore coinsides with the region outside unit space (represented by line ‗0‘

in fig. 1c). Thus the net interregional ratio applicable to the gravitational charge is 1.

Consequently the secondary mass contribution of the gravitational charge is one full unit:

931.152 MeV.

0 R Rv¹+ 0 R RV²

+ 0 R

|

|

|

|

|

|

||

|

1/156.4

1/156.4

1/142.2 1/156.4² 1/156.4

RV²-

a) Electric charge (b) magnetic charge (c) gravitational charge

Fig. 1. Interregional Ratios Pertaining to the Different Regions

REFERENCES

All references are from Nothing But Motion by D. B. Larson, North Pacific Pub.,

Portland, Or. U.S.A., 1979

1. p. 167

2. p. 164

3. p. 128

4. p. 191

5. p. 163

THE LIFETIME OF THE NEUTRON

Theoretical findings of the Reciprocal System indicate that the neutron exists in two

forms: as the massless type, M ½-½-0, and as the compound type,

M 1 - 1 -

(1) ] C (½) - (½) - 1

As matters now stand, while the massless neutron is unobserved, the compound neutron

is identified as the observed neutron. Larson [1] shows how the mass of the compound

neutron, calculated from the Reciprocal System, agrees with the observed value. This

paper attempts to arrive at the compound neutron‘s lifetime on the basis of the same

theoretical system and thus add a further element of validation to the identification of the

compound neutron.

The motional structure of the compound neutron is rather unusual. First, while its net

total displacement is only one unit, like that of the sub-atomic particles, it has two

rotating systems like the atoms. Secondly, it is the only structure (of those that have been

identified so far) in which the two rotating systems are completely ―heteroscalar,‖ that is,

while one system is built up on the material rotational base (with negative vibration and

positive rotation), the second system is built up on the cosmic rotational base (with

positive vibration and negative rotation).

Since basically the gravitation of the cosmic type structure is inward in time, cosmic

rotational units cannot exist in the material reference frame (with its outward time

progression) for not more than one natural unit of time under ordinary circumstances.

This, however, does not apply in the case of the cosmic neutrino type rotation that

constitutes the second rotating system of the compound neutron, for its net effective

three-dimensional rotational displacement is zero. Nonetheless, the association of M 1-1-

(1) and C (½)-(½)-1 should not last for more than one natural unit of time. The reason is

that the corresponding displacements of the two systems, both in the case of the basic

photon vibration and in the case of a rotation in any of the dimensions, are respectively of

opposite space-time directions. Since the relation of space to time constitutes motion, the

two rotating systems must dissociate after the elapsing of one natural unit of time.

The situation, however, is not quite so simple: the two rotating systems belong to

different space-time regions, and the motion that is effective across the regional boundary

is determined by the interregional factors arising out of the limitation on the number of

directions that can be transmitted. We may recall that a material rotating unit—either an

atom or a subatomic particle—exists inside one natural unit of space, i.e., the ―time

region,‖ whereas a cosmic rotating unit exists in the ―space region,‖ which is inside of

one natural unit of time. Now the crucial point to be recognized is that the expulsion of

the c-neutrino motion (from the compound neutron) takes place only if the direction of

the c-neutrino motion, interacting across the inter-regional boundary, happens to be

antiparallel to the direction of the motion of the proton motion, and not otherwise. Thus

the lifetime of the compound neutron is the time elapsed before the eventual occurrence

of this antiparallel encounter that results in the neutron‘s decay.

Had the cosmic type rotation in the second rotating system of the compound neutron been

a one-dimensional motion, the encounter and resultant decay would take place within one

natural unit of time. But the neutrino-type rotation, i.e., C (½)-(½)-1, is three-

dimensional, and it is known that the full influence of spatial (or temporal) effects does

not get transmitted across the boundary, except when it involves only one dimension. On

the other hand, only a fraction of 1/c in the case of two-dimensional effects, and a

fraction of 1/c² in the case of three-dimensional effects gets transmitted.[2] As such, the

effect of the c-neutrino motion existing in the space region and interacting with the

proton motion existing in the time region is reduced by a factor of 1/c².

Here, we must recall that, ―. . . the non-rotating photon remains in the same absolute

location permanently. . . The rotating photon, on the other hand, is continually moving

from one absolute location to another as it travels back along the line of the progression

of the natural reference system, and each time it enters a new absolute location the

vectorial direction is redetermined by the chance process. Inasmuch as all directions are

equally probable, the motion is distributed uniformly among all of them. . .[3] In the

present case, although the net effective rotational displacement of the c-neutrino motion is

zero, its net total rotation is one negative unit, and after the elapse of each natural unit of

time (n.u.t.), its direction is re-determined by chance. Therefore, inasmuch as the chances

of the orientation of the c-neutrino motion taking the correct direction in three-

dimensional time, required for an antiparallel encounter referred to earlier, are reduced by

a factor of 1/c²., the probable time for this encounter to happen is increased from one

n.u.t. to c² n.u.t.

However, it must be noted that the number of possible orientations that the proton

rotation can take in three-dimensional time is not just one but is given by the

interregional ratio, R [4]. As any of these orientations in the time region can deal with the

incoming c-neutrino motion, the chances of the antiparallel encounter are increased by

the factor R. In other words, this means that the previous lifetime arrived at, c² n.u.t. is

decreased to c²/R n.u.t (or c² · tnat/R seconds, where tnat is one n.u.t. as expressed in the

c.g.s. units).

(It can readily be seen that since c²/R represents the total number of possibilities of equal

probability for the antiparallel encounter, R/c² is the probability that the neutron decays in

one unit of time. Thus it can be identified with the classical decay constant).

The value of R pertinent here is not the 128 (1+ 2/9) value computed in Ref.[4]. Firstly,

the proton, M 1-1-(1) is a single rotating system unlike the atoms, which are double

rotating systems. As such, only one of the nine possible vibrational positions is occupied,

bringing the total number of orientations to 128 (1 + 1/9). Secondly, of the two mutually

opposite directions in any dimension of the basic photon vibration, only one results in an

antiparallel alignment (the other resulting in a parallel alignment). Consequently, the

effective vibrational contribution reduces by half. Thus the value of R applicable to the

present situation is 128 (1 + 1/8) = 135.1111.

Adopting the values of c and tnat from Ref.[5], we have the mean lifetime of the

compound neutron as

(2.99793*1010)²

= ——————— × (1.520655 × 10-16)

135.1111

= 1.01154*10³. sec. or 16.859 min.

Or the same result can be expressed in terms of half-life T as

T = · ln 2

= 1.01154*10³ * ln 2

= 701.145 sec. or 11.686 min.

This compares very favorably with the experimental value of 11.7 ± 3 min. (American

Institute of Physics, HB., pp. 8-118) with a discrepancy of -0.144 percent.

References

1. Dewey B. Larson, Nothing But Motion (North Pacific Publ.: Portland, Ore.,

1979), p. 167.

2. Idem, New Light on Space and Time (North Pacific Publ.: Portland, Ore., 1979),

p. 185.

3. Nothing But Motion, p. 58

4. Nothing But Motion, p. 154

5. Nothing But Motion, p. 160

ADDENDUM

Besides the compound neutron and the mass-one hydrogen isotope belonging to the

―intermediate‖ rotating systems, there appears to be another theoretical possibility. The

two rotating systems of this particle are made up of the material neutrino-type rotation

and the cosmic electron rotation respectively. Thus it can be designated:

M (½) - (½) -

(1) ] C 0 - 0 - 1

As can be seen, while the net displacement of one system is zero, there is a net positive

displacement in the other system. As the net total displacement of the combination is

equivalent to that of the neutron, M ½-½-0, this seems to be another version of the

compound neutron. But due to the small mass and the extremely short lifetime of this

combination, it might easily escape detection.

The potential mass of both the neutrino and the c-electron is actualized when the rotations

of these particles enter into combination, constituting this compound neutron. In addition,

there is an initial electric unit as the two rotational bases are heteroscalar. The resulting

mass is 0.00231482.

Since the c-electron has effective rotation in only one dimension, the mean lifetime of

this compound particle, calculated on the basis of the considerations developed in the

paper is:

= tnat/R = 1.520655*10-16/135.1111

= 1.1255*10-18 sec.

RELATIVE ABUNDANCE OF THE ELEMENTS

A general physical theory, like the Reciprocal System, should satisfy two types of

criteria in order to establish its truth. Firstly, it should be able to explain completely

those physical phenomena that remained recalcitrant without explanation in the previous

theories. More desirably, it should lead to predict ions which are definitely in conflict

with those of the preceding theories but c an be validated by observation or

experimentation. The second type of requirement to be satisfied by the general theory is

that it is not inconsistent with any of the definitely established physical facts. This may

be called the negative criterion, whereas the previous one may be called the positive

criterion.

It can be seen that the positive criterion, being more powerful in establishing the new

theory, demands greater attention (and challenge) from the point of view of its

proponents. The negative criterion, on the other hand, is a rather weak condition for

positively establishing the new theory. Further, in view of the extremely vast number of

genuine physical facts that were recognized, it is neither possible nor worthwhile to

bestow more than a limited amount of consideration—especially in the early stages of the

development of the new theory—to showing that the theory is not inconsistent with any

of these facts. However, the negative criterion, though a weak one in establishing the

new theory, is all-powerful in invalidating it if a single instance of inconsistency is

found. For this reason the adherents of the conventional theory not infrequently, tend

to invoke the negative criterion, having already armed themselves with some sort of

explanations for some of these facts. They often ask how the new theory accounts for

some of such recognized facts. In such instances—especially when information of a

quantitative nature is involved—it is incumbent on the proponents of the new theory to

pay more consideration and work out the details to demonstrate that the negative criterion

is well satisfied.

I wish to bring to your attention two such questions which lectures on the astronomical

aspects of the Reciprocal System invariably seem to elicit. The first one of these is about

the genesis of the elements and their relative cosmic abundance. The second concerns

the background microwave radiation and the value of its temperature. These, therefore,

seem to warrant greater consideration in working out the details in the context of the

Reciprocal System. The detailed study of the cosmic abundance problem is also

important from the point of view of stellar evolution and energy generation processes.

In the following I attempt a cursory analysis of the cosmic abundance problem giving

nothing more than a general outline of the argument.

According to the Reciprocal System (i) the element building process starts with the

formation of hydrogen from the decay products of cosmic matter—namely , the massless

neutrons and their equivalents—ejected into the material sector; 1 (ii) the assembling of

the elements with higher atomic numbers then continues by the successive additions of

the positive rotational displacement units (PDU).² Let:

Nd = the total number of PDU in the material sector of the universe , locked up in the

material atoms

Nt = the total number of atoms in the material sector

Ne = the number of rotational displacement units ejected into the cosmic sector from the

material sector

= the number of rotational displacement units ejected into the material sector from the

cosmic sector (under steady state conditions)

Nn = the number of free PDU in the material universe involved in transmuting the

elements

Nz = the number of atoms of the element with atomic number Z

az = the relative cosmic abundance of the element Z = Nz/Nt

We will consider the element with atomic number Z. We find that its population, Nz, is

being increased by the atoms that get transmuted to element Z from lower Z values. At

the same time Nz is being decreased by those atoms that get transmuted to atomic

numbers higher than Z. In addition, some atoms of element Z are lost through Type II

explosions. Since the universe as a whole is under steady state, the number Nz can be

taken as constant. This means that the inflow must be equal to the outflow.

Total PDU

The total number of the positive rotational displacement units contained in a ll the atoms

in the material sector is given by

ND=S zZ*Nz=NT S Z*AZ (1)

Transmutation, Outgoing

Oz, the number of atoms of element Z that are outgoing by getting transmuted to

element(s) of higher atomic number by combining with the free PDU can be arrived at as

follows:

Let Dz be the number of PDU captured by the atoms of element Z, out of Nn, the total

number of PDU available for transmutation. Then, the ratio Dz/Nn must be equal to the

ratio of the PDU locked up in all the atoms of element Z to the total number of PDU in

the material sector. That is,

Dz/Nn = Z*nz/ nd,orDz = Z(Nt*az) Nn/nd (2)

Now, the major portion of the outgoing atoms from element Z end up as atoms o f

element Z+2. This involves the capture of a single PDU by each atom. Let this number

of atoms be 2Oz. In addition, it is also probable that a small fraction of the atoms capture

simultaneously two PDU, resulting in trans mutation to element Z+2. Let this number be

2Oz. Thus Oz is made up of two parts, 1Oz and 2Oz, such that

1Oz = k*Oz and 2Oz = (1-k)*Oz (3)

where k is a distribution fraction.

Of the number of Dz, we take that the number of PDU involved in the single capture

event is 1Dz and the number involved in the double capture event is 2Dz. Then 1Dz =

1Oz, whereas 2Dz = 2* 2Oz. Usin g eq. (3) we have

Dz = 1Dz + 2Dz = 1Oz + 2*2Oz = [k+2(1-k)]Oz = (2-k)*Oz

Substituting for Dz from eq. (2),

Oz = [Nt*Nn/Nd(2-k)]*Z*az (4)

Transmutation, Incoming

From what has been said above, it can be seen that the number of atoms, I, coming in

by getting transmuted to element Z from elements of lower atomic number comprises two

separate streams: Iz-1, the number that is coming in from element Z-1 due to single

capture, and Iz-2, the number coming in from element Z-2 due to double capture (see fig.

2). From eq. (3) we note that

******************************************************

Iz-2 = 2Oz-2 = (1-k)*Oz-2 and

Iz-1 = 1Oz-1 = k*Oz-1

Thus, the total number of incoming atoms adding to the population of element Z i s,

(substituting Z+2 and Z+1 respectively, for Z in eq. (4))

I = Iz-2 + Iz-1

=[Nt*Nn/Nd(2-k)]*[(1-k)(Z-2)az-2 + k(Z-1)az-1] (5)

Ejection

We will assume that the relative abundance in the matter that is ejected to the c-sector

by the Type II explosions is the same as that in the material sector of the universe in

general. If Ez is the number of atoms of element Z that are ejected, we have the total

number of PDU that are leaving the material sector by way of ejection as

Ne = Sz Z*Ez (6)

If the matter is uniformly distributed, we have Ez proportional to N z; that is, Ez = g*Nz,

where g is a fraction less than 1.0. Then.

Ez = g*Nt*az (7)

Therefore, from eq. (6) above,

Ne = SZ*(g*Nt*az) = g*NtSZ*az

Hence, from eq. (1), Ne = g*Nd, or g = Ne/Nd. Finally, from eq. (7),

Ez = (Nt*Ne/Nd)az

= [Nt*Nn/Nd(2-k)] [Ne(2-k)/Nn]*az (8)

Equilibrium

By steady state we mean, in the material sector, uniformity with respect to time. Under

steady state conditions, therefore, the relative abundance does not vary. That is, Nz, the

number of atoms of the element Z is constant. That is, Nz, the number of atoms of the

element Z, is constant. In othe r words, I = Oz + Ez (see fig. 2). Thus, from eqs. (4), (5)

and (8),

[Nt*Nn/Nd(2-k)][(1-k)(Z-2)az-2 + k(Z-1)az-1]

= [Nt*Nn/Nd(2-k)][Z*az + (Ne(2-k) /Nn)az]

Or

az = (1-k)(Z-2)az-2 + k(Z-1)az-1

———————————— (9)

Z +

where s = Ne(2-k)/Nn (10)

Hydrogen

Since with Z = 1, hydrogen is the first element, the case of inflow from elements of

lower atomic number does not arise. On the other hand, the displacement units ejected

from the c-sector form the incoming flow. Since, of the Ne displacement units entering

the material sector, Nn PDU are u sed up for the purpose of transmutation, the number of

PDU that eventually trans form to hydrogen atoms is Ne - Nn. Therefore, from eqs. (4)

and (8), balancing the inflow and the outflow,

Ne-Nn = [Nt*Nn/Nd(2-k)][1*a1 + (Ne(2-k)/Nn)a1]

Or,

Ne-Nn Nd

——— (2-k) —— = (1 +

)a1

Nn Nt

Substituting from eqs. (1) and (10),

- (2-k)

a1 = ———— Z*az (11)

+ 1

Since az is a function of a1, a1 cancels out from both s ides of the equation (11). The

equation, therefore, serves as the compatibility criterion between values of s and k.

Further, since Nt = SNz,

Saz = 1 (12)

Eq. 12 is the normalizing condition which fixes the value of a1, and hence of all az, for

given values of s and k.

Comparison with Empirical Data

The values of the two parameters s and k in the above equations are to be arrived at by

logical processes from the postulates of the Reciprocal System. This still remains to be

done. Meanwhile, a good agreement with the empirical values of the relative cosmic

abundances³ can be demonstrated by appropriate choice of s and k. The theoretical curve

is plotted in Fig. 1, with s = 9.5 and k = 0. 9.

*************************************************

It must be noted that, in the figure, the abundance values are plotted on a logarithmic

scale and hence the discrepancy between the theoretical and the observational values

wherever it occurs should not be underestimated. However, it is clear that, as far as it

goes, the trend of the theoretical curve conforms well to the actual.

Further refinement is in order in considering the possibility of transmutation by triple or

multiple capture of PDU, which have a non-zero probability at t he higher Z values. In

fact, the comparatively higher abundance of the Even-Z elements over those of the Odd

ones can be explained on the basis of the corresponding distribution in the values of k for

the single, double, or higher multiple capture events. Remembering that the atomic

number is the net total electric displacement units, and Even Z can be seen to correspond

to an Odd speed 1/(1+Z) . As Larson explains, Odd speeds (like 1/3 or 1/5) are the direct

result of scalar directional reversals, whereas Even speeds (like 1/4 or 1/6) are obtained

only by way of compounding two Odd speeds. As such, the probability of an Odd s peed

(Even Z) is comparatively higher than that of an Even speed (Odd Z).

Among the assumptions made, the first is that the relative abundance is uniform in the

universe. The second one is that the magnetic ionization level is zero. This may be true

only in the case of interstellar and intergalactic matter, most of which lies undetected.

Consequently, the contribution of this matter t o the cosmic abundance is not reflected

adequately in the observational values. The zero ionization level assumption, therefore,

is likely to give rise to a large error in the predicted values, especially at the higher

atomic numbers. Evaluation based on the consideration of the atomic weight rather than

the atomic number will be more appropriate to the situation as it takes care of the

rotational displacement present as the gravitational charge as well.

Another important factor that has not been taken into account in this primary analysis is

the disintegration of matter that occurs on attaining the destructive thermal limit (as in the

stellar energy generation process). Also to be considered is the effect of supernova

explosions on the abundance of the Fe group of elements, and the possibility that the

relative abundance in the matter ejected out of the material sector in Type II explosions

is considerably different from that applicable at large.

References

1. D. B. Larson, Nothing But Motion, (Portland, Or.: North Pacific Publishers,

1979), p. 215.

2. D. B. Larson, The Structure of the Physical Universe (Portland, Or.,: North

Pacific Publishers, 1959), pp. 105-108.

3. American Institute of Physics Handbook, 1963.

THE INTER-REGIONAL RATIO

Introduction

The inter-regional ratio is an important concept discovered in the development of the

Reciprocal System of theory. The works of Larson, notably Nothing But Motion and The

Structure of the Physical Universe are to be referred to for an explanation of the origin

and significance of this ratio. This paper only attempts to clarify the factors involved in

its calculation, as applied to the basic properties of matter.

At the outset, I feel that the word ―orientation‖ that we have been using in this context

does not seem appropriate because of its strong connotation of direction in space. The

word ―possibility‖ might seem preferable, since in evaluating the inter-regional ratio we

are inquiring as to how many possibilities are there for a motion unit to exist—the

intrinsic existential possibilities, we might say. Another word that comes to mind is

―eigenstate.‖ But ―degrees of freedom‖ seems very much suitable, provided we refrain

from smuggling in some of its spatial connotations.

The Reciprocal System shows that there are several types of regions or domains in the

structure of the physical universe and that there are interactions across the regional

boundaries. During the interactions it is not always the case that the effect of a unit of

motion transmitted across the boundary is also one unit. For example, if there are f

number of equipossible alternatives within the region for a unit of motion, then by

probability laws we know that there is 1/fth chance of the unit effect being transmitted, or

what is tantamount, only 1/fth part of the unit motion gets transmitted. The number of

possibilities or degrees of freedom, f, is called the Inter-regional Ratio.

Rotational Degrees of Freedom in Three-dimensional Time (or Space):

Let us examine rotation in space in order to draw conclusions that are equally applicable

to rotation in time. ―One-dimensional‖ rotation means that one magnitude (or parameter)

is required to fully specify the rotation. A one-dimensional rotation occupies two-

dimensional space. Similarly, a two-dimensional rotation requires two magnitudes for its

full specification and occupies three-dimensional space. Now a unit of one-dimensional

rotation has two possible directions, +1 and -1, within the framework of three-

dimensional space, as shown in fig. 1.

As a result, the total number of possibilities—the degrees of freedom, as we will call

them—in three-dimensional space with two possibilities in each dimension is 2*2*2 = 8.

Notationally we can express the eight possibilities as

(+1,+1,+1) (+1,+1,-1) (+1,-1,+1) (+1,-1,-1)

} (1)

(-1,-1,+1) (-1,-1,-1) (-1,+1,+1) (-1,+1,-1)

In fact, if n is the number of (vector) dimensions and p the number of possibilities per

dimension, then f the number of degrees of freedom available in n-dimensional

(vectorial) space (or time) is given by

f = pn (2)

As such, a unit of one-dimensional rotation has eight degrees of freedom (that is, intrinsic

existential possibilities) in three-dimensional space (or time).

The question is sometimes raised as to whether the two possibilities in each of the three

dimensions do not make up a total of six rather than of eight. This would indeed be true

if we were considering three one-dimensional spaces instead of one three-dimensional

space. If the three dimensions are independent, then the total possibilities are

2 or 2 or 2 = 2 + 2 + 2 = 6 (3)

In fact, this is what we have in the case of space-time dimensions—the dimensions of

scalar motion—in distinction to the dimension of space (or time)—which we have called

the vector dimensions. Since the three space-time dimensions, being scalar, are

independent, the possible number of degrees of freedom is six.(1)

So if n is the number of

scalar dimensions and p the number of possibilities per dimension, we can write down

the formula for the number of degrees of freedom available in the scalar dimensions as

f = n*p (4)

On the other hand, if the three dimensions are interrelated, the total number of degrees of

freedom, as given by eq.(2) is

2 and 2 and 2 = 2 * 2 * 2 = 8 (5)

Another question that is sometimes raised is why two possibilities per dimension and

three dimensions do not imply 32 = 9 possibilities rather than 2

3 = 8. But it is not

difficult to see that this would be the case only if we had three possibilities in each of the

dimensions of a two-dimensional motion, and not otherwise.

As the degree of complexity of the motion increases, the existential states possible to it

decrease. The two-dimensional rotation, it is also remarked, requires two magnitudes to

specify it fully. So the possible degrees of freedom for a two-dimensional rotation in

three-dimensional space (or time) are 8/2 = 4. This can easily be understood with the

help of the diagrams shown in fig. 2.

Fig. 2 The Degeneracy of a Two-dimensional Rotation

The two-dimensional rotation is a coupled rotation of two one-dimensional rotations.

This coupling causes a ―degeneracy.‖ In fig. 2(a), the directions of the two component

rotations are indicated by two plus signs. The characteristic of the two-dimensional

rotation is that if the directions of both of the one-dimensional rotations are reversed, as

in fig. 2(b), the net effect is to leave the sense of the two-dimensional rotation unchanged,

in view of the fact that

(+1) * (-1) = (-1) * (-1)

} (6) and

(+1) * (-1) = (-1) * (-1)

Due to this feature, the eight possibilities listed in statement (1) above reduce to four, for

the case of the two-dimensional rotation, because each of the possibilities listed in the

upper line of statement (1) turns out to be the same as the one listed immediately below

it, in the second line. For example, for the coupled rotation

(+1,+1,-1) = (+1,+1,-1) = (-1,-1,-1) = (-1,-1,-1) (7)

Therefore if d is the vector dimensionality of the motion, then eq.(2) is modified to give

f, the number of degrees of freedom available in vector space (or time) as

f = pn/d (8)

We finally arrive at the total number of degrees of freedom available for a unit of motion

in the atom which comprises two two-dimensional (magnetic) and one one-dimensional

(electric) rotations, as

(23/2) * (2

3/2) * (2

3/1) = 4 * 4 * 8 = 128 (9)

There is another point of relevance that needs to be mentioned at this juncture before

turning attention to the inquiry of the vibrational degrees of freedom. We have already

distinguished between the dimensions of space-time (the scalar dimensions) and the

dimensions of space (or time) (the vector dimensions). If we have an instance of motion

existing in two or three space-time dimensions, then motion in only one of these space-

time dimensions can be represented in either three-dimensional space (or time)(2)

. This is

depicted in fig. 3.

Gravitation (atomic rotation) is three space-time dimensional. The two space-time

dimensions which cannot be represented in three-diomensional time (or space) are fully

occupied by scalar motion and therefore leave no more degrees of freedom than

calculated by eq. (9).

Scalar Motion in this one space-time

dimension only is represented in three-

dimensional time (or space)

Two two-

dimensional

rotations in two

dimensions of time

One one-dimensional

rotation in the third

dimension of time The region of

three-dimensional time

These two space-

time dimensions

are occupied by

scalar motion; but

this motion cannot

be represented in

three-dimensional

space (or time)

Fig. 3 The Limitations of Three-dimensional Time

Vibrational Degrees of Freedom in Three-dimensional Time:

While a one-dimensional rotation has two possibilities (clockwise and counter-clockwise,

as shown in fig. 1), a one-dimensional vibration has only one possibility, since both the

directions (forward and backward) in any dimension constitute one oscillation. This is

true of both one-dimensional linear and rotational vibrations. In view of this, the possible

number of degrees of freedom of a one-dimensional vibration in three-dimensional time

(or space), as calculated by eq.(2), with p =1 and n=3, is

f = 1³ = 1 (10)

However, this number is increased by an additional factor, the freedom available in the

three space-time dimensions, only one of which is occupied by the single unit of photon

vibrational motion. This leaves the remaining two space-time dimensions vacant (unlike

in the case of atomic rotation). Consequently the one unit of vibrational motion has three

possible choices as far as the space-time dimensions are concerned. Notationally we can

list these possibilities as

(1,0,0), (0,1,0), (0,0,1) (11)

Thus the number of degrees of freedom of the one-dimensional vibrational unit becomes,

by eq.(3) or (4)

1³ or 1³ or 1³ = 1 + 1 + 1 = 3 (12)

At this juncture we recall that that we are not so much interested in the degrees of

freedom available to the one-dimensional vibration on its own right, but rather in the

additional degrees of freedom, if any, that this one-dimensional vibration makes available

to the rotational unit that is built on it. Since the atomic rotation is a time-displacement

while the basic photon vibration is is a space-displacement, both belong to different

―regions.‖ As a result, by applying probability laws, we see that N degrees of freedom of

the space-displacement of the photon is equivalent to 1/N degrees of freedom from the

point of view of the time-displacement of the rotation.

The three degrees of freedom calculated by eq.(12) are specifically applicable to the case

of a one-dimensional rotation founded on a one-dimensional vibration, giving the

rotational unit an additional 1/3 degree of freedom. But the rotation basic to the atomic

or subatomic structure is two-dimensional and not one-dimensional.(3)

Therefore, with p

= 3 and n = 2, by eq.(2), we obtain the total vibrational degrees of freedom from the point

of view of the two-dimensional rotation as

32 = 9 (13)

This means that for every rotational degree of freedom in three-dimensional time there is

an additional 1/9 degree of freedom due to the underlying vibration. However, since that

the atomic structure consists of two two-dimensional rotational systems—this is what

distinguishes the atom from subatomic particles, the latter having only one two-

dimensional rotational system in its structure—the additional degree of freedom due to

the vibrational contribution is 2/9 (being 1/9 for each of the rotational systems) in the

case of atoms, whereas it is only 1/9 in the case of the subatoms. The inter-regional ratio,

which is simply the number of total degrees of freedom, is

128 + (128 * 2/9) = 156.44 (14)

in the case of the atomic rotation, and is

128 + (128 * 1/9) = 142.22 (15)

in the case of the subatomic rotation.

Summary

1. Scalar motion (that is, space-time) can at maximum be three-dimensional. These

dimensions of scalar motion are referred to as ―scalar dimensions.―

2. The scalar dimensions are independent. If there are n number of scalar

dimensions and p number of degrees of freedom per dimension, the total degrees

of freedom, f, are n * p.

3. The stationary reference frame we call space is three-dimensional, these being

called the ―vector‖ dimensions.

4. If a multi-dimensional scalar motion exists, motion in only one of these multiple

scalar dimensions can be represented fully in a three-(vector) dimensional space

or time.

5. The three vector dimensions of space (or time) are not independent but

interrelated. If there are p number of possibilities per dimension, then the total

number of degrees of freedom, f, in the three-dimensional vector space (or time)

is given by: f = p³.

6. That the maximum number of degrees of freedom in three-dimensional space or

time is p³ does not mean that a particular motion can have p degrees of freedom.

If the number of dimensions of this motion (as against the number of dimensions

of the vector space (or time) in which it exists) is d, then the available number of

degrees of freedom for this motion is f = p³/d.

References

1. D. B. Larson, The Neglected Facts of Science (Portland Ore.: North Pacific

Publishers, 1982), p. 84.

2. Ibid., p. 19.

3. D.B. Larson, Nothing But Motion (Portland, Ore.: North Pacific Publishers,

1979), pp. 124-125.

ELECTRIC IONIZATION

1. Introduction

R. W. Satz discusses(1) the fundamental motions of the physical universe from the point of

view of the Reciprocal System of theory and derives their mathematical expressions. In a

subsequent paper(2) he shows how the work function, the ionization energy, and the

magnetic resonance frequencies of the atoms and the subatoms can be theoretically

derived from the fundamental postulates of the Reciprocal System. These two works

form the starting point of the present paper. Firstly we note some printing errors that are

found in Ref. 2 cited above:

(i) In figs I and II, the direction of the arrow head on the outermost of the three circles

should be reversed.

(ii) Table I, p. 22: in the column for ―c/vmag‖ for the element B, the entry should be 3 and

not 4. In the first column, in the second line from bottom, it must be Ag and not As.

(iii) p. 29, 8th line from bottom: ―(R/2 )‖ must be there in piace of ―(2R/ ).‖ (Note that it

is mentioned in the text, in the line above it, that the cosmic neutrino rotation takes an

inverse charge.) Only then does the combined energy add up to h * (2R/ ) * (B/Bnat) as

indicated.

(iv) Table II, p. 32: In the column for ―Displacement,‖ for the isotope 5B(11) the entry

should be 2-1-3 and not 2 2-3.

The theory of the electric ionization and magnetization developed in Refs. 1 and 2 leaves

certain unresolved difficulties:

l.l The mass effect of an etectric charge. Satz evaluates the energy necessary for creating

a positive electric charge as 8.68 eV (eq. 7 of Ref. 2 and p. 8 of Ref. 1). Larson,

calculating the individual masses of the subatoms, concludes that the electric charge

produces a mass effect amounting to 0.00004494 amu.(3) This is equivalent to nearly

41850 eV. How such a mass effect of 41850 eV is produced from an electric charge that

came into being from an energy of 8.68 eV is not clear. Similarly, it can be seen that the

energy associated with the unit isotopic charge is 2.17 eV since its rotational frequency is

R/2 (p. 8, Ref. 1). It is once again not clear how this can compare with the mass effect

of an isotopic charge, namely, 931.3 MeV. Further, I have shown(4) that , following

Larson‘s line of argument, a unit magnetic charge gives rise to a negative mass effect

equivalent to -243.19 eV, which also contrasts with the energy required to create a

magnetic charge, namely, 2.17 eV as derived by Satz.

1.2 Under Table I (p. 23, Ref. 2), Satz mentions in a foomote: ―...where value 3 appears

in K.V.K. Nehru Electriclonizarion magnetic rotation, this is the inverse of actual

rotation,‖ whereas in the work(5) from which these values were taken, Larson was more

careful, noting that ―...where the value 3 appears as the magnetic rotation of one of the

higher group elements, this is the inverse of the actual rotation, 5.― However, what both

these authors fail to make clear is how rotation 5 is the inverse of rotation 3 , since in the

magnetic dimension the two ―zero points‖ are separated by 4 units and not 8.

1.3 The photoionization theory developed by Satz(2) seems to give good results, but there

are ceriain inadequate features. The first of these is the rather large discrepancy (16 to 19

%) between rhe calculated and the observed values of the ionization energy of some of

the elements. See, for example, the cases of C, Zn, Cd, Hg, etc. (Table I, pp. 22-23, Ref.

2).

1.4 The appropriateness of taking the magnetic speed as 3 (see Table I, p. 23, ref. 2) when

the magnetic displacement is 3, in the cases of Ni, Cu, Zn, Zr, Nb and Mo or that of

taking the electric speed as 5 and 6 when the electric displacement is (4) and (3)

respectively in the cases of Ge and As is not explained. This lapse occurs in the cases of

Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, etc.

1.5 While Table I(2) covers a good number of the elements for which the calculated values

of the work function and the ionization energy are compared with the observed values,

there is a considerable number of elements left out. Conspicuous among the latter are all

of the inert gases.

1.6 Similarly, while it was mentioned that the electron, the positron, the proton, and

H1can take an electric charge (p. 23, Ref. 2), no reason was given as to why the neutrino

and the neutron do not do so.

1.7 In the case of H1 the Principle of Equivalence was invoked (p. 24, Ref. 2) to show that

the ionization energy is 13.595 eV. However, no attempt was made to derive this value

from the rotational speeds of H1, even though this was done in the case of the ionization

energies of the free positron and proton (eq. 7, ref. 2), as well as atoms (eq. 9a, Ref. 2).

1.8 Developing the equation for the ionization energy of an atom, Satz writes: ―From

mechanical considerations it is obvious that the energy necessary to create a positive-

negative charge pair is twice that needed to create the negative charge on the electron‖ (p.

24, Ref. 2). Thus he takes it as 2 * 2.1 = 4.34 eV. But it can be asked, why should not this

energy be taken as twice the energy needed to create the positive charge on the atom (2 *

8.68 eV), or the sum of the energies required to ;,reate the negative and the positive

charges (2.17 + 8.68 eV), instead of 4.34 eV?

2. Equation for the Ionization Energy

We will now attempt a refmement of the electrical ionization theory developed by Satz(2)

with a view to meet the difficulties mentioned in section 1 above.

We find that the best way to get an insight into the situation is to consider the ionization

energies, EI, of the atoms of the alkali metals, all of which have only one unit of

rotational displacement in the electric dimension. From Ref. 6 we have the following

data:

Element Displacement EIin eV

Li 2-1-1 5.392

Na 2-2-1 5.139

K 3-2-1 4.341

Rb 3-3-1 4.177

Cs 4-3-1 3.894

It can be noted from the observational data that as the displacement in the magnetic

dimension increases, there is a systematic decrease in the ionization energy. On the other

hand, the value calculated by Satz (his Table I, Ref. 2) is the same, 4.34 eV, for all of

these elements. From this it is apparent that there ought to be some missing factor that

accounts for this discrepancy. This factor, whose existence has not been recognized

hitherto, is what might be called the transverse effect of the rotations in the two

dimensions other than the one considered in the Satz eq. 9a (p. 25, Ref. 2):

EI,atom = 4.34 *(c/vmag)½

eV

EI,atom = 4.34 *(c/velec-1)½

eV

That is to say, if u and v are the two magnetic speeds and w the electric speed, and if the

ionization energy happens to be given by

EI = 4.34 * (c/u)½,

the speeds v and w in the orthogonal dimensions do have a transverse effect on EI. Or if

EI happens to be given by

EI = 4.34 * (c/w-1)½,

then the speeds u and v exert the transverse effect.

This transverse effect can be evaluated as follows. Firstly, we note from Satz‗ eq. 9-a(2)

given above that the collinear effect of the atomic rotation on the electric ionization is

arrived at by considering the inverse speed c/vmag or c/velec. The transverse effect is the

inverse of the collinear effect, and as such, is to be arrived at by considering the specific

speeds, namely, vmag/c and velec/c directly.

Secondly, since speeds in two different dimensions are simultaneously involved in the

transverse effect, their net effect can be calculated by talang their geometric mean.(7)

Incidentally, it may be noted that the reason for the geometric mean of the specific

rotations to be the relevant quantity, as Larson(7) takes, is that the force effect of a specific

rotation t is given by ln t (i.e., the natural logarithm of t), and that the average force due

to the two rotations t1 and t2 is

½(ln t1 + ln t2) = ln(t1* t2)½.

That is, it is equivalent to the force effect of a rotation (t1* t2)½.

Finally, the square-root of the expressions is to be taken in order to convert the time

region quantity into the time-space region quantity. Thus the factor responsible for the

transverse effect can be written down as

[(Vx/c * vy/c)½]

½ = (vx * vy/c2)¼ (1)

where vx/c and vy/c are the specific rotations in the other two dimensions.

It is necessary to consider one more item before we can set up the fmal expression for the

ionization energy of the atom. This concerns the energy required to create a positive-

negative charge pair, mentioned in section 1.8 above. This is not twice the energy needed

to create the negative charge as Satz supposes (nor, of course, twice the energy needed to

create the positive charge). In Ref. 1, Satz concludes that the natural frequency of electric

charge is R/ Hertz (his eq. 23, ref 1) and then shows that the frequency of unit negative

charge is R/2 , since the negative charge is one unit of time displacement and its speed is

1/(1 + 1) = ½. Similarly, he shows that since the unit of positive electric charge is a unit

of space displacement, its speed is (1 + 1)/1 = 2, its frequency is 2R/ (also see his eqs. 4

& 7, Ref 2). Now, when a charge pair is created the relevant speed is the geometric mean

(of the speeds of a positive and negative charge), that is, (½ * 2)½ = l. Hence the energy

necessary to create the charge pair is twice h * 1 * R/ (where h is Planck's constant), or

8.68 eV. Therefore, the energy for the first ionization level is given by

EI,atom = 8.68 *(c/vmag)½*(

.vx * vy/c2

)1/4

eV

or (2)

EI,atom = 8.68 *(c/velec-1)½*(

.vx * vy/c2

)1/4

eV

3. Observational Validation

In Table I are listed the values of EI calculated from eq. 2. In column 2 of the Table the

displacements in the three dimensions are given for each element, and in the third column

are given the rotations causing the collinear effect, namely, either c/vmag or c/velec. In

those cases where these speeds are derived from any of the alternative orientations the

atomic rotation is able to assume, as will be presently discussed, they are marked by an

appropriate sign. In the fourth column are listed the two specific rotations that produce

the transverse effect. In column 5 are listed the calculated values and the observed values

according to Ref. 6.

The agieement with the observational values can be seen to improve very materially

compared with that achieved by the Satz equation. (The correlation coefficient is 0.992.)

There are several aspects to the computation:

3.1 The Neutral Particles. As pointed out in section 1.6 above, the neutrino and the

neutron do not take any electric charge. I have shown elsewhere(4) that the ―½

-½‖ type of

effective displacement in both the magnetic dimensions of these particles is what makes

the acquirement of an electric charge impossibie.

3.2 Hydrogen. One of the two intermediate type of particles, H1, has the following speeds

in its two rotating systems:

1/3 - ½ - 2

}

½ - ½ - 2

Since the speeds in the two rotating systems in the primary magnetic dimensions are

unequal, their geometric means, (1/3 *

½)½ = 1/6 is to be taken. This causes the collinear

effect. The transverse effect comes from the two speeds ½ and 2 in the remaining two

dimensions. Thus, from eq. (2) we have:

EI,H1 = 8.68 * ( 6)½ * (½* 2)

¼ = 13.585 eV.

3.3 The Inert Gases. A typical case is that of the inert gases, all of which have zero

electric displacement. It must be recalled that the positive and negative zern-.points (from

either of which the atomic rotation can be alternatively reckoned) are separated by 8 (or

16) displacement units in the electric dimension.(8) Now for the purpose of talang on the

electric charge the rotation in the electric dimension of the inert gases is able to assume

the role of this alternative zero-point. We shall refer to this phenomenon by the term

―zero-shifting.‖

Both He and Ne, with their smaller atomic numbers (net total electric displacement), are

able to take the double leap of 16 units (two 8-unit shift). This has been indicated in

Table I by ¶¶. Kr, Xe and Rn, with higher atomic numbers, take on the 8-unit zero-shift

(indicated in Table I by ¶). Ar, the element next to Ne in the inert gas series, is also able

to take on the 16-unit zero-shift li.ke both of its predecessors. But its net total

displacement being much higher than that of He or Ne, the probability of the 16--unit

shift competes equally with that of the 8-unit shift resorted to by Kr and the higher

members.

We will find in a number of instances where alternative atomic rotational orientations are

possible, as will be seen below, the question of the relative probabilities plays a

significant role in determining the value of the ionization energy observed

macroscopically. Pending detailed study of the relative probabilities we will assume that

the 16-unit shift and the 8-unit shift have equal probabilities in the case of Ar. Thus the

ionization energy of Ar comes out to be the arithmetic mean of the two values resulting

from the 16-unit shift and the 8-unit shift, namely, 15.92 eV.

3.4 Etectro-negative Elements. From the principles of the Reciprocai System it is evident

that positive ionization-that is, acquisition of a rotational vibratory space displacement-of

the atom is not possibie because of the space dispiacement in the electric dimension of

these elements. The rotation in the electric dimension must assume an alternative

orientation, thereby acting as an equivalent time displacement. This alternative

orientation may be achieved by any of the following three expedients.

3.4.1 The first expedient is to revert to the aIl-positive equivalent displacement. Thus, for

example, Ni, with the usual displacement of 3-3-(8) can assume the equivalent

displacement 3-2-10. This all-positive displacement is not normally realized due to its

lower probability. This possibility, therefore, occurs only when the element belongs to

the highest position in Division III (see pp. 223-4, Itef. 3—near the border between

Divisions II and III. In fact, it is encountered in only one more case, that of Lu (4-4-(15)).

3.4.2 If the rotation in the electric dimension is involved only in the transverse effect,

another possibility opens up. In view of the space-time symmetry around unity, a speed n

can achieve the effect of inverting the space-time orientation of the rotation by its ability

to act in the capacity of its reciprocal, namely, the speed 1/n. But this ability to act as its

reciprocal is limited only to the transverse effect and cannot extend to the collinear effect,

since the transverse effect is an inverse effect itself. Thus, in the case of Au (4-4-(7)), for

example, the speed 8 in the electric dimension is able to act as speed 1/8 as far as the

production of the transverse effect is concerned. This type is indicated in Table I by §.

Other examples are Cu, Pd, Ag, Cd, and Iif. The probability of this type of alternative

configuration becomes very low as we move away from the middle of a Group.

3.4.3 Under these circumstances, none of the elements of Division IV nor any of those in

the lowest positions in Division III are able to take up this expedient. The negative

rotation in the electric dimension of these elements is, however, able to achieve the same

result by taking recourse to the expedient of zero-shifting mentioned in section 3.3. As an

example, let us consider the element Se with the displacement 3-3-(2). An 8-unit zero-

shift in orientation turns the space displacement (2) into the time displacemen 6, which

then is able to produce the collinear efiect. It must also be noted that the inversion of the

orientation effected by the zero-shifting enables the rotation to exert either the collinear

effect or the transverse effect with equal facility. In the example of Se cited above, the

two effects seem to have equal probabilities. The macroscopic result, once again, is that

the ionization energy required is the arithmetic mean of the two values.

It will be seen that this alternative of zero-shifting is invariably the expedient adopted by

all the elements of Division IV (and those of Division III nearer the border between

Divisions III and IV, of Groups 2B, 3A, 3B and 4A. In the case of Group 4A elements Ta

(4-4-(14)) through Pt (4-4-(8)) the 8-unit zero-shift is not feasible, since the existing

space displacement in the electric climension is greater than 8 units. These elements,

therefore, take the 16-unit zero-shift. It is worth noting that in the case of the elements S

(3-2-(2)), Se (3-3-(2)), Os (4-4-(10)), Ir (4-4-(9)) and Pt (4-4-(8))--in all of which the

electric displacement is at the bottom of the first or second 8-unit stretch-the positive

rotation effectuated by zero-shifting seems to act either in the collinear or in the

transverse capacity with equal probability.

This leaves the Division IV elements of Group 2A, which have some peculiarity arising

out of their low net total displacement. These elements, N, O and F do resort to the zero-

shifting, like the rest of their electro-negative family, but, by virtue of their low net total

displacements they are able to take on the 16-unit double shift, like the two inert gas

elements, He and Ne, that bracket their group. In fact, the probabilities of the 16-unit and

8-unit shifts are about the same for each of these elements.

4. The Special Cases. There remain two special cases in which the large discrepancy

between the calculated and the observational values of the ionization energy seems to

warrant further study

( i ) The first of these pertains to those elements with displacement 3 in their electric

dimension, irrespective of whether this displacement is the direct positive value of 3, or

the equivalent positive displacement 3 obtained by an 8-unit zero-shifting of the negative

displacement of 5. They are Al (2-2-3), Sc (3-2-3), Ga (3-3-(5)), Y (3-3-3), In (4-3-(5))

and La (4-3-3). The exceptions are B (2-1-3) at the low atomic number end, and Tl (4-4-

(5)) and Ac (4-4-3) at the high atomic number end. The calculated value, in these cases,

exceeds the observational value by about 15 to 35%, as shown in Table II below.

Table II. Cases of Large Discrepancy

Ele. Calc. Obs. discr.(%)

———————————————————————

Al 8.08 5.986 35.0

Sc 7.52 6.54 14.9

Ga 7.52 5.999 30.7

Y 7.52 6.38 17.8

in 7.11 5.786 22.9

La 7.11 5.577 27.5

( i i ) The second special case pertains to the electropositive elements of Group 4A,

namely, the Lanthanides from Ce (4-3-4) through Tb (4-3-11). The average calculated

value of the ionization energy for these elements is 7.87 eV, while the average

observational value is 5.62 eV.

References

1. R.W. Satz, ―Further Mathematics of the Reciprocal System,‖Reciprocity, X (3),

1980.

2. Idem, ―Photoionization and Photomagnetization,‖ Reciprocity, XII (1), Winter

1981-82.

3. D.B. Larson, ―Nothing But Motion, ‖North Pacific Publishers, Portland, Or.,

1979, p.163.

4. K.V.K. Nehru, ―Internal Ionization and Secondary Mass,‖ privately circulated

paper.

5. D.B. Larson, ―The Structure of rhe Physical Universe, ‖North Pacific Publishers,

Portland, Or., 1959, p. 119.

6. J.A. Dean, ed., Lange‘s Handbook of Chemistry, 1973, pp. 3-6 to 3-8.

7. D.B. Larson, ―Solid Cohesion,‖ Reciprocity, XII (1), Winter 1981-82, 15.

8. Idem, Nothing But Motion, p. 222.

Table I. Ionization Energy of the Elements

Specific Speed Ei in eV

Ele. Dsplt, c/vm c/ve Trans.Eff. Calc. Obs.

H M 1-1-(1)

M½-½-(1) 6 1/2 *2 13.585 13.598

He 2-1-0

17¶¶ 1/2 .5*1/1.5 24.95

24.587

Li 2-1-1

2 1/3 *1/2 5.55 5.392

Be 2-1-2 3

1/2 *1/3 9.61 9.322

B 2-1-3 3

1/2 *1/4 8.94 8.298

C 2-1-4 5 1/3*1/2 11.09 11.260

N 2-2-(3) 14¶¶ 1/3*1/3 18.07

6¶¶ 1/3*1/3 11.21

Av.

14.64 14.534

O 2-2-(2) 15¶¶ 1/3*1/3 18.75

7¶ 1/3*1/3 12.28

Av.

15.51 13.618

F 2-2-(1) 16¶¶ 1/3*1/2 .5 20.31

8¶ 1/2 .5*1/2 .5 14.52

Av. 17.42 17.422

Ne 2-2-0

17¶¶ 1/2 .5*1/2 .5 21.96

21.564

Na 2-2-1

2 1/3*1/2 .5 5.25

5.139

Mg 2-2-2

3 1/2 .5*1/2 .5 7.76

7.646

Al 2-2-3 3

1/3*1/4 8.08

5.986

Si 2-2-4 3

1/2 .5*1/4.5 8.21

8.151

P 3-2-(3)

6¶ 1/4*1/3 10.43

10.486

S 3-2-(2)

7¶ 1/2 .5*1/4 11.96

4

1/2 .5*1/7¶ 8.49

Av.

10.22

10.360

Cl 3-2-(1)

8¶ 1/2 .5*1/4 12.91

12.976

————————————————————————————————

Ar 3-2-0

17¶¶ 1/4*1/3 18.65

9¶ 1/4*1/3 13.19

Av.

15.92

15.759

K 3-2-1

2 1/4*1/3 4.66

4.341

Ca 3-2-2

3 1/4*1/3 6.60

6.113

Sc 3-2-3 3

1/4*1/4 7.52

6.54

Ti 3-2-4 3

1/4*1/5 7.11

6.82

V 3-2-5 3

1/4*1/6 6.79

6.74

Cr 3-2-6 3

1/3.5*1/7 6.76

6.766

Mn 3-2-7 4

1/3*1/8 7.84

7.435

Fe 3-2-8 4

1/2 .5*1/9 7.97

7.870

Co 3-2-9 4

1/2 .5*1/9.5 7.86

7.86

Ni 3-3-(8) 4

1/2 .5*1/10.5+ 7.67

7.635

Cu 3-3-(7) 4

1/3.5*1/7.5§ 7.67

7.726

Zn 3-3-(6) 4

1/4*1/3¶ 9.33

9.394

Ga 3-3-(5)

4¶ 1/4*1/4 7.52

5.999

Ge 3-3-(4) 4

1/4*1/5¶ 8.21

7.899

As 3-3-(3)

6¶ 1/4*1/4 9.70

9.81

Se 3-3-(2)

7¶ 1/3.5*1/3.5 11.36

4

1/3.5*1/6.5¶ 7.95

Av.

9.66

9.752

Br 3-3-(1)

8¶ 1/4*1/3.5 11.87

11.814

Kr 3-3-0

9¶ 1/3.5*1/3.5 13.12

13.999

Rb 3-3-1

2 1/4*1/4 4.34

4.177

Sr 3-3-2

3 1/4*1/4 6.14

5.695

Y 3-3-3

4 1/4*1/4 7.52

6.38

Zr 3-3-4 4

1/4*1/5 8.21

6.84

Nb 3-3-5 4

1/4*1/6 7.84

6.88

Mo 3-3-6 4

1/4*1/7 7.55

7.099

Tc 3-3-7 4

1/4*1/8 7.30

7.28

Ru 3-3-8 4

1/3.5*1/8.5 7.43

7.37

Rh 3-3-9 4

1/3.5*1/9.5 7.23

7.46

Pd 4-3-(8) 5

1/3.5*1/8.5§ 8.31

8.34

Ag 4-3-(7) 4

1/4.5*1/7.5§ 7.20

7.576

Cd 4-3-(6) 4

1/5*1/3¶ 8.82

8.993

In 4-3-(5)

4¶ 1/5*1/4 7.11

5.786

Sn 4-3-(4) 4

1/5*1/5¶ 7.76

7.344

Sb 4-3-(3) 5

1/4*1/6¶ 8.77

8.641

Te 4-3-(2) 5

1/3.5*1/6.5¶ 8.89

9.009

I 4-3-(1)

8¶ 1/5*1/4 10.86

10.451

Xe 4-3-0

9¶ 1/4.5*1/3.5 12.32

12.130

Cs 4-3-1

2 1/5*1/4 4.12

3.894

Ba 4-3-2

3 1/5*1/4 5.80

5.212

La 4-3-3

4 1/5*1/4 7.11

5.577

----------------------------------------------------------------------------------------

Dy 4-3-12 4

1/5*1/13 6.11

5.93

Ho 4-3-13 4

1/5*1/14 6.00

6.02

Er 4-3-14 4

1/5*1/15 5.90

6.10

Tm 4-3-15 4

1/4.5*1/15.5 6.01

6.18

Yb 4-3-16 4

1/4.5*1/6.5 5.91

6.254

Lu 4-4-(15) 4+

1/5*1/18+ 5.64

5.426

Hf 4-4-(14) 5

1/4.5*1/14.5§ 6.83

7.0

Ta 4-4-(13)

4¶¶ 1/4.5*1/4.5 7.09

7.89

W 4-4-(12)

5¶¶ 1/5*1/4.5 7.97

7.98

Re 4-4-(11) 5

1/5*1/6¶¶ 8.29

7.88

Os 4-4-(10)

7¶¶ 1/5*1/5 9.51

5

1/5*1/7¶¶ 7.98

Av.

8.74

8.7

Ir 4-4-(9)

8¶¶ 1/5*1/5 10.27

5

1/4.5*1/7.5¶¶ 8.05

Av.

9.16

9.1

Pt 4-4-(8)

9¶¶ 1/5*1/5 10.98

5

1/5*1/9¶¶ 7.49

Av.

9.23

9.0

Au 4-4-(7) 5

1/5*1/8§ 7.72

5

1/5*1/2 ¶ 10.91

Av.

9.31

9.225

Hg 4-4-(6) 5

1/4.5*1/2 .5¶ 10.60

10.437

Tl 4-4-(5)

4¶ 1/5*1/5 6.72

6.108

Pb 4-4-(4)

5¶ 1/5*1/5 7.76

7.416

Bi 4-4-(3) 5

1/5/1/6¶ 8.29

7.289

Po 4-4-(2) 5

1/4.5*1/6.5¶ 8.35

8.42

Rn 4-4-0

9¶ 1/5*1/5 10.98

10.748

Ra 4-4-2

3 1/5*1/5 5.49

5.279

Ac 4-4-3

4 1/5*1/4.5 6.90

6.9

Th 4-4-4

5 1/5*1/5 7.76

6.95

Note:

+ Altemative all-positive displacement

§ Inverse electric speed (in transverse effect only)

¶ 8-unit zero-shift (in the electric dimension)

¶¶ 16-unit zero-shift

THE LAW OF CONSERVATION OF DIRECTION

Introduction

Some students of the Reciprocal Syetem (RS) have been disputing the explanation of the

intrinsic structure of the photons, given by Larson, the originator of the R.S. No amount

of discussion, so far, seemed to throw additional light in overcoming the logical

objections raised. An examination of the situation undertaken by the present investigator

revealed that a crucial fact of fundamental nature is being missed hitherto, both by the

originator and the other students. It is found that a recognition of this fact not only

clarifies the photon situation entirely but also throws light on many collateral issues

where gaps in the logical development of the theory exist, thus rendering the theory more

cogent. Some of these new developments are reported in this Paper.

The Difficulties with Larson‘s Account of the SHM

In the outline of the deductive development of his theory Larson states:

―The continuity of the progresaion within the units enables the exiatence of another type

of scalar motion of physical locations. This is a motion in which there is a continuous and

uniform change from outward to inward and vice versa; that is, a simple hczrmonic

motion.‖¹ A little earlier (item 5 of the Ref. cited) he defines ―outward‖ and ―inward‖ as

being the scalar directions and representing motion away from and toward a ref erence

point in the stationary three-dimensional spatial reference system respectively. The

former results in increasing intervening distance while the latter in decreasing intervening

distance.

Since there is nothing like more outward (inward) or less outward (inward) the question

arises as to the meaning of the statement ―a continuous and uniform change from outward

to inward‖? Outward and inward, as applied to scalar motion, are discrete directions: the

acalar motion could be either outward or inward. There are no intermediate possibilities.

Larson is quite clear about this, at another juncture: ―When the progression within a unit

of motion reaches the end of the unit it either reverses or does not reverse. There are no

intermediate posaibility.‖² As such, the idea of a ―constant and uniform change‖ is

logically incompatible with, this concept of ―outward-inward motion.‖ It muat be

remembered that the mavgnitude of the motion is constant, being unity.

Since simple harmonic motion (SHM) does seem to underlie the structure of photons, the

crux of the problem of understanding the nature of the photon is the explanation of the

genesis of the SHM given only uniform scalar speed. If a vibration of the type Larson

prnposes is to exist, it can not be a SHM. The speed has to be a square wave. SHM seems

possible only if one of the components (space or time) progressea non-uniformly while

the other progresses uniformly. In fact, SHM will be the result under the two

circumstances: (i) when a constant magnitude is continuously and uniformly changing its

direction in the conventional reference system (as in rotation) and its projection in a

constant direction is being considered; or (ii) when there is a constant direction and the

magnitude is continuously and nonuniformly changing. The second alternative is

precluded by definition (see item D of the Basic Principles in the ―Outline‖³).

Is Rotation Primary ?

A scalar motion has magnitude only, and no inherent spatial direction. It therefore has to

be given a direction in order to be represented in a spatial ref erence system. Now a

―constant and uniform change‖ envisaged by Larson can only happen if the

representation in the reference system changes the vectorial direction uniformly as in

rotation. As a matter of fact, SHM will be the result if two such rotations, mutually

opposite in direction, are vectorially combined.

But Larson does not pasit the possibility of rotation prior to the existence of photons.

Thus he states: ―While motion is possible without anything moving, rotation is not

possible unless some physical object is available to be rotated.‖4 The logical basis for this

conclusion is hard to find. Rotation is as much a motion as translation is, and logically it

must be as much possible without any ―thing‖ rotating, as far as the primary motions are

concerned. One wonders, in this context, if the author is completely free of the

unconscious leanings to the frame of mind that underlies the view of the universe of

matter as against the univerae of motion!

Rotation is precluded only if space is onedimensional. Juat as soon as it is established that

the stationary spatial reference system is threedimensional, rotation becomea a

possibility. Larson himaelf, while discussing the status of the uncharged electron, refers

to the general nature of space which includes rotation as much as linear translation. ―Thus

the electron is essentially nothing more than a rotating unit of space. This is a concept

that is rather difficult for most of us when it is first encountered, because it conflicts with

the idea of the nature of space that we have gained from a longcontinued, but uncritical,

examination of our surroundings. ... The ―space‖ of our ordinary experience, extension

space, ... is merely one manifestation of space in general ...‖5. Therefore, what is not

being explicitly recognized is that, in general, space has two intrinsic traits: translational

and rotational.

The translational trait manifests to us as the familiar ―extension space,‖ whereas the

rotational trait-which manifests as difference in directionsia not so readily regarded by

common experience as manifestation of space. Hence the representation of a uniform

scalar motion in the conventional reference system can take either the form a uniform and

continuous change of linear magnitude with a constant direction, or the form of a uniform

and continuous change of direction, with a constant linear magnitude, that is, a rotation.

Conservation of Direction

As already pointed out, a scalar motion does not have a vectorial direction. The latter is a

property acquired due to the coupling with the conventional stationary three-dimensional

spatial reference system, which involves also the identification of a reference point. A

point of universal significance that needs to be recognized is that the representation of a

scalar motion in the conventional reference system conserves direction. This is

accomplished by the representation by substituting two opposite directionswhat we will

call a ‗bidirection‘ for the original lack of direction.

For example, consider the motion of a point 0 that is made the reference point. Consider

two locations, A and B, on a straight line passing through 0, and situated on opposite

sides of 0 (Fig. 1). In the csse of an outward scalar motion we find both A and B receding

from 0 (Fig. 1(a)). On the other hand, if O‘s motion is vectorial we find B (or A) receding

from 0, and A (or B) approaching it (Fig. 1 (b)). Thus a scalar motion gets represented as

a ‗bivector‘ and not merely as a vector. The appearance of a bivectorial motion in the

conventional reference system, therefore, serves to distinguish an intrinsically scalar

motion from vectorial motion.

Representation of linear motion

in the reference system

An analogy might help to demonstrate the universality of the Law of Conservation of

Direction. Imagine a long solid cylinder with a crosssectional area of an arbitrary shape.

If the cylinder is now divided into two by cutting with a plane, two new surfaces, S1 and

S2, will be generated as the ends of the two halves of the cylinder where there were none

prior to the cutting. Adopting the right hand cork-screw representation of areas, we can

see that the two intersection surfaces, S1 and S2, will be of equal area but opposite

directions (one being the mirror image of the other). The original lack of (exposed) area

is substituted by two equal areas of opposite vectorial directions. It is simply not possible

to carry out the intersection such that only one new surface is generated. In an identical

manner, the representation in the conventional apatial reference frame of a scalar motion,

with its inherent lack of direction, is not possible with the ascription of only a single

direction-it requires the imputation of two mutually opposite directions, in other words, a

bidirection.

Photon: an Intrinsic SHM ?

In case the representation of a scalar motion in the stationary three-dimensional reference

system is rotational motion instead of translational motion, the requirement of the

conservation of direction still holds good, the reprssentation taking the form of a

birotation. The birotation is a vectorial combination of two equal and opposite rotations,

clockwise (CW) and counter-clockwise (CCW).

Some students of the RS have argued that the CW or CCW direction of rotation is the

algebraic sign, the sense, of the rotation and not really a direction. Therefore they

concluded that rotation has no true direction. But they are missing the point. What their

conclusion means is that rotation does not have a direction in the sense of a direction of

linear motion. The CW or CCW sense of rotation is relative to the axis of rotation, but the

axis itself can be oriented in any direction in the three-dimensional spatial reference

system. Adopting the right hand cork-screw representation of rotation, the latter can be

vectorially depicted .

Because of the discrete unit limitation a mere change of direction (as in rotation) without

any magnitude is not possible. Hence a unit of birotation involves half a unit of one-

dimensional space element in each of its component rotations. As shown in Fig. 2, let one

component rotation be CW, and the refer ence point for this rotation be O, OA being the

radius of rotation with the axis of rotation perpendicular to the plane of the paper. The

reference point for the second component rotation, which is CCW, will be A, with AB as

radius and axis parallel to that of the first rotation. Since the angular speeds of the two

rotations are of equal magnitude, the visible result of this birotation is a SHM, with

location B oscillating in the XX‘ direction. This, therefore, is how the SHM is

engendered by uniform motion-the basis of photon structure.

Figure 2

Simple Harmonic Motion as Birotation

At this juncture it might be mentioned that, in this Paper, we are endeavoring to discuss

some logical difficulties occurring in the present development of the RS and to clarify

them in the light of the discovery of the Law of Conservation of Direction. It is not

possible, however, to undertake here the full development of the aspects we discuss

beyond supplying the missing links in the logic. It is assumed that the reader is

sufficiently familiar with the account of the development of RS as given by Larson in his

works.

Polarization Suppose now that a light beam is passed through a polarizer and one of the

component rotations of the photons is filtered out. The outcoming photons will be

constituted of a continuous uniform rotation, with the axis of rotation lying parallel to the

direction of propagation. If a blackened disk is suspended by a fine filament and ia

irradiated by such a circularly polarized beam of radiation such that the beam travels

parallel to the suspenaion and atrikea the diak normally, a torque should appear. This, of

course, is experimentally verified. It might be noted that in Laraon's account of the

structure of the photon there is no explanation of thia fact.

Vibration vs. Translation

Since each unit of motion, by the reciprocal poatulate, consists of one unit of space in

association with one unit of time, all motion takes place at unit speed. However, by a

sequence of reversals of the progreasion of either time or space, while the other

component (space or time) continues progressing unidirectionally, an efiective speed

other than unity can result. Explaining this, Larson gives a tabulation² for the example of

an effective apeed of 1/3 (see Table I).

Table I: DIRECTION

unit vibration translation

number scalar vectorial scalar vectirial

1 inward right inward forward

2 outward left outward backward

3 inward right inward forward

4 inward left inward forward

5 outward right outward backward

6 inward left inward forward

It may be seen that in the case of the translational situation the vectorial direction

reverses in unison with the scalar direction. But in the case of the vectorial vibration it is

not so: it is perplexing why the scalar and vectorial directions do not maintain a constant

relationship in the case of the vibrational motion (cp., for example, the third and the

fourth units in the tabulation).

Larson comes up with an explanation of a sort, which sounds more like an apology: ―...in

order to maintain continuity in the relation of the vectorial motion to the fixed reference

system the vectorial direction continues the regular reversals at the points where the

scalar motion advances to a new unit of space (or time).‖6 On the principles of

probability, the alternative possibility, namely, the vectorial directional reversals

occurring in unison with the scalar directional reversals appears more logical.

The present recognition of the fact that the linear vectorial vibration is really the

manifested result of a birotation now clarifies the situation. Both in the case of the

vibration and in the case of the translation the vectorial directional reversal is in unison

with the scalar directional reversal. In the vibrational case, the two component rotations

involved in the birotation do promptly reverse their respective directions at the time of

the reversal of the scalar direction. However, this does not produce any effect on their

vector resultant, which continues uninterrupted as the SHM.

Referring to Fig. 2, let A reach the poaition A‘ and B the poaition B'. Thia is one extreme

position of the oscillation of B. From this position whether OA‘ continues rotate in the

original CW direction or reversea and rotatea in the CCW direction (with the sense of

rotation of the aecond rotation always being opposite to that of the rotation of OA) hardly

matters-in either case the observable result ia the same oscillatory motion of B.

Conclusions

Summarizing some of the concluaions reached:

1. The representation of a scalar motion in the these dimenaional spatial reference

system conserves direction by substituting bidirection for its in herent lack of

direction unit vibration translation number sca,lar vectorial scalar vectorial 1

inward right inward forward 2 outward left outward backward 3 inward right

inward forward 4 inward left inward forward 6 outward right outward backward 6

inward left inward forward

2. The primary displacement from the background condition of the space-time

progression takes the form of a uniform birotation, the vector resultant of which

manifeats as a SHM. This ia identified as the photon.

3. Circular polarization is the result of filtering out one of the component rotationa

of the photon.

References

1. D. B. Lareon, ―Outline of the Deductive Development of the Theory of the

Universe of Motion,‖ Reciprocity XVII(1), Spring 1988, p. 8 (item 16)

2. D. B. Lareon, Nothing but Motion, North Pacific Pub.,Or.,U.S.A., 1979, p.98

3. D. B. Larson, Outline, op. cit., p. 6.

4. D. B. Lsrson, Nothing but Motion, op. cit., p. 57.

5. D. B. Larson, Basic Properties o f Matter Int. Soc. of Unified Science, Utah,

U.S.A ., 1988, pp. 102-3

6. D. B. Lareon, Nothing but Motinn, op. cit., p. 50. -K.V.K. Nehru

IS FERROMAGNETISM A CO-MAGNETIC

PHENOMENON

Introduction

According to the Reciprocal System, magnetism is the manifestation of two-dimensional

scalar motion of the rotational vibration type with space displacement. Since the

stationary three-dimensional spatial frame of reference is capable of representing not

more than one dimension of a scalar motion, only one dimension of the motion of a

magnetic charge, which is two (scalar) - dimensional, is observable while the scalar

motion in the second dimension is unobservable.

In the phenomenon of the ferromagnetism the material exhibits large spontaneous

magnetization in the absence of any externally applied magnetic field, below a

characteristic temperature called the Curie point. Relatively few elements are

ferromagnetic. This is because ―a magnetic charge, as a distinct entity, can exist only

where an atom is so constituted that there is a portion of the atomic structure that can

vibrate twodimensionally independently of the main body of the atom.‖(1) This precludes

many elements from being ferromagnetic.

Another important point that we need to note is that ―Ferromagnetism is a phenomenon

of the time region, and its natural zero point (the Curie temperature) is therefore a

boundary between two dissimilar regions ...‖(2) The rotational vibration which is the

magnetic charge is not a basic motion; it is a modification of a specific portion of the

basic rotation of the atom. In a solid state the atomic motion is already in equilibrium in

the time region. The magnetic charge, therefore, effectively crosses a regional boundary

when the motion falls below the time region unit of space, which is a compound unit and

is smaller than the natural unit of space by the interregional ratio, 156.444.(3)

Into the Time Region

The conventional theory tries to explain the spontaneous magnetization of the

ferromagnetism by the mutual magnetic interaction of the atomic dipoles. The initial

attempts at this explanation ran into trouble when it was found that the strength of this

interaction which is needed to explain the observed high intensity of magnetization had to

be nearly 104 times that of the postulated dipole-dipole interaction. When all rational

attempts to account for the origin of this high interaction streneth have failed. auantum

mechanics was invoked to interpret it as a purely hypothetical ‗exchange interaction.‘

In the Reciprocal System, however, the explanation comes out naturally: it stems from

the second power relation between the corresponding quantities of the inside and the

outside regions. Explaining cohesion in solids Larson points out: ―As we found in

Chapter 12, Vol. I, the equivalent of distance s in the time region is s², and the ... force in

this region therefore varies as the fourth power of the distance rather than the square.‖(4)

The interatomic distance in solids is, on the average, of the order of the compound unit of

space applicable to the time region, namely, the natural unit of space divided by the

interregional ratio, 156.444. Therefore, the dipole-dipole interaction strength worked out

on the basis of the inverse fourth power law would turn out to be (156.44)² or nearly 2.5 x

104 times stronger than that calculated on the basis of the inverse square law. This is

precisely what is needed to account for the observed state of affairs.

Co-Magnetism

In an earlier paper(5) we have shown that when the magnetic motion enters the time

region, the apparent direction of the motion reverse, resulting in an attraction of like poles

and a repulsion of unlike poles. The phenomenon has been referred to as ‗comagnetism.‘

This is illustrated in Fig.l, which is reproduced from the above referred paper.

Figure 1

Magnetism vs. Co-magnetism

It can be gathered from Fig. 1(c) that the minimum energy configuration for two

magnetic dipoles when located adjacent to each other is when the respective dipole

directions are antiparallel, and if placed collinearly is when the dipole directions are

parallel. On the other hand, in the case of co-magnetism, as could be seen from Fig. I(d),

the minimum energy configuration of two dipoles which are adjacent is when their

directions are parallel and if they are collinear when their directions are antiparallel. The

scheme of orientations is illustrated in Fig. 2.

Figure 2

Dipole Orientations for Least Energy

We shall presently show how comagnetism is responsible for the domain structure

characteristic of the ferromagnetic order. The point that is of significance here is that the

magnetic charge (motion) is two dimensional. If p and q are respectively the effective

speeds in the two scalar dimensions concerned of the magnetic charge, the motion of the

charge crosses the regional boundary effectively when the product, p*q, or more

correctly, their geometric mean, falls below the value of the compound unit of space.

This could happen in either of the three ways (see also the Appendix):

Case (i): when the component motion p, pertaining to the dimension parallel to the

dimension of the conventional spatial reference frame, is still outside the compound unit,

while the component q, pertaining to the second scalar dimension (which we shall refer to

as the ‗transverse dimension‘' for the purposes of this paper) crosses the regional

boundary and enters the inside region;

Case (ii): when the component p crosses the regional boundary which the component q is

still outside it; and

Case (iii): when both the components cross the boundary and enter the inside of the

compound unit.

Though ―the motion components in the second dimension are not capable of direct

representation in the conventional spatial reference system, ... they have indirect effects

that are observable, particularly on the effective magnitudes.‖(6). Further, quoting Larson:

―.. a two dimensional (magnetic) charge consists of a rotational vibration in the

dimension of the reference system and another in a second scalar dimension independent

of the first, and therefore perpendicular to it in a geometrical representation.‖(7) Following

our notation, we can conclude that the motion component q pertaining to the transverse

(scalar) dimension, though not observable directly in the conventional reference frame,

nonetheless, has indirect effects that do manifest in the geometric representations, in

directions that are perpendicular to the dipole direction.

Coupling this conclusion with the inferences we have drawn earlier, concerning the least

energy configurations of the magnetic and co-magnetic dipole pairs respectively, we can

deduce the types of ordering that are possible in aggregates of these dipoles for the cases

(i) to (iii) noted above. These are shown in Fig. 3. Figs. 3 (a), (b) and (c) respectively

depict cases (i), (ii) and (iii).

Figure 3

Magnetic/Co-magnetic Ordering

It is at once evident that case (i) results in the all-parallel dipole ordering called the

ferromagnetic. The remaining cases can be seen to result in the antiferromagnetic

orderings. In the case when the adjacent magnetic charges are of differing magnitudes

antiferromagnetism shows up as ferrimagnetism.

Summary

(1) The ferro- and antiferromagnetic phenomena are the result of the magnetic charge

entering the inside of the time region unit of space.

(2) The apparently strong interaction that is responsible for the spontaneous

magnetization stems from the second power relations relevant to the inside region.

(3) The ferro- and antiferromagnetic orderings of the dipoles are the result of either one

or both of the motion components of the twodimensional motion that is the magnetic

charge entering the inside region and thereby turning into the co-magnetic in the the

dimension concerned.

References

1. D.B. Larson, Basic Properties of Matter, Intl. Soc. of Unified Science, 1680 East

Atkin Av., Salt Lake City, Utah 84106, U.S.A, 1988, pp. 215-216

2. Ibid., p. 251

3. Ibid., p. 6

4. Ibid., pp. 7-8

5. K.V.K Nehru, ―Glimpses into the Structure of Sun: Part I, The Nature of Stellar

Matter,‖ Reciprocity, XVII(2), Autumn 1988, pp.14.21

6. D.B. Larson, Basic Pronerties of Matter, op. cit., p. 212

7. Ibid., p. 213

Appendix

Theoretically there could be seven types of the dipole orderings. Let p be the component

of the magnetic charge in the collinear direction, and q be the one in the traverse

direction, of the geometric representations. Splitting q into q1 and q2 to represent each of

the two transverse directions and adopting brackets to indicate that the component is

inside the compound unit of space, we have the following seven possibilities, all of which

exemplify the magnetic charge crossing the interregional boundary:

(i) P - [q1] - [q2]

(ii) [p] - ql - q2

(iii) [p] - [ql] - [q2]

(iv) p - [ql] - q2

(v) p - q1 - [q2]

(vi) [P] - [q1] - q2

(vii) [P] - ql - [q2]

Of these, combinations (iv) and (v) are geometrically identical. So are combinations (vi)

and (vii). Only the first combination gives rise to ferromagnetism. All the remaining lead

to antiferromagnetism. The characteristic common to all the antiferromagnetic

combinations is the occurence of parallel crystal planes such that while the dipoles in any

plane are all mutually parallel, the dipoles in neighboring planes are antiparallel. The

matter in which these combinations differ from each other is in the orientation of these

planes and in the inclination of the dipole direction with respect to these planes.

THEORETIGAL EVALUATION OF PLANCK'S

CONSTANT

The analysis of physical quatities into their space-time components, made possible by the

application of the Reciprocal System, throws fresh illumination on the nature and

significance of these quantities. Larson demonstrates that the result of applying the

discrete unit postulate to the dimensions of physical quantities results in the principle that

the dimensions of the numerator of the space-time expression of any real physical

quantity cannot be greater than those of the denominator. Quoting Larsonl¹:

The most notable of the quantities excluded by this dimensional principle is ―action.‖

This is the product of energy, t/s, and time t, and in space-time terms it is t² /s Thus it is

not admissible as a real physical quantity . . . The equation connecting the energy of

radiation with the frequency is

E = hv

where h is Planck‘s constant . . . expressed in terms of action.

It is clear, however, from the explanation of the nature of the photon of radiation . . . that

the so-called ―frequency‖ is actually a speed. It can be expressed as a frequency only

because the space that is involved is always a unit magnitude. In reality, the space

dimension belongs with the frequency, not with the Planck‘s constant. When it is thus

transferred, . . . the equation for energy of radiation is [in space-time terms]

t/s = t²/s² * s/t <1>

In The Structure of the Physical Universe Larson derives the value of Planck‘s constant

on this basis, making use of the gravitational constant. In this paper I attempt to do the

same, but without bringing the gravitational constant into the picture, with the hope of

showing the factors involved more clearly.

We will adopt the suffix c to denote a quantity expressed in the conventional units, no

suffix to denote the quantity expressed in the natural units, and suffix n to denote the

magnitude of the natural unit of a quantity expressed in terms of the conventional units.

Remembering that, on the natural unit basis, any unit of a physical quantity is also the

unit of the corresponding inverse quantity, every unit of energy is both a unit of t/s and a

unit of s/t, each in its

proper context,z from eq. <1> the quantitative relationship between E natural units of

energy and u natural units of speed can be expressed as

E = (1/1) u

since the numerical magnitude of the t²/s² term is (1/1)² in natural units. The speed u is

given by the quotient of S natural units of space and T natural units of time. Therefore,

E = S/T

Now we will introduce the conventional units into the equation, but will do so only in the

case of those quantities which we want expressed in the conventional units finally. Since

E = Ec /En and T = Tc /Tn, we have

Ec= (En * Tn) S/Tc <2>

However, from what has been quoted earlier, we note that the numerical magnitude S in

eq. <2> is 1, since the vibration is confined to one natural unit of space. The lack of

recognition of the true status of the frequency term as a speed term and expressing every

quantity in terms of the conventional units (i.e., including 1 cm in place of S) therefore

has the effect of overstating the numerical value on the RHS by a factor of 1 cm/Sn. As

such, the RHS must be multiplied by the

reciprocal of this factor. Thus,

E (in ergs) = (En * Tn * Sn /1 cm) 1/Tc (in sec) <3>

Or, replacing 1/T by v, the frequency in Hertz,

Ec =(En* Tn* Sn / 1 cm) v <4>

from which we have Planck's constant as

h = En * Tn * Sn /1 cm <5>

There are two additional factors to be considered before we can arrive at the numerical

magnitude of h. Firstly, since the photon vibration is limited to the time-region while

measurements appertain to the outside region, this value of h is to be reduced by the

interregional ratio R. Hence,

h = (En* Tn* Sn )/(r * 1 cm) <6>

The second factor is concerned with the effect of the secondary mass component s. As

long as mass is expressed in the dynamical unit of gram, it becomes necessary to take

account of the discrepancy between the units of primary mass and inertial mass. Thus,

when adopting the gram-unit, the mass term is to be multiplied by a factor of 1+s, where

1 is the primary mass and s the secondary mass.4 In the present case, since energy is t/s

while mass is ³/³;, the multiplying factor is (1+s).¹/³ Thus,

h = [(En* Tn* Sn ) / (R *1 cm)) * [1+s)¹/³ <7>

Adopting the values from Ref. 3,

En = 1.49175/ * 10 -3

erg

Tn = 1.520655 * 10 -16

sec

Sn = 4.558816 * 10 -6

cm

Rn = 156.4444 (Ref. 5),

and for the secondary mass calculation, from Ref. 6,

m, magnetic mass = 0.00639205,

we have the value of Planck's constant as

h = 6.6243162 * 10 -27

erg-sec <8>

But it must be noted that m, the magnetic mass, is not the only component of the

secondary mass s. This is because in the particles with unit net displacement (like, for

example,

M 1

- 1

- 0 2 2

there is alraays an initial unit of electric mass, of magnitude 0.0005787. Thus 1+s

becomes 1.00697075. Substituting this in equation <7> gives

h = 6.6255857 * 10 -27

erg-sec <9>

This is in close agreement with the experimental value of 6.6256 * 10-27

erg-sec (within

an error of 2.16 * 10-4

percent).

REFERENCES

1. l. D. B. Larson, Nothing But Motion, (North Pacific Publishers: Portland, OR,

1979), p.152

2. Ibid., p. 169 (see lines 6-4 from bottom).

3. Ibid., p. 160.

4. Ibid., p. 170.

5. Ibid., p. 162.

6. Ibid., p. 164.

SUPERCONDUCTIVITY:

A TIME REGION PHENOMENON

1. INTRODUCTION

The chief characteristic of superconductiv ity is the complete absence of the electrical

resistance. As the temperature is decreased, the change from the normal to the

superconducting state takes place abruptly at a critical temperature Tc. Though the

phenomenon was discovered as far back as 1911, it resisted all theoretical understanding

and not until 1957 was the famous BCS theory propounded. According to this theory,

superconductivity occurs when the repulsive interaction between two electrons is

overcome by an attractive one, resulting from a mechanism which gives rise to electron

pairs since then known to be called the ―Cooper Pairs‖- that behaved like bosons and

moved without resistance.

The tunneling and flux quantization experiments firmly established the presence of

electron pairs. However, the phonon mechanism of electron pairing remained

experimentally un proven. Subsequent experimental work brought to light many

anomalies and unexplained results which demonstrated the inadequacy of the BCS

theory. The theoretical trend, in the past decade, has been toward invoking the quantum

mechanical concept of ―exchange interactions‖ for the explanation of the formation of the

electron pairs.

The explanation of the phenomenon of superconductivity from the point of view of the

Reciprocal System, however, has not yet been attempted. Larson himself refers to the

phenomenon with nothing more than a passing remark [1]. As the present author sees,

progress toward this end would not have been possible in the R.eciprocal System, as it

needed the discovery of a new development, which emerged only recently. This is the

new light thrown by the study of the ―photon controversy,‖ leading to the discovery of

birotation [2]. It has been shown there that the two equal, and opposite rotational

components of a birotation manifest as a linear Simple Harmonic Motion (SHM). The

knowledge of this now opens the way toward understanding the phenomenon of

superconductivity.

2. The Origin of the Phenomenon

It has been well-recognized that superconductivity, from the abruptness of its occurrence

at the temperature Tc, is a collective phenomenon—like that of ferromagnetism, for

example—involving all particles co-operatively. We have shown that the ferromagnetic

ordering is the phenomenon of the time region [3]. We now find that superconductivity is

the result of the electron motion entering the time region. In fact, since in solids the atoms

are already in the time region, the region inside unit space, it follows that

superconductivity, like ferromagnetism, results when the motion concerned crosses

another regional boundary, namely, the time region unit of space (which is a compound

unit)

2.1 The Perfect Conductor

Larson points out: ―... the electron is essentially nothing more than a rotating unit of

space.‖ [4] He identifies the movement of the electrons (rotating units of space) through

matter (a time structure) as the electric current. We might note that there is no electric

charge associated with these electrons. One of the causes, according to Larson, of the

resistance to the flow of current is the spatial component of the thermal motion of the

atoms. ―If the atoms of the matter through which the current passes are effectively at

rest..., uniform motion of the electrons (space) through matter has the same general

properties as motion of matter through space. It follows Newton‘s first law of motion .

and can continue indefinitely... This situation exists in the phenomenon known as

superconductivity.‖[1]

We would like to point out that the actual situation is somewhat different. Firstly, as we

will see later, superconductivity is not solely a phenomenon of zero resistance which we

shall call the perfect conduction (that is, infinite conductivity), which is what Larson

seems to imply by ‗superconductivity‘ in the para cited above. The second fact is

concerning the resistance caused by the impurity atoms due to their space displacement.

Since the current moves, according to the Reciprocal System, through all the atoms of the

conductor (including the impurity atoms), and not through the interstices between the

atoms, there is a large contribution by the impurity atoms to the resistance.[5] Mere

reduction of the thermal motion, therefore, cannot serve to eliminate the cause of

resistance to the current.

2.2 The Electron Pair as a Birotation

In the ―uncharged state the electrons cannot move with reference to extension space,

because they are inherently rotating units of space, and the relation of space to space is

not motion. ...In the context of the stationary spatial system the uncharged electron, like

the photon, is carried outward by the progression of the natural reference system.‖[6] But

as the temperature is decreased below the critical value Tc, and the electrons in the solid

enter the region of the inside of the compound unit of space, the direction of the electron

motion changes from outward to inward from the point of view of the stationary

reference system. Thus the electrons start moving toward each other, as if mutually

attracting.

Remembering that the electron is a unit of rotational space, when two of them with

antiparallel rotations approach each other to an effeetive distance of less than one

compound unit of space, the two opposite rotations form into a birotation. As explained

in detail elsewhere [2] a birotation manifests as an SHM. We might call this process the

―pair condensation,‖ following the conventional nomenclature. The formation into the

birotation (that is, SHM) has two distinct effects which need to be noted:

(i) the character of the motion changes from rotational (two-dimensional in extension

space) to linear (one-dimensional in extension space);

(ii) the magnitude of the motion changes from steady (constant speed in time) to

undulatory (varying speed in time).

Let us call these two effects respectively the ―dimension-reduction‖ and the ―activation‖

for ease of future reference.

2.3 The Zero Electrical Resistivity

The rotational space, that is the electron, may be regarded as a circular disk area. We see

that the effect of the dimensional-reduction is to turn the disk area into a straight line

element (of zero area). What causes the electrical resistance in normal conduction is the

finiteness of the projected area of the electron in the direction of current flow. The

vanishing of this pro jected area on pair formation eliminates the cause for the resistance

and turns the material into a perfect conductor (zero resistivity). It should be emphasized

that a dimension-reduction from a three-dimensional spatial extension (say, a spherical

volume) to a two-dimensional spatial extension (a circular disk) could not have

accomplished such an elimination of projected area. This is only possible when the

reduction is from a two-dimensional spatial extension to the one-dimension.

In the conventional parlance we might say that while the single-electron (rotational) is a

fermion, the electron pair (linear SHM) behaves as a boson. In the analogous case of a

photon, we see that the photon is a linear SHM and is a boson. One can, therefore,

conjecture that the circularly polarized photon [2] ought to behave like a fermion. I

suppose that an experimental verification of this prediction could easily be borne out.

3. The Meissner Effect

This an interaction between superconductivity and magnetic field and serves to

distinguish a superconductor from the so-called ―perfect conductor.‖ If we could place a

perfect conductor in an external magnetic field, no lines of magnetic flux would penetrate

the sample since the induced surface currents would counteract the effect of the extern,al

field. Now imagine a normal conductor. placed in the magnetic field and the temperature

lowered, such that at Tc it turns into a perfect conductor while in that field (see top row

Fig.l, which is adopted from R.ef.[7]). The field that was coursing through it would be

continuing to do so (top center, Fig.l). If now the external field is removed (top right) the

change in this field would induce electrical currents in it which would be persisting (as

there is no resistance), and these currents produce tlie internal flux that gets locked in as

shown.

But the situation is quite different in the case of the superconductor. As can be seen from

the bottom row of Fig.l, a metal placed in an external magnetic field and cooled through

the superconducting transition temperature Tc expels all flux lines from the interior

(providing, of course, the field is less than a critical value, Hc) (see bottom center). This

is called the Meissner Effect. In fact, the external field threading the superconductor

generates persistent surface currents, and these currents generate an internal field that

exactly counterbalances the external field resulting in the flux expulsion phenomenon.

Termination of the external field induces an opposing surface cur rent which cancels the

previous one and leaves the superconductor both field-free and current free.

Now the crucial point that should be noted is that a constant magnetic flux threading a

conductor that is stationary relative to it does not induce an electric current. What induces

a current is a change in the magnetic field. In the case of a perfect conductor we

considered above, the field is steady (that is, constant with time) and no induced currents

appear (top center, Fig.l).

The perfect Conductor

The Superconductor

T < Tc T < Tc T < Tc

H > 0 0< H < Hc H = 0

FIG. 1 THE MEISSNER EFFECT

But in the case of the superconductor, the steady field does induce an electric current.

This has been a recalcitrant fact that defed explanation in the conventional theory and

forced the theorists to hazard weird conceptual contrivances like the exchange

interactions. The development of the Reciprocal System has clearly demonstrated that in

all such cases there is no need to devise extreme departures from the otherwise

understandable straightforward explanations. For instance, we have shown in the

explanation of ferromagnetism there is no need to invoke the aid an ―exchange

interaction‖ at all [3]. It was shown that understanding of the origin and charaeteristics of

that phenornenon follows from the recognition that it has crossed a regional boundary

and entered the time region.

Exactly for identical reasons, we find that in the present too, there is no need to resort to

the purely hypothetical exchange interaction explanation. The reason why a steady

magnetic field threading the superconductor induces a current in it follows from the

activation aspect of the electron pairing. That is, while in the case of the normal electron

the rotational space is constant with time, in the case of the electron pair the space is

sinusoidally varying with time. In normal conduction, electric current is induced if the

magnetie flux threading the space of the electrons changes with time. In

superconductivity, the electrical ctzrrent is induced since the space of the electrons

threading the magnetic flux varies with time. We may eall this ―superinduction,‖ and the

relevant current ―activation current.‖

4. The Non-locality of the Pairing

It has been found that ―the size of the electron pairs is on the order of 10-4cm and the

motion of electrons at different points of the metal shows correlations over distances of

this order.‖[8] Richard Feynman points out: ―I don't wish you to imagine that the pairs

are really held together very closely like a point particle. As a matter of fact, one of the

great difficulties of understanding this phenomenon originally was that that is not the way

things are. The electrons which form the pair are really spread over a considerable

distance; and the mean distance between pairs is relatively smaller than the size of a

single pair. Several pairs are occupying the same space at the same time.‖[9] By any

standard of conventional thinking this is rather a strange state of affairs.

From the point of view of the Reciprocal System, however, we see that the two electrons

that form the pair are adjacent in time, and not in space, since the electron motion is in

the time region as has already been noted. As the location of the particles in space is in no

way correlated to their location in time, adjacency in time does not necessarily entail

propinquity in space. Therefore, the components of a pair could be spatially separated

while contiguous in time. Their maximum separation could be the natural unit of space

multiplied by the interregional ratio (nearly 7 x 10-4 cm).

5. Superconductivity and Magnetic Ordering

As both magnetic ordering and superconductivity are the result of the respective motions

entering the time region, it would be of interest to examine whether and how they affect

each other. In the ferromagnetic arrangement of the directions of all the atomic dipoles

are mutually parallel. Sueh a state of ordering precludes the electron pair formation

required in superconductivity since the spins of the electrons are disposed to orient

parallel to each other. As such, we can predict that superconductivity and ferromagnetism

cannot coexist.

On the other hand, in the antiferromagnetic ordering, adjacent magnetic dipoles are

oriented antiparallel to each other. Since the rotational space that is the electron will have

greater chance of assuming the directions of these dipoles, adjacent electrons with

opposite spin directions would be readily available for pairing. Consequently, we can

conclude that the antiferromagnetic ordering can co-exist with or even promote the

electron pairing that underlies superconductivity. If this is so, it might lead to the

development of high Tc superconducting materials by exploiting the potential of the

antiferromagnetic type of structures.

6. Thermodynamical Aspects

The observable relationships among the superconducting and the normal states follow

directly from the quadratic nature of the relationship between the corresponding

quantities of the time region and the outside region [10].

6.1 Specific Heat Relations

Quoting Larson: ―:.. the relation between temperature and energy depends on the

charaoteristics of the transmission process. Radiation originates three-dimensionally in

the time region, and rnakes contact one-dimensionally in the outside region. It is thus

four-dimensional, while temperature is only one-dimensional. We thus find that the

energy of radiation is proportional to the fourth power of the temperature.

Erad = K * T4 . ‖[11]

We have seen earlier that the phenomenon of birotation of the electron pair is identical to

that of the birotation of photons (except for the absence of the rotational base in the

latter). Consequently, the time region energy associated with the electron pairs is

proportional to the fourth power of the temperature. Therefore, considering unit volume

of the material, the expression for the thermal energy in the superconducting state can be

written as

Es=Ks*T4 (1)

where Kg is a constant and suffix s denotes the supercondueting state. Differentiating this

equation one gets the expression for the specific heat in the superconducting state,

Cs=4*Ks*T4 (2)

This cubic relationship is confirmed experimerr tally.

Continuing the quotation from Larson: ―The thermal motion originating inside unit

distance is likewise four-dimensional in the energy transmission process. However, this

motion is not transmitted directly though the thermal oscillation is identical with the

oscillation of the photon, it differs in that its direction is collinear with the progression of

the natural reference system rather than perpendicular to it. ―The transmission is a contact

process ... subject to the general inter-regional relation previously explained. Instead of

E=KT4, as in radiation, the thermal motion is E² = K‘T

4,‖[12] that is,

En=Kn*T (3)

where Kn is a constant and sufiix n denotes the normal state. This, of course, gives the

linear relationship between the normal specific heat Cn, and temperature that Larson uses

in his calculations. [12]

Cn=2*Kn*T (4)

We know that the entropy of both the states, Sn and Ss, must be equal both at Tc and at 0

kelvin (by the third law of thermodynamics). Using dS = dE/T, we have from Eqs. (1)

and (3),

T

(5) Ss(T)= T4*Ks*T²*dT=(4/3)*Ks*T³

0

T

(6) Sn= 2*Kn*dt=2*Kn*T

0

At T = Tc we have Ss(Tc) = Sn(Tc) which gives

Ks =

3 * Kn

———

2 * T²c

Using Eqs. (2), (4) and (7), we can now find that at the transition the excess specific heat

is given by

Cs - Cn = 6KnTc - 2KnTc = 4KnTc = 2Cn (8)

The above result is experimentally corroborated.

6.2 External Magnetic Field

Below the critical temperature Tc superconductivity is quenched by applying an exter nal

magnetic field of intensity greater than the critical value Hc. The fourth power and the

seoond power relations, Eqs. (1) and (3) respectively, pertaining to the two regions across

the boundary lead us to the result (see Appendix)

Hc (T) = 1 - (

T )

²

Hc (0) Tc

where Hc(T) is the critical magnetic field that quenches the superconductivity at the

temperature T (less than Tc). .

This is the well-known parabolic relation that is especially found to hold good in the case

of all the soft (Type 1) superconducting materials. A more rigorous treatment should, of

course, take into consideration the probability of existence of some unpaired electrons at

temperatures greater than 0 kelvin. The Type II superconducting materials have a mixed

state which we cannot consider in a preliminary study such as the present one.

7. Conclusion

The foregoing explanation of supercon ductivity adds one more item that demonstrates

the coherence and generality of the Reciprocal System of theory. It has been shown that

the apparent reversal of direction, from the point of view of the stationary three-

dimensional spatial reference system, that takes place when the scalar motion constitut-

ing a phenomenon crosses a unit boundary of some sort underlies the explanation of such

diverse phenomena as the white dwarfs, quasars, cohesion in solids, sunspots and

ferromagnetism. In this present article we extend this explanation to the phenomenon of

superconductivity as well. Superconductivity is the result of the electron motion

(rotational space) entering the time region and turning into a birotation.

The formation of electron pairs,

the non-locality of the pairing,

the zero electrical resistance,

the expulsion of magnetic field,

the abrupt change in the specific heat at the transition,

the manner of variation of the critical field with temperature, all of these are

shown to follow logically from the theory.

References

1. Dewey B. Larson, Basic Properties of Matter, Intl. Soc. Unified Sc., Utah, U.S.A.,

1983, p.104

ON THE NATURE OF ROTATION AND

BIROTATION

In an earlier paper entitled ‗The Law of Conservation of Direction‘1 I have introduced the

concept of birotation. I discussed there the difficulties with Larson's account of the

intrinsic nature of photon and shown how birotation underlies the photon structure.

Thomas Kirk, in a communication² , refers to this paper and raises two questions. The

present article is writen as a response to these, realizing that more detailed explanations

are necessary than were given earlier, in view of the maiden nature of our explorations of

the Reciprocal System.

The Two Intrinsic Traits of Vector Space

I shall begin by answering Kirk‘s first question: ―How does the simple displacement from

the natural progression become a rotational motion, or if a photon is rotational, what

phenomenon is the negative of the outward progression?‖

I have anticipated this category of difficulty that a reader might feel and included in my

exposition a discussion explaining the nature and primacy of rotation (see pp. 3-4 of

ref.(1]). The real difficulty here stems from the tacit assumption made by the questioner

that the only way a primary displacement from the space-time progression can manifest is

as a uniformly increasing linear magnitude with constant direction (that is , translation).

Quoting Larson: ―The only inherent property of a scalar motion is its positive or negative

magnitude, and the representation of that magnitude in the spatial reference system is

subject to change in accordance with the conditions prevailing in the environment. The

same scalar motion can be either translational, rotational, vibrational, or a rotational

vibration ... ‖³ What distinguishes them is the coupling to the reference system and this

changes according to the circumstances.

I emphasized that space has two intrinsic traits-translational and rotational. In translation

we have uniform and continuous change of linear magnitude with constant direction,

whereas in rotation we have uniform and continuous change of direction with constant

linear magnitude. Both are equally possible. Moreover, ―...a constant and uniform change

of position or direction (my italics) is just as permanent and just as self-sustaining as a

condition of rest.‖4

Letting the linear , magnitude be x and the angular magnitude , we can succintly

describe the representation of a unit of scalar motion in the conventional spatial reference

system as

[

dx/dt

]

[

0

]

[

1

]

=

or

d /dt 1 0

where t denotes time. The first represents rotational space while the second translational

space.

If space were not to have the rotational trait it would not have had the solidity or the

‗volumeness‘ aspect. For example, if we were to have a ‗cube‘ of side 2 units in such a

‗space‘ of three dimensions, its total magnitude would be 6 linear units. It cannot have

the volumetric aspect of 8 volume units. As such, it should be clear that its angularity

nature is as fundamental as its linearity nature.

The difficulty of imagining the existence of rotational motion without it being the

rotation of something is just like the difficulty of Imagining the existence of motion

without it being the motion of something. Both these difficulties originate from our long

— standing habit of regarding matter as primary in this physical universe and treating

motion only as a predicate of matter. The moment we realize that the most primary entity

of the universe of motion is motion, both these difficulties should dissolve together.

There is another reason why it might be difficult for some people to see the equal

primacy of the rotational aspect of space as against its translational aspect. Larson points

out5 that present-day science does not recognize the existence of any motions that cannot

be represented in the conventional reference system. This reference frame is deficient in

more than one way. While some of the true characteristics of scalar motions cannot be

represented in the conventional three-dimensional spatial reference system at all, some

others could be represented only with the help of some auxiliary devices. ―Rotational

motion, for instance, is represented in the spatial reference system with the aid of an

auxiliary quantity, the number of revolutions. Ordinary vibrational motion can be

accurately defined only by a similar expedient.‖6

With the benefit of the above explanations it can now be seen that the genesis of a simple

harmonic motion from uniform motion is only possible through rotation. Since the

emergence of a single rotation from the scalar motion does not conserve angular

momentum, the only logical alternative for the manifestation of the simple harmonic

motion is the birotation delineated in my paper.1 To those who have been following the

development so far it might be apparent by now that the Law of Conservation of Linear

Momentum, the Law of Conservation of Angular Momentum, and Newton‘s Third Law

of Motion-are all corollaries of the Law of Conservation of Direction.

In a separate paper I am presenting several experimental facts that demonstrate in a direct

manner the existence of birotation in photons. I have already alluded1 to the experimental

determination of the angular momenta of photons. This work7 was brought to my

attention by Edwin Navarro. Kirk proposes that the photon comprises of an inward linear

displacement in a second scalar dimension and that the linear inward unit is rotationally

distributed. But this model is inadmissible for two reasons. Firstly, a rotationally

distributed linear motion does not give rise to angular momentum. Secondly, the way in

which Kirk envisages the displacement to manifest is not valid (for reasons I have given

in a separate communication).

The Scalar Direction of Rotation

The answer to the latter part of Kirk's question, ‖ ...if a photon is rotational, what

phenomenon is the negative of the outward progression?‖ also emerges from what has

been said above about the deficiencies of the conventional reference system. See for

example, how it becomes necessary to introduce the concept of positive and negative

reference points to distinguish between the inward/outward scalar directions of a motion,

since the representation in the conventional reference system cannot distinguish between

them, and same vectorial direction may represent both depending on the situation.8

To ask for ‗the negative of the outward progression‘ in connection with rotational motion

would be absurd if we mean by ‗progression‘ a linear motion. However, if we remember

that the term ‗progression‘ is used to connote ‗continuing motion,‘ and as the scalar

motion is basically a magnitude, its scalar direction in the case of rotation can be

represented by clockwise (CW) or counter-clockwise (CCW) sense of the rotation. Since

this is a matter of the coupling to the conventional reference system it is purely

contingent on the circumstances prevailing.

For example, the two counter-rotations, + and - , of a photon are both inward (scalar).

We may attempt to understand this seeming enigma by considering the analogous case of

linear translation. In order to ~ represent a linear movement we require a reference point

and a moving point. In f ig.l we depict a bivector by two points A and B, moving

uniformly toward a reference point R (with velocities - v and + v respectively). Now, in

order to represent a rotational movement we require a reference direction and a moving

(that is, changing) direction. In fig.2 we depict a birotation by two directions OE and OF,

rotating uniformly toward a fixed direction, OD (with angular speeds - and +

respectively).

Figure 1: Inward Bivector Figure 2: Inward Birotation

While the decreasing lengths AR and BR represent inward motion in the translational

situation, the decreasing angles EOD and FOD represent inward motion in the rotational

situation.

It is important to understand that what constitutes an inward motion in rotation is the

decrease in this angle and not always its CW or CCW sense as viewed by us. In this

particular example we see that both the CW and the CCW rotations happen to be

representing inward motion, as the corresponding angles are decreasing. Moreover, just

like the possibility that the bivectorial motion may have additional motion components

superimposed on it, it is possible that the birotation that we are considering may have

additional rotational motion components. Suppose that an additional rotation of + 2 is

superimposed. Then in the new situation we see both OE and OF rotating in the same

(CCW) sense (at angular velocities + and + 3 respectively).

Now one might argue that when OF eventually coincides with OD and continues to

rotate, the inward rotation would have to become outward as the angular distance

between OF and OD then goes on increasing. But as already pointed out, since the

conventional reference system cannot represent rotation directly, we cannot distinguish

between an angular position of ° from that of + 360°, or from that of - 360°. Under

these circumstances it can be seen that the continued rotation of OF past OD could be in

the same scalar direction (inward) despite the fact that the angle represented in the

conventional reference system seems to increase. Suppose that the angle FOD is °. For

all that we know it could also be +360° , +720° or +360n degrees, where n could be

as large an integer as we please. With . this latter possibility, we can easily see that the

rotation of OF may continue in the same sense with its angular distance from the fixed

direction decreasing continuously and indefinitely, thereby retaining its inward character.

The HF versus LF Photons

The intrinsic speed of a photon (that is, its frequency) could be less than 1/l, say 1/n, or

greater than 1/1, say n/1. The former are referred to as the LF (low frequency) photons

while the latter as the HF (high frequency) photons. Some students tended to call the HF

photons the ‗cosmic photons,‘ and regarded them as not being within the purview of the

material sector or the conventional reference system. They presume that neither the unit

frequency nor the HF is observable. This is a serious mistake commonly committed by

many a student of the Reciprocal System.

Larson says: ―When considered merely as vibrating units, there is no distinction between

one photon and another except in the speed of vibration, or frequency. The unit level,

where speed 1/n changes to n/1 cannot be identified in any directly observable way."9

Subsequent research enables him to identify this unit level. ―Inasmuch as the natural unit

of vibrational motion is a half cycle, the cycle is a double unit. The wavelength

corresponding to unit speed is therefore two natural units of distance, or 9.118 x 10-6 cm.

The distribution over 128 positions increases the effective distance to 1.167 x 10-3 cm.

This, then, is the effective boundary between motion in space and motion in time, as

observed in the material sector.‖10 From this the natural unit of frequency, which

demarcates the LF from the HF, turns out be 2.569 x 10 Hz. This should make

abundantly clear that, as a matter of actual fact, both LF and HF vibrations are observable

either from the material sector or from the cosmic sector.

Probably what throws the student off course in this connection is the general statement of

the fact that a speed greater than unity (the speed of light) cannot be represented as

motion in space with reference to the conventional reference system. The catch here is

that this is true of translational motion in space. The situation, however, is different in the

case of rotation, since the conventional reference system cannot represent rotation

accurately. We, for example, not only. Can observe a rotational time displacement (like a

material particle) but also a rotational space displacement (like a cosmic particle as in the

cosmic rays). The following additional explanation should make it clear.

All independent motion (as against the ficticious motion of the space-time progression)

has to be inward in scalar direction. In the case of the LF photon the vibrational speed

being a time displacement (speed 1/n), the motion is inward in space. On the other hand,

in the case of the HF photon the vibrational speed being a space displacement (speed

n/1), the motion is inward in time, which is tantamount to outward in space. As far as

rotation in space Is concerned, we have already seen that the conventional reference

system cannot distinguish whether an angle is increasing from ° or is decreasing from an

indefinitely large angle + 360n. This fact renders the representation of both the LF and

the HF vibrations (that is, the corresponding birotations) in the conventional reference

system possible. The same fact also makes it impossible to observationally distinguish

between these two types of vibration.

Mechanism of Circular Polarization

I shall now turn to Kirk's second question . He enquires: ―How does a phenomenon

which is compound rotation exist after half of its component rotation is removed as in the

postulated polarization? How is this the same phenomenon, a photon?‖

This Is simple: it can, occur In two different ways. Let us represent the photon birotation

by P(+ w,- w), where + w and - w are the two rotational component speeds. On entering

the polarizing medium let it encounter a rotation R(+ w,+ w) pertaining to a particle. The

result would be the replacement of the -w component of the photon as shown below.

P(+ w,- w) + R(+ w,+ w) -~ P(+ w,(- w,+ w),+ w) = P(+ w,+ w)

It must be understood that the rotation pair inside the inner parentheses, (- w,+ w),

reduces to zero since the interaction here is vectorial. This produces the circularly

polarized photon P(+ w,+ w). The disappearance of the rotation R(+ w,+ w) in the

medium is tantamount to the production of net angular momentum.

Alternatively, the incoming photon P(+ ,- ) might encounter an existing birotation B(-

,+ ) in the atomic system, instead of a rotation R as above. The result would be

P(+ ,- ) + B(- ,+ ) P(+ ,+ ) + R(- ,- )

If we remember that the net angular momentum associated with a birotation is zero, we

can at once see that the creation of R(- ,- ) produces an angular momentum that is

identical in effect to the destruction of R(+w,+w). In either case the net result would be

the circular polarization of the photon in the CCW sense and the production of net

angular momentum in the CW sense.

It must be pointed out that the actual situation of the interaction between two rotations in

the time region is much more diverse than is depicted above. This stems from several

factors, which may be summarized as follows: (i) Each rotation could be either inward

(as in the case of independent motion) or outward (as in the case of an outward

component of a compound motion with net inward direction). (ii) The conventional

reference system is insensitive with regard to the fixed reference direction insofar as it

cannot distinguish between whether an angle is increasing from 0° or is decreasing from

an indefinitely large initial angle. Consequently, both inward and outward scalar motions

could be represented either as CW or as CCW. (iii) The conventional reference system is

subject to the limitation that it can differentiate not more than 360° of angle.

Consequently there is an imputed cyclicity and a ‗phase‘ associated with each

representation.

Schematic representations of the several possible cases are shown in fig.3. We depict the

two rotational components of the photon birotation (P + and P -) by two arrows drawn

below the horizontal line pointing inward toward zero, respectively from - to +

values. It is taken that the arrow pointing from left to right represents CW rotation and its

reverse the CCW. ‗B‘ stands for birotation and ‗R‘ for rotation and both are drawn above

the horizontal line to differentiate them from the components of P. On the left hand side

we have indicated the phase difference between the simple harmonic motion of the

photon P and that of the interacting motion B or R by 0° (in phase) or 180° (phase

opposition). The result of the interaction is mentioned on the right hand side of each

diagram; ±L indicating the ‗, angular momentum created in the medium due to the

circular polarization of the photon. In cases (a) through (d), it must be understood that

when the phase difference is 0°, P + or P - interacts with that component of B which is

situated on the same side of the ± to 0 range as itself, whereas for 180° it interacts with

the B component that is situated on the opposite side.

Figure 3 Schematic diagrams of interactions of rotation

Conclusions

The Paper basically attempts at elucidating the nature of rotation in the context of the

Reciprocal System, and correcting some likely minsconception. Some of the important

conclusions are summarized as follows:

1) It is emphasized that rotational motion is as primary as linear motion and that the

simple harmonic motion (which is apparently an accelerated motion) inherent in photons

is uniform birotation.

2) The inability of the conventional reference system to represent rotation completely and

correctly results in a failure to distinguish between the inward and outward scalar

directions of a rotational representation, and renders both the LF and the HF vibrations

observable in the reference system.

3) The circular polarization of photons is the result of interaction with existing

rotation/birotation in the medium and is accompanied by angular momentum.

References

1. K. V. K. Nehru, ‗The Law of Conservation of Direction,‘ Reciprocity, XVIII (3),

Autumn 1989, pp. 3-6 2. Thomas Kirk, Reader's Forum, Reciprocity, XIX (2), Summer

1990 . PP~ 20-21

3. D. , B. Larson, Basic Properties of Matter, Intl. Soc. of Unified Soc ., Utah, U. S. A.,

1988, p. 280

4. Ibid., p. 135

5. Ibid., p. 139

6. Ibid., p. 152

7. R. A. Beth, ‗Mechanical Detection and Measurement of the Angular Momentum of

Light,‘ Physical Review, Vol. 50, July 15, 1936, pp. 115-125

8. D. B. Larson, Basic Properties of Matter, op. cit., p. 151

9. D. B. Larson, Nothing but Motion, North Pacific Pub., Portland, Or., U. S. A., 1979, p.

53

10. D. B. Larson, The Universe of Motion, North Pacific Pub., 1984, p. 202 .

THE PHOTON AS BIROTATION

Introduction

In an earlier paper1, I have discussed some of the conditions under which a scalar motion

manifests in the conventional spatial reference system, and shown that the simple

harmonic motion (SHM) of the photon is really a birotation. While it is clear that a SHM

underlies the photon from the phenomena of interference and diffraction, the genesis of

SHM, given only uniform speed (as in scalar motion), is not possible except through

rotation. In a subsequent paper², I have elaborated on the characteristics of rotation and

birotation, and shown how they result in observed phenomena, like circular polarization

and angular momentum of photons.

In the present paper, several other characteristics of the photon phenomena that

demonstrate, directly or otherwise, that the photon is basically a birotation are

considered.

The Angular Momentum of Photons

We have seenl that the photon is comprised of two equal and opposite rotations about an

axis, with the axis being, normally, in the direction of translation of the photon. The total

energy, E, of the photon is the sum of the energy of translation, T, and the internal energy

of rotation, R. In the absence of any biasing factor, one can see that E is equally

partitioned into T and R. Let

m apparent mass of each component of the photon

I moment of inertia of each component of the photon

± angular velocities of either component

h Planck's constant, h, divided by 2

wavelength of the photon

v frequency of the photon = / 2

c the speed of light = v

Then

T=R=½E= ½ h1 (1)

Considering both component rotations:

T=2(½ m c²)= ½ h1

or

m=h1 /2 c² (2)

R=2(½ ²)=½ h1

or

I = h1/2 (3)

Turning now to angular momentum, l, of each component rotation, we obtain using

Equation(3)

l = I = ±½ h1 (4)

The ± sign occurs since w could be ±. The angular momentum of the photon itself works

out to be

L = ±h1 or 0 (5)

since the two component rotations could either be parallel (l+l or -l -l) or antiparallel

(1-1). It might be noted that L is independent of , and turns out to be the same for

photons of all frequencies. This agrees with experimental observations.

The Doppler Shift

R. A. Waldron³ extends the above analysis to the calculation of Doppler shifts. Suppose a

photon of frequency vo was emitted by a source that is stationary with respect to the

observer, then

Eo = h vo = T+R = m c² + m c² = 2 m c² (6)

since T = R.

However, if the observer is approaching the source with a velocity v, then the

translational energy would be 2 [½ m (c + v)²] instead of 2 (½ m c²), while the rotational

energy remains unchanged at I ² = mc². The measuring apparatus absorbs this energy;

but this cannot be distinguished from the effect of absorbing a photon of frequency v

such that

E = hv = m (c+v)² + m c²

= 2 m c² (1 + v/c + ½ v²/c²)

Substituting from Equation (6) in the above and writing v/c = , we have

v/vo = 1 + + ½ 2 (7)

Changing frequencies to wavelengths, we have the Doppler shift formula

/ o=(1+ +½ 2)-1

= 1- + ½ ² - ¼ 4 +... (8)

which agrees well with the orthodox Doppler formula

{

1 -

}

½

/ o=

1 + (9)

=1- + ½ ²- ½ ³+ ³/84-...

(since is usually small, terms of order greater than 2 could be ignored).

Dispersion

In ordinary refraction, a light beam incident on a medium at an angle i, changes direction

and gets refracted at an angle r in the medium. This change in direction could be shown

as being due to the reduction in the speed of light from c to v in the medium, and that the

following relation holds good:

sin i/sin r=c/v=n (10)

This ratio n is called the index of refraction. The fall in speed is, of course, due to the

additional time involved in the net time displacement of the material medium through

which the photon traverses. At this juncture we would also like to note that, for a given

substance, the refractive index n increases as a power function of the frequency of light,

which implies that the fall in speed on entering the medium is more for higher

frequencies. This, of course, results in the phenomenon of dispersion, which is defined as

the change in speed of light in a medium that is engendered by a change in wavelength or

frequency of the light. Larson has computed the refractive index and the dispersion

coefficient of several substances from the first principles of the Reciprocal System.4

The relation between the refractive index n of a medium and the frequency v could be

derived from the theory we have been developing as follows. On entering the medium,

the photon is located in the time displacement of the atom, instead of the space unit of the

outward progression; rather, it is the atom, which has been moving inward in space,

enters the photon, the latter being stationary with regard to the natural reference system.

Consequent to this, the datum (initial) level from which the photon's apparent mass is

reckoned gets altered.

It might be noticed that we have been calling m the apparent mass of the photon. Since

mass is three-dimensional inverse speed, whereas the photon is only a one-dimensional

(rotational) speed, the photon does not have a true mass. However, it does have intrinsic

angular momentum, since the photon is rotation per se, and this manifests as an apparent

mass, given by

m=I ²/c² (11)

We may truly call it ―spin mass.‖ The reason why the translational energy of the photon

equals its rotational energy (Equation (1)) should now be obvious,

T=mc²=(I ²/c²)c²=I ²=R

The apparent mass of the photon is entirely spin mass.

Let 1, be the rotational speed of the atom of the medium. The reference level for the

rotational energy of the photon on entering the atom gets changed since it must now be

reckoned from the level of the atomic rotation, and not that of free space. Consequently,

the change in rotational energy could be expressed as:

I ²-I 1² (12)

The introduction of the new datum level for rotation has, of course, a corresponding

effect of changing the datum level of the spin mass. This we express by writing (using

Equation (11)):

m1=I 1²/c² (13)

where m, is the mass equivalent of the datum shift of rotation.

In the general situation, a unit of the apparent mass of the photon need not be equal in

(natural) magnitude to a unit of the apparent mass pertaining to atomic rotation, since the

latter has a different reference point and is contingent on the chemical composition and

the crystal structure. This engenders a scale difference between the two. Let this scale

factor be f. Then ml units of the apparent mass from the point of view of the atomic

rotational system are equivalent to f.m, units from the point of view of the photon

rotational system. Thus, the apparent mass of the photon, as reckoned from the atomic

system in which it is now located, turns out to be:

m-f m (14)

With the new initial levels in the medium, the speed of propagation readjusts itself such

that the rotational and the translational energies of the photon become once again equal,

with reference to these new initial levels. Thus:

I 2-I 12=(m-fm1)v2 (15)

where v is the speed of light in the medium. Substituting from Equations (11) and (13),

and dividing throughout by

I:

² - ²1 = ( ² - f ²1) v²/ c²

or c²/v²=( ²-f ²1)/( ²- ²1) (16)

= 1 + ((1 - f ²1) / ( ² - ²1)

Let

a=1/(f-1)and b=4 ²a/w²1 (17)

Since c/v = n, we finally arrive at

n²=1+1/(a-bv²) (18)

It might be noted that the relation derived from the conventional electromagnetic theorys

is identical to this. Comparison with data shows that the equation is quite accurate

(correlation coefficient > 0.999).

In the case where there exists more than one rotation 1 in the medium, we proceed as

follows. Let n1 be the refractive index calculated on the basis of a single atomic rotation 1 (as though it exists alone) and let there be r such different rotations. It can be seen that

the overall refractive index no is the R.M.S. (root mean square) value of nl. In other

words

r

n²o= p1 n²1 (19)

1=1

where pl is the proportion of each 1 among the total number of rotations, such that

r

p1=1 (20)

1=1

This is because the quantity n² (= c²/v²), being the square of the inverse speed in natural

units, actually represents the time region equivalent of energy (remembering the second

power relation pertaining to the time region). Consequently, Equation (19) gives simply

the average time region energy, so that no becomes the effective refractive index.

Anomalous Dispersion

Any complete theory of dispersion must also account for the so-called anomalous

dispersion. Normally, the refractive index increases with an increase in frequency, but

beyond some sufficiently high frequency, it is found that the refractive index becomes

abnormally low. A prism made of an alcoholic solution of fuchsine (an analine dye), for

example, refracts violet light less than red, although red, orange, and yellow appear in the

normal order. An examination of Equation 18 reveals that this would indeed be the case

when the frequency v is very near the value (a+ 1 )/b, but greater than it.

Binfringence

This is the phenomenon of double refiraction and is exhibited by optically anisotropic

crystalline substances, some examples being Icelandic spar, quartz, ice, tourmaline,

apatite, borax, mica, topaz, etc. If a beam of light is made to pass through such a

substance, it has been found that it gives rise to two beams, one of which corresponds to

the single beam which would have been transmitted, had a substance like glass been used.

This beam is called the ordinary (O) beam; the other, the extraordinary (E) beam.

Now in ordinary refraction, n is found to be constant for all incident angles. This is true

of the O beam in the phenomenon of birefringence. But the E beam is found to vary with

direction, thus implying that the speed of the E beam is dependent on direction. In some

crystals, the E beam travels faster, and in some others, slower than the O beam. Moreover

it is also observed that the O and E beams are plane polarized, with their planes of

vibration being perpendicular to each other.

This behavior could readily be understood if we remember the birotational basis of the

photon. If a certain quantity of rotational motion in the form of a birotation (- ,+ )

occurs in the crystal structure such that its axis is parallel to the E beam, and phase

coincident with that of the photons of the E beam, then the component angular speeds, -

and + of the photon get changed such that they become -( + ) and ( + ). This

apparent increase in frequency (relative to the medium) brings forth a corresponding fall

in the translational speed, as in dispersion, causing the E beam to travel slower than the O

beam. In the case that the operating birotation B compounds with the photon component

speeds as -( -a) and ( -a), the result would be that the E beam travels faster than the O

beam.

It might be noted, in passing, that the supervening birotation B does not interact with the

O beam as their respective planes of vibration do not coincide. It must be understood that

the altered value of the E beam frequency within the medium is an effect of the change of

the initial (datum) level (of rotation), and not an absolute change in the magnitude of .

Consequently, on emerging from the medium, the photon frequency shows up as ± only.

Rotary Polarization

Optically Active Substances

There is a class of optically active substances which have the property of rotating the

plane of vibration of light as it traverses them. Some rotate the plane of vibration to the

left, and others to the right, and are consequently classified as laevo-rotatory and

dextrorotatory, respectively. It has been found that the angle of rotation is proportional to

the thickness traversed, and also to the first approximation of the square of the frequency.

The explanation of the phenomenon comes out naturally from the birotational nature of

the photon. Let, as before, - and + be the angular speeds of the two components of the

photon. As it traverses this type of substance, it encounters a rotation, say R(+ ,+ ),

pertaining to the molecules, and the component rotations get modified as -( - ) and

( + ). This decrease and increase in speed magnitudes of the two rotational components

respectively engender corresponding changes in the speeds of propagation, as in

dispersion. This phenomenon may aptly be called circular birefringence. This produces a

phase difference between the two rotational components of the photon which is

proportional to the thickness. The end result is the rotation of the plane of vibration of the

photon.

From the theory we have been developing, the angle of rotation of the vibrational plane

can easily be worked out as follows. Let -( - ) = - l and ( + ) = w². If t is the thickness

of the medium, the time taken by the component w1 to traverse it is

1=t/v1=(t/c)n1 (21)

where vl and n, are the speeds of propagation, and the refractive index, respectively, of

the component. Thus, the angle turned by this component during time T1 is

1 = 1 1 = (t/c)(n1 1) (22)

Considering similarly the other component ² of the photon, the net angle turned through

by the vibration plane will be

= ( 2 - 1)/2 =½(t/c)(n² ² - n1 1) (23)

since 1 and ² are in opposite senses.

Changing from w to v and adopting Equation (18) for n and expanding the right hand side

in series, we arrive at the following result

= ½ (t/c) (A + Bv2 + Cv4 + ...) (24)

where the constants A, B, C, etc., are dependent on the material, and are functions of ,

and the powers of v are all even. Both the dependence on t and v, of are very accurately

represented by Equation (24) as may be checked from observational values.

The parity of this rotatory polarization would be opposite to that of the above if the

encountered rotation in the medium is R(- ,- ), instead of R(+ ,+ ). In this case, the

photon component rotations would be respectively -( + ) and ( - ). It should also be

noted that if the beam is reversed the original rotation (of the vibration plane) is annulled.

Rotation by Magnetic Field

It is also known that when some substances-many solids, liquids, and gases-traversed by

a beam of plane polarized light are placed in a strong magnetic field, a rotation of the

vibration plane occurs. The angle of rotation is found to be proporaonal to the strength of

the magnetic field, and also the length of travel.

This is what is to be expected, since we lmow that the magnetic field is a two-

dimensional rotational vibration. As explained earlier, this super-imposed rotation speeds

up one component of the photon birotation, and slows down the other, resulting in the

phase difference and consequent rotation of the vibration plane. The dependence on the

field strength and the path length are likewise understandable. But what is not so readily

apparent, is the result that if the beam is reversed, keeping the field direction the same,

the sense of the rotation (of the vibration plane) will be opposite to the previous. So much

so, that if a beam is reflected back and forth along the lines of force, the amount of

rotation should be greater for the greater the number of reversals. This, of course, is

exactly established experimentally.

Direct Measurement of the Photon‘s Angular Momentum

Elsewhere,¹ I had already mentioned how the angular momentum of photons could be

directly measured. Richard Beth6 had devised an ingenious experimental setup that

directly detected and measured the effect. The heart of his apparatus consists of a circular

half wave plate of quartz, hung by a fine filament and free to rotate. Beth contrives to

pass a circularly polarized light beam through this plate twice, such that each time the

beam passes, its circular polarization changes from CW to CCW, and thereby imparts to

the disk, four times the angular momentum which would otherwise have been given,

were the beam merely to be absorbed. Avoiding absorption also eliminates the problem

of heating and pressure.

The Zeeman Effect

When a light source is placed in a magnetic field, a single spectral line is replaced by a

number of others. This separation of the spectral lines resulting from the action of a

magnetic field on the source is called the Zeeman Effect. In the so-called normal Zeeman

effect, when the direction of the light beam is perpendicular to the magnetic lines of

force, instead of one spectral line, three are found; one with a wavelength the same as

when the field is absent, a second with a wavelength slightly greater, and a third with a

wavelength slightly less than the first. It is also found that all the three wavelengths are

plane-polarized, the vibration plane of the first line being along the lines of force, and

that of the other two at right-angles to this direction. This is called the transverse Zeeman

Effect.

On the other hand, if the direction of the field lines is parallel to the beam direction, we

have the longitudinal Zeeman Effect. In this case, the original wavelength is replaced by

two, one with a wavelength slightly greater, and the other with a wavelength slightly less

than the normal; the beams being circularly polarized in opposite senses.

Both these effects can be seen to follow directly from the birotational basis of photons. In

Figure 1, the three mutually perpendicular dimensions of space are shown by the lines

OX, OY, and OZ. The beam direction is OZ. The direction of the magnetic field is

indicated by a thick arrow. The three possible orientations for the birotation in the system

are shown by B1, B2, and B3. In Figure 1(a), the field direction is along OY (being

perpendicular to OZ). One or the other of these three birotations can emit photons with

corresponding rotational components. The magnetic field has two effects on the

birotations. Firstly, since the magnetic motion is rotational, the two components of the

birotation with the axis parallel to the field direction alter their speeds of rotation, ± ,

one component speeding up and the other slowing down. In Figure 1 (a) this happens to

B 1. Because of this, these two circular motions of B1 appear as vibrations of two

different frequencies with their plane of vibration perpendicular to the field direction.

Secondly, in the case of the two birotations B2 and B3, the plane of vibration will be

parallel to the field direction. Thus, the vibration emitted from these will be along ab or

cd (Figure 1 (a)); in either case, the vibration appears plane-polarized in the direction of

the field and its frequency, , is unaltered.

In Figure I (b), we have the field direction coincident with OZ. The first result is the

change in the speeds of the components of B1, which, therefore, emit two circularly

polarized photons, one in the CW direction, and the other in the CCW direction, with the

respective frequencies slightly less and slightly more than w. Since the vibration direction

in the case of B2 and B3 (ab and cd in Figure 1 (b)) is along the longitudinal direction

OZ, no beam gets emitted in this direction. We therefore do not have a spectral line with

the original frequency, , in this case.

Summary

We have endeavored to show that deduction from the postulates of the Reciprocal System

leads one to the concept that the simple harmonic motion of the photon is really a

birotation. In fact, the apparent mass of a photon is shown to arise from its angular

momentum.

A complete theory of dispersion of light has been developed. Other phenomena

considered to demonstrate the birotational nature of the photon were the Doppler shift,

double refraction, rotatory polarization, circular polarization, and the Zeeman Effects.

References

1. Nehru, K.V K., The Law of Conservation of Direction, Reciprocity XVIII (3),

(Autumn, 1989), pp. 3-6.

2. Nehru, K.V K., On the Nature of Rotation and Birotation, Reciprocity XX (1),

(Spring, 1991), pp. 8-12.

3. Waldron, R. A., The Spinning Photon, Speculations in Science and Technology,

Volume 5, Number 2, (1983), pp. 171-181.

4. Larson, D. B., The Structure of the Physical Universe, (North Pacific Publishers,

Portland, OR, 1959), pp. 125-131.

5. Robertson, J. K., Introduction to Optics, (Affiliated East-West Press, New Delhi,

India, 1965), p. 307.

6. Beth, R. A., Mechanical Detection and Measurement of the Angular Momentum

of Light, Physical Review, Volume 50 (July, 15, 1936), pp. 115-125.

(a) The Transverse Effect

(b) the Longitudinal Effect

Figure 1: The Normal Zeeman Effect

BIROTATION AND DOUBTING THOMAS

This is a response to Thomas Kirk‘s article in Reciprocity, XX (3), p. 14.

In the course of the study of the Reciprocal System we find that there is a class of persons

who are not merely intelligent but very intelligent — but unfortunately are not intelligent

enough. Most of us, perhaps all of us, belong to this category, the average scientist

included. Let me explain. It must be recognized that, over ages of tradition and habit, the

human mind, in its endeavor to understand the universe, develops what may be termed a

‗frame of mind,‘ which is really a viewpoint. Every concept, old or new, is reckoned or

interpreted from the background of this frame of mind. Anything that does not fit into the

existing frame is summarily rejected; it cannot be felt as understood. The mind complains

that ‗it cannot swallow it.‘

Paradigm Shifts

In the course of the development of science any new idea or concept that may be

proffered would be usually greeted with great enthusiasm and praise if that idea or

concept is in conformity with the popular, prevailing frame of mind. On the other hand,

once in a while there comes some scientific development which is not merely a new

concept but involves a new frame of thinking. Suffice it to cite the examples of the

Copernican revolution and Planck‘s discovery of quanta. Such a development, though it

marks real breakthrough and progress, is never readily accepted by the intelligentsia of

the time. They commit the mistake of trying to understand the new concepts from the

background of the previous frame of thinking whereas, in reality, they must be evaluated

from the new frame engendered by the development. The result, of course, would seem to

be absurd or contradictory.

In the present case, the viewpoint we have all been addicted to for the past millennia is

the one that is germane to the concept of a universe of matter, namely, the inveterate

habit of positing every thing as existing in a framework of space and time. We may call

this the viewpoint of Container Space. With the advent of the Reciprocal System this

viewpoint could be seen to be no more valid. Space and time, according to the Reciprocal

System, happen to be the content of the physical universe. The majority of difficulties in

understanding my presentation or Larson‘s can be seen to stem from the inability to

relinquish the slavish allegiance to the Cartesian reference frame, namely, the container

space, even when the new theory demands it. We shall refer to this as the Fallacy of the

Incongruous Viewpoints.

Direction of Rotation

Larson has shown that space in general is not limited to the spatial aspect of linear

motion, which alone could be correctly represented in the three-dimensional spatial

reference system. He points out that the reference system is deficient in more than one

way. It cannot, for example, represent truly the spatial aspect of rotational motion.[l,2] The

rotational space of the electron is such, for instance.[3]

Some experience difficulty in following the nature of rotation. Since a rotating line

segment sweeps a disk they imagine that (i) rotation is two-dimensional, and (ii) that in

rotation the direction is changing continuously and hence it cannot be scalar. In item (i)

there is confusion between the dimensions of space and the dimensions of motion, and

they don't realize that one-dimensional rotation utilizes two dimensions of extension

space. A quantity is one-dimensional if only one magnitude can completely specify it.

Insofar as a rotation as above can be so specified by the number of revolutions per unit

time, a single magnitude, it is only a one-dimensional motion. And it is also scalar if the

orientation (in threedimensional space) of its axis of rotation is not specified. From the

point of view of motion it is on par with the one-dimensional scalar speed given in, say,

cm/sec. The direction relevant is the direction of this one-dimensional quantity, the

number of revolutions per unit time, which, however, cannot be represented in any direct

way in the extension space, while the one-dimensional quantity, cm/sec, could be so

represented.

The difficulty experienced in this connection is due to the unconscious, mistaken

assumption that the extension space is all-comprehensive and represents rotation truly.

Since the fallacy of container space regards every thing to be existing in the extension

space and time, it perpetuates the belief that anything not so represented in space and

time is unreal, unthinkable or nonexistent. Therefore, one is unable to see that the

direction — which deems it scalar or vectorial — in the context of rotation is not the

changing direction of its radius, but its changed sense of rotation. As Larson amply points

out[2], rotation can be represented in the conventional reference system only with the aid

of an auxiliary device. For example, using the righthand corkscrew notation we might

represent a rotation by a vector of appropriate length pointing in the direction of its axis.

Direction, in the context of the onedimensional rotation then becomes the direction of this

vector.

There is nothing new in this representation. We generally adopt it in common engineering

practice to denote angular momenta and torques. We may call it ‗rotational vector.‘ As

far as any mathematical operation on the rotational vectors is concerned they can be

treated as identical to the ordinary vectors. For example, we can vectorially add two

rotational vectors as we do with ordinary vectors, or decompose a rotational vector into

components. However, we cannot combine ordinary vectors and rotational vectors in any

operation. This is because, while ordinary vectors are correct representations, rotational

vectors are artif'icial constructs employed by us to circumvent the limitations of the

threedimensional reference frame. Hence the rotational vector deserves a separate name,

something like roctor. Their usefulness lies in the fact that within the domain of the

rotational vectors we can carry out all the vectorial operations and hence while they are

only artificial representations they, nonetheless, correctly represent the interrelations

between them.

When we said that one could be very intelligent but not intelligent enough, we meant that

one is unable to see the limitations of the viewpoint of the extension space and is unable

to recognize that he is attempting to view all phenomena, whether they fit this viewpoint

or not, only from such a viewpoint. Once this is realized, all the points that have been

raised can be understood. A re-reading of the articles on birotation without losing the

awareness of this fact might now be able to convey correctly what I meant there about

rotation and birotation.

Other Objections

I did not elaborate on my use of the word ‗fictitious‘ in connection with the space time

progression because I was only paraphrasing Larson‘s explanation, which follows: ―The

sphere generated by the motion of the natural reference system relative to the point of

origin has no actual physical significance. It is a fictitious result of relating the natural

reference system to an arbitrary fixed system of reference.‖[5] And, ―... the postulates

require the existence of real units of motion, units that are similar to the units of motion

involved in the progression of the natural reference system, except that they actually

exist, rather than being fictitious results of relating motion in an arbitrary reference

system. These independent units of motion ...‖[6]

If one is really concerned about truth, one makes sincere attempts to follow the author,

communicate with him for possible enlightenment, or discuss with others. We all have

done that with Larson and with each other. Merely launching into a tirade at the slightest

conceptual difficulty does not lead one very far. Patience, perseverance, and if we may

point out respectfully, lack of conceit are important. They give the higher intelligence a

chance to operate. Of course, in the present instance, it never occurred to me that some

reader might miss the obvious and fail to discern from the context that the rotation under

consideration is the rotation of the atom and not the rotation that constitutes the atom.

Back to the Bivector

Knowing the difficulty one may experience with the analysis of the nature of rotation, we

started our original explanation with linear translational motion.[7] We tried to show how

the representation of a scalar in the conventional reference frame would be a bivector and

not a vector. This explanation proceeds logically and directlv from Larson‘s treatment of

the nature of scalar motion as against vectorial motion.[8] Reading the passage on pp. 33-

34, Nothing but Motion and then my article on The Law of Conservation of Direction[8]

should establish that we are only carrying out Larson‘s development to its logical end,

rather than indulging in ‗free inventions‘. The analysis is next extended logically to

rotation.

Any way we would like to try once more to see if we can be of help. Let us dwell on

linear motion since this does not bring the limitation of the reference frame into the

picture and is consequently easier to grasp. Now the first thing we would like to

emphasize is that the bivector is tantamount to a scalar. Imagine a bivector XAXB as

shown in Fig. 1.

Next consider two mutually perpendicular lines making an arbitrary angle a and 90+a

respectively with the line AB. Let the two components of the vector XA along these two

directions be Xa1 and Xa2 respectively. Similarly Xb1 and Xb2 are the two components of

the vector XB along these two directions (Fig. 2).

On cross-combining the components of the vector XA and XB, such that Xa1 is combined

with Xb2 and Xb1 with Xa2, we arrive at the resultants XA1 and XB1 as shown in Fig. 3.

Thus the original bivector can be transformed into a new bivector XA1XB 1 whose line of

action is at an angle 2a to that of the original. Since the angle chosen, a, is totally

arbitrary, this proves that the bivector XAXB is equivalent to any other bivector of the

same magnitude extending in any direction (actually, bidrection) in the three-dimensional

reference frame. Or what comes to the same, the bivector is tantamount to scalar. Thus

when the scalar motion is placed in the context of a spatial reference frame it manifests as

a bivector, and not as a vector.

It might be noted that while all the first order quantities connected with the bivector (like

momenta) cancel each other out (like mv and -mv), the second order quantities remain

additive (like mv2 and m(-v)2).

All that has been said above the characteristics of a bivector is also true of the birotational

vector (or biroctor, if one prefers to call it so). While a rotational speed has a

onedimensional magnitude and a rotational direction, and hence is a (rotational) vector, a

birotational vector is a pure scalar. Hence if scalar motion manifests in a reference frame

as rotation, it would do so as a birotation and not rotation. Manifestation as a rotation

would entail the creation of a quantity of angular momentum not existing previously,

whereas there is no such need in the case of the birotation.

Finally I have produced the proof of the pudding in a Paper entitled ‗Photon as

Birotation‘ presented at the 1991 Convention (waiting to be published in Reciprocity),

wherein I demonstrated how the manifold phenomena connected with radiation do follow

logically from the birotational nature of the photon.

The difficulty is shared by all of us who fail to realized that we might be making the

mistake of adopting the inappropriate conceptual frame in studying the Reciprocal

System. In fact it is fatally easy to slip back into the Fallacy of the Incongruous

Viewpoints and not realize it. I have separately made a careful analysis of this and other

difficulties we might encounter, in a Paper entitled ‗The Quasar Paradox?‘ sent to

Reciprocity for publication.

We must, however, see that discussions like this have done a great service by showing us

alternate responses to the Reciprocal System. These latter provide us with valuable

insights as to the ways in which an intelligent, well-meaning scientist might

misunderstand discussions of the Reciprocal System and end up passing wrong verdicts.

REFERENCES

1. Dewey B. Larson, ‗The Basic Properties of Matter‘, ISUS, Utah, U.S.A, 1988, p.

139

2. Dewey B. Larson, ‗Nothing but Motion‘, N. P. Pub., Oregon, U.S.A., 1979, pp.

39-40

3. Dewey B. Larson, ‗The Basic Properties of Matter‘, op. cit., pp. 102-103

4. K.V.K. Nehru, ‗On the Nature of Rotation and Birotation,‘ Reciprocity, XX (1),

Spring 1992, pp. 8-12

5. Dewey B. Larson, ‗Nothing but Motion‘, op. cit., p. 38

6. Ibid., p. 45

7. K.V.K. Nehru, ‗The Conservation of Direction ‘ , XVIII (3), Autumn 1989, pp.

8. Dewey B. Larson, Nothing op. cit., pp. 33-34 Law of Reciprocity, 3-6 but Motion,

THE WAVE MECHANICS IN THE LIGHT OF THE

RECIPROCAL SYSTEM

One of the large areas to which the Reciprocal System is yet to be applied in detail is

spectroscopy. The need is all the more urgent as vast wealth of empirical data is available

here in great detail and a general theory must explain all the aspects. To be sure, this was

one of the earlier areas which Larson[1]

explored. But he soon found out, he writes, that

there were complications too many and too involved that he decided to postpone the

investigation until more basic ground was developed by studying other areas.

Coupled with this is also the fact that the calculation of the properties of elements like the

lanthanides is still beyond the scope of the Reciprocal System as developed to date.[2]

The

question of the appropriateness of the Periodic Table as given by Larson is still open.[2-5]

Under these circumstances it is certain that there is lot more to be done toward enlarging

the application of the Reciprocal System to the intrinsic structure of the atom. Perhaps it

is time to break new ground in the exploration of the mechanics of the Time Region, the

region inside unit space. Breaking new ground involves some fresh thinking and leaving

no stone unturned. In this context, it may be desirable to examine, once again, such a

successful theory as the Wave Mechanics in the light of our existing knowledge of the

Reciprocal System.

The Fallacies of the Wave Mechanics

The fundamental starting point of the Wave Mechanics is the correlation, which Louis de

Broglie advanced originally, of a wave with a moving particle. Like every wave has a

corpuscular aspect as shown by Planck's analysis of the blackbody radiation, the

photoelectric effect and the Compton effect (the scattering of photons by particles), it is

hypothesized that every particle has a wave aspect. Since the characteristics of waves and

particles are mutually exclusive in many ways, this concept of associating a wave with a

particle had been beset from its inception with a contradiction that had been euphemized

by stating that the two are "complementary" aspects. This led to many an epistemological

difficulty. The quantum theorists concluded that the phenomena (particles) inside an atom

are not localized in physical space, that the electron in the atom does not exist in an

objectively real sense, that it is but a mathematical symbol, and that the world is not

intrinsically reasonable or understandable in the realm of the very little. One may refer to

The Case against the Nuclear Atom[6]

by Larson for a critical appraisal.

While this is so, it must be noted that the Wave Mechanics was successful in explaining

the vast wealth of the spectroscopic data. The several quantum numbers, n, l, m, etc.

come out in natural way in the theory. Even the "selection rules" that govern the

transitions from one energy state to another could be derived. The fine and the hyperfine

structures of the spectra, the breadth and intensity of the lines, the effects of electric and

magnetic forces on the spectra could all be derived with great accuracy. In addition, it

predicts many non-classical phenomena, such as the tunneling through potential barriers

or the phenomena connected with the phase, which found experimental verification. Thus

we can see that the mathematical success of the Wave Mechanics is accompanied by a

gross mis-understanding of the physical concepts involved. It is the latter which Larson

points out and condemns in his criticism of the conventional atomic theory.[6]

It might be worthwhile to examine if the Wave Mechanics could be purged of its

conceptual errors, drawing from our knowledge of the Reciprocal System, and see if the

transformed version could be integrated into the Reciprocal System scheme with

advantage. After all we have seen this happen in the case of the Special Theory of

Relativity. Some of its mathematical aspects—like Lorentz transformations or the mass-

energy equivalence—could be adopted by the Reciprocal System after purging the

Theory of the wrong interpretations.

Reinterpretation of the Physical Concepts of the Wave Mechanics

Let us take a look at the original points linking the concepts of the wave with that of the

moving particle. The frequency n and the wavelength l of the wave are respectively given

by

n = E/h = M.c²/h (1)

l = h/p = h/(M.v) (2)

where E is the energy, p the particle momentum, M the mass, v the particle speed, c the

speed of light and h Planck's constant. Now the product of n and l gives the wave velocity

u = n. l = c2/v (3)

That is, measured in the natural units, the propagation speed of the wave associated with

the particle is the inverse of the particle speed:

unat = u/c = 1/(v/c) = 1/vnat (4)

As the speed of the particle increases from zero upwards, the corresponding speed of the

associated wave decreases from infinity downwards.

It is at this juncture that our knowledge of the Reciprocal System helps clarify the

physical situation. In particular, we recall that while speed is reckoned from the

standpoint of a three-dimensional spatial reference system, inverse speed is reckoned

from the standpoint of a three-dimensional temporal reference system. While the speed of

the origin of the three-dimensional spatial reference system is zero in that system, the

inverse speed of the origin of the three-dimensional temporal reference system is zero in

the latter system. Or what comes to the same thing, the speed of the temporal zero would

be infinite in the spatial reference system. It can easily be seen that a particular speed vnat

reckoned from the spatial reference system is identical to the inverse speed 1/vnat

reckoned from the temporal reference system. Therefore it follows that the switching

from the particle speed vnat to the associated wave speed unat = 1/vnat is tantamount to the

shifting of the reckoning from the three-dimensional spatial reference system to the three-

dimensional temporal reference system.

This is exactly what needs to be done at the juncture where the phenomena (motion)

under consideration enter the Time Region (see Appendix I). In the Time Region there

could be only motion in time, and the relevant reference frame to represent the motion

would have to be the three-dimensional temporal reference frame. Since changing from

the corpuscular view to the wave view has the significance of shifting from the three-

dimensional spatial reference frame to the three-dimensional temporal reference frame,

the theorists have been unknowingly adopting the right procedure in connection with the

calculations relevant to atomic dimensions. But it is no longer necessary to maintain, as

the theorists do, that an entity is a particle as well as a wave at the same time, since these

two views are irreconcilable. The truth is that the particle viewed from the three-

dimensional spatial reference frame is the wave viewed from the three-dimensional

temporal reference frame. While the particle has a definite location in the former

reference frame, the associated wave, being monochromatic, has infinite extent. In the

temporal reference frame it appears as infinite repetition.

We often come across situations where a change of the coordinate frame, say, from the

rectangular to the polar, facilitates the mathematical treatment. In such cases, the same

geometrical form—or more generally, the space-time configuration, namely, motion—

takes on different mathematical forms in the different coordinate frames. In the present

context we have the converse situation, wherein different coordinate frames engender

different space-time configurations from the same underlying reality (see Appendix II).

In other words, a change of coordinate frames transforms one physical object (space-time

configuration) into an apparently different physical object.

Time and again we find the theorists being compelled to resort to similar transformations

(without, of course, the benefit of the insight given by the Reciprocal System). Consider,

for example, the phenomenon of diffraction of particles/waves by crystal lattices. Here

they customarily work out the interaction in terms of the wave vector k and the

reciprocal lattice, instead of the wavelength l and the direct lattice respectively.

The quantity k = 2p / l is called the wave number. The vector with modulus k and an

imputed direction is the wave vector k. From Eq.(2) it can be seen that the wave vector

represents momentum. If a1, a2 and a3 are the sides of the unit cell of a crystal lattice, then

the array of points drawn with unit cell sides b1 = 2p /a1, b2 = 2p /a2 and b3 = 2p /a3 is

called the reciprocal lattice. Without genuine insight, it is regarded as the invariant

geometrical object whose properties are fundamental in the theory of solids. However,

from the Reciprocal System we know that in solids the motion equilibrium is in the Time

Region, where space is replaced by equivalent space (reciprocal space). Therefore we can

readily see the rationale in adopting the wave vector (reciprocal length) and the reciprocal

lattice in place of the wavelength and the direct lattice respectively.

The Uncertainty Principle

The quantum theorists, being uninformed about the existence of the Time Region,

naturally thought that these waves, associated with the particles, exist in the space of the

conventional reference system, while the truth is that they exist in the equivalent space of

the Time Region. Now a particle is localized whereas its associated wave is spread out

infinitely. Since the theorists have been mistaking that both the particle and the associated

wave exist in the space of the conventional reference frame, they thought if D x is the

region in which the particle is located then it is reasonable for the wave too to be limited

to the same extent D x. So they took recourse to the concept of wave packet. The latter is

a superposition of plane waves, with their wave numbers in the range D k centered

around the de Broglie wave number k (= 2p /l) and producing a resultant wave whose

amplitude is non-zero only for a space of D x, equal to the "size" of the particle. They

then identify the wave packet, rather than the original monochromatic wave, with the

particle. The so-called uncertainty principle stems from this procedure, because the range

of size D x, and the range of wave number D k, of the waves composing the wave packet,

are inversely related as could be seen from Fourier analysis.

D x @ 1/D k (5)

Using Eq.(2) we have

D x. D p @ h/2 p (6)

which is the conventional statement of the uncertainty principle.

But now, one realizes that while the particle is localized in space, it does not entail that

the associated wave is also to be somehow localized in space, since the latter is to be

reckoned from the point of view of the three-dimensional temporal reference frame and

not the spatial reference frame.

It may be a practical difficulty to measure both the location and the momentum of a

system of atomic dimensions with unlimited accuracy simultaneously. But the conclusion

drawn by the theorists from the uncertainty principle that a system of atomic dimensions

does not possess these properties of precise location and precise momentum

simultaneously can be seen to be invalid. As Larson rightly points out, conclusions such

as these are applicable only to the theorists' model, not to the actual system. The

uncertainty principle is merely the statement of the fact that the characteristic length

belonging to space, namely D x cm, and the characteristic length belonging to equivalent

space, namely D k cm-1

, are reciprocally related (Eq.(5)).

The Probability Interpretation

The next thing to be recognized is that the wave information is not to be visualized as

mapped out in the space of the conventional spatial reference system. The reference

frame for the wave is a temporal manifold. As creatures of the material sector we have

no direct access to the three-dimensional temporal reference frame: rather we are

anchored to the three-dimensional spatial reference frame. But fortunately, we can

accomplish the equivalent of the transformation from the spatial to the temporal frame by

the contrivance of adopting the wave picture in place of that of the particle. It must

continually be borne in mind that the three-dimensional spatial manifold being used in

this context is so used as a temporal analogue. This is why the wave function

(specifically, the square of the amplitude) takes on the probability interpretation. The

action itself is unambiguous and precise, but since it takes place in the temporal reference

frame, the outcome in the three-dimensional spatial reference frame is governed by

chance and therefore statistical.

The randomness of the radioactive disintegration is another example to the point. When

the total mass (rotational + vibrational) of the atom builds up to the upper zero point for

rotation, the time-zero as we might call, the (excess) motion reverts to the linear status

and is jettisoned as radiation or other particles. Since it is the result of reaching the time-

zero point the action is in time instead of space. The radioactive disintegration proceeds

continuously and contiguously in three-dimensional time. But since locations in the three-

dimensional temporal frame are only randomly connected to the locations in the three-

dimensional spatial frame, the apparent disintegration of the atoms (as observed from the

conventional spatial standpoint) seems utterly random.

Again the interference of light is another example. The crests and troughs of the resultant

wave in the two-slit experiment coincide respectively with the regions where the

maximum and the minimum number of photons reach. But if the beam intensity is very

low, say only a few photons are passing the slits, then all that we can say is that a photon

has a greater likelihood of arriving at the location indicated by the wave crest rather than

at any other place. In other words, the wave (square of the amplitude) takes on a

probability interpretation.

This is also precisely the reason why the theorists find some of these forces to be non-

local in nature—a totally non-classical phenomenon—namely, that they originate in the

Time Region and the connection between the locations in three-dimensional time and the

locations in three-dimensional space is random. We have discussed this point in

connection with the phenomena of ferromagnetism[7]

and superconductivity.[8]

Wave Mechanics without the Nucleus

In The Case against the Nuclear Atom[6]

Larson advances arguments to establish that the

concept of the nucleus of the atom is untenable. He points out that, in fact, the "size" of

the nucleus obtained by the scattering experiments is rather the size of the atom itself.

Our calculations in the next section corroborate this. While Larson's confutation of the

nuclear concept proceeds from his original arguments, his criticism of the Quantum

Theory, given in the same work, was based entirely on citations from other experts in the

field, including those of the pioneers of the Theory. Larson himself does not directly

analyze or comment upon any part of the Quantum Theory or the Wave Mechanics. And

all those criticisms he quotes deal with the epistemological difficulties only—such as the

"lack of rationality," etc. which we mentioned at the outset—none deal with the

mathematical aspects.

Now since we realize that the entire confusion in the area arises from the fact that the

theorists do not distinguish between the space of the conventional reference system and

the equivalent space of the Time Region (of which they do not know), if we set this right

by explicitly recognizing that the associated wave is reckoned from the three-dimensional

temporal reference frame, we would have achieved much progress.

Since according to the Reciprocal System there is no nucleus, we need to give new

interpretation to the energy term occurring in the Schrödinger equation for the wave. It

cannot be regarded as the energy level of an orbiting electron. But as we shall see below,

this can be treated as the energy level of the atom itself.

The Size of the Atom

Larson[6]

has pointed out that as the three-dimensional motion that constitutes the atom

extends in the Time Region, its measured size in the time-space region (namely, the

conventional three-dimensional spatial frame) would be much smaller than one natural

unit of space, snat. It is reduced by the inter-regional ratio, 156.444, which was calculated

earlier[9]

as the number of degrees of freedom in the Time Region, and 8, which is the

number of degrees of freedom in the time-space region. Since the atomic rotation is

three-dimensional, the cube of 156.444 is the applicable value. So the measured atomic

radius would be the following

snat/(8 * 156.4443) = 1.4883 x 10

-13 cm

(adopting snat = 4.558816 x 10-6

cm from Larson[10]

). Since actually it is the volume with

which the equation is concerned, rather than the length (radius), there is an additional

geometrical factor, f, relating the volume of a cube (of side f*x) with that of a sphere (of

diameter x) given by

(f * x)3 = p * x

3/6

which gives f = 0.806. Adopting this, the measured radius, based on the natural unit of

volume concerned, would be

f * 1.4883 x 10-13

cm = 1.1995 x 10-13

cm

But this is specifically the measured radius of an atom of unit atomic weight. If the

atomic weight of the atom is A units, then the measured radius of the atom turns out to be

rA = 1.2 * A1/3

fm (7)

As can be seen, this agrees well with the results obtained from the scattering experiments

for the so-called nuclear radius. This therefore confirms Larson's view that the

experimenters are confusing the atom with the nucleus.

The Region of One-dimensional Motion

We recall that the atom is constituted of three rotations a-b-c. "a" and "b" are two-

dimensional rotations (three-dimensional motion) in two of the scalar dimensions, and

"c" is the one-dimensional reverse rotation in the third scalar dimension. Since this one-

dimensional rotation is not the basic rotation of the atom, the inter-regional ratio

applicable to this is the purely rotational factor 128. As the degrees of freedom in the

time-space region is 8 as already pointed out, the range of sizes associated with the one-

dimensional rotation in the Time Region is

snat/(8 * 128) = 4.45 x 10-9

cm (8)

Hence we can expect the discrete speeds which exist within this spatial range, as far as

the one-dimensional type of rotation is concerned, to be part of the atomic structure and

the origin of the energy levels that explain the line spectra. Our preliminary study

suggests that further prospects for the understanding of the spectroscopic data lie in this

zone of one-dimensional rotation of the Time Region.

Conclusion

It is shown that while the Wave Mechanics has been very successful and accurate

mathematically, it is fraught with some fundamental errors. A review of the latter in the

light of the Reciprocal System of theory shows that the principal stumbling block was the

ignorance of the existence of the Time Region and its peculiar characteristics.

Knowledge of the Reciprocal System enables us to recognize two crucial points: (i) that

the wave associated with a moving particle, in systems of atomic dimensions, exists in

the equivalent space of the Time Region; and (ii) that the switching from the particle

view to the wave view is equal in significance to shifting from the standpoint of the three-

dimensional spatial reference frame to that of the three-dimensional temporal reference

frame. This recognition not only throws new light on the intriguing wave-particle duality,

but also corrects the conceptual error that eventually led the theorists to the wrong

conclusion that the world of the very small does not conform to the rational laws that are

applicable to the macroscopic world.

It is shown that the uncertainty principle does not stem from the intrinsic nature of the

atomic phenomena, as the theorists would have us believe, but is rather the result of

gratuitously assuming that the wave associated with a moving particle is spatially co-

extensive with the particle.

The probability connotation of the wave function is shown to arise from the two facts that

the wave is existent in the three-dimensional temporal manifold, and that locations in the

three-dimensional temporal manifold and the three-dimensional spatial manifold

respectively are randomly connected. The non-local nature of the forces in the Time

Region also follows from this.

Calculations based on the inter-regional ratios applicable confirm Larson's assertion that

the measured size of the atom is in the femtometer range and hence the actual atom is

being confused with the non-existent nucleus.

It is suggested that the investigation of the one-dimensional motion zone of the Time

Region, in conjunction with the adoption of the Wave Mechanics corrected of its

conceptual errors, will lead to greater understanding of the atomic structure and thereby

pave the way for the complete explanation by the Reciprocal System, of the spectroscopic

data, as well as the other recalcitrant problems connected with the properties of rare-

earths etc.

References

1. Larson D.B., The Structure of the Physical Universe, North Pacific Pub., Portland,

Oregon, USA, 1959, pp. 122-125

2. Gilroy D.M., ―A Graphical Comparison of the Old and New Periodic Tables,‖

Reciprocity, Vol. XIII, No. 3, Winter 1985, pp. 1-27

3. Sammer J., ―The Old and New Periodic Tables - Again,‖ Reciprocity, Vol. XX,

No. 4, Winter 1991-92, pp. 7-13

4. Tucek R.V., "New Periodic Table," Reciprocity, Vol. XXI, No. 1, Spring 1992, p.

20

5. Kirk T., "Periodic Table, Revisited," Reciprocity, Vol. XXI, No. 2, Autumn 1992,

pp. 10-13

6. Larson D.B., The Case Against the Nuclear Atom, North Pacific Pub., Portland,

Oregon, USA, 1963

7. Nehru K.V.K., "Is Ferromagnetism a Co-magnetic Phenomenon?" Reciprocity,

Vol. XIX, No. 1, Spring 1990, pp. 6-8

8. Nehru K.V.K., "Superconductivity: A Time Region Phenomenon," Reciprocity,

Vol. XIX, No. 3, Autumn 1990, pp. 1-6

9. Nehru K.V.K., "The Inter-regional Ratio," Reciprocity, Vol. XIV, No. 2-3, Winter

1985-86, pp. 5-9

10. Larson D.B., Nothing but Motion, North Pacific Pub., Portland, Oregon, USA,

1979, p. 160

Appendix I

According to the Reciprocal System space and time occur in discrete units only. If two

atoms approach each other in space, they cannot come any nearer than one natural unit of

space, snat. Within one natural unit of space no decrease in space is possible since one

natural unit is the minimum that can exist. However, since the basic constituents of the

physical universe are units of motion, or speed, in which space and time are reciprocally

related, an increase in time (t) with space constant is equivalent to a decrease of space

(1/t). This is referred to as the equivalent space in the Reciprocal System. Therefore,

though the atoms cannot approach each other nearer than one natural unit of space, they

can do so in the equivalent space by moving outward in time. As all changes in this

region inside unit space are in time only, it is referred to as the Time Region.

Appendix II

Consider, for instance, a wave motion in the three-dimensional temporal reference frame,

of amplitude given by

r = A + B.cos q (i)

with A and B constants, and q the time coordinate. In order to return to the spatial

reference frame, we (i) transform the time coordinate q into f , a rotational space

coordinate—rotational because all our time measurements are based on cyclical

processes; and (ii) transform r into 1/r, since equivalent space and actual space are

reciprocally related. We then find that the above equation (of the wave configuration)

becomes the equation of an ellipse (or hyperbola) that represents the locus of a planetary

mass point revolving around a central force

1/r = A + B.cos f (ii)

where A/(A2-B

2) is the semi-major axis and B/A the eccentricity. (It must be cautioned

that though the above example illustrates the point in question, it is not a complete

analogy.)

―QUANTUM MECHANICS‖ AS THE

MECHANICS OF THE TIME REGION

The preliminary results of a critical study of the Wave Mechanics carried out in the light

of the knowledge of the Reciprocal System of theory have been reported earlier.[1]

Some

of its important findings are as follows. While the Wave Mechanics has been very

successful mathematically, it contains some fundamental errors. The principal stumbling

block has been the ignorance of the existence of the Time Region and its peculiar

characteristics. The crucial points that need to be recognized are that the wave associated

with a moving particle, in a system of atomic dimensions, exists in the equivalent space

of the Time Region: and that switching from the particle view to the wave view is equal

in significance to shifting from the standpoint of the three-dimensional spatial reference

frame to that of the three-dimensional temporal reference frame that is germane to the

Time Region. To imagine that even gross objects have a wave associated with them is a

mistake: the question of the wave does not arise unless the phenomena concerned enter

the Time Region.

One corollary is that the theorists ―assumption that the wave associated with the moving

particle is spatially co-extensive with the particle is wrong since the former exists in the

equivalent space, not in the extension space of the conventional spatial reference system.

The Uncertainty Principle stems from the theorists‖ practice of resorting to wave packets.

It has further been shown that the probability connotation of the wave function arises

from the two facts that the wave is existent in the three-dimensional temporal manifold,

and that locations in the three-dimensional temporal manifold are only randomly

connected to locations in the three-dimensional spatial manifold. The non-local nature of

the forces (motions) in the Time Region also follows from these facts.

Calculations based on the inter-regional ratios applicable confirm Larson‘s assertion that

the measured size of the atom is in the femtometer range and hence what is found from

the scattering experiments is the size of the atom itself—not of a nucleus.

From the above study it became abundantly clear that the critics‘comments that the

small-scale world is not intrinsically rational, and that the Quantum theory cannot be

understood intuitively were wrongly founded. What was really missing was the

knowledge of the existence and characteristics of the Time Region, the region inside the

natural unit of space, where only motion in time is possible. Since our knowledge of the

Reciprocal System helped straighten some of the conceptual kinks of the Wave

Mechanics and has indicated that its original basis has been rightly (though

unconsciously) founded, an attempt has been made to inquire into its mathematical

aspects in order to see whether they are valid in the light of our understanding of the

Reciprocal System. The results of this inquiry are reported in this article.

1. Where Do We Stand

Before proceeding further it would be desirable to take a stock of the atomic

situation form the point of view of the Reciprocal System.

Firstly, Larson[2]

asserts that the atom is without parts, that it is a unit of

compound motion, motion being the basic constituent of the physical universe.

This means that both the nucleus and the so-called orbital electrons are non-

existent.

Secondly, he argues that there is no electrical force either, involved in the atomic

structure. This, therefore, leaves gravitation and the space-time progression as the

only two motions (forces) that operate inside the Time Region with, of course, the

appropriate modifications peculiar to the Time Region introduced into them.

Under these circumstances the question of a ―nuclear‖ force does not arise at all.

But it is perfectly legitimate to inquire what forces (motions) are encountered by a

particle as it approaches the vicinity of an atom, and indeed, as it enters the very

atom itself. Equally important is to inquire into the mechanics of the converse

process of the emission of a particle by the atom.

2. The Wave Equation

The most fundamental starting point for the mathematical treatment in the

Quantum Mechanics is the wave equation. The wave equations in the quantum

theory govern the wave functions associated with the particles, and correspond to

Newton‘s laws of classical mechanics. From our earlier study we have seen that

changing from the particle picture to the wave picture is a legitimate strategy that

needs to adopted on entering the Time Region, as it is tantamount to shifting from

the conventional three-dimensional spatial reference frame of the time-space

region to the three-dimensional temporal reference frame of the Time Region.

Therefore the next logical step is to examine how the governing equations of the

wave phenomena have been arrived at, and see if it is in consonance with the

Reciprocal System.

Since it is always possible to constitute a wave of any shape by superposing

different sinusoidal waves of appropriate wavelengths and frequencies, we shall

limit our discussion to these elementary sinusoidal waves. The relation between

the wave number k and the wavelength on the one hand, and that between the

angular frequency and frequency on the other, are as follows

k = 2 / ; = 2 (1)

The wave speed u is given by

u = . = /k (2)

The general functional forms of sinusoidal waves are

sin (kx t) ; cos (kx t) (3)

and in complex exponential form (see Appendix I)

ei(kx t)

(4)

where the imaginary unit i is defined by i2 = -1.

Complex functions involve a real part and an imaginary part. Since at this stage of

our discussion the nature of the wave function of particles is yet unknown, there is

no theoretical reason to exclude complex functions. Let us bear in mind that the

criterion of judgment is what is possible in the Time Region, not what is possible

in the time-space region. To be sure, observable quantities in the time-space

region ought to be real. However, by virtue of the second power relation between

corresponding quantities in the Time Region and the time-space region, the

observable value of a Time Region quantity would still be real even if it were to

be imaginary in the Time Region (e.g.: a quantity i.v in the Time Region would

appear as (i.v)2, that is, -v

2 in the outside region).

3. Radiation Waves

Let us derive the governing equation for the wave propagating at constant speed,

like that of radiation. First we note the relation between the momentum p of the

wave and the wave number k, and the energy E and its angular frequency ,

p = k ; E = (5)

where is Planck‘s constant h divided by 2 .

From the energy-momentum relationship of the wave, p2c

2 = E

2, (c being the

constant wave speed) we have

p2 = E

2/c

2;

2k

2 =

2 2/c

2; k

2 =

2/c

2 (6)

Assuming the simplest wave form, that of a sine wave, we write the wave

function in complex exponential form as

(x,t) = A.ei(kx- t)

(7)

where A is an arbitrary constant. For such a function,

/ x = ik. and / t = -i . (8)

That is, taking the derivative with respect to x is equivalent to multiplying by ik,

and taking the derivative with respect to time t is equivalent to multiplying by -i .

Thus

2

/ x2 = (ik)

2. = -k

2. and

2 / t

2 = (-i )

2. = -

2. (9)

Substituting these in the last of Eq.(6) we obtain

2

/ x2 = (1/c

2)

2 / t

2 (10)

which is exactly the wave equation we are seeking (see Appendix II).

4. Matter Waves

At the instance of his mentor Peter Debye, Erwin Schrödinger made a detailed

study of the wave hypothesis advocated in 1924 by de Broglie. Schrodinger noted

that the energy-momentum relationship of a free particle (not acted by forces) of

mass m

p2/2m = E (11)

leads to the wave number-angular frequency relation

2k

2/2m = (12)

From Eqs. (2) and (12) we see that the wave speed in this case is given by

u = k/2m (13)

Therefore the speed of the matter waves is not constant like that of the radiation

waves, but is a function of the wave number k. Eq. (12) could be rearranged as

-( 2/2m) (ik)

2 = i (-i )

Multiplying both sides by , we can at once see from Eqs. (8) and (9) that

-( 2/2m) (

2 / x

2) = i ( / t) (14)

which is the governing equation for the wave associated with the free particle that

we are looking for. This is the Schrödinger equation for the free particle. It is the

equation in the Time Region which corresponds to Newton‘s first law of the time-

space region.

In order to include interactions of the particles with the environment we note that

the total energy of such a particle consists of the kinetic energy and the potential

energy. The latter could be taken to be dependent only on position and

represented by a potential energy function V(x). Thus for a conservative system

we have the constant total energy E given by

p2/2m + V(x) = E (15)

The corresponding wave number-frequency relation, associating frequency with

the total energy, is

2k

2/2m + V =

Adopting Eqs. (8) and (9) as before, we arrive at the Schrödinger wave equation

with interaction present

–( 2/2m) (

2 / x

2) + V(x) = i ( / t) (16)

This corresponds in the Time Region to Newton‘s second law in the time-space

region.

As can be seen from the foregoing derivations, nothing against the principles of

the Reciprocal System has been introduced so far. Hence the Schrodinger

equations can be admitted as legitimate governing principles for arriving at the

possible wave functions of an hypothetical particle of mass m traversing the Time

Region, with or without potential energy functions as the case may be. We may

note in the passing that often considerable mathematical dexterity is required in

solving these differential equations, though computer-oriented numerical methods

are fast replacing closed-form solutions.

Any wave corresponding to a state of definite energy E has a definite frequency

= E/. Therefore from Eq. (7) we can write

(x,t) = A.e–iEt/ . (x) (17)

where (x) is a function of space variable only. Inserting the above into Eq. (16)

and dividing out the factor e–iEt/

throughout, we get the differential equation to be

satisfied by (x)

-( 2/2m) (

2 / x

2) + V(x) (x) = E. (x) (18)

which is referred to as the time-independent Schrödinger equation. This equation

is less general and is valid only for states of definite total energy.

5. States of Negative Energy

It is instructive to see what the solutions of Schrödinger equation turn out to be.

Firstly, in any region of constant potential energy V, we see that the solution of

Eq. (18) is a sinusoidal function,

(x) = A.sin kx or A.cos kx, and k2 = 2m(E-V)/2

(19)

(E-V) being the kinetic energy.

6. The Step Function

In Fig. 1(a) we picture a step-function potential energy, which is constant at V1

and V2 respectively in two different regions. A possible wave function

corresponding to this case is shown in Fig. 1(b). The particle‘s greater kinetic

energy (E-V1) in the region x>0 is reflected in its larger wave number (smaller

wavelength) in this region. Also since its speed in this region is greater, it spends

comparatively less time in this region, and this reflects as its smaller amplitude in

this region.

An interesting case occurs when the potential energy V in any region is greater

than the total energy E. Here the kinetic energy, E-V, becomes negative! This is

physically impossible in the time-space region and the particle can never enter

such region. However, the situation is different in the Time Region: Eq. (18) has

valid solutions in the region, with k from Eq. (19) taking on imaginary values,

(x) = A.e bx

, and b = ik (20)

The sign of the exponent is so chosen as to see that tends to zero for large x.

Fig. 2 illustrates this case: in the region x 0 we see that E is less than the

potential energy. The wave function is sinusoidal in the region of positive kinetic

energy and is exponential in the region of negative kinetic energy. Both functions

join smoothly at x=0 with a first order continuity. The penetration of the wave

function into the region of negative kinetic energy has no classical analog and is

purely a phenomenon of the Time Region.

7. Explanation of the Negative Energy States

When we turn to the Reciprocal System for an explanation of the possibility of the

existence of negative energy states, what we find is as follows. In the time-space

region, that is, in the context of the three-dimensional spatial reference frame,

speed (space/time) is vectorial, that is, can have direction in space and therefore

could take on positive or negative values. This is because in this case space is

three-dimensional and time is scalar. In this frame, energy, which is one-

dimensional inverse speed (time/space), is scalar, and can take on zero or positive

values only. On the other hand, the Time Region is a domain of the three-

dimensional temporal reference frame. In this case time is three-dimensional and

space is scalar. Consequently the inverse speed (namely, energy) is the quantity

that is ―directional,‖ that is, can take on a ―temporal direction‖ in the context of

the three-dimensional temporal reference frame. Therefore it is perfectly possible

for it to take on negative values as well. (It must be cautioned that ―direction in

time‖ has nothing to do with direction in space; it is to be understood that we are

only speaking metaphorically.) Further, in the Time Region, speed is the quantity

that is scalar, an example being the net total speed displacement of the atom,

namely, the atomic number Z.

Moreover the possibility that even potential energy (being an inverse speed) could

be ―directional‖ in the three-dimensional time, and hence be represented by

complex numbers in the Time Region, cannot be overlooked. Indeed the Quantum

theorists find it necessary to adopt the complex potential V+iW in place of V in

scattering theory. Here the wave number k becomes complex and is written as

k+iq. b of Eq. (20) becomes b = i(k + iq) = -q + ik, and we have

= (A.e-qx

)(eikx

) (21)

We can at once see that this is the wave function of a travelling wave of whose

amplitude decreases as it advances, and therefore represents a beam of particles

some of which are getting absorbed.

8. The Potential Energy Barrier

An interesting situation arises when two regions of positive kinetic energy occur

separated by a potential energy barrier that is higher than the total energy as

shown in Fig. 3(a). In the central region (of negative kinetic energy) the wave

function is exponential, while it is sinusoidal on either side as shown in Fig. 3(b).

At either boundary the function and its first derivative are continuous. From this it

is apparent that the particle represented by the wave has a non-zero probability of

appearing on the other side of the barrier! While this is a real Time Region

phenomenon that has been observed (the ―tunneling‖ ), it has no analog in the

time-space region (classical mechanics).

9. The Potential Energy Well

The last case of interest we wish to consider is that of a potential well as shown in

Fig. 4(a), wherein the total energy E is less than the potential energy V1 in the

outer regions. As before, we find that the wave function is sinusoidal in the

(central) region of positive kinetic energy, and is exponential in the (outer)

regions of negative kinetic energy, maintaining first order continuity at the

boundaries. But here a new factor emerges, namely, that if we choose an arbitrary

value of E, it might become necessary to adopt growing exponentials in the outer

regions (for example, e+bx

for x L) so as to satisfy the continuity conditions at the

boundary. This therefore leads to an unreal state of affairs. The physical

requirement is that the wave function goes towards zero with increasing space

coordinate in the outer regions. This necessitates the choice of shrinking

exponentials in the outer regions (for example, e-bx

for x L). This requirement,

coupled with the continuity constraints at the boundary, limits the possible

energies to a series of distinct levels, each with its own wave function. Thus, well-

type potential energy functions give rise to set of possible discrete energy levels.

This fact can be seen directly to lead to the explanation of several observable facts

including the atomic spectra.

10. Origin of the Pauli Exclusion Principle

The so-called exclusion principle was originally promulgated by Wolfgang Pauli.

This is an empirical law to which no exception was ever found. It has been a

heuristic guiding rule for understanding many an important quantum

phenomenon. In spite of its important role, the explanation of its origin has defied

the theorists. Therefore that this explanation is now forthcoming from the

Reciprocal System is a point in favor of the general nature of the latter theory.

i. The Spin

But first we must recognize a point that we have been emphasizing,[3,4]

namely, that rotational space is as fundamental as the linear (extension)

space. Larson explains: ―...the electron is essentially nothing more than a

rotating unit of space. This is a concept that is rather difficult for most of

us when it is first encountered, because it conflicts with the idea of the

nature of space that we have gained from a long-continued, but uncritical,

examination of our surroundings. ...the finding that the ―space‖ of our

ordinary experience, extension space, as we are calling in this work, is

merely one manifestation of space in general opens the door to an

understanding of many aspects of the physical universe...‖ [5]

He points out

that an atom, for example, can exist in a unit of rotational space as it can in

a unit of extension space.

In a Paper entitled Photon as Birotation[6]

we have derived that the basic

unit of angular momentum is ½ . Now we find that the Quantum theorists

have been referring to this basic unit of rotational space as the spin. In

addition to the three space coordinates spin is treated as a fourth

coordinate. Thus two different particles can occupy the same location in

extension space at the same time if their spin coordinate differs.

ii. Indistinguishability

In connection with a class of elementary particles, we know that any two

individual particles (say, two electrons) are absolutely alike. In the time-

space region, the fact that two particles are identical presents no

complications since they can be kept distinguished by their respective

locations. But in the quantum phenomena, because of the non-local nature

of the Time Region, no such distinction is possible. This intrinsic

indistinguishability gives rise to some special constraints. Let us take

(1,2) to be the wave function of two indistinguishable particles with

particle 1 at location r1 (whose coordinates include the spin coordinate

also) and particle 2 at location r2. Then [ (1,2)]2 represents the

probability distribution for particle 1 to be at r1 and particle 2 to be at r2.

Since we cannot distinguish between the particles, the wave function

should be of such a form that it results in the same probability distribution

if we interchange the two particles in . That is

[ (1,2)]2 = [ (2,1)]

2

This can be satisfied in two ways,

(1,2) = + (2,1) and (1,2) = - (2,1) (22)

The first type of wave functions are referred to as the symmetric and the

second as the antisymmetric functions.

Now the empirical finding is that the wave functions of particles like

protons and neutrons which are known to have half-integral spin (½ h ) are

antisymmetrical, and those of particles with integral spin (like the

photons) are symmetrical. The most fundamental statement of Pauli

exclusion principle goes somewhat like this: ―Any permissible wave

function for a system of spin-½ particles must be antisymmetric with

respect to interchanging of all coordinates (space and spin) of any pair of

particles.‖ But enunciating a principle is quite different from explaining its

origin, and the fact is that no theoretical explanation has been found for

this empirical finding. One author writes: ―For reasons that are not clearly

understood, for electrons, protons, neutrons, and all other spin-½ particles,

the minus sign is chosen...‖ [7]

iii. The Two Types of Reference Points

From the Reciprocal System we have now the explanation. Let us recall

that in the universe of motion there are two types of reference frames—the

conventional, stationary three-dimensional spatial reference frame (or its

cosmic analog, the three-dimensional temporal reference frame) and the

moving natural reference frame. We also have two kinds of objects, those

having independent motion like the gravitating particles and those having

no independent motion of their own and hence are stationary in the natural

reference frame, like the photons and those particles having potential

mass[8]

only. The reference point for the scalar inward motion of the

gravitating particle is the particle itself. Thus if there are two locations A

and B in the three-dimensional reference frame with this particle situated

at A, say, its gravitational motions appears in the direction BA, because it

is inward, toward itself. If now the particle is shifted to location B, the

direction of its gravitational motion seems reversed, being in the direction

AB. This is the origin of the antisymmetry of the wave functions of such

particles.

As already remarked a unit of one-dimensional rotation carries unit spin

(½ ). The resultant spin of a two-dimensional rotation with unit spin in

each dimension is 1x1 = 1 (that is, ½ h ) or is 1x(-1) = -1 (that is, -½ ).

On the other hand, the resultant spin of a birotation (like the photon) is

1+1 = 2 (that is, ) or 1-1 = 0. Since gravitation arises out of the two-

dimensional rotation, we can see that a gravitating particle carries spin-½.

Thus the wave function of spin-½ particles turns out to be antisymmtric.

On the other hand, the reference point for the motion of particles like the

photons is the location in the natural reference frame, or what Larson calls

the absolute location. The natural reference frame is not a spatial

manifold; not is it a temporal manifold. It is a speed manifold: each

location in it is moving at unit speed, one unit of space per unit of time.

Suppose that the spatial separation between two locations in this frame

(the absolute locations) increases by n natural units of space. Because of

the unit speed criterion, there is concomitant increase in the separation in

time by n natural units of time, making n/n = 1. The expansion in space is

completely nullified by the expansion in time (because an increase in

space is equivalent to a decrease in time and vice versa), and from a

space-time point of view there is no separation between absolute locations.

In the context of the three-dimensional reference frame, photons appear to

move outward from the point of their origin. But we have already seen

that the photon is stationary in the absolute location. Its apparent motion is

the outward motion of the absolute location (in which it is situated) away

from all other absolute locations. The crucial point that should now be

recognized is that outward from one absolute location is still outward

from any other absolute location because of the equivalence of these

absolute locations as explained above. Therefore, interchanging the

location of the photon between two such absolute locations has no effect

on the sign of its wave function. That is, the wave function of such

particles is symmetric. One final word is in order: all that has been said

above is also true in the Time Region, except that the scalar direction

outward in the time-space region manifests as inward in the Time Region

and vice versa.

11. Potentials in the Time Region

Finally it might be of interest to explore the nature and type of the potential

energy functions V (see Eq. (15)), in the Time Region. In view of the maiden

nature of the investigation and the insufficient time available, the results reported

in this section may have to be treated as tentative.

i. Dimensional Relations across the Regions

Discussing the effect of the inversion of space and time at the unit level on

the dimensions of inter-regional relations, Larson[9]

shows that the

expressions for speed and quantities related to speed in the Time Region

are the second power expressions of the corresponding quantities

belonging to the time-space region. This is because motion (speed) has a

spatial component and a temporal component. Since unit space is the

minimum that can exist, within the Time Region—the region inside unit

space—the spatial component of a speed remains constant at 1 unit and all

variability can be in the temporal component, t, only. By virtue of the

reciprocal relation between space and time the t units of time are

equivalent to 1/t unit of space and manifest so in the Time Region. That is

why Larson uses the term equivalent space (that is, inverse space) as

synonym for Time Region. The equivalent speed in the Time Region is,

therefore, given by the ratio of the equivalent space to time, (1/t)/t = 1/t2.

This quantity is the second power expression of the speed in the time-

space region with 1 unit of space component and t units of time

component, namely, 1/t.

In an earlier article[1]

we have identified two different zones of the Time

Region, namely, the one-dimensional and the three-dimensional. The

second power relation mentioned above could be seen to apply specifically

to the one-dimensional zone, the zone of one-dimensional rotation

associated with the atoms or subatoms. On the other hand, for the three-

dimensional zone—where the compound motions constituting an atom

exist—the situation is different because the basic rotation that constitutes

the atom is two-dimensional. The temporal component of a two-

dimensional rotation in the Time Region would be t2, and its spatial

equivalent is 1/t2. So the equivalent speed in the case of two-dimensional

rotation turns out to be (1/t2)/t

2 = 1/t

4. As could be seen, this is the fourth

power expression of the corresponding time-space region speed 1/t. (Note

that in the time-space region time is scalar and there cannot be anything

like two-dimensional time.)

Looking back, we can now easily see why the quantum theorists required

complex numbers to deal with the so-called ―electronic energy levels‖ of

the atom adequately: they needed to cope up with the two-dimensional

character of the equivalent speed pertaining to the one-dimensional

rotation in the Time Region. It also suggests itself that we require to adopt

quaternions to handle the so-called ―nuclear energy levels‖ since the

dimensionality of the equivalent speed pertaining to the two-dimensional

rotation in the Time Region is four.

ii. Potentials in the Time-space Region

At this stage of our study we have only two scalar motions (forces) to

consider: the space-time progression and gravitation. In the outside region

(the time-space region), the forces due to the space-time progression and

gravitation are respectively given by

FPO = KPO and FGO = -KGO/r2 (23)

where all the quantities concerned are in the natural units, the K‘s are

positive constants and r the distance factor. Suffix G refers to gravitation,

P to space-time progression and O to outside region. From the definition

of potential, F = - V/ r, we obtain the expressions for the corresponding

potentials due to the space-time progression and gravitation, in the outside

region respectively as

VPO = -KPO.r and VGO = -KGO/r (24)

The potential due to the space-time progression is repulsive while that due

to gravitation is attractive as can be seen.

iii. Potentials in the One-dimensional Zone of the Time Region

Potential energy being inverse speed, the expressions for the potentials in

the one-dimensional zone of the Time Region would be the second power

expressions of the corresponding ones in the time-space region (Section

5.1). Consequently the space-time progression and gravitational potentials

in this zone could be written as

VP1 = KP1.r2 and VG1 = KG1/r

2 (25)

with suffix 1 referring to the one-dimensional zone. We can at once verify

that gravitation is repulsive and the space-time progression attractive in

this region. In addition there could be a constant term KI1, representing the

initial level of the Time Region potential. Thus the total Time Region

potential in the one-dimensional zone turns out be

VT1 = KP1.r2 + KG1/r

2 KI1 (26)

The values of KG1 and KI1, and possibly KP1, are functions of the

displacements of the atom in the three scalar dimensions.

It is instructive to see what the expressions for the corresponding forces

would be: differentiating with respect to r and taking the negative sign, we

have

FP1 = -2.KP1.r and FG1 = 2.KG1/r3 (27)

Larson[10]

however, while calculating the inter-atomic distances in solids,

basing on the equilibrium of the Time Region forces, adopts

FP1 = -1 and FG1 = K/r4 (28)

where K is a function of the several atomic rotations. These expressions

can be seen to differ from Eqs. (27) above. But whether we take Eqs. (27)

or Eqs. (28), the force equilibrium equation, FP1 = FG1 can be seen to lead

to the same fourth power dependence on the distance factor.

Consequently, even if we find that Eqs. (27) are to adopted in preference

to Eqs. (28), Larson‘s original inter-atomic distance calculations would

remain unaltered.

The Time Region potential Eq.(26) results in a potential well and therefore

the solutions of Schrödinger‘s Eq. (18) yield a set of discrete energy levels

for the atomic system (see Section 3.4). It remains to be verified whether

these truly correspond to the values inferred from the spectroscopic data.

iv. Potentials in the Three-dimensional Zone of the Time Region

Turning now to the potentials in the three-dimensional zone, following our

earlier analysis of the dimensional situation (Section 5.1), we adopt the

fourth power expressions of the corresponding outside region (that is, the

time-space region) quantities from Eqs. (24)

VP3 = KP3.r4 and VG3 = KG3/r

4 (29)

with suffix 3 denoting the three-dimensional zone.

We know that the space-time progression acts away from unit space. In

the time-space region away from unit is also away from zero (the origin of

the conventional spatial reference frame), whereas in the Time Region

(that is, in less than unit space) away from unit is toward zero. This is the

reason why the space-time progression is an outward motion in the outside

region while it is inward in the Time Region. This is true in the one-

dimensional zone of the Time Region as much as in the three-dimensional

zone. But the 'unit' of the three-dimensional zone does not coincide with

the 'unit' of the one-dimensional zone. Its boundary is determined by the

apparent size of the atom in question. This is because the atom and the

three-dimensional zone are one and the same thing. (We must avoid

falling into the trap of imagining that first there is an atom, and that it

'occupies' the pre-existing three-dimensional zone!) In Eq. (7) of the

article on Wave Mechanics[1]

we have derived the following expression

for the size of the atom,

rA = 1.2 * A1/3

femtometers

where A is the atomic weight. Expressing this in the natural units as rAn,

we now note that the reference point for reckoning distance in the case of

VP3 is not the origin of the reference system but the point at rAn. Finally,

since the potential due to progression has to be attractive a minus sign has

to be introduced. Thus the expressions for the two potentials are

VP3 = -KP3.(rAn -r)4 and VG3 = KG3/r

4 (30)

Adding a constant term KI3 to take care of initial level of the potential

energy, we have the total expression for the potential of the three-

dimensional zone of the Time Region as

VT3 = -KP3.(rAn -r)4 + KG3/r

4 KI3 (31)

We note that this corresponds to what the conventional Quantum theorists

would call the nuclear potential. Our study indicates that Eq. (31) bears a

remarkably close qualitative resemblance to the potentials arrived at

through the scattering experiments. An unexpected feature of the

experimental data analysis was the occurrence of a repulsive core of small

radius. The Reciprocal System, on the other hand, actually predicts this

repulsive core, namely, VG3.

12. Conclusions

Let us summarize the highlights. Having resolved the riddle of the wave-particle

duality in an earlier article[1]

and understood the legitimacy of the wave picture in

the Quantum theory, attempt has been made to examine the foundation of its

mathematical formalism with the benefit of our knowledge of the Reciprocal

System. This proved productive in two ways: firstly it clarified the situation in

connection with the Quantum Mechanics, identifying some of its conceptual

errors. Secondly it gave scope to expand our knowledge of the Reciprocal System

in the form of new insights that would not have been possible otherwise.

i. The Schödinger equations were found to be valid general rules for the

exploration of the wave functions in the various situations.

ii. In the time-space region, speed can be vectorial (that is, directional in the

context of the three-dimensional spatial reference frame), whereas inverse

speed (like, energy) is scalar. In the Time Region, speed is found to be

scalar, whereas inverse speed is directional—directional in the three-

dimensional temporal reference frame. Variables of the latter type,

therefore, could take on inherently negative values and be represented by

complex numbers or quaternions as the case may be.

iii. The penetration of the wave associated with particle into the regions of

negative kinetic energy resulting from potential energy barriers is found to

be a genuine Time Region phenomenon.

iv. In a similar vein, it is found that the occurrence of a well-type potential

energy function in the Time Region leads to the limiting of possible values

of total energy to a discrete set.

v. Such an important empirical law as Pauli exclusion principle, which has

no theoretical explanation in the context of the conventional theory, could

easily be understood form the knowledge of the positive and negative

reference points brought to light by the Reciprocal System.

vi. Reasoning from the principles of the Reciprocal System the possible

potential energy functions of the Time Region relevant to atomic systems

are surmised. While they evince a close qualitative resemblance to the

empirically found potentials, detailed further study needs to be carried out

to see if they lead to the correct prediction of the properties pertaining to

spectroscopy, radioactivity and the scattering experiments.

On the whole there seems to be a prima facie case in favor of adopting the Quantum

Mechanics after purging it of its conceptual errors.

References

1. Nehru K.V.K., ―The Wave Mechanics in the Light of the Reciprocal System,‖ R

eciprocity, Vol. XXII, No. 2, Autumn 1993, p. 8

2. Larson D.B., The Case Against the Nuclear Atom, North Pacific Pub., Oregon,

USA, 1963

3. Nehru K.V.K., ―The Law of Conservation of Direction,‖ Reciprocity,Vol. XVIII,

No. 3, Autumn 1989, p. 3

4. Nehru K.V.K., ―On the Nature of Rotation and Birotation,‖ Reciprocity, Vol. XX,

No. 1, Spring 1991, p.8

5. Larson D.B., Basic Properties of Matter, International Society of Unified Science,

Utah, USA, 1988, pp. 102-3

6. Nehru K.V.K., ―The Photon as Birotation,‖ Reciprocity, Vol. XXV, No. 3, Winter

1996-97, pp. 11-16

7. Cohen B.L., Concepts of Nuclear Physics, Tata McGraw Hill, India, 1971, p. 38

8. Larson D.B., Nothing But Motion, North Pacific Publishers, Oregon, USA, 1979,

pp. 141-2, 165-7

9. Ibid., p. 155

10. Larson D.B., Basic Properties of Matter, op. cit., p. 8

Appendix I: Euler‘s Relations

Often calculations are facilitated by adopting exponential functions with imaginary

arguments in place of the sine or cosine functions, making use of Euler‘s relations

eia = cos a + i.sin a

e–ia

= cos a - i.sin a

which directly follow from the series expansions of these functions.

A number containing imaginary as well as real parts is called a complex number.

Complex numbers may be represented graphically on a rectangular coordinate system,

with the real part corresponding to the horizontal axis and the imaginary part to the

vertical axis. Any complex number can then be represented by a vector extending from

the origin and inclined at the angle a to the real axis. Thus A.ei t

represents a (radial)

vector of magnitude A rotating at the angular speed (t being time). It may be noted that

each of the inverse relations,

sin a = (eia - e

-ia)/2i

cos a = (eia + e

-ia)/2

represents a birotation.

Appendix II: The General Equation of a Constant Speed Wave

Let a wave of arbitrary but unchanging shape be traveling in the X-direction of the

stationary reference frame X-Y at a constant speed u. This wave appears stationary in a

reference frame X1-Y1 which moves at the same speed u along the X-direction. We can

then write

x1 = x - u.t ; y1 = y (i)

If the wave shape in the co-moving frame is given by y1 = f(x1), we have from Eq. (i)

y = f(x - u.t) (ii)

By the chain rule for derivatives we have

y/ x = (dy/dx1)( x1/ x) = (dy/dx1).1,

y/ t = (dy/dx1)( x1/ t) = (dy/dx1).(-u).

Therefore the relation between the two derivatives is

y/ x = -(1/u)( y/ t) (iii)

Similarly for a wave traveling in the -X direction we obtain

y/ x = +(1/u)( y/ t) (iv)

Now a repeated application of the above procedure yields

2y/ x

2 = (1/u

2)(

2y/ t

2) (v)

which is the governing equation of the wave function; and it is the same for waves

traveling in either direction of the X-axis.

—Reciprocity, Volume XXIV, Number 1, Spring 1995, p. 1; Revised Feb. 1998

NON-LOCALITY‘ IN THE RECIPROCAL SYSTEM

Though quantum theory is phenomenologically successful, it fails to throw any light on

the nature of the underlying physical reality. The Reciprocal System, true to its claim of a

unified and general theory, not only covers the ground of the quantum theory, but also

provides insight into the reality, basing on the new paradigm of motion as the sole

constituent of the physical universe. Its most important finding is the existence of

different domains of physical action, in which the rules of the game apparently differ.

Larson resolves all the difficulties the conventional theory is facing, by the knowledge of

the characteristics of these domains.

Thomas Kuhn, the renowned historian of science and its methodology, writing in The

Structure of Scientific Revolutions1, points out that as paradoxes and unsolved puzzles

mount up in the science of an era, a state of crisis results. This initiates the development

of new theories basing on a totally new paradigm. General acceptance of the new

paradigm, however, is not automatic. Old theories die hard because emotional

commitment, rather than pursuit of truth, invariably becomes the driving force. Continued

endeavor to consider and study the new paradigm by open-minded students will gradually

establish it in the scientific field. An interesting fact brought to light by Kuhn‘s study is

that as more and more human effort gets spent in understanding the new paradigm, it

becomes easier and easier for all people to understand it—as though entire mankind is

one at deeper levels. Kuhn also points out that as more people accept the new theory,

more evidence of it appears. Therefore, consideration of the recalcitrant problems in

science—especially, in physics—and showing how the Reciprocal System of theory

resolves them should be of interest to us. We shall consider a few of these:

Problem #1: Unification of the four fundamental forces of nature.

Scientists have not been successful in this enterprise of creating a grand unified theory;

especially gravitation has not yielded to the unification efforts.

Problem #2: The quantum measurement problem.

In essence, this may be described as follows: Consider, for example, the two-slit electron

interference experiment. While the intensity of the wave function represents the

probability of finding a particle, the actual measurement reveals the arrival of a particle

somewhere on the detector—say, at x1—which is a discrete event. In a sequence of

identical measurement situations, the location xi where the ith

particle makes its

appearance on the detector screen is totally random. But, the relative proportion

(frequency) of the particle appearances at any location strictly follows the wave pattern

predicted by quantum theory. How do the later particles ‗know‘ the history of the earlier

particles, and maintain the overall pattern? Even though individual particles come at

different times, there seems to be some sort of connection through time existing among

these!

Problem #3: Instantaneous connectedness in space.

Most accurate experimental verification of Bell‘s theorem has positively established that

correlated quantum entities—as in the EPR experiment—maintain a strong nonlocal

connection, however far they are separated in space. The surprising feature of this

nonlocality is that it is immediate, not attenuated by distance and not mediated by any

medium. Even though quantum theory predicts the experimental results correctly, the

inference of the existence of nonlocality is actually based on experimental facts—not on

the quantum theory—plus Bell‘s Inequality theorem. Therefore, nonlocality has to be

explained by any new theory that might encompass the quantum theory in the future.

Nonlocality has been one of the most baffling features of quantum phenomena, defying

all attempts to understand the nature of the reality underlying them.

Larson has discussed problem #1 in great length in some of his works2-6

and developed

the thesis sufficiently to establish that, in fact, the Reciprocal System is a unified and

general theory. The application of the Reciprocal System to the study of the quantum

domain, however, is urgently desiderative. Therefore, in the present discussion, we shall

limit ourselves to the consideration of problem #2 and #3, only. Let us begin by briefly

recapitulating the Reciprocal System of theory.

Conjugate Sectors of the Physical Universe

The two Fundamental Postulates of the Reciprocal System with which Larson7 starts are:

The physical universe is composed of one component, motion, existing in

three dimensions, in discrete units, and with two reciprocal aspects, space

and time.

The physical universe conforms to the relations of ordinary commutative

mathematics, its primary magnitudes are absolute, and its geometry is

Euclidean.

The motion which is the basic constituent of the physical universe is conceived by Larson

as scalar motion, or speed, the ratio of space magnitude to time magnitude. All

phenomena—radiation, matter, gravitation, electric charge, magnetism—come out as

different possible modes of motion. Larson deduces the following:

Corollary #1 (quantization): The two components of motion, namely space and

time, are quantized;

Corollary #2 (reciprocity): Space and time are reciprocally related to speed—an

increase in space is tantamount to a decrease in time, and vice versa;

Corollary #3 (symmetry): Both space and time have identical characteristics:

time has three dimensions like space, and space, too, progresses like time does.

Further, we find that the possible speeds in the physical universe fall into two natural

ranges: from speed zero to unity, and from unity to infinity. However, from the

Reciprocal System we learn that speeds exceeding unity do not manifest as motion in

space; instead, they manifest as motion in time (not the time travel of science fiction).

Larson calls the domain of the physical universe in which the speeds range from zero to

unity the material sector, and that in which the speeds range from unity to infinity (or

what comes to the same thing, the inverse speeds range from zero to unity) as the cosmic

sector. By virtue of the symmetry, all the phenomena of the material sector, which is the

sector we inhabit, are duplicated in the cosmic sector with the roles of space and time

interchanged.

Unit speed—which Larson identifies as the speed of light—is the boundary between the

two sectors, and forms the background of the physical universe. Larson refers to this

ever-present space-time progression at unit speed as the natural reference frame (which

we shall refer to as the N-frame). An immediate consequence of the space-time

progression is the observed recession of the galaxies (which is being mistakenly

attributed to a hypothetical ‗big bang‘). It also resolves the mystery of the propagation of

radiation. Radiation is not propagated at all; the space unit, in which the photon is

situated permanently, itself progresses.

For reasons explained by Larson4, gravitation always acts in opposition to the ubiquitous

progression of space-time. Since space-time progression acts outward in space (as well as

outward in time), gravitation in the material sector acts inward in space, and gravitation

in the cosmic sector (that is, cosmic gravitation) acts inward in time. So, to observers

anchored to material aggregates, like we are, space appears stationary and three-

dimensional, while time seems progressing one-dimensionally. The reference frame that

is natural to us is the familiar stationary, three-dimensional spatial reference frame

(which we shall refer to as the S-frame. See Figure 1).

In the cosmic sector, the result of cosmic gravitation acting inward in time is that the

three dimensions of time and the one-dimensional progression of space stand out. The

reference frame that is natural to the cosmic sector is the three-dimensional, temporal

reference frame (which we shall refer to as the T-frame).

In passing, we might recall that cosmic background radiation is the radiation emitted by

cosmic stars of the cosmic sector, and cosmic rays are the cosmic matter ejected from the

cosmic quasars. The uniformity and isotropy of both these items—which have no good

explanation in conventional theory—can be seen to stem from the fact that they originate

from cosmic matter which aggregates in three-dimensional time, but is randomly

distributed in the S-frame of the material sector.

The Time Region

Imagine two material particles moving towards each other in space. By virtue of the

quantization corollary, less than one natural unit of space cannot occur in physical

interactions. Therefore, the particles cannot approach each other nearer than one effective

unit of space in the S-frame. However, they can accomplish the equivalent of this, by

virtue of the reciprocity corollary, by moving outward in time. Inside an effective unit of

space, there cannot be motion in space; all motion has to be in time only. For this reason,

Larson refers to the domain of physical action inside the effective unit of space as the

time region.

According to the Reciprocal System, the natural direction of the space-time progression

is always away from unity. In the outer region (beyond unit space) away from unity is

also away from zero, and hence the space-time progression acts outward (1/1). In the

region inside unit space (the time region), however, away from unity is toward zero.

Hence, the apparent direction of the space-time progression in the time region is inward

(-1/1). Gravitation, as it always opposes the space-time progression, acts apparently

outward in the time region. In the Reciprocal System, the physical state—not to be

confused with the quantum mechanical state—is the result of reaching motion

equilibrium between these two above motions in the time region, and pertains to the

individual atom or molecule. It is not a group characteristic as in the conventional theory.

Corollary #4 (physical state): The solid state is the result of reaching motion

equilibrium in the time region in all three dimensions. The liquid state results when the

motion in at least one dimension comes out of the time region, and the gaseous state

when the motion is outside the time region in all three dimensions (that is, it is entirely in

the S-frame).

We have now come to an important juncture. Outside unit space, since all motion is in

space, the appropriate frame of reference is the conventional, three-dimensional

stationary reference frame (the S-frame). However,

Corollary #5 (frame-inversion): in the time region, since only motion in time can take

place, the appropriate frame of reference that should be adopted is the three-dimensional

temporal reference frame (the T-frame) (see Figure 2).

Summarizing: the physical universe comprises two sectors, the material and the cosmic

sectors, with the applicable reference frames being the S-frame and the T-frame,

respectively. In the material sector, there is a sub-region called the time region, whenever

interactions take place in less than one (effective) space unit, with the applicable

reference frame being the T-frame. (By symmetry, we have in the cosmic sector a sub-

region, which we can call the space region, with the applicable reference frame being the

S-frame.) We have depicted these schematically in Figure 3.

Quantum Nonlocality

The crucial point that should now be realized is that as a quantum entity—like an electron

or a proton—enters the time region, we should change the reference frame to reckon its

motion(s) from the S-frame to the T-frame, for the reasons delineated above. We note

that the origin (the zero-point) of the conventional reference frame (the S-frame) is at

zero speed in that frame. Similarly, the origin (the zero-point) of the temporal reference

frame (the T-frame) is at zero inverse speed in that frame. But zero inverse speed is

tantamount to infinite speed. Consequently,

Corollary #6 (spatial nonlocality): the origin of the T-frame would be apparently at all

places in our familiar S-frame and at the same time. In other words, it is nonlocal in

space.

Furthermore, Corollary #7 (non-trajectory): the concept of a particle trajectory in the S-

frame is not applicable from the point of view of the T-frame, for the obvious reason that

the origin of the T-frame is‗everywhere‘ in the S-frame.

In an earlier paper, Wave Mechanics in the Light of the Reciprocal System8, we have

shown that, by a consideration of the dynamical relationships,

Corollary #8 (w-p equivalence): a particle localized in the S-frame is equivalent to a

plane monochromatic wave from the point of view of a T-frame and vice versa.

We further pointed out that even though one should adopt the T-frame for the description

of the interactions in the time region, there is no way to accomplish this since we—as

creatures of the material sector—are unavoidably anchored to the S-frame. However, we

can achieve the same result by adopting the expedient of shifting from the particle picture

to the wave picture by virtue of Corollary #8. We can now see that to depict a quantum

entity as both a particle and a wave is wrong. It is a particle, as viewed from the S-frame,

and a wave as viewed from the T-frame (See Reference 8).

Before proceeding further, we have to note that there are two significant differences

between the T-frame of the time region, and the T-frame of the cosmic sector. Referring

to Figure 3, we would like to point out:

(i) the speed and inverse speed ranges pertaining to the S-frame of the material sector and

the T-frame of the cosmic sector respectively meet at unit magnitude;

(ii) the speed and inverse speed ranges pertaining to the S-frame of the material sector

and the T-frame of the time region respectively meet at zero magnitude. The

mathematical fact that while the inverse of unity is unity, the inverse of zero is infinity,

introduces a profound difference here.

Firstly, the time region is the result of crossing the unit space boundary, while still in the

material sector (S-frame), whereas the cosmic sector is the result of crossing the unit

speed boundary in all the three dimensions of motion—mark it: three dimensions of

motion, not three dimensions of space—and consequently moving out of the material

sector, altogether. The motion germane to the cosmic sector is true motion in time, and

cannot be represented in the S-frame. On the other hand, the motion in time germane to

the time region, does not manifest to us as motion in time, per se, but, by virtue of the

reciprocal corollary, shows up as equivalent motion in space (or as Larson puts it—

motion in equivalent space, which is reciprocal space). This is, in fact, a general

principle:

Corollary #9 (equivalent space): so long as the net speed is on the material sector side

of the speed range, the motion in time that might occur as a minor component of the

overall speed configuration, acts as a modifier of the motion in space which is the major

component. In other words, it manifests as motion in equivalent space, rather than motion

in time.

Secondly, we have seen by Corollary #6 that as we switch from the S-frame to the T-

frame on entering the time region, the origin of the T-frame appears ‗everywhere‘

at‗infinite speed.‘ Further, temporal dimensions are related to spatial dimensions only

scalarly, that is, there is no geometrical (vectorial) relationship between temporal and

spatial dimensions. Consequently, if we have a case of two distinct particles of the S-

frame entering the time region, there is no reason why the three switched dimensions

pertaining to one particle should hold any geometrical relationship to the three switched

dimensions pertaining to the second particle. The origin (that is, the zero-point) of the

two switched frames, however, is common since it is ‗everywhere‘ at ‗infinite speed.‘ So,

Corollary #10 (multiple dimensions): in the case of the frame-inversion (Corollary #5)

of two interacting particles, unless inhibited by special conditions, we end up with six

apparently different dimensions, three each of the two T-frames, respectively. Indeed, we

require 3n dimensions to represent n particles.

Scientists call this multi-dimensional manifold the configuration space to distinguish it

from the conventional, three-dimensional space. We would like to emphasize here that

this multiplicity of dimensions arises solely out of the scalar nature of the relation

between temporal dimensions and spatial dimensions, and not because the physical

universe has a plethora of dimensions. Their occurrence is limited only to the sub-

regions.

Corollary #11 (temporal nonlocality): when the interaction eventually comes out from

the time region back into the conventional frame, as at the measurement site, the

reference frame has to be switched from the T-frame of the time region, back to the

familiar S-frame. Like in the case of Corollary #6, this frame-switching entails the

phenomenon of nonlocality. But this time, it is nonlocality in time, since the switching is

T->S rather than S->T, and so the origin of the S-frame appears ‗everywhen‘ at ‗infinite

inverse speed‘ from the point of view of the T-frame.

Quantum Interpretation Problem

The quantum theory has been successful and accurate in predicting the results of all the

experiments related to quantum phenomena. But, it is a theory that does not provide any

insight into the nature of the physical reality underlying these phenomena. It merely

works like a recipe book for cookery. Therefore, scientists have subscribed to different

views regarding reality—varying all the way from the ‗official‘ Copenhagen view, which

denies the existence of any underlying reality, to the other extreme view of the‗many

worlds‘interpretation of Everett. The question is yet unsettled. We shall show how the

Reciprocal System, with its new paradigm, resolves the mystery and knits all the strange

and seemingly weird features of the quantum world into one, logical whole.

Let us first note two quantum facts:

(i) The attributes of the quantum entities fall into two types. The static attributes, like

mass, spin and electric charge, are innate to the entity. The dynamic attributes, like

position and momentum, seem to depend jointly on the entity and the reference frame of

the measurement.

(ii) Even in the case of dynamic attributes, so long as the quantum entity is not forced to

go through tiny holes, or confine itself to tiny volumes; the entity appears to have a

definite position and momentum—like a classical entity.

Both these above facts are in total consonance with the Reciprocal System finding that

the non-classical behavior stems from the entry into the time region, which is a sub-

region (tiny hole, tiny volume) of the translational motion (position, momentum or

velocity).

Let us consider the familiar electron interference experiment. We have an electron source

that shoots a coherent beam of electrons toward a phosphor screen target. Initially, we

find a bright spot on the screen where the electrons hit. We then introduce a barrier into

the beam provided with two small slits. If the width of the slit is of the order of the

wavelength of the electrons in the beam, we observe the light and dark fringes of the

interference pattern on the screen, instead of the single, bright spot.

There are four versions of quantum theory: the Matrix Mechanics (Heisenberg), the

Wave Mechanics (Schrödinger), the Transformation Theory (Dirac) and the ‘sum-over-

histories‘approach (Feynman). All of these give the same final result, but Feynman‘s

method gives us a better clue as to the nature of the wave function than, for example,

solving Schrödinger‘s wave equation. Feynman makes two unusual assumptions, that:

(1) a single electron takes all possible paths, and

(2) no path has a greater preference.

He implements these by assigning the same amplitude to each path. The history of each

path, then, determines its phase for any location on the target screen. Feynman then

arrives at the amplitude of the electron‘s wave function by summing up the wave

amplitudes of all possible paths the electron can take to reach that particular location

from its source.

Feynman‘s assumptions, that the single electron takes all possible paths, at the same time

and with equal probability, are extremely outlandish. But the conclusions that we reach

from the deductions of the Reciprocal System are exactly the same! Firstly, on entering

the time region, the particle picture is to be replaced by the wave picture, due to the

frame-inversion and the p-w equivalence corollaries. Then, the simultaneous existence of

all possible paths is the result of the spatial nonlocality corollary.

As the electron beam brightness is gradually reduced such that we have electron by

electron hitting the target, rather than an ensemble all at one time, we fail to observe the

interference pattern in real time. However, if we place a photographic plate adjacent to

the phosphor screen and wait long enough for sufficient electrons to accrue, the pattern

could once again be seen, despite the fact that the individual electrons that are arriving hit

the screen at purely random locations. It appears as though it does not matter whether the

electrons come at once as an ensemble, or they come at different times—the statistical

wave pattern, observed in either case, is exactly the same. But, this is exactly what we

should expect by the temporal nonlocality corollary! The same S-frame would appear to

be present at all moments, nullifying the time delays between the individual electron

events, as though merging them into a single ensemble.

The EPR Experiment

In certain atomic events, two correlated photons in what is called a twin state are emitted

in opposite directions. In the particular experiment, the photons are polarization-

correlated. In this state, either of the photons does not seem to have any definite

polarization until measured, even though it is definite that they have mutually opposite

polarization. Experiments show that, if we force one of them to take up a specific

polarization direction at the first measurement site, the polarization of the twin invariably

shows up (at the second measurement site) in the opposite direction, even if the two

photons are so far separated in space as to be beyond the reach of the signal that could

travel at light speed between them. The results apparently indicate that twin photons are

casually connected even if they are beyond the ‗'light cone.‘

Discussing the primary motions in the physical universe, we have pointed out9 that an

intrinsically scalar quantity (motion) can manifest in the reference system as a pair of

oppositely directed vector quantities, and not as a lone vector. A bivector acts as a true

scalar: it does not have a specific direction before manifestation, and can assume any

bidirection on manifestation. The twin state is a state of bi-polarization—bi-momentum,

in the EPR original version—which can split into two oppositely directed polarizations in

any specified direction.

Explaining the EPR phenomenon, Larson states in a communication10

: ―A photon

occupies a position in the three-dimensional spatial reference system and also a position

in the analogous three-dimensional temporal reference system. If two photons originate

coincidentally in such a manner that they separate spatially, they may remain coincident

in time; that is, in the same time unit or an adjacent unit. In this case, a change that takes

place in one photon will cause an appropriate change in the photon to which it has a

connection in time, just as it would if the two were connected in space.

"This idea that contact in time is subject to the same considerations as contact in space is

not new to the students of the Reciprocal System of theory. It enters into a number of

physical situations, particularly in the reverse application, where contacts in space are

maintained unchanged when separation takes place in time. As an example...{see} The

Universe of Motion11

, in which I point out that this explains the containment of the high

speed matter in the interiors of the giant galaxies.‖

The Junction of the Living and the Non-living

In Figure 3, we have depicted the various speed domains of the physical universe which

we derived from the theory. We now pursue the logical deduction further. We have seen

that the space-time progression in the time region is inward in space (1/1), whereas in the

space region of the cosmic sector it is inward in time (1/1). The time region begins at the

zero inverse speed of the T-frame, and ends at -1 inverse speed of the M-frame.

Similarly, the space region begins at zero speed of the S-frame and ends at -1 speed of the

M-frame. At unit level, speed and inverse speed are effectively identical (1/1 = 1/1).

Consequently, we get the complete picture if we unify the M-frame of the space region

and the M-frame of the time region. This is depicted in Figure 4.

Since gravitation always acts in opposition to the space-time progression, it acts outward

in the time region. It also turns out that since the space-time progression acts inward in

time in the space region of the cosmic sector, cosmic gravitation in the space region acts

outward, too.

Corollary #12 (frame-merging): the final result is that the action of gravitation in the

time region of the material sector, on one hand, and of cosmic gravitation in the space

region of the cosmic sector on the other, are both outward.

Larson, in Beyond Space and Time12

extends the application of his theory to the realms of

life and consciousness. He notes that in the material sector, all structures spontaneously

move from states of greater organization (or order) to states of lesser organization. In

other words, the available energy goes on decreasing. But, in the case of living units, like

the cells or higher life, the organization level is either maintained or increases, against all

odds. It is still an enigma how life is possible at all, in the material universe, if we stick to

purely mechanistic explanations.

Larson notes that while available energy goes on decreasing in the material sector, the

inverse is true in the cosmic sector, namely, the available inverse energy decreases

spontaneously. That is, the available energy increases! He, therefore, discovers that what

we call a living cell comes into being when the purely material structural unit is

connected to and governed by a control unit built of the cosmic structures. By Corollary

#12 above, we can readily see how the linking of the cosmic unit with the material unit is

possible, and how they can interact, since the nature of the governing force (motion) is

identical in both of them. This control, of course, appears nonlocal.

Conclusion

The development of the Reciprocal System of theory finds space and time to be discrete,

reciprocally related, and of symmetrical properties. It discovers another sector of the

physical universe wherein the applicable speeds range above the speed of light. Inside the

quantum of space there is a sub-region, called the time region, with non-trivial space-time

characteristics that directly lead to peculiar quantum phenomena. To a large extent, the

development is in consonance with the procedures of quantum theory. In addition, it

supplies what quantum theory fails to offer—a lucid understanding of the nature of

quantum reality.

The Reciprocal System has rational explanations for perplexing quantum issues like:

wave-particle duality

spatial nonlocality

temporal nonlocality

breakdown of the trajectory concept

multi-dimensional configuration space

connection between the living and the non-living

In closing, we need to remind ourselves that the Reciprocal System is not just another

new theory, but one that stems from an entirely new paradigm. The new paradigm, that

motion is the sole and fundamental constituent of the physical universe, immediately

repudiates the age-old practice of viewing space as a container for physical objects and

time as a canvas on which the drama of the universe unfolds. Even though they appear so

in the local environment, in reality they are the contents of the universe. The recognition

that Reality need not be limited to what is representable in space and time opens the door

for a truly scientific approach not only to the study of the physical universe, but also of

living systems, para-psychological phenomena, and, indeed, consciousness itself.

References

1. Kuhn, Thomas S., The Structure of Scientific Revolutions, (University of Chicago

Press, Chicago, IL, 1976).

2. Larson, Dewey B., The Case Against the Nuclear Atom, (North Pacific Publishers,

Portland, OR, 1963).

3. Larson, Dewey B., Beyond Newton, (NPP, 1964).

4. Larson, Dewey B., Nothing But Motion, (NPP, 1979).

5. Larson, Dewey B., The Neglected Facts of Science, (NPP, 1982).

6. Larson, Dewey B., Basic Properties of Matter, (International Society of Unified

Science, Salt Lake City, UT, 1988).

7. Larson, Dewey B., Nothing But Motion, op. cit., p. 30.

8. Nehru, K.V.K., ―The Wave Mechanics in the Light of the Reciprocal System,‖

Reciprocity XXII (2), Autumn, 1993, pp. 8-13.

9. Nehru, K.V.K., ―The Law of Conservation of Direction,‖ Reciprocity XVIII (3),

Autumn, 1989, pp. 3-6.

10. Larson, Dewey B., Letter to David Halprin, Nov. 3, 1984.

11. Larson, Dewey B., The Universe of Motion, (NPP, 1984), p. 385.

12. Larson, Dewey B., Beyond Space and Time, (Tucek and Tucek Book Publishers,

Tuscon, AZ, 1996).

SOME THOUGHTS ON SPIN

Detailed study of the characteristics of the so-called nucleus of the atom has not been

carried out by Larson. Therefore we have undertaken this much needed investigation and

been reporting our results.[1-3]

It has been our experience that such investigation hardly

ever proceeds in a strictly serial manner. Rather, it is more akin to the process of fitting

the pieces of a jigsaw puzzle together. Nascent understanding gradually builds up and

evolves from various seemingly diverse starting points, the concepts on each line of

thinking modifying the ones on other lines, and in turn themselves getting modified by

the latter. Eventually a nexus of coherent structure ensues. The thoughts presented in this

article too constitute such a preliminary group of ideas that might serve to crystallize

some of the earlier concepts enunciated on the topic of the so-called atomic nucleus.

§1. Spin-1 and Spin-½.

The one-dimensional rotational space (angle) as well as the two-dimensional rotational

space (solid angle), both are customarily regarded as dimension-less in the context of the

conventional three-dimensional spatial reference system (the time-space region). This

practice, therefore, does not distinguish between one-dimensional spin (angular

momentum) and two-dimensional spin (angular momentum). We end up measuring both

in units of erg-sec. In order to clarify the issue let us first note that the dimensions of

momentum are energy/speed. In the present case these are Planck's constant, h, divided

by space unit. If the motion is translational the space unit concerned is taken as

centimeter. If the motion is rotational the space unit concerned is taken as radians. The

basic unit (quantum) of one-dimensional angular momentum is taken as erg-sec (spin-

1), which is the same thing as (h ergs)/(2¶ radians/sec). The denominator, 2¶ radians/sec,

can be seen to be one-dimensional rotational speed. On this basis the quantum of two-

dimensional angular momentum is to be taken as (h ergs)/(4¶ steradians/sec), which is the

same thing as ½h erg-sec (spin-½). We can immediately see that particles like photons

(the bosons), which have integral spin, are based on one-dimensional rotation, whereas

those like proton and electron (the fermions), which have half-odd integral spin, are

based on two-dimensional rotation.

In the conventional theory it is recognized that the quantum state of the integer-spin

particles cycles at 2¶ radians and that of the half-odd-integer-spin particles cycles at 4¶

radians. What is needed to clarify the physical fundamentals is to recognize that in the

latter case the value is 4¶ steradians rather than 4¶ radians--and hence it really pertains to

two-dimensional rotation.

§2. Unbounded Phase

There is yet another unforeseen feature of rotation in the Time Region. In the

conventional time-space region, after rotating through an angle of 2¶ radians one comes

back to the starting point. An angle of radians cannot be distinguished from an angle of

+ 2n¶ radians. In the Time Region, however, this need not be true. Speaking of spin-½

particles Bhandari states: "...studies... bring out the additional fact that phase changes of

2n¶ are real, physical and measurable, something that is often ignored. For example, our

experiments make it obvious that the difference between +¶ and -¶ or the difference

between ¶ and 3¶ is measurable and that it is unnatural to restrict the value of the phase

that is being continuously monitored to be between 0 and 2¶ . The need to incorporate

this unbounded nature of the phase variable presents a promising program for the

future."[4]

§3. Non-degenerate Spin

A one-dimensional spin is represented by a single spin coordinate, say 1, and could be

either {+} or {-}. The two-dimensional spin requires two spin coordinates, 1 and 2,

and is categorized into four domains: {+ +}, {- +}, {- -} and {+ -}. From the point of

view of the time-space region there is a degeneracy: {+ +} and {- -} are effectively

identical, and {- +} and {+ -} are effectively identical. However, these four domains

remain distinct in the three-dimensional zone of the Time Region itself, necessitating a

quaternion representation rather than one of an ordinary complex number.

§4. Helicity

Unlike in the case of the one-dimensional rotation, there is an internal chirality or

handedness arising in the case of the two-dimensional rotation out of the multiplication

of the two constituent one-dimensional rotations. Thus the combinations {+ +} and {- -}

both result in the positive sign and may be treated as Right-handed. In similar manner,

the combinations {- +} and {+ -} both result in the negative sign and may be treated as

Left-handed. The Quantum theorists recognize the existence of this internal chirality

when they posit the characteristic of Helicity. They do not, of course, have the benefit of

the insight given by the Reciprocal System regarding its origin.

§5. Photon Wave

According to the Reciprocal System the photon is situated permanently in the space unit

(of its origin) of the background space-time progression. As these space units are ever

moving scalarly outward, away from one another, no two photons can ever contact each

other. However, both may be able to contact a gravitating particle since the latter is

moving scalarly inward, and can enter the space unit in which a photon is situated. That

bosons, the class of particles of which photon is a member, do not interact with each

other is an observed fact. If this is so, one may ask, how do we explain the phenomena

like interference and diffraction, wherein the waves associated with the photons are

apparently interacting! The answer from the Reciprocal System has already been

explained in detail elsewhere[3]

where we have shown that the photon interacts with itself,

by virtue of the nonlocality feature of the Time Region. The wave associated with the

photon is actually in the Time Region and is to be represented by complex vibration

rather than a real vibration. The projection on the real axis appears sinusoidal.

§6. Point Particles

The reason why photons and electrons appear to measurement as point particles is this:

they are units of rotational space--not of linear space.

§7. Complex Wave

The wave function of a particle in the one-dimensional zone (that is, the zone of one-

dimensional rotation) of the Time Region is to be represented by a complex wave. This

follows from the fact that the equivalent speeds pertaining to this zone that correspond to

the one-dimensional speeds of the conventional spatial reference frame (the time-space

region) are two-dimensional.[2]

Thus

= { 1 i 2},

where 1 and 2 are real and the symbol i represents the operation of orthogonal rotation,

from the real to the imaginary axis, such that i2 = -1. It must be noted that denotes a

one-dimensional rotation. The probability density as applicable in the time-space region

is, of course, given by the square of the modulus, | |2 (or * where * is the complex

conjugate of ).

§8. Quaternion Wave

What we have called the three-dimensional zone of the Time Region is the zone of two-

dimensional rotation of the atom. We have shown[2]

that the equivalent speeds pertaining

to this zone that correspond to one-dimensional speeds of the time-space region are four-

dimensional. Consequently, the wave function germane to this zone needs to be

represented by a four-component mathematical object. Since we have represented the

one-dimensional rotation pertaining to the Time Region by a complex quantity { 1 i 2},

we recognize that to represent two-dimensional rotation (pertaining to the Time Region)

we need to introduce an additional imaginary dimension j. Thus, replacing 1 and 2

respectively by 1 (={ a j b}) and 2 (={ c j d}) which are complex, we have for the

wave function of this zone

= { 1 i 2} = {{ a j b} i{ c j d}} = { a i c j b ij d}

= { a i c j b k d},

where we define k = ij, and a, b , c and d are all scalar.

As can be seen this is a quaternion, with the following basal elements: the identity

operator 1 (which keeps a quantity unchanged) and the three orthogonal rotation

operators i, j, and k. The properties of the operators are:

12 = 1; 1i = i1 = i; 1j = j1 = j; 1k = k1 = k;

i2 = j

2 = k

2 = -1;

ij = -ji = k; jk = -kj = i; ki = -ik = j.

The probability density, once again, is given by

* = a2 + c

2 + b

2 + d

2.

In the conventional theory the theorists find that the speeds of the nucleons approach the

light speed because of the large ‗nuclear‘ interaction energies (on the order of tens of

MeV) concerned. In view of these large speeds they find it necessary to resort to the

Relativistic Quantum Mechanics. Some of the celebrated theoreticians who worked on

the relativization of the wave equation, like Paul Dirac, were led by mathematical

necessity to adopt wave functions with four components like we have been talking of.

§9. Dimensionality of Space

In a closed group of operators, like [1 i j k], the result of the combination of any number

of the basal elements is also a member of the same group. The result of any such

combination can be known only if all the possible binary combinations of the elements

are first defined in terms of the basal elements i, j and k themselves (besides, of course,

the identity operator, 1). Let there be n basal elements (excluding the unit operator 1) in a

group. Then the number of unique binary combinations of these elements, in which no

element occurs twice, is n(n-1)/2. We can readily see that a group becomes self-sufficient

(finite) only if the number of binary combinations of the basal elements is equal to the

number of those basal elements themselves, that is

n(n-1)/2 = n.

The only definite solution for n is 3. (Zero and infinity are other solutions.) Therefore if

we regard space (time) as a group of orthogonal rotations, its dimensionality has to be

three in order to make it self-sufficient dimensionally. Otherwise the number of

dimensions either has to shrink to zero, or proliferate to infinity.

References

1. Nehru K.V.K., ―Wave Mechanics in the Light of the Reciprocal System,‖

Reciprocity, Vol. XXII, No. 2, Autumn 1993, pp. 8-13

2. Nehru K.V.K., ―Quantum Mechanics as the Mechanics of the Time Region,‖

Reciprocity, Vol. XXIV, No. 1, Spring 1995, pp. 1-9. (See especially Section 5.1)

3. Nehru K.V.K., ―Non-locality in the Reciprocal System,‖ Reciprocity, Vol. XXVI,

No. 1, Spring 1997, pp. 7-14

4. Bhandari R., ―Geometric Phase in Interference Experiments,‖ Current Science,

Vol. 67, No. 4, 25 August 1994, p. 230

HIGH ENERGY PHYSICS AND THE RECIPROCAL

SYSTEM

―...during times of crisis new theories arise. Meanwhile, adherents of the old paradigm in

crisis fight to retain it against the revolutionaries who are outrageously explaining

anomalies by treating nature as if she were a rabbit or squirrel instead of what every self-

respecting scientist knows she is: a duck.‖

J.P.Briggs and F.D.Peat, Looking Glass Universe, p. 28

Great advances in technology in the recent decades of this century have made it possible

to amass a wealth of experimental data of unprecedented scope and variety. Theory in the

areas of Particle Physics and Astrophysics has been subjected to repeated revisions to

cope up with the observed facts. Especially in the field of High Energy Physics (HEP)

exciting things have been happening. The Orthodoxy is becoming more tolerant to wild,

if not crazy ideas and inventions of thought. In this backdrop, it might be desirable to

survey the vicissitudes of the physical theory, hoping that we might learn something from

the history.

Little Fleas on Little Fleas on Little Fleas on...

Physicists recognize two revolutionary experiments in the 20th

century that resulted in

significant revision of the previous ideas about the fundamental particles. One was the

Rutherford scattering experiment of 1911, which revealed that the atom was not a

uniform solid object it was thought to be, but is largely hollow with a compact solid

nucleus which is nearly five orders of magnitude smaller than the atom itself. Subsequent

theory conjectured that the nucleus is made up of particles even more fundamental,

namely, the protons and the neutrons. The second experiment was the electron-proton

scattering experiment of 1968 at Stanford. With the probing energies scaled up to the

MeV range the scattering pattern revealed that the proton and the neutron were not the

solid compact objects they were thought to be, but are largely hollow with extremely

compact, point-like objects inside. The theoreticians named these point-like particles the

quarks.

Originally only three quarks (‘u,‘ ‗d‘ and ‗s‘) were invented to explain protons, neutrons

and pions. But soon, a theoretical inconsistency cropped up as the unstable hadron

resonance known as delta++

was experimentally discovered. According to the existing

quark scheme this resonance has to be composed of three u-quarks in a configuration that

is symmetric under interchange of any two quarks. This, however, was not in accordance

with the well-established Pauli Exclusion Principle, which states that no two fermions

can be in the same quantum state. Therefore, instead of abandoning the quark model, the

inconsistency was evaded by inventing purely ad hoc, a new quantum attribute—

fancifully called the ‗color‘ charge—which serves to distinguish the three u-quarks.

That now we have u, d and s quarks each in three color states is, of course, not the end of

the story. The discovery in 1974 of the J or psi particle required the positing of a fourth

quark (the ‗c‘), and in 1977 of the Upsilon particle necessitated another quark with a

brand new quantum attribute (the ‗b‘). At the present time, we have as the fundamental

particles six types of quarks, each in three different color states, along with equal number

of antiquarks. In addition, the Standard Model (SM) propounds the existence of six

leptons—particles which do not experience the ‗strong‘ force. These are the electron, the

muon and the tau- particle and their corresponding neutrinos ve, vµ and vT along with, of

course, the antiparticles of all of these.

Problems in the Current Theory

Though the SM is a highly successful theory of the HEP and covers the ‗weak,‘ the

electromagnetic and the ‗strong‘ interactions, its most flagrant shortcoming is the

omission of gravitation. Physicists have come up with the characteristic length at which

‗quantum gravity‘ is expected to manifest as nearly 10-35

m. This is seventeen orders of

magnitude smaller than the characteristic length of the ‗weak‘ interaction, namely, about

10-18

m. Such a stupendous scale difference is quite baffling to them.

It is an embarrassing fact that free quarks have never been observed. Consequently it is

theorized that interactions between quarks must be extraordinarily strong and perhaps

irrevocably confining. The theorists do not know whether quarks are truly fundamental

entities or have further structure. Nor do they know if quarks are ever-lastingly stable or

decay spontaneously. Further, the SM contains many parameters, such as the masses of

the quarks and leptons, the values of the fundamental charges etc. which cannot be

derived from the theory but have to be taken as given. Then there is the generation

problem: even though only two quarks (u and d) and two leptons (e- and ve) occur

preponderantly in nature, yet nature possesses two more copies (four more quarks and

four more leptons) of this basic structure, which latter are assumed to be relevant, if at all,

in the first few seconds after the so-called Big-bang.

Occurrence of infinities plagues the mathematics of the theory, at the various levels of the

energy ranges. Solving one problem introduces new problems at the new levels. For

instance, solving the mass problem of the ‗weak‘ bosons, W± and Z

0, by the Higgs

mechanism involves the prediction of a new particle—the Higgs boson—the

experimental discovery of which is an outstanding problem. The concept of

supersymmetry—wherein all bosons have fermionic superpartners and vice versa—is

invented to circumvent the infinities. However, in the bargain, a host of new particles are

predicted, generating new ignorances at the same rate as developing new understanding.

Finally, the theorists are investing great hopes in the superstring theories, in which one-

dimensional singularities, instead of point-like particles, are envisaged as the ultimate

constituents of the universe. Supersymmetry is an essential ingredient of the theory. One

of the problems besetting the superstring theory is the occurrence of several versions of

it, without a clear hint of the actual one. The theory requires the superstrings to exist in

large number of space-time dimensions (like 10). This requires figuring out ways of

reducing the superabundance of the dimensions.

Vindication of these ideas comes from experimental confirmation and the future of HEP

is threatened by a serious crisis. The range of energies that would be needed to test the

new theories is 105 to 10

19 GeV. The known acceleration technologies can take us up to

the 104 GeV level in the coming decade. Beyond that, the veterans in the field fear that

the HEP is near its end. The deepening crisis is making the physicists look for

unconventional ideas, no matter how weird they might appear. Unfortunately, they are

looking for these new ideas still within the ambit of the old paradigm only. They seem to

be committing the mistake of the proverbial drunkard, who was found searching in the

middle of the night, right under the street light, for something he lost in the darkness

beyond! Recognition of the truth of the Reciprocal System of theory, which is based on a

totally new basic paradigm, is getting procrastinated because it upsets some of our most

cherished notions. But this is what a paradigm change at the most basic level is bound to

do. Planck‘s discovery of the quantum nature of energy is a good example. It was greeted

with indifference and disbelief, if not open hostility.

The Deepening Crisis

It is now apparent that applying iteratively the program that ‗particles are built out of

more fundamental particles‘ has resulted in the proliferation of ‗fundamental‘ particles

and led us from complex theory to more complex theory. The situation is reminiscent of

the accumulation of epicycles in the Ptolemaic system. Once again it might be pointing

out to us, if we are able to take the hint, that the basic paradigm underlying the whole

edifice of the HEP has been wrong.

Particle physicists have innovated the concept of force, which was originally defined as

acceleration times mass. The idea of action-at-a-distance was repugnant to the modern

scientist who thought it was spooky and belonged to the dark era of scientific ignorance.

He rather believed in the localness of interaction: a force could be passed on from A to B

only if A is physically touching (contiguous in space to) B, or through some other thing

touching both. This belief logically led him to the idea of ‗exchange force,‘ that when

two entities are separated in space a force could be transmitted between them only

through the intermediary of a particle—the field quantum—propagating in space. This is

part of the paradigm on which the superstructure of modern physics has been erected.

The physicists have even disregarded factual information from their own field and

subscribed unstintingly to this paradigm. For example, there is no empirical evidence that

gravitation is propagated at finite speed or that it is propagated at all. But current

Orthodoxy presumes that gravitation has a field quantum, the graviton, and that it

propagates at the speed of light.

Meanwhile a new factor has emerged into the situation. Carefully conducted experiments

in the recent decades have established beyond doubt that quantum non-locality is a fact—

particles widely separated in space are able to influence each other, without the need for

any medium or intermediary and without any effects of attenuation by distance, even

when they are beyond each other‘s light cone. Since this is a factual finding, it must be

incorporated into whichever theory of physics that might come into ascendancy if it has

to be true.

Notwithstanding these developments HEP has continued on its program of building

particles out of more fundamental particles, postulating at each structural level the

existence of ‗carriers of interaction‘—the mesons, the ‗intermediate vector bosons,‘ the

gluons and the like. Now the question arises whether there is a way to build physical

theory basing on established facts including non-locality without having to re-introduce

the unacceptable spooky action-at-a-distance? Well, this is exactly what Larson has

accomplished!

The New Paradigm

Larson has laid out, in his published works1-6

the general outline of his theory, covering

all the physical fields. All of the phenomena whose origin is a mystery in the current

theory—like that of the high energy cosmic rays—come out as logical deductions from

his fundamental Postulates about the characteristics of motion. He has carried out the

development far enough to establish a prima facie case for a general theory. However,

considerable amount of theoretical work still needs to be done to extend the application

of the Reciprocal System to greater detail.

Following the lead given by observational facts, and not based on speculations, Larson

has endeavored to review the entire physical situation and come up with a new structure

of physical theory, which has come to be called The Reciprocal System of theory.

Larson‘s principal finding is that the physical universe is composed entirely of discrete

units of motion. Space and time occur only as the two reciprocal aspects of motion and

are quantized. In the new paradigm, space-time plays the role of the

GRAVITATIONAL DEFLECTION OF LIGHT BEAM

IN THE RECIPROCAL SYSTEM

The gravitational deflection of light beam owes its origin to the same factor as that

causing the excess perihelion precession of the planets—namely, the coordinate time

component associated with independent motion [1]. But there is a significant difference

between the movement of a planet and the movement of a photon in the sun‘s

gravitational field. In the former case, the motion of the planet is an independent motion.

On the other hand, the motion of the photon is due to the background space-time

progression and is introduced by our use of the stationary reference system. This has an

important bearing on the manner in which the spatial effect of the coordinate time

manifests itself in the motion, in the two cases, as will be explained below.

Gravitational Motion and the Gravitational Potential

The gravitational motion of a material atom is inward in space. But in a celestial object

like a star, which is a spatial aggregate of such units, the inward motion of each unit is

counterbalanced by the interaction with the contiguous neighbors. The scalar space-time

direction of this counterbalancing force is in opposition to that of gravity and has the

same magnitude as the gravitational motion and is equal to the escape velocity, v, at that

location. The escape velocity can be evaluated by noting that the centrifugal force on a

mass m situated at a radial distance r will be equal to the gravitational force on it by the

central mass M. Thus

m v²/r = G Mm/r² or, v² = GM/r (1)

where G is the gravitational constant.

Coordinate Time

The coordinate time increase associated with a speed v is given by

v²/c² fraction of unit/unit (2)

This is in the radial direction of the counterbalancing force explained in the para above

[2].

Let the radial distance of the photon at its closest approach to the sun be r0. Since v² is a

point function of the radial distance given by eq. (1), the increase in the coordinate time

for a change of radial distance from the ―outer gravitational limit‖ [3] to r0 will be given

by

g-0 = (v0²/c²) - 0 = v0²/c² (3)

(where v0² = GM/r0. The circumferential space equivalent [2] of this coordinate time

increase is v0²/c². But the photon is already moving at unit speed—one unit of space per

unit of time—in the forward dimension. As such no further spatial shift is possible in the

direction of its motion (unlike in the case of the planetary motion). However, in view of

its scalar nature, the spatial effect of this coordinate time increase will manifest itself in a

spatial dimension other than the one in which the photon is already progressing at unit

speed. Thus the photon gets displaced in the inward radial direction coinciding with the

direction of gravity.

Now the question arises why this effect should manifest radially inward instead of

radially outward direction. The situation here can be easily understood if we look to an

analogy from the motoring/generation principle in electrical engineering. Current flowing

in a particular direction, in the conductor of a motor armature situated in a magnetic field

forces the armature to rotate. But the rotation of the conductor (in the same magnetic

field) now generates what we call the ―back e.m.f.‖ and causes a current flow in the

conductor in the opposite direction (opposing the original current), establishing a natural

equilibrium. Analogously, in the present case, the coordinate time increase resulting from

a radially outward equilibrium motion manifests as a circumferential spatial shift. While

this gives rise to the excess perihelion motion in the case of orbitting planets, in the case

of the photon such motion not being possible, the spatial shift, v0²/c², shows up in the

radial direction opposite to that of the originating motion: that is, it manifests in the

radially inward direction.

We have so far considered the increase in coordinate time only during half of the transit,

from the outer gravitational limit to r0. The coordinate time change associated with the

remaining journey, from r0 onwards to the outer gravitational limit on the other side, will

similarly be

g-0 = (0 - v0²/c²) = - v0²/c² (4)

This will again manifest as a spatial shift of magnitude v0²/c². It must be noted that the

negative sign of the coordinate time increase, in eq. (4) above, has no relevance in

deciding the direction of its spatial effect. The spatial effect is always additive,

irrespective of the sign of the coordinate time because of the scalar nature of the reiation

between the dimensions of time and the dimensions of space. Thus the total spatial shift

in the direction perpendicular to that of progression is given by

0 = v0²/c² (5)

in fraction of unit/unit or simply the deflection in radians.

Interaction Cross-section

However, this deflection, given by eq. (5) is not necessarily effective in its entirety. This

requires the consideration of the way in which an independent motion, as against the

fictitious motion of the space-time progression, can be brought to bear on a photon or a

material particle. An independent motion can be imparted to a material atom, for

example, because it can offer a resistance in the direction of the motion being applied.

The resistance to motion is due to the speed displacement in that dimension. For instance,

the reason why we don‘t find sub-atomic particles participating in the scalar inversion

from the cosmic sector to the material sector, which gives us the cosmic rays, is that they

are unable to build up speed in the vacant dimension in which they do not have any

displacement. In contradistinction, the motion of the space-time progression applies in

the vacant dimension, as in the case of a photon, for example.

As such, in the present case, the full force of the deflection motion is applicable to the

photon only if the plane of vibration of the photon is parallel to the deflection motion:

that is, if it is in the direction of the gravity.

Let us take a look at the photon in the direction of its progression. Referring to the figure,

let the direction perpendicular to the plane of the paper represent the direction of the

photon progression.

The diameter of the circle is one natural unit of space

representing the amplitude of the photon vibration. Any

diameter of the circle, like PP, now represents the plane of

vibration of the photon (looking end-on). OD is the

direction of the deflection motion. Suppose the photon

vibration happens to be in the YD direction, the full

impact of the deflection motion, 0 , can be imparted to it.

On the other hand, if the plane of vibration is XB, since

the photon does not carry any displacement in the YD

direction, none of the deflection motion can be imparted to

the photon. In fact, when the plane is tilted at an angle ø to YD, the fraction of the

deflection motion that can be transferred to the photon is proportional to cos ø.

In an unpolarized beam all orientations are equally existent and the average value of the

resistance—which I will call the ―interaction cross-section‖—that makes the motion

transfer possible can be obtained by

½

-½ p(ø) cosø dø 2

p ————————— = — (6)

(½ (-½

So finally, from eqs. (5) (6), the total effective deflection is

= v0²/c²) · (2/ ) = v0²/c² (7)

Or, using eq. (1), we have

= GM r0c²) (8)

Polarized Beam

It may be noted that the above result is identical to what General Relativity predicts.

However, the result differs from the Relativity value in the case of a polarized beam of

radiation. Consider the case of a fully polarized beam. Let the piane of polarization be

represented by PP (fig. 1), inclined at angle ø to the direction of gravity, YD From what

has been said above, the total effective gravitational deflection will be

p = v²/c² cos ø = 2 (GM/r0c²) cos ø (9)

In the more general case where the degree of polarization in each direction varies, we

proceed as follows. Let the power p in any plane (of polarization) be a function of the tilt

angle ø:

p = p (ø).

Then the average interaction cross-section is given by

½

-½ p(ø) cosø dø

p ————————— (10)

½

-½ p(ø) dø

The total effective deflection, then, is

p = 0 · p

This aspect of the theory, namely, the dependence of the gravitational deflection on the

polarization characteristics of the traversing beam provides a possibility to

observationally test it in comparison with the theory of Relativity.

References

1. Larson, Dewey B., Nothing But Motion, North Pacific Pub., Portland, Oregon,

1979, pp. 99–100.

2. Larson, Dewey B., Beyond Newton, North Pacific Pub., Portland, Oregon, 1964,

p. 126.

3. Larson, Dewey B., Quasars and Pulsars, North Pacific Pub., Portland, Oregon,

1971, p. 166.

NEW LIGHT ON THE GRAVITATIONAL

DEFLECTION OF RADIATION PATH

In an earlier paper I have discussed the effect of gravitation on the bending of the locus of

a photon.(1)

Even though the role played by the coordinate time associated with the

gravitational motion in deflecting the path of light was correctly depicted therein, I

believe that the mathematical implications were not correctly brought out. Especially, in

the case of equation (6) there, though its existence was correctly recognized, its physical

significance was misconstrued. The present paper, therefore, attempts to overcome these

shortcomings and derives the mathematical expression for the angle through which the

path of a light beam is deflected in the vicinity of a mass.

According to the Reciprocal System, an independent motion of speed v has associated

with it an increase in the coordinate time amounting to (v/c)² sec/sec (c being the speed of

light). In the case of a one-dimensional motion, like that of a planet orbitting the sun, or

of a photon grazing the sun‘s limb, I have pointed out(2)

that the circumferential spatial

effect arising out of the coordinate time amounts to 3(v/c)² sec/sec. It was further

explained that, in the case of a photon this spatial effect manifests itself in the radially

inward direction since no further circumferential effect is possible, as the photon is

already moving at unit speed in the latter direction.(3)

The gravitational speed v at any radial distance r from a mass M is shown(4)

to be

v² = GM/r

where G is the gravitational constant. Thus, we have the rate of coordinate time increase

at a radial distance r outside a mass M as

dtc/dt = 3(v/c)² = 3 GM/rc² (1)

where tc represents the coordinate time and t the clock time.

As shown in Fig. 1, let the straight line ABC represent the locus of a photon passing the

sun situated at S. With SB perpendicular to AC, B is the point of closest approach to the

sun. Let SB = ro. The equation of the line ABC in polar coordinates, with the origin at S,

is given by

r0 = r cos (2)

where r is the radial distance at any angle q measured counterclockwise from SB.

Substituting r from eq. (2) into eq. (1), we have

dtc/dt = (3 GM/roc²) cos (3)

Now we note that the gravitational effect of any mass aggregate, according to the

Reciprocal system, does not extend up to infinity, but becomes zero at a limiting distance,

which Larson calls the ―outer gravitational limit,‖ d1. As such, we need to compute the

coordinate time increase in the case of the transitting photon, starting from the outer

gravitational limit on one side (toward A, in Fig. 1), up to the outer gravitational limit on

the other side (toward C, in Fig.1). Larson worked out the value of the outer gravitational

limit for the sun to be nearly 13350 light years. As this will be very large compared to ro,

we find that the limits on the two sides are given by 1 = – /2 and 2 = + /2.

Hence, using eq. (3), the average rate of coordinate time increase during this transit from

1 to 2 is given by

dtc

av

2 dtc

— ( —— d / ( 2 - 1)

dt 1 dt

/2

= (3 GM/roc²) cos d /

- /2

= 6 GM/ ro c²

sec/sec (4)

Since the total distance traveled is 2 d1, the total transit time is

t = 2 d1/c sec (5)

Therefore the total coordinate time gained during this clock time t is

dtc

av

tc,tot = t * — = (6 GM/ ro c²)*(2d1/c)

dt

= 12 GM d1/ ro c³ sec (6)

In Fig. 2 the directions of approach and departure of the light beam are shown as ABC‘

and BC respectively. CC‘ represents the spatial shift in the radial direction arising out of

the coordinate time component and is given by

x = c * tc,tot = 12 GM d1/¹ ro c² cm (7)

Finally, from Fig. 2 we can see that the angular deflection, according to the Reciprocal

System is given by

dRS = x/d1 = 12 GM/ ro c² radians (8)

The corresponding expression from General Relativity is

dGR = 4 GM/ro c² (9)

The discrepancy between the two formulae can be seen to be

dRS/dGR = 3/ (10)

The value calculated from the Reciprocal System formula, for the sun, is 1.67 arcsec,

whereas the General Relativity value is 1.75 arcsec. The reported values vary from 1.5 to

1.8 arcsec.

References

1. K.V.K. Nehru, ―Gravitational Deflection of a Light Beam in the Reciprocal

System,‖ Reciprocity XI(1) (Spring, 1981), 28.

2. Idem, ―Precession of Planetary Perihelia due to Coordinate Time,‖ Reciprocity

XIV(1) (Autumn, 1985), 11-13.

3. Idem, ―Gravitational Deflection. . .‖ op. cit., 29.

4. Ibid., eq. (1), p. 28.

5. D. B. Larson, The Universe of Motion (Portland, Ore.: North Pacific Publishers,

1984), p. 201.

GRAVITATIONAL REDSHIFT ACCORDING TO THE

RECIPROCAL SYSTEM

If the frequency of a photon is f ‘, at a location where the gravitational potential is GM/r,

then according to Relativity the gravitational redshift is given by

zg = (f ‘- f)/f = -GM/rc² (1)

where

f = frequency of the radiation in its inertial rest frame

G = gravitational constant

M = mass of the object

r = radial distance of the photon, and

c = speed of light.

The account of the gravitational redshift in the Reciprocal System may be given as

follows:

The gravitational motion of any material particle is inward in space, toward all other

space-time locations. In a celestial object such as a star, which is an aggregate of such

material units, this scalar inward motion of the individual units is counterbalanced by the

physical continguity of the neighboring units. This counterbalancing force is in the scalar

direction of the space-time progression, being opposite to gravity, and has the same

magnitude as that of the gravitational motion at that location. Thus its measure is equal to

the escape velocity, v. Now, we can identify the coordinate time increase at a particular

location to be v²/c² (in fractions of units/unit), just like in the case of excess perihelion

shift. This means that the total time involved per unit of clock-time is [1 + (v²/c²)] units.

The frequency, f, denotes the number of oscillations per unit of time in a gravity-free

situation. In the location under gravity, then, this frequency becomes f number of

oscillations per [1 + (v²/c²)] units of time. Thus

f ‘ = f/(1 + (v²/c²), or f ‘/f = 1/[1 + (v²/c²)] (2)

Therefore, the redshift is

zg = f ‘/f - 1 = -(v²/c²)/[1+ (v²/c²)] (3)

Comparison of the Results of the Two Theories

The escape velocity, v, is evaluated as follows: The centrifugal force on a mass m

rotating at the orbital speed of v at radius r is equal to the gravitational force by the

central mass M, under equilibrium situation. Thus

mv²/r = G Mm/r², i.e., v² = GM/r (4)

Substituting this in eq. (1) and rearranging, we have, according to Relativity,

f ‘/f = 1 - (v²/c²) (5)

Comparing this with eq (2) we can see that 1 - v²/c² 1 + (v²/c²)-1 for small values of v.

The divergence between them can be detected only (i) if the present experimental

accuracies can be improved by many orders of magnitude, or (ii) if the test could be

carried out for extremely large gravitational potentials such as encountered in the white

dwarfs etc.

PRECESSION OF THE PLANETARY PERIHELIA

DUE TO CO-ORDINATE TIME

1. Introduction

The first of the two Fundamental Postulates of the Reciprocal System from which Larson

derives every aspect of the physical universe is:

―The physical universe is composed entirely of one component, motion, existing in three

dimensions, in discrete units, and with two reciprocal aspects, space and time.‖ [1]

The primary implication of the Postulate is that the properties of either space or time are

the properties of both space and time, except that space and time are reciprocally related

as motion. This means, inter alia, that space is a progression like time is, and that time is

three-dimensional. While the space progression is observable as the recession of distance

galaxies, the three-dimensionality of time is not so directly apparent.

It is essential to note that the three dimensions of time are not the spatial dimensions: nor

is there anything space-like in them. In any situation, the total time comprises of two

components: (i) the clock time, which is a uniform progression and (ii) the three-

dimensional coordinate time (analogous to the three-dimensional coorinate space of a

stationary reference system).

Besides other things, the concept of coordinate time in the Reciprocal System explains

and derives the characteristics of supernovae, the white dwarfs, the pulsars, the quasars,

the compact X-ray sources and the cosmic rays–without taking recourse to concepts like

degenerate matter, the curvature of space-time, etc... All the so-called Relativistic effects

come out, in the Reciprocal System, of the existence of this additional time component.

In fact, the effect of the excess advance of the perihelion of an orbiting planet arises out

of the accumulation of the coordinate time from its orbital motion. ―As long as the orbital

velocity is low, the difference between the clock time and the total time is negligible, but

the velocity of Mercury is great enough to introduce an appreciable amount of

coordinate time and during this added time the planet travels through an additional

distance.”[2]

2. The Theoretical Evaluation

According to the Reciprocal System, an independent motion (like gravitation) of speed v

has associated with it an increase of coordinate time amounting to v²/c² unit per each unit

of clock time (c being the speed of light). [3] In order to calculate the excess orbital

movement, Larson argues like this: ―Since the gravitational motion is inward, the scalar

space-time direction of the orbital motion is outward, and the computed time increase is

radial. To obtain the circumferential space equivalent of this linear time increase, we

must multiply by ¶.‖[4]

Thus, according to Larson the total coordinate time increase is ¶ v²/c² s/s. In the quotation

just cited, what Larson states regarding the scalar direction of the orbital motion as being

outward, is understandable. But what the expression ―the computed time increase is

radial‖ is expected to connote is difficult to see. For, ―...no matter how many dimensions

it may have, time has no direction in space.‖ [5] To be sure, it is true that time has a

property called ‗direction in time‘, but this is a purely temporal property and ‗directions

in time‘are not in any way determined by directions in space. Consequently, the

coordinate time increase associated with gravitation (or with any independent motion) is

a scalar addition. The words ―...to obtain the circumferential space equivalent of this

linear time increase, we multiply by ¶,‖ do not, therefore, depict the truth, except

pointing out that the necessity of having to include in the calculations a factor amounting

to ¶ has been recognized.

The true state of affairs can be understood if we recall that gravitation is a three-

dimensional scalar motion. If v is the gravitational speed, then the coordinate time

increase per each scalar dimension is v²/c². The total coordinate time increase, therefore,

is 3 v²/c². The orbital motion of the planet is one-dimensional (scalar). As such, the

effective coordinate time increase, as applied to the orbital motion, is 3 v²/c². The same is

true in any other case where the motion is one-dimensional, like, for example, that of a

photon grazing the sun. On the other hand, if we are considering the effect of the

coordinate time increase due to gravitation on an atom situated in the gravitational field,

the result is different. Since the atomic rotation is three-dimensional, the coordinate time

increase effective per dimension is 3 v²/c² / 3 = v²/c² only. This is the value which causes

the gravitational redshift, for instance.

Thus, the rate of coordinate time increase at any speed v is given by:

where tc represents the coordinate time and t the clock time.

Consider the elliptical orbit of a planet around the sun, with the sun situated at the focus.

The equation of the ellipse in polar coordinates, with the center at the focus is given by

where

r = the radial distance of the planet, at any angle ø measured from the perihelion

l = the semi-latus rectum = a (1 - e²) (2-a)

e = the eccentricity of the ellipse

a = the semi-major axis

In an earlier article [6] I have pointed out that the gravitational speed, v, at any distance r

outside of a mass M is given by

where G = the gravitational constant.

Using equations (1), (2), & (3), we have the rate of coordinate time increase at a given

location on the orbit as

in units of s/s or radians/radians. The incrase over an angle of dø radians is

Therefore, the total increase from ø = 0 to 2 ¶ radians (that is, one revolution) is

(Note that equation (7) is applicable to parabolic, as well as hyperbolic orbits with l as the

semi-latus rectum). Finally, using relation (2-a), the perihelion advance, according to the

Reciprocal System, is given by

The corresponding formula from the General Relativity is

where P = the orbital period of the planet. In order to compare the two formulae, we use

the relation

for the solar system. Then equation (8) becomes identical to the Relativity expression,

given in equation (9).

References

1. Larson, Dewey B., Nothing But Motion (North Pacific Publishers, Portland, OR,

1979), page 30.

2. Larson, Dewey B., Beyond Newton (North Pacific Publishers, Portland, OR,

1964), page 85.

3. Larson, Dewey B., Nothing But Motion, op. cit., pages 99-100.

4. Larson, Dewey B., Beyond Newton, op. cit., page 126.

5. Larson, Dewey B., Nothing But Motion, op. cit., page 73.

6. Nehru, K.V.K., ―Gravitational Deflection of Light Beam in the Reciprocal

System,‖ Reciprocity XI (1), Spring 1981, page 28.

GLIMPSES INTO THE STRUCTURE OF THE SUN

PART 1- THE NATURE STELLAR MATTER

1. Introduction

Larson has discussed the development of the Reciprocal System of Physical Theory to a

great extent in his two works, Nothing But Motion [1] and The Universe of Motion, [2]

the latter work especially dealing with the astronomical applications. Stars are the basic

building blocks of the large-scale universe. As such, the knowledge of their internal

constitution and dynamics constitutes an important step in the understanding of the

macroscopic universe. Larson developed the general structure and the details of evolution

of the stars of various types. [2] The detailed study of their internal structure has not yet

been carried out in the context of the Reciprocal System. Therefore, such a study was

taken up as an initial attempt to fill this gap and some of the results obtained are reported

herein.

In Part I, we will discuss the general properties of matter at very high temperatures,

applying the principles and concepts developed by Larson in his works cited. Since the

sun is the only star about which a wealth of obserational information is available in great

detail, an attempt is made to explain some of the solar phenomena–phenomena so well

known but whose nature is by no means clearly understood by the scientists–utilizing the

conclusions reached in Part I. This is reported in Part II. It is hoped that these will be

found interesting to the researchers of the Reciprocal System and stimulate further

investigations.

According to the Reciprocal System, the energy generation in the stars is by the atomic

disintegration process. [3] Larson shows how the operation of this source at the central

regions of the stars gives rise to a fluctuating energy output, its periodicity showing up

even in the case of the stable stars, though not as conspicuously as in the case of the

intrinsic variables. Thus, he attributes the 11-year periodicity of the sun to this fluctuation

of the internal energy generation. [4]

The basic scalar motion that constitutes the material atoms is a speed displacement in

time. Both the thermal motion and the electric charge of the atoms are displacements in

space. At a large enough temperature, called the thermal destructive limit, the combined

space displacement due to the thermal motion and the positive electric ionization is

sufficient to neutralize one of the rotational time displacement units constituting the atom

and reduce it to the linear status (radiation). Preliminary calculations indicate that the

thermal limit of the elements is greater than two natural units of temperature. [5]

Accordingly, the material in the central region of a star has to be at temperatures beyond

the unit level, and this gives rise to significant results as explained below.

2. Discovery of a New Source of Magnetism

Larson refers to the speeds in the range of one to two natural units as the intermediate

speeds, and those above two units as the ultra high speeds. In a similar manner, we will

refer to the temperatures greater than one natural unit, but less than two natural units, as

intermediate temperatures, and those beyond as ultra high temperatures. In addition, we

will call the temperatures below the unit level as the low temperatures. This connotation

of ―low‖ will be used throughout our discussion, and must be so remembered.

In the intermediate range, the motion is in time instead of space. However, where the net

total motion is still in space, the motion due to the intermediate speed component will be

in the space equivalent of time, that is, in equivalent space. [6] As such, the effects of the

thermal motion when the temperature is in the intermediate speed range, are in equivalent

space, rather than in the space of the conventional reference system. An important, direct

consequence is that this thermal motion would be two-dimensional, as is all motion in

equivalent space. [7]

In view of the fact that both the thermal motion, and the motion constituting the positive

electric charge, are of the same type–namely, one-dimensional vibratory space

displacements (except that the former is a linear vibration, and the latter is a rotational

vibration), thermal motion readily engenders electric ionization when present in sufficient

intensity. This thermal ionization, of course, is a known phenomenon.

In a similar manner, the thermal motion in the intermediate range, being of a two-

dimensional linear vibratory space displacement, readily produces on the basic units of

matter present, a two-dimensional rotational vibration, with space displacement. We can

immediately recognize that the latter, namely the two-dimensional rotational vibration

with space displacement, is nothing but the magnetic charge! Thus, throughout the

stellar interiors, where the thermal motion is above the unit level, magnetic fields of

intensity proportional to the strength of the thermal motions are always generated.

Instead of relegating the role of the magnetic fields as minor, we now find that the

presence and configuration of these thermally generated magnetic fields largely

determine the structure and dynamics of the stellar phenomena. Since the interiors of all

stars have to be at temperatures above the unit value if energy generation by thermal

destruction is to take place at all, intense magnetic fields must invariably be present in all

of them. This does not, however, mean that these fields reach up to the stellar surface in

their full intensity. Only few field lines seem to penetrate through the outer bulk of

material that is at lower (that is, less than the unit) temperature, as we will see later.

While fields as strong as 10,000 gauss might be generated at the core, the surface field

may be of the order of tens of gauss to a fraction of a gauss.

3. Nature of the Matter and Radiation at Very High Temperatures

We will now summarize some important conclusions reached by Larson, and add our

own discussion to their further implications concerning the states of matter and radiation

at the upper range speeds.

3.1 The Radiation Intensity

Larson states:

―...thermal radiation originates from linear motion of the small constituents of the

material aggregates in the dimension of the spatial reference system. The effective

magnitude of this motion is measured as temperature.‖

―Inasmuch as motion at intermediate speeds is in the same scalar dimension as the motion

at speeds below unity, the vibrational motion that produces the thermal radiation

continues into the upper speed ranges. But because of the reversal at the unit speed level,

the temperature gradient in the intermediate region is inverse; that is, the maximum

intensity of the thermal vibration, and the resulting radiation, is at the unit speed level,

and it decreases in both direction.‖[8]

In the intermediate region, an increase in temperature (equivalent to a decrease in inverse

temperature) decreases the thermal radiation.

As a consequence of this, if we try to identify a thermal source at the upper end of the

intermediate temperature range by observing the intensity of its radiation, it would appear

to be at a low temperature, of an order that is not beyond the ken of terrestrial experience.

A further fact of significance is that, ―...all radiation from objects with upper range

speeds ... is polarized as emitted. Where a lower polarization is observed, this is due to

depolarizing effects during travel of the radiation. A three-dimensional distribution of

radiation is impossible in a two-dimensional region.‖ [9]

3.2 The Inverse States of Matter

3.2.1 Radiation Spectrum

―Furthermore, the radiating units of matter are confined within one unit of time, at the

upper end of the intermediate temperature range (the lowest inverse temperatures), just

as they are confined within one unit of space at the lower end of the normal temperature

range.‖[10] ―The physical state of this material is the temporal equivalent of the solid

state: a condition in which the atoms occupy fixed positions in three-dimensional time,

and the emission is modified in the same manner as in the solid state.‖ [9] This radiation

has a continuous spectrum.

3.2.2 Analogy Between the Phenomena of the Time Region and Those of the

Space Region

Corresponding to the three states of matter in the low temperature range–solid, liquid,

and gaseous–there ought to be three more states in the intermediate temperature range,

which we may call the inverse gas, the inverse liquid, and the inverse solid, in that order

of increasing temperature (decreasing inverse temperature).

In order to see how the effects of motion in the space region (occuring at the far end of

the intermediate speed range) manifest themselves to observation in the time-space

region (the conventional three-dimensional, spatial reference system), we will first

consider how the effects of motion in the time region are known to manifest in the time-

space region, and then draw an analogy. We can tabulate:

Motion

Originating Effects as manifested in the conventional reference frame

In the time

region

(i) discontinuous (or limited in extent) in the space of the reference

system

(ii) continuous in the time of the reference system

In the space

region

(iii) discontinuous (or limited in extent) in the time of the reference

system

(iv) continuous in the space of the reference system

An example of the time region phenomena is the crystal or grain of the solid state–which

is of limited spatial extent, but exists continually in time. In the case of the space region

phenomena, in view of item No. (iii) tabulated above, the spatial aggregations of the

atoms concerned do not persist continually: they keep forming and dissolving into fresh,

new aggregates.

3.2.3 The Lifetimes

The lifetimes of these space region aggregates, that is, the times elapsed before they

dissolve to give place to new aggregates, depends upon the rate at which the heat transfer

is taking place. In the case of solidification from liquid to solid state, a high heat transfer

rate produces smaller grain size (more number of grains per unit of space). In the case of

the inverse states we are considering, this should result in less number of ―grains‖ per

unit of time. This means that the lifetimes are longer with higher heat transfer rates.

3.2.4 The Spatial Configuration

The motion in time has no direction in space, and does not manifest as a movement of

individual atoms, as such, in space. However, there are some observable effects on

aggregates of atoms. For instance, the scalar direction of thermal motion is always

outward. The expansion in time resulting from the intermediate temperature shows up as

a contraction in equivalent space. Or conversely, if matter at the upper temperature

ranges is cooling to the low temperature region, we would expect it to expand. We will

have occasion to refer to this phenomenon in the context of sunspots, later.

3.3 Thredules: the Seventh State of Matter

We have seen how the intermediate range temperatures give rise to three more states of

matter–the inverse states, as we are calling them–in addition to the three known states

pertaining to the low temperature range. The entry of the temperature into the ultra high

range, beyond the two-unit limit, results in a yet another, seventh, state of matter.

The third unit of motion is already beyond the two-unit limit of the dimension of scalar

motion that is coincident with the dimension of the conventional spatial reference system.

It pertains to a second scalar dimension incapable of representation in the conventional

reference system.

But:

―...some of the change of position due to the unobservable ultra high speeds is

represented in the reference system in an indirect manner... the outward motion of the

ultra high speed... is applied to overcoming the inward gravitational motion... . Inasmuch

as that gravitational motion has altered the position (in the reference system) of the

matter..., elimination of the gravitational motion results in a movement of this matter

back to the spatial position that it would have occupied if the gravitational motion had not

taken place. Since it reverses a motion in the reference system, this elimination of the

gravitational change of position is observable.‖ [11]

―Thus, even though the speeds of the particles... are in the ultra high range, the

observable thermal effect is in the low speed range, and the radiation that is produced has

a line spectrum like that of an ordinary hot gas.‖ [9]

―Inasmuch as the spatial motion component of the ultra high speed motion is in a second

scalar dimension, it is perpendicular to the normal dimension of the reference system.

This perpendicular line cannot rotate in a third dimension because the three-dimensional

structure does not exist beyond the unit speed level. Thus the representation of the motion

in the reference system is confined to a fixed line...‖

―... this type of motion does not distinguish between the direction AB and the direction

BA, since the only inherent property of the motion is a magnitude... any linear motion

originating at a given point is therefore divided equally between two opposite directions

by the operation of probability.‖ [12] The matter at ultra high temperature, therefore,

takes the shape of a sheaf of expanding rectilinear threads. We will call these

unidirectional filaments ‗thredules.‘ There is ample observational evidence of this

slender, thread-like structure associated with the ultra high speeds like in the cases of the

remnants of Type II supernovae, [13] and quasar explosions. [14]

Before passing on to the next section, we must mention that since beyond the unit

temperature the magnetic field is a concomitant phenomenon, we find that every thredule

is invariably associated with magnetic flux lines running along its longitudinal axis.

4. Magnetism and Co-Magnetism

In section 2 we have seen how the upper range temperatures generate magnetism. The

basic motion constituting this magnetic charge is a two-dimensional space displacement

of rotational vibration type, and so is the same as that of a magnetic charge in the material

sector, in general. However, the fact that the thermally-generated magnetism we have

been considering occurs in equivalent space, rather than the space of the conventional

reference system, introduces a new element into the situation that produces some

unfamiliar effects as viewed from that reference system.

4.1 The Lines of Force

It is usual to try to understand the action of magnetic charges with the help of the concept

of ―lines of force.‖ This is a legitimate practice inasmuch as force is a property of scalar

motion, as Larson explains. [15] Referring to Figure 1a, we see that the magnetic lines of

force are in tension in the longitudinal direction, and have a positive pressure in the

transverse direction; that is, they tend to contract along their length, and to diverge out in

the perpendicular direction.

Figure 1 - Magnetic vs Co-magnetic Lines of Force

Because the direction, in the context of the conventional reference system, reverses

whenever a motion crosses a unit boundary (even though it continues in the same natural

direction), the behavior of the magnetic lines of force in the equivalent space would be as

shown in Figure 1b. They tend to expand in the longitudinal direction, and to concentrate

in the transverse direction. In other words, like poles attract and unlike poles repel (see

Figures 2a and 2b). In view of this reversal of the apparent directions, we will give this

phenomenon a new name, and call it co-magnetism.

Figure 2 - Magnetic vs Co-magnetic Poles

4.2 Domain Configurations of Magnetism and Co-magnetism

We will now highlight some significant patterns of the field line arrangements that are

derived from the nature of magnetism and co-magnetism respectively, as these will have

a bearing on the explanation of the magnetic field structure of the sun.

Figure 3 - Least Energy Configuration

Consider two pairs of parallel field lines, with the field directions as shown in Figure 3a.

Let us refer to the field line coming out of the plane of the paper and represented by a

plus sign as the ―north line‖ and the one antiparallel to it, and represented by the minus

sign, as the ―south line.‖As can be seen from the figure, in the case of normal magnetism,

two parallel north (or south) lines repel each other, while north and south lines attract

each other. If we now imagine a process that generates equal numbers of south and north

lines, all of which remain parallel to each other, but are free to move in the lateral

direction, the least energy configuration would be one in which there are no large-scale

magnetic domains, as shown in Figure 4a.

Figure 4 - Least Energy Arrangement

Turning now to the case of co-magnetism, we find that two north (or south) lines attract

each other, while north and south lines repel each other (Figure 3b). Suppose that in a co-

magnetic process, equal numbers of north and south lines are generated in such a way

that they are constrained to remain parallel to each other, but are free to migrate laterally.

If initially the south and north lines are randomly distributed in space, lines of the same

type tend to aggregate and form separate magnetic domains. At the same time, domains

of opposite polarity tend to repel each other and move apart (see Figure 4b). If the total

volume in which these domains exist is restricted, then the eventual result of the gradual

merging of the domains of the same polarity would be the complete bifurcation into two

domains of opposite polarity.

5. Summary of Part I

Summing up some important conclusions reached regarding the structure of matter at

very high temperatures:

1. Matter in the ultra high temperature range manifests as slender, unidirectional,

expanding threads that keep forming and dissolving. These have been named

Thredules.

2. Thermal motion beyond unit level produces magnetic fields.

3. Inasmuch as these fields are in equivalent space, the magnetic effects in the three-

dimensional reference system are the opposite of the normal magnetic effects.

This phenomenon is named Co-magnetism.

References

1. Larson, Dewey B., Nothing But Motion (North Pacific Publishers, Portland, OR,

1979)

2. Larson, Dewey B., Universe of Motion (North Pacific Publishers, Portland, OR,

1984)

3. ibid., page 41.

4. ibid., pages 61-62.

5. Nehru, K.V.K., "Intrinsic Variables, Supernovae and the Thermal Limit,"

Reciprocity XVII (1), Spring, 1988, page 20.

6. Larson, Dewey B., Universe of Motion, op cit., pages 70-73.

7. Larson, Dewey B., Nothing But Motion, op.cit., page 155.

8. Larson, Dewey B., Universe of Motion, op cit., page 215.

9. ibid., page 224.

10. ibid., page 215-216.

11. ibid., page 213.

12. ibid., page 214.

13. ibid., page 223.

14. ibid., page 364.

15. Larson, Dewey B., The Neglected Facts of Science (North Pacific Publishers,

Portland, OR, 1982), pages 9-12.

16. Sakurai, Kunitomo, Physics of Solar Cosmic Rays (University of Tokyo Press,

Japan, 1974), page 53.

17. ibid., page 55.

18. Bray, R.J., and Loughhead, R.E., Sunspots (Chapman & Hall, New York, 1964),

page 244.

19. Sakurai, Kunitomo, op. cit., page 64.

20. ibid., page 63.

21. ibid., page 94.

22. Bray, R.J., and Loughhead, R.E., op. cit., pages 242-243.

23. ibid., page 276.

24. ibid., pages 151, 154.

25. Larson, Dewey B., Nothing But Motion, op. cit., page 107.

26. Bray, R.J., and Loughhead, R.E., op. cit., page 132.

27. ibid., page 140.

28. ibid., pages 66-67.

29. Bray, R.J., Loughhead, R.E., and Durrant, C.J., The Solar Granulation (Dover

Publishers, 1979), pages 41, 86.

30. ibid., page 88.

31. Larson, Dewey B., Universe of Motion, op. cit., pages 248-249.

Part I: The Nature of Stellar Matter

Part II: The Solar Interior and the Sunspots

GLIMPSES INTO THE STRUCTURE OF THE SUN

PART II- THE SOLAR INTERIOR AND THE

SUNSPOT

In Part I of this paper, we have endeavored to develp some important properties of matter

at very high temperatures–those that prevail in the stellar interiors. Utilizing the

principles developed there, we will now attempt to deduce the internal structure of the

sun. For ease of reference, the section numbers, the figure numbers, and the reference

numbers are all continued from Part I.

6. Morphology of the Solar Core

We have noted that the energy generation in the stars is by the thermal destruction

process, and that preliminary calculations [5] establish that the thermal destructive limits

of the elements are in the ultra high temperature range. So the central region of the sun is

composed of matter at the intermediate and the ultra high temperatures. The matter in the

ultra high temperature core manifests as an ensemble of thredules, which we have seen to

be thin, straight, continuous filaments (Section 3.3). We now note that both these

thredules, and the embedded co-magnetic field lines that run along the length of these

filaments are expanding in the longitudinal direction (Section 4.1).

The directions of the thredules have to be randomly oriented in the three-dimensional

space of the reference system when no factor providing for a preferred direction exists.

But since the sun is rotating, the axis of rotation does provide such a preferential

direction. As such, the great majority of the thredules form in a direction parallel to the

axis of rotation.

Once the general direction of the thredules is fixed, we can deduce that, by the operation

of probability, half of these will have north magnetic flux lines threading through their

length, while the remaining half will have south magnetic lines (the qualifications ―north‖

and ―south‖ being merely chosen for the sake of convenience of reference, and do not

mean to point to any external magnetic field).

6.1 Formation of the Two Sheaves of Thredules

For reasons explained in Section 4.2, the south and north thredules segregate into two

principal domains of opposite magnetic polarity. Given no other factors, therefore, one

would expect the ultra high temperature core to assume a configuration in which two co-

axial, cylindrical sheaves of north and south thredules respectively occur.

Since we have seen (Section 4.2) that two parallel co-magnetic lines of the same

magnetic field direction attract each other, the minimum energy configuration for either

of the sheaves mentioned in the preceding paragraph would be one in which all the

thredules are mutually parallel. However, at the interface between the two sheaves we

find thredules of opposite magnetic field direction occuring adjacent to each other. Since

parallel co-magnetic lines of opposite field directions tend to repel (Section 4.2), we see

that the above arrangement of the two sheaves does not yield the least energy

configuration for the interface.

Therefore, the above configuration would give way to another in which the interficial

energy is also reduced. This could be readily achieved by tilting the adjacent thredules of

the two sheaves in opposite directions, while, at the same time, keeping the adjacent

thredules of any one sheaf mutually parallel. This would render the cylindrical shape of

each sheaf into a hyperboloid. The final configuration of the two sheaves of thredules at

the beginning of a solar cycle will be that of two co-axial hyperboloids, as shown in

Figure 5. For the sake of clarity, only a few of the thredules of each sheaf are shown in

the figure.

Figure 5 - Formation of Thredules in the Solar Core

(schematic diagram only–not to scale)

Let us denote the angles of inclination of the thredules of the inner and outer sheaves with

respect to the direction of the axis of rotation of the sun by øi and øo respectively.

Remembering that the thredules tend to maximize their length (Section 3.3) and so do the

co-magnetic lines (Section 4.1), one can easily compute that the optimal values of øi and

øo would be ±45°. (More involved calculations point out that øi would be around 50°, and

øo around -40°.) In Figure 5, the inner thredules are shown inclined such that øi = +45°,

while the outer thredules with øo = -45°.

6.2 Effect of the Progress of the Solar Cycle

The thredule structure does not extend beyond the ultra high temperature core. The co-

magnetic field lines running along the thredules, however, jut out into the outer layers.

When they emerge out into the low temperature regions where the magnetic effects are in

the space of the reference system, instead of in equivalent space, lines of opposite field

directions join in U-loops and start exerting attractive force. This tends to effectively

anchor the tips of the thredules of opposite field directions. We might imagine the

circular edges of the inner and the outer hyperboloidal sheaves respectively to be jointed

at each end.

Now while retaining these anchorages at the ends, if the inclination of all thredules is

altered by some angle, say ø, then øi becomes ø + 45° and ø0 becomes ø - 45°. This

means that the inner thredules would be pointing to lower latitudes and the outer ones to

higher latitudes. The effect on the shape of the two hyperboloids would be such that the

inner one gets more separated from the outer. Consequently, the repulsive interficial

energy decreases further. Therefore, this is what happens with thte progress of the solar

cycle, as shown in Figure 6: the inner thredules go on tilting toward lower and lower

latitudes, and their average length increases, while the outer thredules of opposite

magnetic polarity go on tilting toward higher and higher latitudes, and their average

length decreases.

Figure 6 - Change of the Thredule Orientation with the Progress of the Solar Cycle

7. Birth of the Sunspots

The sun‗s atmosphere consists of three distinct layers; the lowest is the photosphere with

an estimated depth of 200-400 km, followed by increasingly rarefied and transparent

layers of the chromosphere and the corona. The bulk of the energy is emitted by the

photosphere as continuum radiation. The opacity of the photosphere increases very

rapidly with depth, producing the illusion of a sharply defined outline of the sun. The

effective temperature of the photosphere, on the basis of blackbody assumption, is

estimated to be 5780° K.

7.1 Observational Description

Sakurai gives a graphic account of how sunspots form:

―At first, a localized magnetic field appears... In general, sunspots start out as pores,

which are small regions much darker than the surrounding photosphere... the magnetic

field strength increases significantly... and a full-fledged sunspot group develops. The

sunspots are concentrated in the preceding... and the following... ends of the group...‖

―The magnetic field has different polarity in the spots belonging to the preceding and

following ends... It is well-established that most sunspot groups appear as bipolar.‖

―... a fully developed sunspot consists of the central dark umbra, through which most of

the magnetic flux is channeled, and the less dark penumbra.‖

The magnetic field strength has a maximum value near the center of the spot, or where

the spot is darkest, i.e., the core of the umbra. The strength of the magnetic field is about

1,000-5,000 gauss for well-developed sunspots... The fully developed sunspot may exist

for days, weeks, or months...‖ [16]

7.2 Explanation of the Origin

We will see that the explanation of the structure of the solar core we have delineated

earlier logically leads to the explanation of the origin and properties of the sunspots and

the associated phenomena. In the beginning of the previous section, we have noted that

the thredules (as well as the co-magnetic lines embedded in them), tend to expand in the

longitudinal direction. As they do so and penetrate into the lower temperature outer

regions, they give up heat to the surrounding material and eventually drop into the

intermediate temperature region and cease to exist as thredules. However, at times due to

the local variations in the energy generation process, thredules with large enough energy

shoot outwards with sufficient violence as to reach the top of the atmosphere before

getting dissolved.

As this ultra high temperature matter breaks through the photosphere, it makes its

appearance as a sunspot of low temperature (for reasons explained in Section 3.3) and is

seen as a sunspot. Thus, the sunspots are hotter and not cooler than the surrounding

photosphere. The characteristic of the co-magnetic field lines to bunch together in the

transverse direction naturally produces a field intensity sharply increasing toward the

center or core of the spot umbra, which is the hottest (though ostensibly the coolest)

portion.

Between the two sheaves of thredules oppositely inclined to the rotation axis (Figure 5),

the inner one is naturally at a higher temperature. Moreover, as the solar cycle advances,

the thredules in the inner sheaf become longer, while those in the outer become shorter

(Figure 6). Consequently, the great majority of the sunspots arise out of the shooting of

the more energetic inner thredules. In fact, the magnetic polarity of the precursors of an

emerging bipolar spot group is that of these inner thredules. Thredules of opposite

magnetic polarity, being induced outwards by the action of the precursors, emerge to

form the spots of opposite polarity of the sunspot group. As we will see presently, these

latter always appear on the "following" end of the group, and a little while later than the

precursors.

As those of the thredules belonging to the inner sheaf, and which will be emerging at the

photospheric level as the leader spots travel through the matter of the intermediate

temperature shell surrounding the core, that matter in the immediate vicinity of these

passing thredules gets heated up. Some of this matter in the line of travel rises to the ultra

high temperature level and transforms into the thredule state (see Figure 7). The co-

magnetic lines in these induced thredules will, of course, be of opposite polarity. These

induced thredules, therefore, appear as the spots of the opposite polarity when they

emerge at the photospheric level. The general finding that the preceding spot appears

first, develops first, and disappears last, is exactly what is to be expected from our above

theoretical account if we remember that the induced thredules are less energetic, as well

as time-lagged, compared to the inducing thredules.

Figure 7 - Preceding and Following Spots in the two Hemispheres

The reason why the induced spots always form behind, with reference to the direction of

rotation of the solar surface may not, however, be readily understood. We have already

noted in Section 3.3 that the motion at the ultra high speed pertains to a scalar dimension

altogether different from the scalar dimension that is coincident with the conventional

reference system. [11] Even though such motion does not produce direct effects in the

reference system, being itself a motion in space it always acts to oppose the motion

represented in the reference system. Inasmuch as the motion in the dimension of the

reference system did produce changes of position in that system, the overcoming of that

motion (by the ultra high speed motion in the second scalar dimension) reverses those

changes of position. The position of the induced thredule, thus, would be located at a

little angular distance backwards compared to the position of the inducing thredule

relative to the direction of rotation of the sun. This produces the separation between the

preceding and the following members of a spot group.

8. Sunspot Properties

8.1 Characteristics of the Spot Groups

Figure 7 illustrates one of Hale‗s polarity laws of sunspot groups: namely, that the

polarity of the preceding (following) spots in each hemisphere is opposite. We have just

now explained its origin.

Currently, the formation of spot groups is being attributed to the buoying up of toroidal

magnetic flux tubes supposed to be subsisting below the photosphere. If this were to be

true, all spot groups have to be bipolar. The occurrence of unipolar and those classified as

complex groups cannot be accounted for.

Large-scale, low intensity magnetic regions of the photosphere within which sunspots

rarely appear are referred to as the bipolar magnetic regions (BMR), and the unipolar

magnetic regions (UMR). Like the bipolar sunspot groups, the BM regions also are found

to obey Hale‗s polarity laws. It is not difficult to see that these regions arise as the

thredules and the embedded co-magnetic lines shoot outwards, but the thredules give up

heat and completely dissolve prior to reaching the visible layers of the photosphere,

whereas the co-magnetic lines emerge out. Since they are no longer in equivalent space

when they so emerge, these lines no longer bunch together, but tend to diverge and their

intensity falls to a low value. This is the origin of the magnetic regions. Once again, in

the conventional theory it is difficult to account for existence of the UM regions.

―The belts where sunspots most frequently appear migrate from high latitudes around

35° - 40° at the start of the new solar activity cycle, to the low latitude region around 5° -

10° at the end of the solar activity cycle. This migration of the sunspot producing areas

occurs at almost the same time in both the northern and southern hemispheres.‖ [17] We

have already arrived exactly at this finding by theoretical deductions toward the end of

Section 6 above. Bray and Loughheed, who have done extensive work on sunspot studies,

comment, ―The cause of the latitude drift is very obscure.‖ [18]

Solar prominences are arch-like structures, which appear as dark filaments against the

solar disk, but appear luminous at the limb. There are two types of prominences: one type

appears in the region of 45° latitude where sunspot groups are born and migrates with

them toward the equator, as shown in Figure 8. The other type is not associated with

sunspots, and appears around 45° latitude and tends to migrate polewards, reaching the

pole toward the maximum of the solar activity cycle. Both types of prominences are

known to form along the borders between magnetic regions of opposite polarity. The

magnetic polarity distribution around the polar prominences is opposite to that around the

spot prominences, as indicated in Figure 8. Sakurai states, ―... as yet we do not know the

cause of this relationship... This subject is not yet fully understood in spite of extensive

efforts to discover the cause of the formation of solar magnetic fields, both sunspot and

‗general‘.‖ [20]

Figure 8 - Migration of Prominences

(adopted from Reference 19)

But our theoretical derivation correctly predicts this state of affairs: in Section 6 we have

shown that the thredules of the outer sheaf assume higher latitude positions with the

advance of the solar cycle. These thredules are shorter and less energetic and succeed in

producing only the bipolar magnetic regions in the photosphere, and not the sunspots. It

is evident that the polar prominences are associated with these regions. Since the inner

and the outer thredules are of opposite polarity, the preceding and following members of

the BMR associated with spot prominences (arising from the inner thredules) are of

opposite polarity compared to the corresponding members of the BMR associated with

polar prominences (arising from the outer thredules). The migration of the two classes of

BMRs, one poleward, and the other toward the equator, is similarly explained (see the

end of Section 7.2).

Before leaving the subject of prominences, we should mention that scientists find it hard

to explain why the gaseous material arching out in space sustains the filamental shape,

when there is nothing to prevent its lateral expansion. Sakurai remarks, ―Even now we do

not have a definite explanation of how the cool gas constituting the prominences is

supported by the magnetic lines of force of the sunspots, because this gas may easily

diffuse out without resistance from the magnetic lines of force.‖ [21] But we have already

seen why the matter in the very high temperature range retains the thread-like structure

and how expansion in the context of such temperatures is observed as contraction.

We will now move on to the explanation of another observational fact–a fact which the

conventional theories find most difficult to explain–namely, the reversal of the polarity

scheme of the bipolar spot groups in both the hemispheres with each new cycle of solar

activity. This is expressed as another of Hale‗s polarity laws: ―The entire system of

polarities remains unchanged during any one 11-year cycle of sunspot activity, but

reverses with the beginning of the next cycle...‖

―The reversal... begins with the appearance of spots of the new cycle in high latitudes

before the spots of the old cycle have completely disappeared.‖ [22] (See Figure 8.)

The beginning of the next cycle of the energy generation process takes place at the center

of the sun as the temperature there once again reaches the thermal destructive level of the

element present there. This creates a fresh pair of inner and outer sheaves of thredules

lying inside the pair of sheaves belonging to the old cycle. The thredules of either sheaf

of the new cycle also will be inclined at nearly 45° on either side of the axis, respectively.

In view of the fact that the co-magnetic lines of like polarity have an affinity to each

other, two things happen. Firstly, the thredules of the outer sheaf of the new cycle will

form inclined to the axis on the same side in which the thredules of the inner sheaf of the

previous cycle happened to be inclined. Secondly, the magnetic polarities of the thredules

of these two sheaves will be identical. Since the polarity of the thredules of the inner

sheaf is opposite to that of the thredules of the outer sheaf, we have the final result that

the polarity of the thredules of the inner sheaf (and hence of the preceding spots) of the

new cycle is opposite to the polarity of the thredules of the inner sheaf (and that of the

preceding spots) of the old cycle.

8.2 The Sunspot Penumbrae

Soon after the appearance of a sunspot, the surrounding material of the photosphere in its

immediate neighborhood starts becoming darker and at some subsequent stage, thin

filaments directed more or less radially outwards from the spot umbra form. These

annular regions around the umbrae are referred to as the penumbrae. The lengths of these

radial filaments are known to vary according to the spot size and complexity. The

radiation intensity in the penumbra gradually decreases inwards from the photosphere to

the penumbra-umbra border, where it falls very steeply. The filaments end abruptly such

that this border is sharply outlined.

Bray and Loughhead state: ―It must be admitted that neither the mode of origin of the

penumbra nor the role it plays in the sunspot phenomenon as a whole is yet properly

understood.‖ [23] However, we can readily see that the penumbra must comprise of the

photospheric material heated up to the intermediate temperature by the thredules that

form the spot unbra. Both its filamental configuration, and sharply demarcated interface

with the umbra suggestive of the phase change that occurs on crossing the boundary

between the ultra high speed region and the intermediate speed region, clearly point to

this.

Observations of sunspots near the solar limb show a marked asymmetry in the penumbral

width (the Wilson effect) that seemed to suggest that the sunspots are saucer-like

depressions in the photosphere. But recent observations with improved resolution never

revealed such depressions when seen right up to the limb. The Wilson effect results if the

umbra is much more transparent, rather than the penumbra, as compared to the

photospheric material. This, of course, is what is to be expected. Opacity is a result of the

absorption of radiation by the processes of photoionization and photoexcitation. With

increasing temperature, more and more atoms are completely ionized, and the scope for

the above absorption processes decreases. Therefore the matter in the penumbra is more

transparent than the low temperature photospheric matter and that in the umbra more

transparent than both of these.

8.3 The Evershed Effect

Radially outward motions in the sunspot penumbrae (parallel to the photospheric

surface), named as the ―Evershed velocities‖ (after their discoverer) are known to exist.

No vertical or tangential velocities were ever observed in the penumbrae. The radial

velocity–radial to the spot–increases from about 1.0 km/sec at the boundary between

umbra and penumbra, reaches a maximum of about 2.0 km/sec near the center of the

penumbra and comes to zero at the outer edge of the penumbra. It is also known that the

Evershed velocity increases with the depth.

According to Bray and Loughhead:

―... The simplest interpretation of the Evershed effect is that it consists of a laminar flow

of matter outwards from the umbra along the filaments...

―One piece of evidence against the hypothesis is the observed variation of the Evershed

velocity with height: this would seem to be of sufficient magnitude to prevent the

occurrence of a purely laminar flow... the shearing effect of the vertical velocity gradient

would quickly lead to the disintegration of the filaments. Yet individual filaments are

observed to persist...

―No trustworthy mechanism for the origin of the driving force of the Evershed flow has

yet been proposed. It is rather interesting to note that at the photospheric level the

direction of the motion is opposed to the pressure gradient, the pressure in the umbra

being less than that in the photosphere.‖ [24]

All the above description of the Evershed effect exactly fits our theoretical conclusion

that the penumbral matter is in the intermediate temperature range. The commencement

of the radial velocity with a finite value (instead of a zero value) at the boundary of the

umbra, the sustained laminar-like flow, despite the existence of a steep velocity gradient

in the vertical direction, the apparent motion against the pressure gradient, all of these

point to the same thing, namely, that the motions in the penumbra pertain to the region of

equivalent space.

In Section 3.2.4 we have shown that thermal motion beyond the unit level tends to

contract a material aggregate. Therefore the decrease in the intermediate temperature with

the increase in the penumbral radius involves a re-expansion that extends all along the

radius. Although this manifests as a flow in the penumbral filaments, in reality, its true

nature is altogether different.

We shall let Larson explain it:

―At this time we will take a look at another of the observable effects of motion in time...

its effect in distorting the scale of the spatial reference system.

―... in the physical universe we are able to use the spatial reference system only on the

basis of an assumption that the rate of change of time remains constant ... the scale of

spatial co-ordinate system is related to the rate of change of time ... At speeds in excess of

unity, space is the entity that progresses at the fixed normal rate, and time is variable.

Consequently, the excess speed above unity distorts the spatial co-ordinate system.‖[25]

Thus at higher intermediate temperatures there will be a greater scale distortion (in the

manner of contraction) and vice versa.

The Evershed flow is not a genuine change of position of the particles of matter in the

space of the reference system: it is, rather, the effect of the occurrence of a scale gradient

accompanying the temperature gradient in the intermediate region.

8.4 Evidence Against the Apparent Low Temperature of the Spots

8.4.1 Intensity Measurements

The radiation intensity of the sunspots is measured at several frequency ranges. The

current practice of treating this radiation as conforming to the continuum spectrum of the

blackbody radiation has lead to conflicting results.

Bray and Loughhead remark, ―As a direct consequence of the umbra's low temperature,

its spectral class is later than that of the photosphere–dKo as compared to dGo-2 for the

photosphere.‖ Then on making a comparison with the observed intensity values they

conclude: ―It follows that the spectral class of the umbra is decidedly earlier than the

temperature derived from intensity measurements made in the continuous spectrum

would lead one to expect. The origin of this discrepancy is unknown.‖ [26] This must be

so, as long as the true status of this radiation is not recognized.

Quoting again from them: ―... numerous weak [spectral] bands due to unidentified

compounds have so far been seen only in spots, and ... unidentified bands in the sunspot

spectrum are more numerous than those now accounted for.‖ [27]

8.4.2 Sunspot Effects on the Surrounding Granulation

The entire surface of the photosphere appears covered with uniformly bright cells, called

the granules, separated by the darker intergranular material. These granules are believed

to be convection cells. Observations show that there is an increase in intensity at the

Violet and UV wavelengths giving rise to the appearance of bright, ring-like regions

around the spots.

Bray and Loughhead report that it is ―found that the intensity of the bright ring is greatest

immediately outside the penumbra and decreases slowly outwards... the bright rings are

unusually intense around spots showing large Evershed velocities.

―No satisfactory explanation of the presence of the bright rings in the photosphere

around spots ... has yet been given.‖ [28] Rightly so. But the moment we realize that the

spots are hotter and not cooler than the photosphere, then enhanced brightness can be

attributed to the energy transfer from the spot.

Moreover, from heat transfer studies, it is known that an increased heat transfer rate is

correlated with smaller size of the convective cells. We see from Bray et al that ―the size

distribution of the solar granulation is extremely uniform over the solar surface...

... Several authors have observed a reduction in the granule diameter or mean spacing in

the close neighborhood of sunspots..., which so far has received no theoretical

attention.‖ [29] In addition, these areas of reduced granule size adjacent to the spots are

found to coincide with the regions of enhanced brightness mentioned above. [30]

8.5 Polarization of the Radiation

Polarization measurements on the integrated radiation from the sunspots indicates that it

is partially plane polarized. This, of course, is what is to be expected (see the end of

Section 3.1).

9. Radiation Associated with Sunspots

We have already discussed some aspects of the magnetic fields, the prominences, and the

granulation in association with the spots.

In addition to the continuum and line emission, different other patterns of radiation

emission are observed in conjunction with sunspot groups. Non-thermal radio emission in

the metric frequency range is often found above spot groups and is known as the Type I

continuum storm. Such sunspot groups with Type I emission are also found responsible

for the generation of solar flares (sudden, local increases in the surface brightness of the

sun).

Emission of micro-waves, soft thermal X-rays, high energy particles (of MeV-BeV

range), hard non-thermal X-rays, gamma rays, and non-thermal burst emissions at radio

frequencies are all known to occur in the several phases of the solar flares. Some of the

radiation is seen to be strongly polarized. The scientists admit that as yet no satisfactory

and consistent explanation of the complex nature of these radiation phenomena is

available.

Larson discusses at length the processes that generate non-thermal X-rays and radio

waves. [2] He explains how stable isotopes become radioactive and emit radiation at

radio wavelengths when they are transported from the low temperature region to the

intermediate temperature region. In a similar manner, he shows that when matter which

has attained isotopic stability in the intermediate temperature region is transported to the

low temperature region, it again becomes radioactive and emits X-rays and gamma rays.

[31] As such, it is not difficult to account for the origin of the variety of the observed

radiations in association with the sunspots, once the presence of the ultra high and the

intermediate speed matter in and around them is recognized.

10. Epilog

We have shown that reasoning from the principles embodied in the Reciprocal System it

is possible to explore the internal structure of the sun. The theoretical understanding so

obtained is in consonance with the observations of sunspot and relevant phenomena.

The main thesis derived is that sunspots are produced by the surfacing of the ultra high

temperature matter in the solar core in the form of ―thredules‖ to the photospheric level.

It must be mentioned that the theoretical account of the solar interior herein reported is a

simplified one that is meant to serve as the basis for further, more detailed, work.

References

Glimpses Into the Structure of the Sun 1. Larson, Dewey B., Nothing But Motion (North Pacific Publishers, Portland, OR,

1979)

2. Larson, Dewey B., Universe of Motion (North Pacific Publishers, Portland, OR,

1984)

3. ibid., page 41.

4. ibid., pages 61-62.

5. Nehru, K.V.K., "Intrinsic Variables, Supernovae and the Thermal Limit,"

Reciprocity XVII (1), Spring, 1988, page 20.

6. Larson, Dewey B., Universe of Motion, op cit., pages 70-73.

7. Larson, Dewey B., Nothing But Motion, op.cit., page 155.

8. Larson, Dewey B., Universe of Motion, op cit., page 215.

9. ibid., page 224.

10. ibid., page 215-216.

11. ibid., page 213.

12. ibid., page 214.

13. ibid., page 223.

14. ibid., page 364.

15. Larson, Dewey B., The Neglected Facts of Science (North Pacific Publishers,

Portland, OR, 1982), pages 9-12.

16. Sakurai, Kunitomo, Physics of Solar Cosmic Rays (University of Tokyo Press,

Japan, 1974), page 53.

17. ibid., page 55.

18. Bray, R.J., and Loughhead, R.E., Sunspots (Chapman & Hall, New York, 1964),

page 244.

19. Sakurai, Kunitomo, op. cit., page 64.

20. ibid., page 63.

21. ibid., page 94.

22. Bray, R.J., and Loughhead, R.E., op. cit., pages 242-243.

23. ibid., page 276.

24. ibid., pages 151, 154.

25. Larson, Dewey B., Nothing But Motion, op. cit., page 107.

26. Bray, R.J., and Loughhead, R.E., op. cit., page 132.

27. ibid., page 140.

28. ibid., pages 66-67.

29. Bray, R.J., Loughhead, R.E., and Durrant, C.J., The Solar Granulation (Dover

Publishers, 1979), pages 41, 86.

30. ibid., page 88.

31. Larson, Dewey B., Universe of Motion, op. cit., pages 248-249.

Part I: The Nature of Stellar Matter

Part II: The Solar Interior and the Sunspots

INTRINSIC VARIABLES, SUPERNOVAE

AND THE THERMAL LIMIT

Introduction

According to the Reciprocal System the main energy generation process in stars is by

way of thermal destruction of the atoms of the elements present in the stellar core.

―....both the thermal energy of the matter in the star and its ionization energy are space

displacements, and when the total of these space displacements reaches equality with one

of the rotational time displacements of an atom, the opposite displacements neutralize

each other, and the rotation reverts to the linear basis. In other words, both the ionization

and a portion of the matter of the atoms are converted into kinetic energy. ...

―....Inasmuch as the entire structure ... is fluid, the heavy elements make their way to the

center. As the temperature in the central regions rises, successively lighter elements reach

their destructive limits and are converted to energy.‖[1]

The Destructive Limit

The destructive limit Td, that is, the temperature at which the neutralization of one of the

two-dimensional displacements of the atom takes place can be worked out as follows. A

temperature T in Kelvin, expressed in the natural units, is given by

T/Tnat (1)

where Tnat is the natural unit of temperature in the time-space region (that is, the three-

dimensional spatial reference frame) expressed in the conventional units [2] as

Tnat = 7.20423 x 1012 K (2)

Since speed displacement is the deviation of the speed from the natural datum—the

natural datum in the universe of motion being unity—the space displacement.

corresponding to a temperature T is

(T/Tnat) -1 (3)

This, therefore, is the space displacement available per each rotational unit of the atom

when it is at a temperature of T Kelvin. If the net number of rotational units (the atomic

number) of the atom is Z, the total space displacement available due to the thermal

energy is

Z * ((T/Tnat) - 1) (4)

The temperature of the atom is a linear (vibratory) motion in the time-space region while

the rotational motion that constitutes the atom is in the time region (inside unit space).

The total number of equipossible orientations for a unit of linear motion in the time-space

region is shown to be 8 [3]. As such, the portion of the space displacement of the

temperature that becomes effective in the time region is

Z * ((T/Tnat ) -1)/8 (5)

Thermal destruction of the atom implies the neutralization of one of its two-dimensional

time displacement units since the basic rotation constituting an atom is two-dimensional.

The one-dimensional equivalent of a two-dimensional displacement of magnitude n being

2 * n² , where the atomic displacements are a - b - c , the time displacement units needing

to be neutralized would be either 2 * (a - 1)² or 2 * b². Thus, we have, at the destructive

limit Td‘

2 * n² - Z * ((T/Tnat )-1)/8 (6)

where

n = either (a - 1) or b, whichever is bigger. (7)

It must be pointed out at this juncture that though the space displacement of the electric

ionization does add to that of the thermal motion in neutralizing a unit of the magnetic

time displacement of the atom, its contribution is comparatively small—amounting to not

more than a fraction of a percent of the temperature displacement. Hence, no appreciable

error will be introduced by dropping the ionization displacement from consideration at

the present stage.

In fig. 1 are shown plotted the values of the thermal destructive limit of the elements

against Z. As can be seen, this temperature increases as the atomic number decreases. But

the most conspicuous feature of the curve is that, instead of being monotonous, it dips at

several locations where there is a change in the displacement of the atom in one of the

magnetic dimensions. These dips, occurring respectively at Z = 70, 27 and 6 are of

paramount significance in determining the course of stellar evolution as we will presently

see.

Figure 1: Destructive Limits of the Elements

The Intrinsic Variables

Under normal stellar conditions, where there is no severe large-scale turbulence,

gravitational segregation of the elements according to their masses would take place, the

heavier ones migrating toward the core. Taking this gravitational segregation into

consideration, if we plot the thermal limit Td of the material of the star at different radii

we obtain a curve of the general nature shown in fig. 2.

Figure 2: Regular Burning

The distribution of the actual temperature Ts in the star at various radii is also shown

plotted in the figure. We see at the center, P, that the temperature is the same as the

destructive limit of the heaviest element present. As such, this element gets thermally

neutralized to yield the energy output of the star. We shall refer to this process as the

‗regular burning‘ in order to distinguish it from the ‗secondary burning‘ which we will

presently explain.

As the element burning (that is, the thermal neutralization) continues, elements of lower

Z (and with higher Td) keep arriving at the center. At the same time the stellar

temperature gradually keeps on rising so that each of these lower Z elements reaches the

thermal limit successively at the center. Thus, the Td vs. radius curve goes on shifting

horizontally to the left in the diagram, while the Ts vs. radius curve gradually keeps on

rising, signifying higher stellar temperatures, as evolution progresses. Eventually the

group of elements with Z = 74 to 70 arrives near the center. The state of affairs is now as

shown in fig. 3.

Figure 3: Onset of Secondary Burning

It can be seen that the stellar temperature curve now begins to intersect the Td curve at

two points P and Q. Therefore we find that while principally elements 74 and 73 are

burning at the center P, element 70 also arrives at its destructive limit at location Q,

slightly farther out. The consequent ignition of element 70, however, upsets the previous

equilibrium between the thermal and the gravitational forces, for three reasons.

Firstly, the element 70 is relatively more plentiful compared to the elements of higher Z

and thus a potentially larger energy source is switched on, and switched on suddenly, in

addition to the existing source. This new source we shall refer to as the ‗secondary

source.‘ Secondly, this happens not quite at the center (where the regular source has been

operating) but at a slightly larger radius rs (see fig.3), which we shall call the ‗secondary

burning radius,‘ where there was no energy generation previously. Thirdly, the extent of

the spherical area at radius rs, where s the thermal limit of the secondary fuel is reached,

is comparatively larger than available to the regular fuel at the center, and in consequence

the proportion of the secondary fuel that is ignited is much greater.

The additional energy thus released causes an expansion of the star. This drops the stellar

temperature and acts as a negative feedback, shutting off the new energy source.

Subsequent contraction repeats the cycle and we have the phenomenon of the intrinsic

variable. In fact, the Cepheids could be identified as the stars burning elements around

the ytterbium-dip at Z = 70 (fig.l).

Larson proposes [4], in the context of the Reciprocal System, that in the regular course of

the energy generation process, with elements of lower atomic numbers successively

arriving at the center to be neutralized, the appearance of an element such as lead (Pb),

with comparatively higher-than-normal abundance, initiates the variability cycle. This

might well be one of the causes of the variability and the long period variables seem to

fall into this category. However, as the stellar mass (and consequently its temperature)

increases, the ratio of the additional energy produced to the total stored energy decreases.

As such, the variations become damped out and unobservable. In the case of the higher

temperature stars, therefore, the principal cause for the variability could be attributed to

the Yb-dip as explained in the foregoing.

The phenomenon of the intrinsic variable occurs whenever there is a cyclic upsurge in the

energy production. This also happens when the central temperature of a gravitationally

contracting aggregate first reaches the destructive limit of the heaviest element present

there. In fact, Larson identifies this category of stars as the long period variables [4].

The Main Sequence Stars

The phenomenon of the variable luminosity manifests only in case the accretion rate is

high and the star follows the path AC shown in the Color-Magnitude diagram (see fig.6

of Reference [SD] The story of a main sequence star, with about the same surface

temperature as that of the variable is somewhat different. This is primarily because when-

the stellar temperature archives at the Yb-dip, the temperature gradients in the variable

and the main sequence star are markedly different. In the variable the Yb-dip occurs

much farther from the core as compared with the main sequence star. As shown in fig.4

(a) and (b) the temperature gradient in the core is much steeper in the main sequence star.

(a) Main sequence star (b) Intrinsic variable

Figure 4: Effect of Temperature Gradient on the Dip

If dZ is the difference between the atomic number of the element currently burning at the

center and that of the new arrival (the secondary source), the effect of the steep

temperature gradient is to keep dZ to a small value (1 or 2). Therefore no marked

difference in the magnitude of energy generation will result by the initiation of the

secondary burning. Whatever little difference there may be is successfully damped out by

the larger heat capacity and the larger mass of the overlying material (in view of the

smaller secondary burning radius rs). Consequently the main sequence star of comparable

surface temperature passes less conspicuously than the variable through this Td dip. In the

case of the variable the dZ is larger (4 or 5) (see fig.4 b)) which results in considerable

amount of secondary energy production.

The Type I Supernova

As the element-burning continues and the cobalt-dip (at Z = 27) arrives at the core while

element 31 or 30 is burning at the center, a spectacularly different result ensues. Firstly,

the secondary source triggered suddenly is proportionately very large—not just three or

four times the regular, as in the case of the Yb-dip, but nearly a hundredfold bigger—

owing to the much greater relative abundance of the Co-group of elements. Secondly,

because of the large size of the dip in Td at Z = 27 the secondary burning radius is

appreciably large. As such, a large number of elements (with Z between 32 and 27), and

in quantities more plentiful than the regular fuel now burning at the center, are present

within the sphere of radius rs, waiting to be ignited but for their higher destructive

temperatures.

The initial spate of the secondary energy released by the onset of the thermal destruction

of Co at the radius rs does two things: on the one hand, it causes the expansion of the

overlying material and results in a drop in the temperature, which thereby acts as a

negative feedback switching off the Co ignition. On the other hand, it compresses the

material inside the radius rs . This sudden implosion raises the temperature in the region

sharply and brings all the high-Td material within the radius rs catastrophically to its

destructive limit. Consequently, a pilot explosion takes place in the core, liberating

considerably large quantities of energy greater nearly by a magnitude or two than was

being released hitherto—and liberating this energy in a short interval. This acts as a

positive feedback and retriggers the burning of the Co-Fe group of materials at the radius

rs at a substantially high rate. This high rate of temperature rise raises the temperature of

a large portion of. the Co-group well above its destructive limit, culminating in the

supernova explosion before the negative feedback of the drop in temperature owing to the

expansion of the outer layers has time to operate. In fact, if the star is quite large, a few

outer luminosity pulsations may be apparent before the core explodes, activating the final

cataclysm of the cobalt explosion.

As Larson points out [6], the supernova explosion disperses the major portion of the Co-

group out into space before it had a chance to get destroyed in the event. Hence their

cosmic abundance keeps on building up unlike that of the other elements of higher Z. The

elements of Z = 28 through 30, which are inside the secondary burning radius, and are

involved in the pilot explosion, also seem to share this good fortune to a limited degree

by virtue of their higher destructive limits.

Conclusions

Highlighting the effect of the Td dip on stellar evolution we summarize:

1. In the course of the regular burning in the stellar core, the element that reaches the

thermal limit next in the succession is that with dZ = 1 or 2. The effect of the dip

is to activate a source with dZ = 4 or 5, with the concomitant larger difference

between the relative abundances of the regular and the secondary energy sources.

This is one of the causes of the variable luminosity.

2. The secondary energy source thus activated by the dip is an extra source,

operating in addition to the regular source existing at the center.

3. The secondary source is located not at the center but at a larger radius called the

secondary burning radius.

4. The long-period variables could be identified as the stars burning element Pb at

the center or the ones that just started their energy production by thermal

neutralization while the Cepheids are the ones passing the ytterbium-dip (Z = 70).

5. The Type I supernova explosion is the result of the cobalt-dip (Z = 27) reaching

the stellar core.

References

1. Dewey B. Larson, The Universe of Motion, North Pacific Pub., Portland, Oregon,

1984, pp. 41-42

2. Dewey B. Larson, The Basic Properties of Matter, The International Society of

Unified Science, Salt Lake City, 1988, p. 59.

3. K. V. K. Nehru, ―The Inter-regional Ratio,‖ Reciprocity, XIV (2 - 3), Winter

1985/86, p. 5

4. Dewey B. Larson, The Universe of Motion, pp. 61 - 63.

5. Ibid., fig.6, p. 64

6. Ibid., p. 5.

THE QUASAR PARADOX?

Paradoxes Galore

Paradoxes bring to light flaws in the logical structure of a theory. We have had the

famous twin paradox of the Special Theory of Relativity. In our attempts to understand

the Reciprocal System of theory some paradoxes seem to be coming up for consideration.

One such paradox, which we will name the Quasar Paradox, has recently been mentioned

by a student of the Reciprocal System, in a privately circulated communication. Since the

correspondent opines therein that this paradox requires revision of Larson‘s theory, it

might be educative and worthwhile to discuss the issue with a hope to see the truth.

Simply stated the paradox is as follows.1 Larson establishes that the total redshift of a

quasar is the sum of the recession redshift z, and that due to the explosion that created the

quasar amounting to n*z(1/2)

, (where n is normally 3.5). As the distance increases and the

recession redshift reaches the value 0.326 the explosion redshift arrives at the 2 unit limit.

At this juncture, according to Larson, the gravitation inverts and ceases to be inward in

space, resulting in the final disappearance of the quasar into the cosmic sector of the

physical universe. Now, in the words of the correspondent,

The problem is that an observer closer to the quasar would see the relation z +

3.5*z(1/2)

as less than that seen by a more distant observer (z being less) and so the

speed [in the explosion dimension] would be less than 2 for the closer observer. I

feel... that a quasar cannot both fly apart and not fly apart at the same time

depending [on] one‘s point of observation.

The New Paradigm

We submit that before undertaking an analysis of the paradox it would be fruitful to draw

attention to certain factors which act as preconditions for an unbiased appraisal of the

Reciprocal System. The first thing to be recognized is that the Reciprocal System

involves a fundamental change in our viewpoint concerning the basic constituent of the

physical universe. Its principal tenet is that the universe is constituted entirely of motion.

The previous viewpoint regards it as a universe of matter. The most important implication

of this new viewpoint is that motion (space-time) is the content of the universe, whereas

the concept of the universe of matter regards space and time as the background or setting

on which matter plays. Throughout the ebb and tide of scientific thinking for the past

3000 years, Larson points out, the one unchanging element has been the ‗setting‘ concept

of space and time. This has become a thoroughly entrenched habit in the thinking of

scientists and laymen alike.

Man‘s endeavors to understand Nature have always been impaired by his limited and

local viewpoints. He has tended to extrapolate what he perceived and experienced of the

local and peculiar environs by merely enlarging their extent, without in the least

suspecting that he might not be the centre of the universe. Only the increased power and

scope of his observations have brought to light the fact that his global view is vitiated by

his local viewpoint. He first thought that the earth was flat before realizing it is spherical.

Then he went on thinking that his earth is the centre of the universe. The proliferation of

epicycles eventually led to the discovery that it is the sun that is the real centre and so on.

Every time such fundamental revolution in the view points had occurred it encountered

bitter antagonism and a cold reception because the old and the new viewpoints were so

disparate that the common man and the common scientist of the day could not grasp the

truth.

We can now see history repeating itself as Larson discovers that our viewpoints about the

most fundamental aspects of the physical universe, namely, space and time, have been,

after all, local and limited. The view that space is stationary and three-dimensional and

that time is one-dimensional and progressive is only apparently true and applicable only

to the gravitationally bound system. Emancipating from this anthropocentric view and

recognizing that both space and time are three-dimensional in their own right and

progressive and that they are reciprocally related comprise the new revolution in human

thought.

Larson states:

Previous investigators have not realized that the ―setting‖ concept is a creature of

the ―matter‖ concept; that it exists only because that basic concept envisions

material ―things‖ existing in a space-time setting. In attempting to construct a

theoretical system on the basis of the concept of a universe of motion while still

retaining the ―setting‖ concept of space and time, these theorists have tried to

combine two incompatible elements, and failure was inevitable. ... What is needed

is to discard the ―setting‖ concept of space and time along with the general

concept of a universe of matter, to which it is intimately related, and to use the

concept of space and time that is in harmony with the idea of a universe of

motion.‖ (2)2

Realizing this, Larson has repeatedly cautioned in his works that the findings of the

Reciprocal System ought to be adjudged from the standpoint of its basic premise(s) and

that endeavors to evaluate the new concepts from the viewpoint of the untenable matter

concept of the universe (and the associated ―setting‖ concept) are going to lead to absurd

results. We shall term the practice of using this old viewpoint in the context of the new

theory the Fallacy of Incongruous Viewpoints.

The danger is especially strong for all of us who happen to live at the junction of the new

paradigm of the universe of motion and the old untenable one of the universe of matter

existing in a framework of space and time. Since none of us is in a position to maintain

that we are absolutely infallible, it becomes imperative, whenever we encounter a

difficulty or paradox in the Reciprocal System, to first establish that we have not

unconsciously fallen prey to the Fallacy of Incongruous Viewpoints, before we can

legitimately conclude that the logic of the theory is faulty.

Content vs. the Container

Now the crucial point to see is that it is not legitimate to imagine that the quasar is

located ‗out there‘ in our co-ordinate space. When we picture the large-scale universe we

tend to imagine that the stationary co-ordinate reference frame--namely, the container

space--as extending indefinitely in the three spatial dimensions and picture quasars and

other distant galaxies as studded at specific locations in that stationary reference frame.

This, of course, is an unconscious habit of thought carried over from the previous

paradigm of ‗container space‘ belonging to the concept of the universe of matter.

On examining we find that the stationary reference frame is an artifact applicable only to

a gravitationally bound system of material aggregates. The very existence of the

stationary reference frame requires unit inward motion to counter the ever-present unit

outward motion of the natural reference system. Otherwise we cannot have a stationary

reference frame. This needed inward motion is supplied only by a material system that is

gravitationally bound. Therefore, whether we explicitly acknowledge or not, the

stationary reference frame can exist only in conjunction with a gravitationally bound

system3

Since the domain of the net inward motion of a gravitationally bound system ends at its

gravitational limit, each such system has its own stationary reference frame. Beyond the

gravitational limit the domain of the familiar three-dimensional space does not exist: it is,

thereafter, a domain of equivalent space.4 The familiar three-dimensional space, the space

adopted in all our picturizations, ends at the gravitational limit of the gravitationally

bound system to which the stationary reference frame is anchored.

The truth that there cannot be one universal stationary co-ordinate reference frame and

that each gravitationally bound system has its own stationary reference frame is not

immediately and sufficiently recognized. Larson denies ―that all spatial locations could

be defined in terms of an absolute spatial reference system, and that time could be

defined in terms of a universal uniform flow.‖5 ―In order to get the true picture,‖ Larson

remarks, ―it is necessary to realize that no single reference system is capable of

representing the whole of physical reality.‖6

The Two-Galaxy Paradox?

Imagine two galaxies A and B of unequal masses, each beyond the ambit of the

gravitational limit of the other, and two stationary reference frames attached to each

respectively. The spatial separation between the two stationary reference frames need not,

in general, be the same as measured from A and B individually. This is because each such

stationary reference frame is reckoned from the background of the gravitational motion of

the gravitationally bound system to which it is anchored and the magnitude of this (the

gravitational motion) is contingent on the mass of the gravitationally bound system. The

estimate of the intervening distance according to the observers belonging respectively to

either stationary reference frame need not be the same since the observer is observing

from the background of the gravitational motion in which he is situated, and this differs

for both of them.

In fact, this distance is proportional to the recession speed and the reciprocal of the

Hubble constant. ―... the astronomers have assumed that the Hubble constant is a fixed

characteristic of the physical universe...‖ Larson explains, ―The Hubble ―constant‖... like

the gravitational limit... is a property of each individual mass aggregate. In application to

the galactic recession this so-called constant is a function of the total galactic mass ...‖7

More specifically, we have shown elsewhere8 that the Hubble constant is inversely

proportional to the fourth-root of the galactic mass. We have shown there how the

consideration of the mathematical relations that are applicable to the region beyond the

gravitational limit directly leads us to the observed linear relationship between the

recession speed and the distance that the Hubble law states. More recently we have also

shown9 how the large-scale structure of the distribution of galaxies and voids that has

emerged from the latest astronomical observations follows from the theory--both

qualitatively and quantitatively--by considering the limitation of the conventional three-

dimensional spatial reference frame and applying the mathematical relations appertaining

to the region beyond.

Thus, if vAB is the velocity of recession of galaxy A, as measured by the observer

belonging to the stationary reference frame anchored to B; and xand H represent the

distance and Hubble‘s constant respectively, we have:

vAB = HB * xAB and vBA = HA * xBA [1]

and

(xAB/xBA)*(vBA/vAB) = HA/HB [2]

Then all that we can say about the intervening distance is that XAB need not, in general,

equal xBA. Seeing that the basic constituent of the universe is motion, a plausible

*assumption* is that these two galaxies are connected by the common speed of recession,

rather than by a common intervening distance (which would probably be more

appropriate to assume in the context of the concept of container space). Then:

xAB/xBA = HA/HB = (MB/MA)¼ [3]

where M represents the mass of the galaxy. This might seem an absurd result, but only if

looked at from the unacceptable viewpoint of the ―setting‖ concept.

Resolution of the Quasar Paradox

Eq.[2] gives enough clue to resolve the quasar paradox. Whatever happens to the quasar

due to the 2-unit explosion speed happens to it in an objectively real manner. But since

each observer is making his observation from within his gravitationally bound system,

the phenomena pertaining to the excess speed components that cannot be directly

represented in his ‗absolute space‘ and ‗absolute time‘ frames manifest variously

depending upon the local gravitational motion. It must be realized that the inversion of

gravity that marks the entry of the quasar into the cosmic sector is relative to the local

spatial co-ordinate frame--not relative to the natural reference frame.

An analogy might help. Imagine an object of mass m situated on the surface of the earth

and two scientists located vertically below the object ad depths d1 and d2 and estimating

its potential energy. They would measure it to be respectively mgd1 and mgd2. Then it

would seem that the object has a potential energy mgd1 and at the same time a different

potential energy mgd2, depending on which observer‘s standpoint one takes. The paradox

disappears as soon as it is recognized that the datum levels from which the potential

energy is regarded are different.

The term ―at the same time‖ occurring in our statement of the quasar paradox can now be

seen to be referring to a concept that is not applicable to the quasar situation under

consideration, since this turns on the assumption of the existence of a universal, unique

co-ordinate frame. What has given rise to the quasar paradox is the committing of the

Fallacy of Incongruous Viewpoints: it is not, after all, as contended, due to any flaw in

the structure of the Reciprocal System. The quasar paradox typically demonstrates (i)

how difficult it is for us to cast off our allegiance to the concept of a universal container

space and uniform absolute time that pertain to the concept of universe of matter that no

longer is admissible in the context of the concept of the universe of motion; and (ii)

consequently, how we might be misled to wrong evaluations of the Reciprocal System.

Perhaps it is not out of place here to note how rashly and caustically the correspondent

condemns Larson‘s theory, in the communication in which he refers to the quasar

paradox, and discredits his monumental work. It would seem that one tends not only to

underestimate Larson‘s calibre but also to overestimate one‘s own infallibility. Sure and

faster progress in the study and research of the Reciprocal System will be accomplished

only if we are seeking truth and thoroughly understand the pitfalls a student might

encounter. Therefore it might be of some value to dwell on a few more items, in the

context of the Reciprocal System, and examine how the unconscious slipping into the old

habit of positing everything in the container space might confound our thinking.

Other Conceptual Difficulties

The Time Region. One concept that led some students astray has been that of the time

region, the region inside unit space. Since the Reciprocal System asserts that less than a

(natural) unit of space does not exist, some tended to interpret that the time region is

some kind of pseudo-space. The principle mistake, however, has been to conceptually

locate the time region in the frame of the container space. It is not realized that what it

really alludes to is a region (or domain) of physical action. The inside of a unit of space,

to which the concept refers, is still a region of space, not of any pseudo-space. This

example typically illustrates how desperately we tend to hang on to the known concept of

space by some stratagem of using such terms as ‗pseudo-space.‘

Travel through Time. Another concept that might mislead students is the manner in

which the radiation from an object moving away from us at a speed greater than unity

reaches us. Larson points out that such radiation reaches us through time rather that

through space. Any conclusion that might be reached by inadvertently and unwarrantedly

assuming universal reference frames is bound to create mischief.

The Spatialization Syndrome. In the speakers of English ( and of languages of kinder

grammatical structure), unfortunately, there is a strong tendency to spatialize everything,

even those items that have no noticeable spatial structure (such as thoughts and emotions,

say). This, therefore, predisposes the speaker of such a language to picturize/localize all

items of knowledge in the container space. This language habit is so thorough that it

requires the utmost detachment and awareness to recognize its illegitimacy whenever

such is the case.

Moreover, our sentence structure divides reality into ‗actors‘ and their ‗actions,‘ largely

due to the occurrence of the grammatical categories of substantive and verb. This practice

is so ingrained that we are assisted to imagine that there is necessarily an ‗actor‘ in each

fact which, in reality, is only the necessity of a substantive in the sentence structure. For

example, our sentence structure requires us to say ‗it is raining‘ while, in truth, ‗raining‘

is sufficient. Another example: we seem to be regarding ‗the thinker‘ as distinct from

‗thinking,‘ while in reality there is no separate thinker disassociated with thinking.

Larson explains at length in his Beyond Space and Time that we divide reality into two

categories, answering respectively to the two questions ‗what it is‘ and ‗what it does‘ . In

the context of the old paradigm of the universe of matter suppose one asks these

questions, say, about the earth, one would answer ‗what it is‘ by ‗matter‘ and ‗what it

does‘ by ‗moves.‘ However, from the point of view of the Reciprocal System, the answer

to both these questions is ‗motion.‘ Therefore one has to be wary not to fall prey to the

attitude of misreading what in truth are only the necessities of English grammar as the

characteristics of reality. We may call this attitude the Fallacy of Misplaced Categories.

The Space-Time Progression. Another source of potential misconception is the space-

time progression, the background or datum of physical action. it would be educative to

inquire as to how we visualize the uniform ubiquitous space-time progression. Do we

visualize it as empty space spread out to infinity and ever expanding? do we tend to miss

(or misunderstand) the significance of the concomitant expansion of time? Since space

and time are reciprocally related, the expansion in space is nullified by the expansion in

time, and each unit of space is not separated by other units of space but all are connected

by the unit speed. The space-time progression is a speed manifold--not a space manifold,

as is commonly visualized. The entire background of the space-time progression without

displacements is a ‗point‘ in the speed manifold--not an expanse in the space manifold

(the container space).

In the stationary reference frame all spatial locations are at the same time. But this frame

is not valid for the entire universe. Larson states:

‖... It follows that the motions can be represented in the conventional fixed system

of reference only by the use of multiple reference points... further elaboration of

this point is necessary in order to avoid misunderstandings. The principle

stumbling block seems to be a widespread impression that there must be some

kind of a conceptually identifiable universal reference system to which the

motions of photons and other objects that remain in the same absolute locations

can be related. The expression ―natural reference system‖ probably contributes to

this impression, but the fact that a natural reference system exists does not

necessarily imply that it must be related in any direct way to the conventional

three-dimensional stationary frame of reference.‖10

Summary

Paradoxes in a theory point to defects in its logical structure. However, paradoxes and

difficulties encountered in the Reciprocal System might arise out of another source. One

of such is the unconscious practice of looking at the concepts of the Reciprocal System

from the standpoint of regarding space and time as setting or background for physical

action rather than regarding them as the contents of the universe. This has been termed

the Fallacy of Incongruous Viewpoints. The quasar paradox is seen to belong to this

category. Other such unconscious factors identified are e spatialization syndrome and

what has been termed the Fallacy of Misplaced categories, both of which were seen to

have their origin in the linguistic habits. Before branding the Reciprocal System as

fallacious on the strength of any paradoxes that might be proffered, it is mandatory to

establish that the proponent is not guilty of committing any of the above fallacies. This

danger is especially so with our generation since we are at the change over point and are

still steeped in the old frame of thinking.

References

1. The Universe of Motion, (Portland, 1984), p. 210.

2. Nothing But Motion, pp. 18-19.

3. Ibid., pp. 66-67.

4. The Universe of Motion, p. 197.

5. Nothing But Motion, p. 40.

6. Ibid., p. 41.

7. The Universe of Motion, p. 200.

8. K.V.K. Nehru, ―The Gravitational Limit and Hubble‘s Law‖, Reciprocity, XVI

(2), Winter 1987-88, pp. 11-16.

9. ―The Large-Scale Structure of the Physical Universe,‖ Reciprocity, XX (2),

Summer 1991, pp. 5-8 and XX(3), Autumn 1991, pp 23-28.

10. D. B. Larson, Nothing But Motion, p. 34

RADIO COMPONENT SEPARATION

IN QUASARS

In The Universe of Motion,l the volume dealing with the astronomical applications of the

Reciprocal System (RS), Larson gives a complete account of the explanation of the

quasars and the related phenomena. He deduces that the redshift of the quasars has two

components, z, that due to the recession, and q, that due to the speed imparted by the

galactic explosion that ejected tlie quasar. He relates these two components by the

equation

q =3.5z½ (1)

In Chapter 22 of the work cited, he adduces observational evidence supporting his

inferences. Among the items he considers there is the observed separation of the radio

emitting regions of the quasars. He observes: ―The... angular separation of such large

proportion of these radio components of quasars stands out as an observed fact for which

conventional astronomical theory has no explanation.‖² According to the RS, the

explosion speed of the quasar is incapable of representation in the conventional three-

dimensional spatial reference system, since it exceeds unit speed (the speed of light), the

limit of such reference system. However, under appropriate circumstances, the motion in

the second dimension appears in the reference system with a direction perpendicular to

the line of motion in the original dimension. An example is electromagnetism. In the case

of quasars this direction is perpendicular to the line of sight.

Component Separation Data

In Table VI of his book² Larson lists the quasar component separation data. These data

are relisted in Table I below, with the redshift data added and in increasing order of the

redshift. Larson states: ―The recession speed in the second dimension is the same as in

the dimension coincident with the reference system, but as observed it is reduced by the

inter-regional ratio...‖³ Therefore, denoting the inter-regional ratio applicable by R, and

the lateral separation by y, expressing it in the same units as those of the recession

distance z, we have according to Larson

y = Rz (2)

However, as could be seen from the last column of Table I, the y/z values are not

constant. Larson asserts: ―...the observed separations vary, and are generally less than the

calculated 33.3 seconds of arc.‖3³ He attributes the variation in the values to the

differences in the times elapsed since the explosion event in the several cases.

Table 1. Quasar Redshift and Component Separation Data

Designation Larson‘s

classification q z

y/z

(arcsecs)

3C 273

3C 249.1 II B

I L

0.156

0.303

0.002

0.008

19.6

18.8

3C275.1

3C 261

MSH 13-011

3C 207

I E

I E

I L

I E

0.534

0.586

0.596

0.650

0.023

0.028

0.030

0.034

13.2

10.8

7.1

6.7

3C 336

3C 205

3C 288.1

3C 208

II B

II B

II A

0.866

0.895

1.024

0.061

0.066

0.086

21.7

15.8

6.4

10.5

3C 204

3C 181

3C 268.4

3C 280.1

3C 432

II A

II A

II A

II A

II A

1.026

1.254

1.269

1.480

1.597

0.096

0.128

0.131

0.179

0.208

31.4

6.0

9.4

19.0

12.9

I want to demonstrate that the quasar component separation data listed in the Table

indicate a relationship between the recession, z, and the component separation, y,

stronger than is suggested by Larson. Class I quasars with q less than 1.0 and Class II

quasars with q greater than 1.0 seem to show two distinct patterns. Regression analysis of

the data on the first six quasars in Table I (all of which are Class I with q less than 1.0,

with the sole exception of 3C 273) yields the following relationship.

y/z = A - Bz (3)

with A = 21.44, B = 413.9, and the correlation coefficient = -0.98, which is highly

significant.As regarding the Class II quasars with q greater than 1.0 (excepting 3C 208),

that is, the last five quasars in Table I, the following relationship shows up.

y/z = C + D/z³ (4)

with C = 8.8, D = 0.0124, and the correlation coefficient = 0.75, which is also fairly

significant.

Discussion

Rewriting equations (3) and (4) respectively as

y = Az - Bz² for q < 1.0 (5)

y = Cz -D/z² for q > 1.0 (6)

and comparing them with Eq. (2) it can readily be seen that in addition to the factor z,

suggested by Larson, there is another factor z², that contributes to the lateral shift in the

coordinate space.

Further it might be of interest to note that the following equalities hold good very nearly.

B = A², D = 1/C² (7)

Tentatively assuming their validity, we obtain by regression analysis

y = 20.9 z - (20.9 z)² for q < 1.0 (8)

with a correlation coefficient of 0.98, and

y = 8.96 z + 1/(8.96 z)² for q > 1.0 (9)

with a correlation coefficient of 0.75.

Recalling that z is the recession speed, we can see that the explanation for the z²

component that occurs in these equations could be as follows. Larson shows that

associated witb a speed v (expressed in natural units) there is a shift in coordinate time

amounting to v² (in natural units). For example, in the case of gravitation, effects like the

excess perihelion shift of a planetary orbit or the deffection of a light beam grazing the

sun's limb, are shown to be the result of this coordinate time component.

Now it can easily be seen that the second power expression in Equations (5) and (6) is a

similar effect of shift in coordinate space, proportional to z². The speed imparted to the

quasars on ejection is always greater than unity (in fact, this is what makes them the

quasars), and in this speed range we would expect the shift to be in coordinate space

rather than in coordinate time. Tbis, therefore, shows up as the additional component in

the lateral recession.

Further, for values of q , the explosion redshift, greater than unity, the relevant factor to

be considered is not the speed but the inverse speed, due to the reversal of the space-time

direction from the point of view of the conventional reference system. Hence the

coordinate spatial shift is proportional to 1/z².

We encounter similar state of affairs in the case of the formation of the planetary system

of a star. The planets condense from what Larson calls the B component of Type I

supernovae, a white dwarf moving in the intermediate speed range. Discussing the Bode's

Law, Larson deduces4 that tbe distances of the inner planets fiom the sun are related to

the factor n², where n is the number of units of motion in time on the spatial side of the

neutral point. The distances of the outer planets are related to the factor 1/n² since they

pertain to the temporal side of the neutral point of the motion in time.

On analysis we find that, for the inner planets, the following equation holds good with a

correlation coefficient of 0.999.

d = 0.868 n - 0.1028 n² (10)

where d is the distance from the sun in AU, and n the number of units of motion in time.

Tbe regression equation for the outer planets (including the asteroids) comes out with a

correlation coeffcient of 0.999 to be

d = 0.1184 n + 76.28/n² (11)

The values of n are as follows: for Mercury 8, Venus 7.5, Earth 7, Mars 6, Asteroids 6 to

5, Jupiter 4, Saturn 3, Uranus 2, Neptune and Pluto 1.5.

Conclusions

l. Larson has shown that the lateral shift, y, of the radio components of the quasars is due

to the speed in the second scalar dimension and is a constant (the inter-regional ratio)

times z, the recession redshift.

2. We find that there is an additional shift in the coordinate space that is given by the

following relationships

y = Az-Bz² forq<1.0

y = Cz+D/z² forq>1.0

where q is the speed of the quasar in the explosion dimension, and A, B, C, D are

constants.

References

1. D.B. Larson, The Universe of Motion, Portland OR: North Pacific Publishers,

1984.

2. Ibid., p. 300.

3. Ibid., p. 301.

4. Ibid., pp. 98-99

ANOTHER LOOK AT THE

PULSAR PHENOMENON

Astronomers have recognized in the pulsars, the extremely compact pulsating stellar

objects, opportunities to test the correctness of the predictions of different theories of

gravitation. In fact, the substantial amount of accurate observations accrued on the binary

pulsar PSR 1913+16 by J.H. Taylor et al.¹,² brings this goal nearer to achievement. It is,

therefore, possible to test the Reciprocal System on the basis of the information now

available on PSR 1913+16 and other pulsars.

According to the Reciprocal System, a pulsar is the ultra-high-speed product of a Type II

supernova explosion–the result of reaching the upper rotational limit of matter. In

Quasars and Pulsars³ Larson gives a brief account of the origin and characteristics of

pulsars. Arnold Studtman&S‗4 in his doctoral dissertation Towards a Unified

Cosmological Physics gives a critique of Larson‗s theory of pulsars. A study of these

raises some issues that need clarification.

1.0. Firstly: we recall that quasars, too, like the pulsars, are the result of gigantic Type II

explosions which impart sufficient speed to carry them past the neutral point and into the

region of motion in three-dimensional time. The overcoming of the gravitation that gives

rise to the pulsation phenomenon is present in the quasar situation as well. As such, the

reason why the pulse phenomenon is not apparent in the case of quasars must be

explained.

2.0 If Larson‗s account of the pulse mechanism is correct, it can be seen that the duration

of each pulse cannot be more than a few natural units of time (n.u.t.), at the most, beyond

the point where gravitation has decreased to half of unit value. But such a conclusion is

not consistent with the observed fact, since the pulse widths range from about 5 to 30

milliseconds. For instance, at the point where gravitation is down to 0.500, half of the

radiation from the ultra high speed explosion product is observable in space and the other

half is unobservable. We thus receive radiation for 0.152 x 1015 seconds, after which

there is a quiet interval of 0.152 x 1015 seconds, then another flash of radiation, and so

on.5 Here it is important to note that the fraction to which the unit gravitational speed is

reduced gives the ratio of the pulse duration to the pulse period. Thus, in the above

example, when gravitation has come down to 0.5, we find that there is radiation for a

duration of one n.u.t. succeeded by a quiet interval of one n.u.t. Thus the period is two

n.u.t., and the ratio of pulse duration to pulse period is 1 n.u.t./2 n.u.t. = 0.5.

Now suppose that gravitation has come down to 0.4. In this case, as far as the radiation is

concerned, the proportion of the spatially active time units to the spatially inactive time

units is 0.4 to 0.6. Since there are no fractional units, we find that there will be a radiation

pulse for a duration of 2 n.u.t., followed by a quiet interval of 3 n.u.t., yielding a pulse

period of 5 n.u.t.–the .us smallest whole number of n.u.t. possible. However, the ratio 2/3

of the spatially active to the spatially inactive units is not the only one which is equal to

the ratio 0.4/0.6. The ratios 4/6, 6/9, 8/12, etc. are all mathematically equal to it. But the

2/3 ratio is the most probable one since it involves the least number of consecutive units

of any one kind, spatially active or spatially inactive, in continuous succession. Thus, as

the gravitation goes on attenuating, the pulse period increases, but the pulse duration does

not grow, being constrained by the discrete unit postulate and the probability principles.

By the time the pulse period has grown to an observationally detectable size, the pulse

duration remains in the range of one n.u.t. to a few femtoseconds. But this conclusion is

at variance with the actual observed pulse widths. Neither Larson nor Studtmann points

out this discrepancy.

2.1. One way to get over this problem seems to be by realizing that the magnetic

explosion which drives the stellar matter to the superluminal speeds does not impart those

speeds to all parts of the affected material at the same instant of time. Presumably the

inception of the explosion takes place at the center of the star and spreads to the outer

layers at the speed of light. Consequently, different portions of the star enter the region of

motion in three-dimensional time at different instants. This engenders a phase difference

among the radiation pulses given out by these various portions, while their respective

pulse periods will be the same, since the period is determined by the degree of attenuation

of the gravitation and not by the epoch of their reaching the gravitational limit. Thus the

observed pulse can be seen to be the result of juxtaposing individual subpulses (from the

different portions), each of duration not more than a few femtoseconds.

A total pulse width of 10 milliseconds, say, implies that the portion of the original stellar

material that became the pulsar is of radius

(10 x 10³ sec) x (2.99793 x 105 km/sec),

equal to 0.0043 solar radii; the outlying material being dispersed into space to form the

SNR (supernova remnant). This does not mean that only material within a radius of 3000

km underwent the catastrophic explosion. The explosion might continue to larger radii,

but the speed imparted to it becomes less than is necessary to transport the matter to the

region of three-dimensional time. Thus, knowledge of the pulse width will enable one to

estimate the fraction of the original star‗s mass that went into the pulsar.

3.0. The next difficulty with Larson‗s account of the pulse mechanism concerns the

occurrence of two separate peaks in the pulses of many pulsars (like CP 0834, CP 1133,

NP 0532, PSR 1913+16, etc.) No explanation has been offered for this from the

framework of the Reciprocal System. In the conventional lighthouse model, the double

peak is explained by suggesting that the pulsar beam is a hollow cone and the peaks could

be the two sides of the cone sweeping past our earth. Though this suggestion is perfectly

legitimate, the process whereby such a hollow cone beam of polarized radiation can be

generated in the pulsar is far from being understood.

3.1. Two ways of accounting for this pulse structure seem possible in the context of the

Reciprocal System. Larson points out that the distribution of emitted radiation takes place

two-dimensionally ―. . . when (it) originates in the region of ultra high speeds, where

physical action takes place only in two scalar space-time dimensions, and not in 3-

dimensional space or time.‖ -6 Furthermore, this is also the reason for the radiation to be

polarized, as it is constrained to the two dimensions. It is not clear why Larson, while

asserting both the two-dimensional distribution of radiation and its polarization in the

case of the quasars, highlights only the polarization aspect with nothing more than a

passing reference to the planar emission in the case of the pulsars.

The double peak can easily be explained if the pulse production is regarded as being due

to the 2-dimensional distribution of the pulsar radiation coupled with the fact of the rapid

spinning of the pulsar. Two peaks are the result if the angle between the spin axis and our

line of sight is greater than the angle of tilt of the radiation plane relative to the spin axis.

3.2. The second alternative is the explanation offered in item 2.1. above. As the total

pulse is seen to be made up of an ensemble of phase-shifted micropulses originating from

different zones that are transported to the realm of motion in 3-dimensional time at

different moments, the general shape of the pulse gives an idea of how the explosion

progressed.

Obviously the first material to reach superluminal speeds is that nearer the center of the

star where the explosion begins. In the normal course, the explosion spreads radially

outward in an expanding spherical shell. Therefore, as the explosion progresses, the

quantity of the material involved in the explosion increases nearly as the square of the

radius, in the initial stages, with the consequent rise in the magnitude of the explosion.

This manifests itself as the corresponing increase in the amplitude (luminosity) of the

successive subpulses, starting from zero. However, as the explosion front progresses to

larger radii it encounters material at lower and lower densities–the decrease in the density

eventually more than offsetting the increase in the spherical area. This results in a fall in

the intensity of the explosion and shows up as a decrease in the amplitude of the

successive subpulses.

However, if the size of the exploding star is very large, the above phenomenon is

modified. The densities in such a star in the regions beyond the initial parts of the

explosion are greater compared to a star of smaller size. Under these conditions, the

advancing compression wave due to the explosion in the inner regions is usually

sufficient to raise the material density at a larger radius and to step up the strength of the

explosion again, resulting in the second peak. It may also be noted that in such a case the

height of the second peak has normally to be less than that of the first. In the case of a

smaller star the second peak does not occur for the reason that the pressure wave simply

ejects the low density matter in the outer layers outward, forming the remnants.

The Type II supernova, which is the origin of the pulsar, is the result of reaching an age

limit. This also means that the general size of the star is comparatively large (due to

accretion) and hence the double peak in the pulse need not be a rare feature. As already

remarked, the shape of the pulse is the signature of the explosion. With a knowledge of

the density profiles in stars and the kinetics of the explosion it is not difficult to calculate

the critical size of the star necessary to produce two peaks in the pulse. Since, as already

noted, the pulse duration gives an idea of the radius of the parent star involved in the

explosion, it is possible to estimate the mass of the pulsar, its radius, period of rotation,

density, luminosity, and average temperature.

4.0.1. The next difficulty is concerning the calculations of the lifetimes. In .us Quasars

and Pulsars Larson explains that the pulsar is continuous until the inner gravitational limit

is reached in the explosion dimension. Beyond this distance there is a pulsation with an

increasing period. There is also another distance, the outer gravitational limit, beyond

which there is no gravitational effect at all and hence the pulsar is not visible as it ―leaves

the material sector‖ of the universe. In the .us Structure of the Physical Universe Larson

evaluates these two gravitational limits for a star of one solar mass as being 2.26 and

13350 light years respectively. Consequently, he points out that the life of a one-solar-

mass pulsar is limited to about 13,000 years.

Further, as the continued attenuation of the gravitation–which is responsible for the

gradual increase of the pulse period–is related to the inverse square of the distance

traveled (in time) Larson arrives at the following relation between the period P and the

age A: P = KA² where K is a constant. Since both the age and the period of the Crab

Nebula pulsar, NP 0532, are known, he calculates the value of the effective inner

gravitational limit in the case as being 6 x 105 light years7.

The inner and outer gravitational limits of a star of m solar masses are respectively given

by d = 2.26 m½ and d = 13350 m½ light years.

Therefore, their ratio:

d /d = 13350/2.26 = 5907.1

is seen to be independent of the mass. Thus the outer gravitational limit in the above case

of NP 0532 works out to be

d = 5907.1 x (6 x 105 ) = 0.354 light years.

This means that its life is limited to 0.354 years, of 130 days! Thus there is an unresolved

incompatibility between the requirement of a small inner gravitational limit as little as 6 x

105 light years (to account for the pulsar‗s present period) and the requirement of an outer

gravitational limit as being nearly 13350 light years (to account for the lifetime).

4.0.2. Studtmann8 estimates the masses of several pulsars on the basis of a relation

involving the maximum possible age of a pulsar. For example, the maximum pulse

period, for the Vela pulsar, PSR 0833, is computed to be 5.2345 seconds. Then on the

basis of P = KA² relation, the A of PSR 0833 is calculated to be1503 x (5.2345/0.0892) =

11514 years where 0.0892 seconds is its present (1969 value) pulse period at the age of

1503 years. Comaring this maximum age with that of a one solar mass pulsar, namely

13350 years, he calculates the mass of PSR 0833 as (11514/13350)² = 0.74 solar masses.

However, there is an inconsistency in the calculations. This stems from the fact that the

present age of the Vela pulsar, 1503 years, used in the above computation is, in the first

instance, arrived at in an earlier calculation5 on the basis that its mass is one solar mass.

To be precise, the fact that the value of the constant K in P = KA² is dependent on the

mass of the pulsar seems to have been overlooked. The period P of the pulsar at an age A

, when it just arrived at the inner gravitational limit d , is one n.u.t. Since d = A (when the

former is expressed in light years and the latter in years)10 we have

A = 2.26 m½

(see item No. 4.0.1. above). Thus

K = P /A² = 1.52 x 1016 / 2.26²m

Moreover, it will be seen that if P = KA² is to be true, the maximum possible period,

whatever might be the pulsar‗s mass, turns out to be

P = (13350/2.26)² x 1.52 x 1016

= 5.31 x 109 seconds!

Once again the inference seems to be that the inner gravitational limit of 2.26 light years

is too large.

4.0.3 The next difficulty of the same category is concerning the time derivative of the

period, P. Studtmann¹¹ describes how Larson, from the three relations, P = KA², A is

inversely proportional to P, and 3 = P, concludes that Pis inversely proportional to P

raised to the power of 1.5. But since age A is time, from P = KA² we have P = 2KA. How

A is taken to be inversely proportional to P is not clear.

5.0.1. The next category of difficulty is about the pulsar gravitation. Do pulsars exhibit

additional redshift like the quasars, which according to the theory arises out of the motion

in time?

5.0.2. Because of the ultra high range of speeds imparted to the pulsar material, the

material is expanding in time and the gravitation that seems to be acting is gravitation in

time. If pulsar gravitation is in time, it is not clear how a pulsar can ever form a binary

system (like PSR 1913 + 16, for example).

5.0.3. Further, it must be recalled that gravitation is an inward scalar motion .us inherent

in the very scalar motion forming the material atoms. So long as the material type of

atomic rotation is extant, it is not clear how the concomitant gravitation can be anything

other than spatial. In the case when the gravitation in space is completely offset by the

speed imparted by the explosion, it must be recognized that the explosion speed can only

counteract the .us translational aspect of the gravitation, and cannot nullify the positive

scalar .us rotation;, much less convert it to the negative rotation of the cosmic atoms

which is the source of the gravitation in time. Consequently, even though the two extra

units of speed transport the material into the cosmic sector where the gravitation in time

is operative, the atoms with the material type rotation cannot form aggregates in 3-

dimensional time–they move outward in time as well as space.

6.0. Explaining the pulsing at X-ray frequencies occurring in the case of some pulsars,

Larson says ―. . . accreted low-speed matter will interact with the adjacent portions of the

pulsar, and will reduce the speed of some of its constituent particles below the unit level,

causing the emission of x-rays . . . Inasmuch as all of the three types of radiation, radio,

X-ray, and optical, originate in the rapidly moving pulsar, the pulsation rates will be the

same for all.‖¹²

But the retarding of the superluminary matter to the region below unit level (thereby

causing X-ray emission) will also eliminate the cause for the pulsing phenomenon, since

in that speed range radiation is emitted continuously, that is, in every unit of clock time. .

6.1 It is suggested that, on the other hand, the x-ray emission could be the result if some

portions of the pulsar material are .us accelerated from the 2-x speed range to the 3-x

range, since this speed range brings the motion back into space again (in the second

scalar dimension).

7.0. Larson states: ―At this . . . 0.500 distance, half of the radiation from the ultra high

speed explosion product is observable in space and the other half is unobservable.‖5 This

description, I think, can be misunderstood by imagining that though the other half of the

radiation is unobservable in space, it nevertheless exists. But this is impossible because

the photons of radiation, having no independent motion, progress scalarly outward at unit

speed and are observable either from the naterial sector or from the cosmic sector. ―The

other half‖ which Larson refers to as being ―unobservable‖ must be radiation which .us

was never emitted. The term ―radiation observable in space‖ could be misleading too.

In his .us Structure of the Physical Universe, Larson very clearly explains the mechanism

of the emission of radiation, making use of the Principle of Inversion. ―From this

principle we find that the thermal motion of the atoms of matter is in equilibrium with a

similar vibratory motion of the space units in which they are located. . . . and as space-

time progresses it carries this vibrational motion of the space units along as radiation.‖13

The atoms enter new space units as they are moving inward in space (while space-time is

progressing outward), and these new units also acquire the vibration and become photons.

So long as the material atoms are continuously moving from one space location to

another (in the inward direction) by virtue of their gravitational motion, each successive

space unit traversed turns into a photon, and the radiation is continuous. If the radiation is

to be intermittent–as in the case of the pulsars–this can happen only if the motion of the

atom is intermittent. For instance, in the example cited by Larson, where the gravitation

is down to 0.500, the atoms move inward to the adjoining space unit in one unit of time

and in the next unit of time their movement is coincident with the background space-time

progression. From the foregoing it can be seen that if L is the luminosity calculated from

the Stefan-Boltzmann Law, the actual luminosity L is proportional to L /P where P is the

pulse period, because the energy leaves the atoms only intermittently. If this argument is

legitimate it must lead to the correct theoretical identification of the relationship between

the radio luminosity and the period.

REFERENCES

1. Scientific American, May 1979, p. 75.

2. J. M. Weisberg et al., Scientific American, Oct. 1981, p. 66.

3. D. B. Larson, Quasars and Pulsars, North Pacific Publishers, Portland, Oregon,

1971), p. 159.

4. A. D. Studtmann, Toward a Unified Cosmological Physics (1979).

5. Larson, Quasars and Pulsars, pp. 166-67.

6. Ibid., p. 100.

7. Ibid., p. 169.

8. Studtmann, op. cit., p. 595.

9. Ibid., p. 588.

10. Ibid., p. 591.

11. Ibid., p. 592.

12. D. B. Larson, Astronomical X-ray Sources, (North Pacific Publishers, 1974) p. 9.

13. Larson, The Structure of the Physical Universe, (North Pacific Publishers, 1960),

p. 119.

THE COSMIC BACKGROUND RADIATION:

ORIGIN AND TEMPERATURE

The Cosmic Sector

One of the outstanding achievements of the Reciprocal System of Theory is the discovery

of the fact that the physical universe is not limited to our familiar world of three

dimensions of space and one dimension of time, the material sector as Larson calls it. By

virtue of the symmetry between the intrinsic natures of space and time, brought to light

by Larson, he demonstrates the existence of a cosmic sector of the physical universe,

wherein space-time relations are inverse of those germane to the material sector.

The normal features of the cosmic sector could be represented in a fixed three-

dimensional temporal reference frame, just as those of the material sector could be

represented in a fixed, three-dimensional spatial reference frame. In the universe of

motion, the natural datum on which the physical universe is built is the outward

progressional motion of space-time at unit speed (which is identified as the speed of

light). The entities of the material sector are the result of downward displacement from

the background speed of unity (speeds less than unity), while those of the cosmic sector

are the result of upward displacement from unit (speeds greater than unity). But entities—

like radiation—that move at the unit speed, being thereby at the boundary between the

two sectors, are phenomena that are common to both these sectors.

Gravitation, being always in opposition to the outward space-time progression, is inward

in scalar direction in the threedimensional spatial or temporal reference frames. Since

independent motion in the material sector (three-dimensional space) is motion in space,

gravitation in our sector acts inward in space and results in large-scale aggregates of

matter. Gravitation in the cosmic sector acts still inward but it is inward in three-

dimensional time rather than in space. Consequently the cosmic sector equivalents of our

stars and galaxies are aggregates in time rather than in space.

Further, as Larson points out, ―... the various physical processes to which matter is

subject alter positions in space independently of positions in time, and vice versa. As a

result, the atoms of a material aggregate, which are contiguous in space, are widely

dispersed in time, while the atoms of a cosmic aggregate, which are contiguous in time,

are widely dispersed in space...

―Radiation moves at unit speed relative to both types of fixed reference systems, and can

therefore be detected in both sectors regardless of where it originates. Thus we receive

radiation from cosmic stars and other cosmic objects just as we do from the

corresponding material aggregates. But these cosmic objects are not aggregates in space.

They are randomly distributed in the spatial reference system. Their radiation is therefore

received in space at a low intensity and in an isotropic distribution. Such a background

radiation is actually being received.‖1

2. The Radiation Temperature

An approach to the derivation of the temperature of this cosmic background radiation is

described now. This can be seen to involve the consideration of several other previously

derived items like the relative cosmic abundances of the elements and their thermal

destructive limits. To this extent, therefore, the present analysis has to be treated as

provisional—a revision in the derivation of these items would entail a corresponding

modification in the present derivation. Notwithstanding this, the general approach to the

derivation described herein continues to be valid as far as it goes.

The basis for a quantitative enquiry into the properties of the phenomena of the cosmic

sector, in general, is the fact that the space-time relations are inverted at the unit level.

For instance, ―... the cosmic property of inverse mass is observed in the material sector as

a mass of inverse magnitude. Where a material atom has a mass of Z units on the atomic

number scale, the corresponding cosmic atom has an inverse mass of Z units which is

observed in the material sector as if it were a mass of 1/Z units.²

―Because of the inversion of space and time at the unit level, the frequencies of the

cosmic radiation are the inverse of those of the radiation in the material sector. Cosmic

stars emit radiation mainly in the infrared, rather than mainly at the optical frequencies ..

and so on.‖³ Therefore, we expect the background radiation to be at a low temperature

(that is, high inverse temperature).

2.1 Averaged Energy Density

We shall attempt to calculate the temperature of the background radiation by adopting the

energy density approach. The energy density in space of blackbody radiation at a

temperature of T kelvin is given by

U = b * T4 erg-cm-3 (1)

where b = 7.5643 x 10-15 erg-cm-3 K-4.

The major contribution to the background radiation is from the cosmic stars. As such, we

shall attempt to arrive at the average energy density of the cosmic star radiation by

finding the lumped average of the energy density of the radiation from all the stars in the

material sector and then taking its inverse. At this juncture we should recognize a point of

crucial importance which renders the analysis simple: to an observer in the cosmic sector

the atoms at the center of a material sector star are as much exposed as the ones at its

periphery, and the radiation from the interior atoms is as much observable as that from

the outer atoms. This is because, as already mentioned, the locations of the atoms of a

spatial aggregate are randomly and widely dispersed in the three-dimensional temporal

reference frame. Analogously, to an observer in the material sector all the atoms of the

cosmic sector star are observable. Since (i) the temperatures in the stellar core are larger

by many orders of magnitude—nearly a billion times—than the temperatures in the outer

regions of a star and (ii) energy density is proportional to the fourth power of temperature

(eq. 1), no appreciable error would be introduced if the energy density of the stellar

radiation, originated in one sector but as observed in the opposite sector, is calculated on

the basis of the central temperature alone.

The temperature prevailing at the center of a star is determined by the destructive

temperature Td of the heaviest element in it that is currently getting converted to

radiation by the thermal neutralization process. On theoretical grounds we expect stars

‗burning‘— that is, undergoing thermal neutralization—elements with atomic numbers

ranging all the way from 117 down to a limiting value, Zs, to occur. Zs is the atomic

number of the element which, as explained in detail elsewhere4, when it arrives at the

center of the star, leads to a chain of events culminating in the thermal destruction of the

Co/Fe group of elements, in other words, in Type I supernova explosions. No star

burning an element with atomic number less than Zs is possible because it would have

disintegrated in the supernova explosions. Theoretical considerations suggest that Zs

could be between 30 and 26.4. The relevant energy density of the radiation of a star

burning element Z at its center is

Uz = b * (Td,z)4 erg-cm-3 (2)

where Td,z is the thermal destructive limit of element Z, in kelvin.

Now it becomes necessary to estimate the proportion each of the stars with central

temperature are the same as the destructive limit of the element Z, for Z = 117 to Zs.

Since the more abundant an element happens to be, the larger would be the number of

stars burning it, on the basis of the cosmic abundance of the elements that is taken to be

uniform throughout the universe, we can deduce the ratio of the number of stars burning

element Z to the total number of stars as

fz = az / S(az) (3)

where az is the relative cosmic abundance of element Z and S( ) stands for,

117

Z=Zs

Hence the expected energy density of the radiation from all the stars can be given by

U = S(fz * Uz) ={b / S(az)} * S(az * (Td,z)4) erg-cm-3 (4)

2.2 The Inverse Energy Density

Because of the reciprocal relationship between corresponding quantities of the material

and cosmic sectors, the energy density of the radiation from the cosmic stars would be the

inverse of this quantity. But before taking the inverse we must convert the concerned

quantities into the natural units from the conventional units. Thus the energy density in

natural units is

u = U / (En * Sn-3) (5)

Where En = natural unit of energy expressed in conventional units5 = 1.49175 x 10-3 erg

and Sn = natural unit of space expressed in conventional units5 = 4.558816 x 10-6 cm

We need to recognize now that radiation in the cosmic sector is dispersed in three-

dimensional time whereas the material sector progresses linearly in one-dimensional

time. A one-dimensional progression in the cosmic sector has two mutually opposite

‗directions‘ in time (say, AB and BA), only one of which is coincident with the

‗direction‘of the time progression of the material sector. The total radiation from the

cosmic sector is distributed equally between the two temporal directions and

consequently the energy density apparent to us would be only half of the total. That is

uapp = u/2 (6)

Larson brings out this point of the relationship between the actual and the apparent

luminosities while discussing the quasar radiation.s Finally, the energy density of the

radiation from the cosmic stars as observed by us is in the inverse of this quantity

uc = 1/uapp =2/u in natural units (7)

2.3 Thermal vs Inverse Thermal Distribution

At this juncture a question that naturally arises is that whether the nature of this radiation

from the cosmic sector would be thermal or not. Especially, recalling what has been

quoted from Ref.[3] earlier, it is clear that this radiation is of the inverse thermal type.

Under these circumstances the adoption of eq. (1) is questionable since it pertains only to

thermal radiation.

On examining the values of the thermal destructive limits of the elements, we find them

all larger than the unit temperature, that is, the temperature corresponding to unit speed.4

If we remember that the demarcations of the speed ranges of the material sector are as

much applicable to the linear vibratory speeds (thermal motion) as to the linear

translational speeds, it becomes apparent that the central temperatures of the material

sector stars are in the intermediate range, that is, on the time-zero side of the one-

dimensional range (see fig. 8 of Ref.[7])

Quoting from Larson: ―... ordinary thermal radiation is ... produced by matter at

temperatures below that corresponding to unit speed. Matter at temperatures above this

level produces inverse thermal radiation by the same process, ... with an energy

distribution that is the inverse of the normal distribution applicable to thermal radiation.‖8

From the foregoing the following syllogism suggests itself:

1. The energy distribution of a cosmic sector phenomenon would be the inverse of

the energy distribution of the corresponding material sector phenomenon.

2. The phenomenon under consideration is the distribution of radiation from the core

of a cosmic sector star.

3. The distribution of the radiation from the core of a material sector star is inverse

thermal, since it originates in the intermediate temperature range.

4. Hence the distribution of the radiation from the core of a cosmic sector star would

be the inverse of inverse thermal, that is, thermal.

2.4 Comparison with Observations

Reverting to the conventional units, we have the apparent energy density of the

background radiation as

Uc = uc * (En * Sn-3) erg-cm-3 (8)

Finally the derived temperature of the background radiation, with the energy density

given by eq. (8) is (adopting eq. ( 1))

Tc = (Uc / b)¼ K (9)

Substituting from eqs. (4), (5), (7) and (8) in eq. (9) and simplifying

Tc = 5.4257 x 1013 * [S(az) / S(az * (Td,z)4)]

¼ K (10)

Adopting the theoretically calculated values of az, the relative cosmic abundance9 and

Td,z, the thermal destructive limits4 of the elements, the background temperature Tc are

worked out for Zs = 117, 116, ..., 26. The listing of a Pascal program for this calculation

is given in the Appendix. Some of the conputed values of Tc are listed in Table 1 for Zs

values ranging from 31 to 26.

Table l. Computed Values of the Cosmic Background Radiation Temperature

Zs Tc (Kelvin)

---------- ---------------

31 2.989

30 2.798

29 2.614

28 2.435

27 2.587

26 2.739

--------------------------

The most probable candidate for Zs, either from the theoretical considerations4 or from

the empirical cosmic abundance data turns out to be 30. The expected temperature of the

background radiataon corresponding to Zs = 30 can be seen to be 2.798 kelvin. The

observed values reported in the literature range from 23.74 to 2.9 kelvin. It is instructive

to note that the value of this temperature calculated on the basis of the element Fe (that is,

Zs = 26) which according to Larson is the element responsible for the supernova

explosion, turns out to be 2.74 kelvin. This is in fair agreement with the recently

published value of 2.75 kelvin estimated from accurate observations.10 Even though the

derivation of the temperature of the background radiation described herein is cursory, if

suffices to demonstrate that it could be derived from theory alone in the context of the

Reciprocal System.

3. Conclusions

To highlight some of the important points brought out:

1. The stars of the cosmic sector of the physical universe are aggregates in time and

are observed atom by atom, being randomly distributed in the three-dimensional

space.

2. The radiation from these is observable as the cosmic background radiation: its

absolute uniformity and isotropy resulting from item 3.1 above.

3. The distribution pattern of this radiation is inverse of inverse thermal, that is,

thermal.

4. Since the radiation originating from the cosmic stars gets equally divided between

the two opposite ‗directions‘ of any single time dimension, the apparent

luminosity as observed from the spatial reference Reciprocity, Pol. XX, No. 1

(Spring, 1991) system of our material sector (which progresses ‗unidirectionally‘

in time) is half of the actual luminosity.

5. The energy density of the background radiation is the apparent energy density of

the cosmic star radiation, which is the reciprocal of the energy density of the

material star radiation after accounting for item 3.4 above.

6. The temperature of the background radiation computed for Zs = 30 is 2.798 kelvin

and for Zs = 26 is 2.739 kelvin (where Zs is the atomic number of the element at

stellar core responsible for Type I supernova). These are in close agreement with

the observational value of 2.75 Kelvin.

References

1. Dewey B. Larson, The Neglected Facts of Science, North Pacific Pub., Oregon,

U.S.A, 1982, pp. 72-73

2. Dewey B. Larson, Nothing but Motion, North Pacific Pub., 1979, p. 190

3. Dewey B. Larson, The Universe of Motion, North Pacific Pub., 1984, p. 387

4. K.V.K. Nehru, Intrinsic Variables, Supernovae and the Thermal Limit,

Reciprocity, XVII (1), Spring 1988, p. 20

5. Dewey B. Larson, Nothing but Motion, op. cit., p. 160

6. Dewey B. Larson, The Universe of Motion, op. cit., p. 341

7. Ibid., fig. 8, p. 72

8. Ibid., p. 246

9. K.V.K. Nehru, Relative Abundance of the Elements, Reciprocity, XII (3), Winter

1985, p. 28

10. David T. Wilkinson, Anisotropy of the Cosmic Blackbody Radiation, Science,

Vol. 232, 20 June 1986, pp. 1517-1522

THE LARGE-SCALE STRUCTURE OF THE

PHYSICAL UNIVERSE

Extensive astronomical observations carried out during the decade that passed have for

the first time revealed a most unexpected picture of the universe on a cosmic scale. The

picture that emerged is defying all the present cosmological theories. In the present

Paper, therefore, an attempt has been made to apply the principles developed in the

Reciprocal System of theory with a view to show that the conclusions reached are in

consonance with these recent observational findings. In order to demonstrate the power

of the Reciprocal System as a truly general physical theory, in Part II of the Paper, a

mathematical treatment of the concepts developed herein will be undertaken and the

results compared with facts.

1. The Bubbles in Space

In the 1980‗s, astronomers have surveyed billions of lightyears into space and millions of

galaxies and analyzed their redshifts. These studies show that the galaxies are not

distributed evenly in space but tend to occur in clusters and then these clusters themselves

occur in large groups (the superclusters). The most unexpected discovery, however, is the

occurrence of immense voids in space, empty of galaxies, between the superclusters.1,2

Three-dimensional maps of the universe prepared from the redshift surveys indicate that

―...the universe is made up of gigantic bubbles: spherical or slightly elliptical regions of

space apparently void of matter, whose outer surfaces are defined by galaxies. ... All the

galaxies... lie on the surfaces of bubbles that measure from about 60 to 150 million

lightyears across.‖³

The investigations of Geller and Huchra4 have brought to light large-scale clustering of

galaxies stretching in the form of ―gigantic filaments and sheets‖ 170 Mpc (megaparsecs)

by about 15 Mpc. The group led by Faber5 finds the `Great Attractor,‗ a stupendous

concentration of galaxies with ―...a diameter of about 80 Mpc and a mass of 3x1016

Suns.

That would be the mass of tens of thousands of typical galaxies, including the dark matter

one infers from the dynamics of galaxies.‖6 Reference [2] gives a graphic description:

―Three-dimensional maps of the distribution of galaxies... show features quite unlike

those of most other astronomical objects: the galaxies are concentrated in enormous

sheets and filamentary structures whose greatest dimension, roughly 100 million

lightyears, is an order of magnitude larger than its lesser dimensions. ...Moreover, within

each structure the galaxies are not evenly distributed: one can distinguish more densely

populated clumps and strings... Finally, interspersed among the largest structures are

huge voids, virtually free of galaxies, that are between 100 and 400 million light years

across.‖

Broadhurst and his collaborators7 have investigated the galaxy redshifts out to a distance

of 2000 Mpc in two narrow regions in the direction of the Galactic north and south poles

where the obscuration by dust is the least. Their measurements reveal periodic oscillation

of the density of galaxies with distance, all the way out to 2000 Mpc. The Fourier

spectrum of these oscillations peaks sharply at a spacing of 128 Mpc (about 417 million

lightyears), as though dense globs of galaxies are alternating with regularly spaced voids.

2. Trouble for the Conventional Theories

There are two diametrically opposite views of galaxy formation. Some astronomers hold

that the galactic structures form as ascending cascades. According to their `bottom-up‗

theory galaxies form out of a soup of gas and dust and subsequently coalesce to form

clusters and superclusters. Other theorists advocate the ‗top-down‘ theory which proposes

that the matter in the universe first collapses into vast pancake-like sheets, which then

fragment, giving rise to superclusters, clusters and galaxies (the descending cascades).

But neither model predicts the formation of bubbles which have the sharply-defined

surfaces of galaxies that are now observationally revealed.

John Horgan8 commenting in Vigyan (Scientific American, Indian edition) states: ―The

cold dark matter model predicts that most galaxies take at least several billion years to

form, so few should be found at distances greater than 10 billion lightyears. ...

Astronomers have now identified a score of galaxies more than 10 billion lightyears

away.‖ Since astronomers currently assume that the universe began in a big bang about

13 billion years ago, Horgan remarks that: ―Theorists have a hard time explaining how

galaxies formed so soon after the big bang.― While models positing cold dark matter thus

have difficulty producing such large structures as now discovered, Powell9 remarks that:

‖... models that assume fast-moving dark particles–―hot dark matter‖–do not accurately

mimic the smaller-scale details seen in the universe. ... Cosmologists ... agree, at the very

least, that current theories are far from complete.‖

Among other things, the universality and the immensity of the spherical voids have

caught the theorists utterly unawares. ―Valérie de Lapparent and Margaret J. Geller note

... that the immense size of the bubbles suggests that powerful stellar explosions–and not

the force of gravity, as is widely thought–had the primary role in the formation of the

universe.‖³ Some astronomers suggest that supernova explosions drove matter into

spherical shells, but the predicted shell sizes are orders of magnitude smaller than those

of the observed bubbles.

Another severe problem that now plagues the astronomers is concerning the recent

findings by the Cosmic Background Explorer (COBE) satellite which show the

temperature of the microwave sky to be uniform to within one part in 10,000. At much

finer angular resolution than that of COBE, recent measurements of selected patches of

microwave background by Readhead10

find no fluctuations down to two parts in 100,000.

Since astronomers conventionally regard the microwave background radiation as the relic

from the primordial (hypothetical) big bang, its absolute isotropy implies that the early

universe was extremely uniform. The current theories of cosmology–including the

‗inflationary theory‘–are unable to account how the large-scale structure of the

distribution of galaxies now evident emanates from the prevenient absolute uniformity.

3. The `Cycle' of the Universe

We will now try to examine what the Reciprocal System of theory has to offer in this

regard. The most important factor that is relevant to our present discussion is the finding

of the Reciprocal System that the vista of the physical universe is not limited to the

familiar three-dimensional space of the conventional reference system but that, by virtue

of the reciprocal relation between space and time, there exists another half, the cosmic

sector, the region of motion in three-dimensional time. For a complete description of the

logical development of the Reciprocal System that leads to the discovery of the various

‗regions‘of the universe Larson‗s original works11,12,13

must be consulted. We will give

here a brief outline of the evolutionary process of the dual sector universe to serve our

present purposes.

Quoting from Larson14

: ―1. Because of the reciprocal relation between space and time in

scalar motion, there is an inverse sector of the universe in which motion takes place in

time rather than in space. All scalar motion phenomena in three-dimensional space are

thus duplicated in the cosmic sector...

―2. There is a limiting size for galaxies, and ... some of those that reach this limit explode,

ejecting fragments, known as quasars, at speeds in the ultra high range, between two and

three times the speed of light.

―3. When the retarding effect of gravitation is reduced enough by distance to bring the net

speed of a quasar above two units (twice the speed of light) the gravitational effect

inverts, and the constituents of the quasar are dispersed into three-dimensional time (the

cosmic sector of the universe).

―4. The effect of the explosion and its aftermath is to transform a quantity of matter from

a state in which it is highly concentrated in space to a state in which it is widely dispersed

in time.

―5. By reason of the reciprocal relation between space and time in scalar phenomena, it

follows that the inverse of the foregoing processes likewise take place, the net effect of

which is to transform a quantity of matter from a state in which it is highly concentrated

in time to a state in which it is widely dispersed in three-dimensional space.

―We thus find that there is a constant inflow of widely dispersed matter into the material

sector from the cosmic sector.‘

4. Origin of the Bubbles

The two principal forces deciding the course of events in the universe are gravitation and

outward progression of space-time. The ultimate ejection of quasars into the cosmic

sector takes place when the net speed reaches two units. Then gravitation ceases to

operate in space. This leaves the outward progression of the natural reference system

unopposed, and that progression carries the constituent units of the spatial aggregates

outward in all directions at unit speed (the speed of light). Thus, centered around the

physical location of the erstwhile quasar, a spherical void starts growing. All the matter

that constituted the quasar now gets either uniformly dispersed over the expanding

spherical surface or ejected out of the material sector altogether. This leaves the inside of

the void genuinely empty.

Meanwhile there is a continual inflow of matter, which has been similarly ejected from

the cosmic sector. Since it comes from sources that are not localized in the three-

dimensional space it emerges in the conventional reference frame spread absolutely

uniformly throughout its extent. In addition, the rate of inflow of this matter is constant,

since the Reciprocal System posits a steady state on the large scale. Therefore the density

of matter in the expanding bubble rises steadily, starting from zero.

This diffuse matter in the bubble, however, is not observable until such time that it

condenses into stars and becomes self-luminous. In the meantime the bubble appears as a

void. (The reason why we prefer to call it bubble rather than void must now be apparent.)

Since the phenomena that give rise to these bubbles, namely, the ejection of quasars and

their ultimate exit into the cosmic sector of the universe, are the necessary end results of

the evolutionary process in the material sector, one must see the whole of space strewn

with these bubbles. Their diameters, of course, reflect their lifetimes. We will show in

Part II that the sizes of these bubbles predicted from the Reciprocal System do indeed fall

within the observed range.

5. Growth and Decline of the Bubbles

Consider a large sphere of diffuse (unconsolidated) matter of uniform density. We note

that while the inward speed due to gravitation, being proportional to the total mass,

increases with radius and density, the outward speed due to the progression of the natural

reference system is constant. Therefore, at the center of the sphere there is a net outward

speed, and as we move away from the center this net outward speed decreases and

eventually reaches zero at some radius. Let us call this radius the ‗zero-point

radius.‘Beyond this point gravitation predominates and the net speed becomes inward.

The zero-point radius varies inversely as the density of matter in the sphere.

In the early stages of the bubble the density is extremely low and the zero-point radius far

outspans the actual radius. Thus the net speed everywhere in the bubble is outward. Since

the bubble is already expanding at unit speed, which is the maximum that is possible in

the dimension of the conventional reference system, the net positive (outward) coordinate

speed has no further effect on the rate of expansion.

It must be seen that the expansion of the bubble is a scaling expansion, that is,

corresponding locations in the bubble at two different stages are related by the same

geometrical relationship. The matter density in the bubble always remains uniform,

although this uniform density steadily increases due to the ever-present inflow. As the

density increases, the zero-point radius decreases. Meanwhile the actual radius is

increasing. Therefore, at some point of time these two radii become equal. That is, the net

scalar speed at the bubble periphery becomes zero. We will call this the ‗point of

criticality,‘ the corresponding radius the ‗critical radius‘ and the time when it happens

(measured from the instant of creation of the bubble) the ‗critical time‘ of the bubble.

Beyond this point, with further accumulation of matter, the zero-point radius becomes

smaller than the actual radius and the scalar direction of the net coordinate speed of the

spherical shell of matter between these two radii becomes inward. This net inward speed

can now act to oppose the outward progression and slow down the expansion of this

portion of the bubble, while the portion inside of the zero-point radius continues

expanding unabated at unit speed. The speed differential occurring across this shell at the

bubble periphery raises the density there relatively rapidly. This rise in density acts as a

positive feedback to augment the inward speed of gravitation in this shell further, and

makes possible the collapsing and condensing of the matter in the peripheral regions of

the bubble.

In due time, it can be shown, this collapsing matter forms into the Globular Star Clusters

and becomes observable. The ostensible effect is the seeming cessation of the expansion

of the bubble or its retardation. As the density of matter in the bubble continues to rise,

more Globular Clusters start precipitating, in successive spherical layers towards the

bubble center, and we see that the observable radius of the ‗void‘ (zero-point radius)

decreases.

If conditions are unaltered it takes infinite time for the matter at the center to reach the

stage of star formation. But long before that, the concentration of the consolidated and

aggregated matter, in the form of the Globular Clusters and groups of these clusters in the

outer stretches of the bubble, rises high enough for the central mass to be brought into the

ambit of their gravitational limits. (See Reference [15] for gravitational limits.) This

finally terminates the existence of the bubble as its diffuse material is swallowed up by

the surrounding stellar aggregates.

6. The Uniformity of the Microwave Background

The problem of reconciling the high degree of uniformity of the cosmic microwave

background radiation with the observed large-scale non-uniformity of the galaxy

distribution does not arise in the Reciprocal System for the simple reason that the source

of the background radiation is not set in the conventional three-dimensional space at all.

Both its absolute isotropy and lack of connection with the spatial distribution and

evolution of the material aggregates result from the fact that the background radiation

originates from ‗aggregates‘ in the three-dimensional temporal reference frame of the

cosmic sector.

Larson16

explains :―... electromagnetic radiation is being emitted from an assortment of

sources in the cosmic sector, just as it is here in the material sector. Radiation moves at

unit speed relative to both types fixed reference systems, and can therefore be detected in

both sectors regardless of where it originates. Thus we receive radiation from cosmic

stars and other cosmic objects just as we do from the corresponding material aggregates.

But these cosmic objects are not aggregates in space. They are randomly distributed in

the spatial reference system. Their radiation is therefore received in space at a low

intensity and in an isotropic distribution.‖ Of its low intensity we have had occasion to

elaborate elsewhere.17

There is another point of significance that emerges from the nature of the origin of the

background radiation and is noteworthy. It is not the case that this radiation starts its

journey entirely at the edges of the universe and reaches us after traversing long stretches

of space. Insofar as the locations in three-dimensional space through which the atoms of

the cosmic aggregates happen to pass are randomly distributed, the background radiation

originates ubiquitously. So long as large enough volumes of space are considered (in

view of the low energy density of this radiation) the existence of absorbing media does

not have any effects on its overall isotropy and uniformity. The possible attenuation by

intervening dust and gas–whose occurrence is an almost certainty–is not alluded to in the

astronomical literature for the simple reason that the large-scale anisotropy it introduces

is patently contrary to the observed fact, and thus it poses an additional problem for the

current theories.

7. Summary of Part I

Recent astronomical observations reveal the occurrence of large-scale voids/bubbles in

space. Galaxies and their clusters appear distributed in sheet-like and stream-like

structures at the peripheries of these cosmic bubbles. None of the current cosmological

theories is able to accommodate these facts, leave alone predict them.

It is shown that, in contradistinction, the Reciprocal System of theory not only explains

their occurrence but also predicts their existence.

Recent observations of the cosmic microwave background radiation reveal its absolute

uniformity to an accuracy that leaves no room for the current theories to reconcile this

uniformity with the observed large-scale non-uniformity of the distribution of galaxies.

In the case of the Reciprocal System, however, this difficulty does not arise since it

shows that the cosmic background radiation originates not in the region of three-

dimensional space but in the region of three-dimensional time.

Part II: Mathematical Aspects of the Cosmic Bubbles

In Part I of this Paper (Reciprocity, XX (2), Summer 1991, pp. 5-8), we have highlighted

the recent observational findings in the field of astronomy leading to the discovery of

large-scale voids in space coupled with the distribution of galaxies as clumps at the

peripheries of these voids. We called these voids bubbles. We have demonstrated there

how the new facts could be readily explained in a natural way by the Reciprocal System

of theory. In the present Part we attempt to develop the mathematical consequences of

those concepts delineated in Part I. Since we cannot afford to repeat, Part I must be read

in order to be able to follow the present treatment. For ease of referring, section numbers

and reference numbers are continued from Part I.

8. Analysis of the Motion in the Bubble

With the knowledge of the origin and nature of the bubbles we can now attempt to

evaluate some of their properties. Let

c = the speed of light = 2.99793 x 1010

cm/s

G = the universal constant of gravitation = 6.673 x 10-8

cm³/g.s²

r = radius of the bubble, cm

t = time since creation of the bubble, s

[sigma] = rate of mass inflow into the material sector, g/cm.³s

[rho] = [sigma].t = mass density in the bubble at time t, g/cm³

M = total mass of a material aggregate, g

M0 = mass of the Sun = 1.99 x 1033

g

d0 = gravitational limit of a consolidated material aggregate, cm

k0 = a constant = 3.5664 x 1018

cm

P = the universal constant of progression = 1.044 x 10-11

cm/s²

v = speed, cm/s

a = acceleration = v (dv/dr), cm/s²

We note from Reference [15] the following:

d0 = k0 (M/M0)½

<1>

P = G.M/d0² = G.M0/k02 <2>

We will first evaluate the expressions for the speed due to progression and the speed due

to gravitation in the bubble. In the beginning stages, (see Section 5), the net speed in the

entire mass is outward and we have to consider the expressions relevant to motion in

equivalent space. Only when gravitation balances (or predominates) progression does the

motion come back into the space of the conventional three-dimensional reference frame.

8.1 Speed due to Progression

In the conventional reference system

ap = vp (dvp/dr) = P, or

vp = (2.P.r) ½

<3>

On the basis of the explanation given in Reference [15] the corresponding speed in

equivalent space is given by

vp,e/v0 = (vp/v0)²/2

where v0, the zero-point speed, is given by

v0 = (2.G.M/d0) ½

= (2.P.d0) ½

<4>

Therefore we get

vp,e = [alpha] (r/[rho])¼

<5>

where

[alpha] = (P/2.k0) ½

(0.75 M0/[pi])¼

= 1.7861 x 10-7

cgs unit <6>

8.2 Speed due to Gravitation

In the conventional reference system, considering a location at the periphery of the

bubble

ag = vg (dvg/dr) = 4.[pi].G.[rho].r/3, or

vg = (4.[pi].G.[rho]/3) ½

r <7>

The corresponding speed in equivalent space is given by

vg,e/v0 = (vg/v0)²/2.

Adopting v0 from Eq. <4> we get

vg,e = ß [rho]¾ r

5/4 <8>

where

ß = [pi] (2.G.k0/9) ½

(0.75/M0 [pi])¼ = 2.391 x 10

-3 cgs unit <9>

8.3 Net Speed

In the conventional reference system, the net speed is (using Eqs. <3> and <7>)

vn = vp - vg = (2.P.r) ½

- (4.[pi].G.[rho]/3) ½

r <10>

and in equivalent space (using Eqs. <5> and <8>)

vn,e = vp,e - vg,e = ([alpha] - ß.[rho].r) (r/[rho]) ¼

<11>

8.4 Zero-Point Radius

We have called the radius of a uniform spherical mass at whose periphery the net speed

becomes zero the zero-point radius, rz. Equating Eq. <11> to zero and using Eqs. <6> and

<9>, we obtain

[rho].rz = [alpha]/ß = (3.P)/(2.[pi].G) = 7.47 x 10-5

g/cm2 <12>

This relationship gives, for any given value of mass density, the corresponding radius

where the net speed becomes zero.

8.5 Advent of Criticality

In Section 5 we have set forth that the mass of the expanding bubble reaches a critical

state when its actual radius equals the zero-point radius. We have called this radius the

critical radius rcr and the corresponding age of the bubble the critical time tcr. Substituting

in Eq. <12> [rho] = [sigma].tcr and rz = rcr , and noting that

rcr = c.tcr <13>

we get

tcr = ([alpha]/(ß.c.[sigma]))½ seconds <14>

Now if the rate of mass inflow, [sigma], could be evaluated, one obtains the time it

requires for the bubble to reach criticality and the corresponding size of the bubble. We,

therefore, proceed as follows.

8.6 The Universal Constant of Materialization

We may call [sigma] the universal constant of materialization, like we call G and P

respectively the corresponding universal constants. Noting that r = c.t and [rho] =

[sigma].t we rewrite Eq. <11>

vn,e = ([alpha] - ß.[sigma].c.t²)(c/[sigma])¼

<15>

At the moment of the quasar exit (that is, the start of the bubble expansion), we take t = 0.

Therefore, at this moment, vn,e reduces to

vn,e,0 = [alpha] (c/[sigma])¼ <16>

This is an outward speed and can be equated to the speed that is coming in, vi, with the

inflowing matter from the cosmic sector, wherein gravitation acts inward in time

(equivalent to outward in space). It is not yet attenuated by gravitation in space (as could

be seen from ß.[sigma].c.t² = 0). The inter-sector transition of matter takes place on

individual mass unit basis. Normally, the speed effective on unit mass basis is the unit

speed c. However, as elaborated in Reference [15], the scalar rotation of atoms that is the

origin of gravitation is distributed over 156.444 directions (degrees of freedom) in the

time region (the region inside unit space) and 8 directions in the time-space region (the

region of motion in three-dimensional space). In the corresponding situation of the

cosmic atom, the cosmic gravitation gets distributed over 156.444 directions in the space

region (the region inside unit time) and 8 directions in the space-time region (the region

of motion in three-dimensional time). Consequently, the incoming speed, vi , is given by

vi = c/(156.444 * 8) <17>

remembering that the contact between motion in space and motion in time is one-

dimensional. Equating Eqs. <16> and <17> we arrive at the important value

[sigma] = 9.2679 x 10-47

g/cm³ s <18>

9. The Bubble Parameters

We can calculate the critical time by Eq. <14>, the corresponding critical density by

[rho]cr = [sigma].tcr , and the total mass of the bubble at criticality:

tcr = 1.643 x 108 years

rcr = 1.643 x 108 lightyears

[rho]cr = 4.8055 x 10-31

g/cm³

Mcr = 3.7994 x 1015

Solarmasses

We will examine these results one by one to see if they tally with the observations.

9.1 Matter Density

All the above values can be seen to be within the range of corresponding actual observed

values. Current estimates of the density (in g/cm³) of matter are as follows18

:

Interstellar space 10-24

Space near edge of galaxy 10-28

Intergalactic space 10-31

The calculated critical density is slightly higher than the estimated density in intergalactic

space but very near it.

9.2 Globular Clusters

As the net speed at the bubble periphery changes its scalar direction from outward to

inward (on reaching criticality), it initiates the collapse of a large number of individual

masses of diffuse matter all around the spherical boundary of the bubble. Each of these

masses, as it collapses, further splits into a number of aggregates of stellar size,

eventually resulting in a Globular Cluster. We will not here enter into detailed discussion

of the mechanics of the formation of the Globular Clusters for want of space. The

interested reader may refer to Larson.13

At this juncture we would merely want to make

an estimation of the collapse time of these Globular Clusters.

Let us consider the condition at the bubble periphery. There the net speed is given by Eq.

<10>. Letting [rho] = [sigma].t, r = c.t (strictly r < c.t since gravitation now

predominates: but its effect is negligible in the initial stages of the post-critical phase),

and x the radius of a proto-Globular Cluster of mass Mg, we have

dx/dt = vn = (2.P.c.t)½ - (4.[pi].G.[sigma].c².t³/3)

½ <19>

The equation can now be integrated between the limits x = xg to 0 and t = tcr to tg, where

xg = [Mg/(4.[pi].[rho]cr/3)]1/3

<20>

The following Table gives the calculated collapse time as a function of the proto-

Globular Cluster mass.

Mg (Solarmasses) Collapse Time (years)

10³ 0.41 x 108

104 0.59 x 10

8

105 0.85 x 10

8

106 1.22 x 10

8

The relationship between the collapse time and Mg obtained by regression is

Collapse Time = 0.138 x 108 (Mg)

0.158 <21>

and indicates that a star of, say, one Solarmass would condense in 0.138 x 108 years.

Thus the individual stars form well before the Globular Cluster as a whole arrives at its

final stage of equilibrium.

In passing, we would like to remark that while it is possible for the Globular Cluster to

form from a matter density of about 5 x 10-31

g/cm³ under the gravitational assistance of

the bubble as a whole, simple calculation from Eq. <12> shows that, left to itself, it

requires a density of nearly 10-26

g/cm³ to accomplish the same result.

9.3 The Bubble Size

The above calculations indicate that it takes nearly 0.4 to 0.6 x 108 years for the Globular

Clusters to form and become observable after the bubble attains criticality. During this

period the original bubble continues to expand, though not at the speed of light, at a

slightly slower rate. Adding, therefore, a distance of 0.4 x 108 lightyears to the radius at

criticality we find that the bubble diameter at this juncture works out to be

2 (1.643 x 108 + 0.4 x 10

8) = 4.1 x 10

8 lightyears.

It must be noted that this result gives the maximum possible size. Beyond this stage the

observed size actually decreases because (i) gravitation retards/nullifies the expansion

and (ii) continued formation of Globular Clusters and dwarf galaxies shifts the spherical

boundary between the visible and the dark matter ever inward, toward the bubble centre.

From Eq. <12> we can see that the apparent void radius (equal to the zero-point radius)

varies with time as

r = rcr .tcr/t <22>

Since the number of clusters grows as time passes, their combined gravitational effect

draws up the matter at the bubble core and simultaneously they close in on it. A

preliminary calculation on the basis of the gravitational limit of the surrounding group of

clusters indicates that the last stage of the bubble, before it rapidly dissipates, will occur

at a bubble diameter of about 84 million lightyears.

The observed bubble sizes reported in the literature range from 60 to 400 million

lightyears. Broadhurst's survey,7 though covering only two narrow regions but extending

to depths of 2000 Mpc, puts it at 417 million lihgtyears (see Section 1). Thus the results

of calculations made on the basis of the Reciprocal System of theory are entirely in

agreement with the facts.

9.4 Total Mass

The bubble mass at criticality has been calculated to be 3.8 x 1015

Solarmasses. But as the

formation of the Globular Clusters and other galaxies continues in the post-critical stage,

the incessant inflow of matter from the cosmic sector adds to the total mass. When the

bubble eventually reaches the supercluster stage its mass–that is, the mass of that portion

of the original bubble that condenses into groups of clusters and clusters of stars–would

be well within the 1016

Solarmass range of the current estimates.

10. Computer Simulations

B.B. Mandelbrot,19

investigating fractal shapes in nature, has studied the distribution of

galaxies and clusters of galaxies in three-dimensional space. By postulating the existence

of intergalactic voids he tried to evolve models of clustering. His findings are very

interesting and pertinent.

He starts with a completely filled space and keeps on removing spherical volumes of

matter. Both the size of the spherical hole and the location of its centre are chosen

randomly. The size of the hole is treated as a Poisson random variable with a distribution

N (>v) [proportional] 1/v <23>

which reads as the number of holes with volume greater than v is inversely proportional

to v.

The model is simulated on computer. His results–both the covariance between two points

in space and the covariance between two directions in the sky–indicate a very good fit of

data. The graphics output shows the views of the material remained after removing the

spherical chunks and bear an amazing resemblance to the actual sky maps.

10.1 Unforced Clusters

A rather significant and unforeseen result of Mandelbrot‗s model above is that the

distribution of the remaining points shows an apparent hierarchical structure. Mandelbrot

exclaims: "Each point stands for a whole minicluster ... In addition ... the miniclusters are

themselves clustered. They exhibit such clear-cut hierarchical levels that it is hard to

believe that the model involves no explicit hierarchy, only a built-in self-similarity."20

Or

again, "Increasing clustering is not provoked by the concentration of all points around a

few of them but by the disappearance of most points, leading to an increasing number of

apparent hierarchical levels."21

Hence he refers to them as ‗unforced clusters.‘

His finding is directly in line with the conclusions which Larson obtains from the

Reciprocal System. ―... the largest units in which gravitation is effective toward

consolidation of its components are the groups of galaxies. These groups begin separating

immediately, but until the outward movement produces a clear-cut separation, their

identity as distinct individuals is not apparent to observation. Here, then, is the

explanation of the large ―clusters‖ and ―superclusters‖ of galaxies. These are not

structural units in the same sense as stars or galaxies, or the groups of galaxies that we

have been discussing.‖22

(Emphasis added.) These are default clusters with apparent

hierarchical structure brought into relief by the randomly generated bubbles.

10.2 Difficulties with Mandelbrot‘s Model

The above model suffers from two shortcomings, and Mandelbrot has to introduce two ad

hoc assumptions to make it successful. These concern the hole size distribution assumed

by him (Eq. <23>). Firstly, while the model shows reasonable verisimilitude when

limited portions of sky are considered, the overall sky maps are completely wrong in that

they include voids as immense as one-tenth of the sky or more. This defect could be

traced to the unrealistically large hole sizes allowed by the hyperbolic distribution

function N (>v) [proportional] 1/v and could be eliminated by imposing an ‗upper cut-

off,‘ vmax , on the hole size.

Secondly, the unrealistically large number of small-sized holes allowed by this

hyperbolic distribution leaves no portion of the sky not covered by the holes. In fact,

Mandelbrot imposes the constraint that

P (>v) = 1, for v < 1 <24>

(where P stands for probability) to save the model. It would, therefore, be interesting to

see what the Reciprocal System has to offer in this context.

10.3 Distribution of the Hole Size According to the Reciprocal System

According to the Reciprocal System the large-scale universe is in a steady state. That is,

both the rate of inflow of matter from the cosmic sector and the rate of final quasar

transitions to the cosmic sector are uniform in time (as well as in space) and equal each

other. Therefore, for a given volume of space, the number of bubbles created per unit

time, which is the number of quasars exiting per unit time, is given by

dN/dt = b <25>

where b is a constant directly calculable from [sigma] and the average mass of a quasar.

Assuming an average quasar mass of 109 Solarmasses, b works out to be 1.37 x 10

-15 per

second per cubic megaparsec of space.

For 0 <= t <= tcr :

We have seen that till criticality the radius is given by the relationship r = c.t.

Differentiating this we get dt/dr = 1/c , and finally

dN/dr = (dN/dt)(dt/dr) = b/c <26>

Integrating we have

N1 (>r) = b (rcr - r)/c <27>

where N1 is the number of bubbles of radii larger than a specified radius r. It may be seen

that N1 is the contribution to the bubble population from the pre-critical phase of the

bubble evolution.

For t >= tcr :

Beyond the critical point, we have seen that the bubble size decreases according to Eq.

<22>. We obtain on differentiating it

dt/dr = - rcr . tcr/r² = - rcr²/c.r²

since rcr = c.tcr by Eq. <13>. Finally

dN/dr = (dN/dt)(dt/dr) = - b.rcr²/c.r2

<28>

On integrating

N2 (>r) = b ((rcr²/r) - rcr)/c <29>

where, again, N2 is the number of bubbles of radii larger than r. N2 is the contribution to

the bubble population from the post-critical phase. We have shown in Section 9.3 that in

the post-critical phase there is lower cut-off to the bubble size due to its quick dissipation.

Let this lower cut-off radius be r0. On adding N1 and N2 from Eqs. <27> and <29>

respectively we get the following total distribution.

For 0 <= r <= r0 :

N (>r) = b ((rcr²/r0) - r)/c <30>

For r0 <= r <= rcr :

N (>r) = b ((rcr²/r) - r)/c <31>

We take the one-dimensional analogue of Mandelbrot‗s Eq. <23> for the sake of

comparison

N (>r) = C‘/r <32>

where C‘ is a constant. It can readily be seen that the difficulty of unrealistically large

number of small-sized holes that occurs in Mandelbrot does not arise here because N (>0)

is not infinite but a finite constant (see Eq. <30>). Similarly the difficulty of occurrence

of unrealistically large-sized holes does not arise either. This is because there is a

maximum possible size, rcr ; and this comes out as a natural consequence of the

development of the theory in the case of the Reciprocal System–not as an arbitrary

constraint imposed on the model to make it conform to the reality.

11. Summary

The astronomical observations of the recent decade have brought to light the large-scale

distribution of galaxies in the universe and the near perfect uniformity of the cosmic

microwave background to an extent that has not been possible earlier. An unexpected fact

that has come to be established is the ubiquitous occurrence of spherical voids of gigantic

proportions throughout space. Current theories are nonplussed.

Larson has shown that galaxies, on reaching an age limit, explosively eject fragments of

their cores, imparting to them ultra high speeds. These fragments are quasars. When

gravitation is attenuated by distance (time) the net speed of quasars reaches two units, the

limit of the material sector. Then gravitation–which always acts inward–ceases to act in

space and starts operating in time. This leaves the outward progression of space

unchecked and all the constituent matter of the quasar, which hitherto stayed put, is

dispersed in all directions in space at the speed of the progression. Thus, centred at the

location of the original quasar, a spherical void starts growing.

Since the ejection of quasars and their exit are inevitable stages in the evolution of

material aggregates these voids ought to be a universal phenomenon. Preliminary

calculations demonstrate that their observed sizes and other parameters are in consonance

with the theoretical predictions.

All these latest observational findings that the current theories are at a loss to account for,

are logically explained by the Reciprocal System starting from the foundation of its

Fundamental Postulates. This Paper, thus, demonstrates once again the cogency and

power of the Reciprocal System as a general physical theory.

References

1. Stephan A. Gregory and Laird A. Thompson, ―Superclusters and Voids in the

Distribution of Galaxies,‖ Scientific American, 246 (3), March 1982, p. 88

2. A. S. Szalay and Y. B. Zel‗dovitch, ―The Large-scale Structure of the Universe,‖

Scientific American, 249 (4), October 1983, p. 56

3. Science and the Citizen section, ―Cosmic Cartography,‖ Scientific American, 254

(3), March 1986, p. 49

4. Margaret J. Geller and John P. Huchra, Science, 246, 1989, p. 897

5. A. Dressler and S. M. Faber, Astrophysics J. Letters, 354, 1990, L. 45

6. Bertram Schwarzschild, ―Gigantic Structures Challenge Standard View of Cosmic

Evolution,‖ Physics Today, 43 (6), June 1990, p. 20

7. Thomas J. Broadhurst et al., Nature, 343, 1990, p. 726

8. John Horgan, ―Universal Truths,‖ Vigyan, October 1990, p. 88

9. Corey S. Powell, "Up Against the Wall," Scientific American, 262 (2), February

1990, p. 12

10. Anthony Readhead et al., Astrophysics J., 346, 1989, p. 566

11. Dewey B. Larson, Nothing but Motion, North Pacific Pub., Portland, Oregon,

U.S.A., 1979

12. Dewey B. Larson, The Neglected Facts of Science, North Pacific Pub., Portland,

Oregon, U.S.A., 1982

13. Dewey B. Larson, The Universe of Motion, North Pacific Pub., Portland, Oregon,

U.S.A., 1984

14. Dewey B. Larson, The Neglected Facts of Science, op. cit., pp. 112-113

15. K. V. K. Nehru, ―The Gravitational Limit and the Hubble‗s Law,‖ Reciprocity,

XVI (2), Winter 1987-88, pp. 11-16

16. Dewey B. Larson, The Neglected Facts of Science, op. cit., p.73

17. K. V. K. Nehru, ―The Cosmic Background Radiation: Origin and Temperature,‖

Reciprocity, XIX (4), Winter 1990-91, p. 20 and XX (1), Spring 1991, pp. 1-4

18. William K. Hartmann, Astronomy: the Cosmic Journey, Wadsworth Pub. Co.,

U.S.A., 1978, p. 309

19. Benoit B. Mandelbrot, The Fractal Geometry of Nature, W.H.Freeman & Co.,

U.S.A., 1983

20. Ibid., p. 294

21. Ibid., p. 298

22. Dewey B. Larson, The Universe of Motion, op. cit., p. 2

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