On Experimental Confirmation of the Einstein Equation

and

the Charge-Mass Repulsive Force

C. Y. Lo & C. WongApplied and Pure Research Institute

7 Taggart Drive, Unit E, Nashua, NH 03060 USAJuly 2010

Abstract

Einstein gives three predictions to support general relativity. However, the Einstein equation, which was first derived by

Hilbert, has not been accurately confirmed beyond what the Maxwell-Newton Approximation can do. The gravitational red -

shifts, the bending light, and radar echo delay can be obtained from the Maxwell-Newton Approximation derived from Ein -

stein’s equivalence principle. As Gullstrand suspected, it is proven that there is no dynamic solution and thus the perihelion of

Mercury cannot be derived from the Einstein equation. Moreover, the Hulse-Taylor experiment of binary pulsars actually sup-

ports a modified Einstein equation. So far, the only exception is the derivation of the metric for a charged particle because the

electromagnetic energy-stress tensor is involved. It has been shown that this metric implies a repulsive force mq 2/r3 between a

charge q and a mass m, separated with a distance r. Thus, the experimental confirmation of this neutral force provides the only

case to verify the static Einstein equation. Although it has been shown experimentally that a metal ball becomes lighter after

charged with electrons, more detailed data are needed to confirm the repulsive force and distinguish its formula from claims of

other theories.

04.20.-q, 04.20.CvKey Words: pioneer anomaly, repulsive force, charge-mass interaction, charged capacitors, E = mc2.

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1. Introduction

Einstein’s general relativity was regarded as a top scientific achievement, although it was very difficult to under-

stand. Observations accurately confirm the three predictions of Einstein [1, 2], namely: 1) the gravitational redshifts, 2) the

perihelion of Mercury, and 3) the deflection of light. Einstein’s accurate predictions created a faith to his theory. Recently it

was found, however, that the difficulties arose, in part, due to its being not a self-consistent theory [3-8].

There are issues relating to the confirmation of the predictions of Einstein’s theory:

1) The gravitational redshifts were first derived from Einstein’s 1911 preliminary assumption of the equivalence between ac -

celeration and Newtonian gravity. However, Fock [9] found that it is impossible to have a metric that is consistent with

uniform Newtonian gravity. 1) This shows that the gravitational redshifts can be derived from an invalid theory.

2) The observed bending of light is inconsistent with Einstein’s theory of measurement [10]. However, the observed bending

is consistent with the measurement based on the Euclidean-like structure if Einstein’s equivalence principle is valid [8].

3) Gullstrand [11] suspected that the Einstein equation may not produce a solution for a two-body problem. For the dynamic

cases, it has been proven that the Einstein equation needs to be modified [5].

4) From both the Schwarzschild and the harmonic solution, Einstein obtained the same first order deflection of light in terms

of the shortest distance from the sun’s center [1, 2]. Then, in support of his covariance principle, Einstein [2] remarked,

“It should be noted that this result, also, of the theory is not influenced by our arbitrary choice of a system of coordi -

nates.” However, it has been shown [6] that such requirements of gauge invariance, actually are not satisfied.

Thus, Einstein’s covariance principle is proven to be invalid [6], and diffeomorphic solutions with the same frame of reference

are not equivalent in physics although they are equivalent in mathematics. Recently, it is found [8] that Einstein’s justifica -

tions for his theory of measurement are based on invalid applications of special relativity which is applicable only for a flat

space. This discovery is the last straw that breaks the back of the camel of Einstein’s erroneous theory of measurements [8].

Fortunately, the Maxwell-Newton approximation has been proven to be a valid first order approximation for gravity due

to massive sources [12], so that the binary pulsar radiation experiments can be explained satisfactorily [5, 13]. Thus, Einstein’s

notion of weak gravity is valid [12, 13]. Moreover, the Hulse-Taylor experiments of the binary pulsars validity necessitate that

the coupling constants have different signs [5]. Thus, the assumption of a unique coupling sign for the singularity theorems

[14] of Penrose and Hawking are invalid. Moreover, it leads to the investigation that Lo [15] discovered the static charge-mass

neutral repulsive force, and thus proves the famous formula E= mc2 being only conditionally valid.

Nevertheless, as shown in the 1993 press release of the Nobel Committee for the Physics Prize [16], the “experts”

failed to see that the Einstein equation does not have a dynamic solution for a two-body problem. Consequently, they also

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failed to see that there are energies that are not equivalent to mass [15, 17]. As a result, they also over-looked that the Einstein

equation actually necessitates the existence of a charge-mass interaction [15, 18, 19].

Fortunately, in 2005 the effect of such a repulsive force was inadvertently detected by Tsipenyuk & Andreev [20].

They discovered that the weight of a metal ball is reduced after it is irradiated with high energy electrons. However, they could

not explain this phenomenon 2) because they did not account for the static charge-mass repulsive force discovered by Lo [15] in

1997. However, by the time of 2005, there is another explanation for the reduction of weight by Yarman [21] whose theory is

based on unconditional validity of E = mc2 and Newtonian gravity, but he rejected general relativity [21, 22].

Based on Einstein’s equation, 3) the neutral repulsive force derived by Lo [15, 18] is: For a charge q and a mass m

separated by a distance r, the charge-mass repulsive force is mq2/r3 (in the units, light speed c = 1, and Newtonian coupling

constant = 1 [23]). Thus, in view of the 1/r3 dependence, the formula of Lo is distinguishable from the theory of Yarman

[21].

In this paper, we suggest an experiment with the “torsion balance” to find out more detailed data such that one can

verify whether Lo’s formula originated from general relativity or the theory of Yarman, which maintains the 1/r 2-dependence,

is appropriate. To this end, we will first start with a discussion of the Einstein equation.

2. The Einstein Equation in General Relativity and E = mc2

The Einstein equation (in the units, the light speed c = 1 and the Newtonian gravitational coupling = 1 [23]) is,

G R – 1

2gR = – 8 T , (1)

where G is the Einstein tensor, R is the Ricci curvature tensor, and T is the sum of energy stress tensor. 3) In general

relativity [1, 2], Einstein and his followers discussed only the special case when the source is of massive matter, i.e.,

G R – 1

2gR = – KT (m) , (2)

where T(m) is the energy-stress tensor for massive matter, and K (= 8c-P2 = 1.8710-27 [1]). Thus,

G R – 1

2gR = 0, or R = 0, (2’)

in a vacuum. However, (2') implies that there is no gravitational wave to carry away energy-momentum. This violates the prin -

ciple of causality since a wave carries away energy and momentum. This is the physical reason that the Einstein equation can -

not have a bounded dynamic solution [5, 7, 13] as the Hulse-Taylor experiments requires. 4)

To deal with experiments of the binary pulsars, our modified Einstein equation of 1995 [5] is necessarily,

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G R – 1

2gR = – K T(m) – t(g), (3)

where t(g)μν is the energy-stress tensors for gravity. 5) From (3), the equation in vacuum is

G R – 1

2gR = K t(g) . (3’)

Note that t(g)μν is equivalent to Einstein's gravitational pseudotensor in terms of his radiation formula.

Then, the linearization of equation (3) is the Maxwell-Newton Approximation [5],

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2 cc = – K T(m) , where = – 1

2(cdcd), = g – , (4)

where μν is the flat metric. Moreover, with the help of (4), the binary pulsars experiments support the validity of the eq. (3)

[5, 13], 6) although the modification is not yet complete since the exact form of t(g) remains to be found. However, the lin-

earized equation (4) may be physically invalid if the source is not massive matter [24]. Nevertheless, Wald [14, p. 183] erro -

neously extended the process to the case when the initial metric of the perturbation is not flat. This illustrates that those “ex -

perts” do not understand the mathematics related to the Einstein equation, and particularly the dynamics case.

For the static case, accurate predictions were made for the bending of light, and radar echo delay with different

gauges for the same frame of reference [23]. However, the accuracy of experiments has not been able to tell whether the static

Einstein equation is better than the Maxwell-Newton Approximation. Thus, it is difficult to say that the Einstein equation has

been established for the static case. However, a metric for a charge particle is the case that the Maxwell-Newton Approxima -

tion has not covered. Thus, this problem provides a unique opportunity to establish the static Einstein equation.

However, it should be noted that in the literature of general relativity, almost all the attention was on the sources of mas -

sive matter. If all the energy is equivalent to mass (since E = mc 2 being unconditional), there is little point to study gravita-

tional sources other than massive matter; and all the coupling constant should have the same sign. This is clear invalid accord -

ing to equation (3) which is necessary because equation (2) does not have a bounded dynamic solution [5].

The misinterpretation of E = mc2 as being unconditional has a deep root of errors starting from Einstein’s assumption

of photons having only electromagnetic energy [1]. In 1905, Einstein thought that he has proven that electromagnetic energy is

equivalent to mass [1]. Then, at least from 1905 to 1909, Einstein attempted, but failed to prove that other forms of energy

also equivalent to mass [25]. Such attempts were natural since energy conservation would suggest that all types of energy

would be equivalent. What Einstein failed to see is that the electromagnetic energy is not equivalent to mass, although the en -

ergy of photons does [26]. In fact, it is natural that photons include the gravitational waves since a charged particle is always

massive.

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3. The Neutral Charge-Mass Repulsive Force Originated form General Relativity

The misinterpretation of the formula E = mc2 as unconditionally valid, has been proven a great obstacle to the

progress of theoretical physics. First, if photons include gravitational energy, it is difficult to continue claiming that quantum

mechanics, which is based on the assumption that photons includes only electromagnetic energy, is a finally theory. Second, if

photons must include gravitational energy, general relativity is obviously not just a theory only for macroscopic phenomena.

Moreover, if E = mc2 is only conditionally valid, the existence of black holes can no longer be guaranteed even in the -

ory since gravity may not always be attractive as assumed [27]; the singularity theorems of Penrose and Hawking [14] may not

be relevant to physics since their crucial assumption of unique coupling sign has been proven invalid. Thus, both the big bang

theory and the big crunch assumption lost their theoretical foundation.

Understandably, Lo’s paper on conditional validity of E = mc2 [15] was reviewed for more than four and a half year

before it is published in 1997 because Will [28] and other theorists failed in defending the unconditional validity. Nevertheless,

the misinterpretation was revived in 2003 [29]. Moreover, the editor of the Physical Review D, Eric J. Weinberg demanded a

proof beyond electromagnetism 7) for the conditional validity of E = mc2. Now, such a proof has already been inadvertently

provided by Tsipenyuk & Andreev [20] since a charged metal ball has increased its total energy, but the weight is reduced.

The failure in discovering the static charge-mass interaction lies on misinterpretations and conceptual errors [17, 29].

The derivation is straight forward from the Reissner-Nordstrom metric [30, 31] for a charge particle Q. The metric is as fol -

lows:

, (5)

where q and M are the charge and mass of the particle Q and r is the radial distance (in terms of the Euclidean-like structure

[32, 33]) from the particle center. Here, the gravitational components generated by electricity have not only a very different ra -

dial coordinate dependence but also a different sign that makes it a new repulsive gravity. Nevertheless, journals such as Sci -

ence and Nature still hold on to unconditional validity of E = mc2 [28, 34], due to an inadequate understanding of general rela-

tivity.

Moreover, some argued that the effective mass could be considered as M – q2/2r (c =1) since the total electric energy

outside a sphere of radius r is q2/2r [18]. Then, if any energy has a mass equivalence, an increase of energy should lead to an

increment of gravitational strength. However, although energy increases by the presence of a charge, the strength of a gravita -

tional force, as shown by metric (5), decreases everywhere. Thus, the unconditional validity of E = mc 2 is a misinterpretation.

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Nevertheless, theorists such as Herrera, Santos & Skea [35] argued in 2003 that M in (5) includes the external electric en-

ergy. They overlooked that this would create a double counting of the electric energy in two different ways [18, 23]. Moreover,

the gravitational forces would be different from the force created by the “effective mass” M – q2/2r. In addition, if M included

the external electric energy, then the inertial mass m0 of the electron would be much smaller than M.8) Moreover, according to

the Einstein equation for the metric [14], since the electromagnetic energy-stress tensor is traceless, curvature R is independent

of the electromagnetic energy-stress tensor. Therefore, the electric energy cannot be equivalent to the mass.

To show the static effect, one needs to consider only gtt in metric (5). According to Einstein, the equation of motion is

where (6)

and . Let us consider only the static case, dx/ds = dy/ds = dz/ds = 0. Thus,

, where (7)

since g would also be static. Note that the gauge affects only the second order approximation of g t t [36]. For example,

and (8)

are with respect to the harmonic gauge and the Schwarzschild solution, but the second order term is negligible.

For a particle P with mass m at r, since gr r -1, the force on P in the first order approximation is

. (9a)

Thus, the second term is a repulsive force. If the particles are at rest, then the action and reaction forces are equal and in oppo-

site directions. The force acting on the charged particle Q has the same magnitude

( ) , where is a unit vector. (9b)

Thus, the first term is the attractive interaction between two masses M and m, and the second term is the repulsive force be -

tween the charged particle Q and the neutral particle P. The second term is very small for this two particles.

Now, consider a metal ball charged with electrons, whose charge is e and mass m 0. Then, the term M is increased by

Nm0 that is linearly with respect to the number N of electrons, but the term q 2 would be increasing with respect to N2e2.

Thus, a net repulsive force would results after the metal ball is sufficiently charged [18]. This is why the metal ball would

appear to have less weight than before charged. This explains the observed reduction of weight [20].

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If approximation (9a) is valid as shown, then one would observe the 1/r 3 distance dependence of the repulsive force,

where r is the distance from the center of the metal ball. This can be measured with the “torsion balance” at different dis-

tance r from the center while the metal ball is charged with different charges. When the number of electrons is sufficiently

large, the increased attractive force due the mass of the additional electrons would be smaller than the increased repulsive

force. This effect would be observed at smaller “r” first. This experiment is also a test of general relativity since equation

(9a) is based on general relativity. Moreover, this new force would lead to the existence of a five-dimensional space (see

Appendix).

4. Unification of Electromagnetism and Gravitation and the Five Dimension Theory

If the particles P and Q are at rest, then the action and reaction forces are equal and in opposite directions as shown in

(9b). However, if one calculates the space-time metric according to the particle P of mass m, only the first term would be ob -

tained. Thus, the geodesic equation is inadequate for the equation of motion. Moreover, since the second term is proportional

to q2, it is not a Lorentz force, nor the radiation reaction force since the charged particle remains static.

Thus, it is necessary to have a repulsive force with the coupling q 2 to the charged particle Q in a gravitational field

generated by masses. It thus follows that, force (9b) to particle Q is beyond current theoretical framework of gravitation +

electromagnetism. In other words, as predicted by Lo, Goldstein, and Napier [37], Einstein’s general relativity leads to a real -

ization of the inadequacy of general relativity just as electricity and magnetism lead to the exposition of their shortcomings.

Since this repulsive force is independent of the charge sign, an immediate question would be whether such a neutral repulsive

force mq2/r3 is subjected to electromagnetic screening. It is conjectured that this force, being independent of a charge sign,

would not be subjected to such a screening [19] although it should be, according to general relativity.

A theoretical framework to accommodate the necessity of unification and the new neutral force being not subject to

electromagnetic screening, would be the five-dimensional theory of Lo et al. [37]. From the viewpoint of their five-dimen -

sional theory, this new force can be considered as a result of a field created by the mass m and the field interacts with the q 2

[19]. Thus such a field is independent of the electromagnetic field and is beyond general relativity. A test of this five-dimen-

sional theory would be to measure the effect due to possibly such a force acting on a charged capacitor since it has concen -

trated charges and is self-screening. To verify their five-dimensional relativity, the existence of such a force on a capacitor

was first performed by Liu [38] 9) although the weight reduction of charged capacitors have been found much earlier [39-41].

However, the r -3-dependence (unlike r -2-dependence) is difficult to test because it would be sensitive to the local surround-

ings [29].

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Attempts to explain weight reduction of a capacitor after charged have been made; but all failed since the 50s. 10) For

instance, Buehler [39] concluded that the force could not be directly associated with the interaction of the electric and mag -

netic fields of the earth. Masha et al. [40, 41] also conceded that we must search for an explanation on their experiments. This

is consistent with the fact that the charge-mass repulsive force on a capacitor is not derivable from a four-dimension theory.

5. Conclusions and Discussions

It is interesting that effect of the static charge-mass interaction was first discovered as a weight reduction of charged

capacitors. Thus, to explain this phenomenon is beyond general relativity, and very likely incomprehensible in terms of a four

-dimensional space. This is the first physical evidence of a higher dimensional space that the string theorists assumed without

any supporting evidence from physics. Now, the establishment of the static charge-mass interaction is possibly the most impor -

tant consequence of general relativity.

The electromagnetism is an interaction among charges and the gravitation is an interaction among masses. A naive

question would be whether there is an interaction between charge and mass. From the viewpoint of physics, it should have be -

cause any charged particle has a mass. Now, we have derived such a static interaction and verified it with experiments. Thus,

such an interaction is real and can no longer be regarded as just a speculation as before. Obviously, just electromagnetism is

not limited to the Coulomb force; and there should be a current-mass interaction.

If the electric energy leads to a repulsive force toward a mass, according to general relativity, the magnetic energy

would lead to an attractive force from a current toward a mass [19, 27]. The existence of such a current-mass attractive force

has been inadvertently discovered and verified by Martin Tajmar and Clovis de Matos [42] from the European Space Agency.

They found that a spinning ring of superconducting material increases its weight much more than expected. Thus, they be -

lieved that general relativity had been proven wrong. However, according to quantum theory, spinning superconductors should

produce a weak magnetic field. Thus, they are measuring also the interaction between an electric current and the earth!

Einstein was really a genius and the full meaning of general relativity is still emerging after 100 years although he

also made mistakes. It is interesting that while his proposal of the photon earned Einstein a Nobel Prize in Physics, his imper-

fect assumption of photons having only electromagnetic energy prevented him from discovering the charge-mass interaction.

Now, with discovery of the charge-mass interaction, the door for research in physics is again wide open in both the

area of theoretical and experimental physics. Fundamental researches in physics are no longer limited to the standard model

based on the Yang-Mill theory and the string theory based on mathematical speculations! Unfortunately, some well known the-

orists still try very hard to make physical sense out of just any solution of Einstein’s equation [6, 8, 43, 44].

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To facilitate the developments of physics, the Nobel Committee should rectify the errors due to invalid mathematic in

the 1993 press release for the Nobel Prize in Physics [16]. This is meaningful because general relativity has a unique problem,

which is exceptional among all branch of physics, there is no expert in the field of general relativity [5, 6, 8] after 95 years of

being perceived as the towering theory that can provide guidance to other branches of physics.

Acknowledgments

The author gratefully acknowledge stimulating discussions with S. -J. Chang, A. J. Coleman, Z. G. Deng, G. R. Gold-

stein, J. Ho, A. Napier, D. Rabounski, G. Sobczyk, Eric J. Weinberg, and T. Yarman,. Special thanks are to Sharon Holcombe

for valuable suggestions. This work is supported in part by Innotec Design, Inc., USA and the Chan Foundation, Hong Kong.

Appendix: Einstein’s Principle of Equivalence, the Einstein-Minkowski Condition

Einstein’s equivalence principle is stated clearly in “The Meaning of Relativity” [2] as follows:

‘Let now K be an inertial system. Masses which are sufficiently far from each other and from other bodies are

then, with respect to K, free from acceleration. We shall also refer these masses to a system of co-ordinates K’,

uniformly accelerated with respect to K. Relatively to K’ all the masses have equal and parallel accelerations;

with respect to K’ they behave just as if a gravitational field were present and K’ were unaccelerated. Overlook -

ing for the present the question as to the “cause’ of such a gravitational field, which will occupy us latter, there is

nothing to prevent our conceiving this gravitational field as real, that is, the conception that K’; is “at rest” and a

gravitational field is present we may consider as equivalent to the conception that only K is an ”allowable” sys -

tem of co-ordinates and no gravitational field is present. The assumption of the complete physical equivalence of

the systems of coordinates, K and K’, we call the “principle of equivalence;” this principle is evidently inti -

mately connected with the law of the equality between the inert and the gravitational mass, and signifies an ex-

tension of the principle of relativity to coordinate systems which are non-uniform motion relatively to each

other.’

This principle is different from Einstein’s 1911 assumption of equivalence with Newtonian gravity [1].

The Einstein-Minkowski condition [1, p. 161] has its foundation from mathematical theorems [45] as follows:

Theorem 1. Given any point P in any Lorentz manifold (whose metric signature is the same as a Minkowski space) there

always exist coordinate systems (x) in which g/x = 0 at P.

Theorem 2. Given any time-like geodesic curve there always exists a coordinate system (so-called Fermi coordinates)

(x) in which g/x = 0 along .

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Thus, the local space of a particle is locally constant, although not necessarily Minkowski. What Einstein added to these theo-

rems is that physically such a locally constant metric must be Minkowski. Such a condition is needed for special relativity [2].

In fact, Einstein [1, p. 144] has given an example that illustrates Pauli’s errors. However, like Pauli [46], few understand Ein-

stein’s equivalence principle correctly [47] because of inadequate background in pure mathematics.

Pauli’s version is mistakenly regarded [48] as Einstein’s equivalence principle [1]. Pauli’s [46] version is as follows:

“For every infinitely small world region (i.e. a world region which is so small that the space- and time-variation of

gravity can be neglected in it) there always exists a coordinate system K 0 (X1, X2, X3, X4) in which gravitation has no

influence either in the motion of particles or any physical process.”

Based on Einstein’s equivalence principle, it is proven that a physical space must have a frame of reference with a Euclidean-

like structure [32]. However, Einstein’s equivalence principle was still not understood until the space contractions and the time

dilation for the case of a rotating disk were explicitly derived [49, 50]. 11) In fact, in the 1993 press release on the Nobel Prize

in Physics [16], 12) Einstein’s equivalence principle is implicitly rejected, in addition to other theoretical errors.

ENDNOTES:

1) Fock [9], Ohanian & Ruffini and Wheeler [51] and etc. have mistaken the equivalence assumption of 1911 that a uni -

form Newtonian gravity (generated by a scalar potential) is equivalent to a uniformly accelerated frame, with the equiv -

alence principle of 1916 [1, 2]. Moreover, Fock [9] found it impossible to express a uniform Newtonian gravity in terms

of a spacetime metric. Based on the above misidentification, they claimed that Einstein’s equivalence principle is in -

valid (see also Appendix A). Recently, they are proven wrong because the metric for a uniform gravity has been derived

[50].

2) Recently, G. Sobczyk and T. Yarman informed us the important results of reference [20].

3) The Einstein equation with a source of massive matter is actually first derived by Hilbert [52]. However, with a source

involved electromagnetism, such an equation is first proposed by Einstein [1, 2].

4) An evidence that Einstein equation has no bounded wave solution is that the calculated gravitational radiation depends

upon the method of approximation used [53].

5) The energy-stress for gravity t(g)μν should be a tensor [5] although Einstein considered it to be a pseudo-tensor.

6) P. Morrison of MIT also recognized errors in the 1993 press release of the Nobel Committee. He went to Princeton a

few times to discuss with Taylor the calculations of the pulsar radiation [49]. Note also that Christodoulou & Klainer-

man [54] of Princeton incorrectly claimed their success in constructing dynamic solutions [55, 56].

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7) For this, one of the authors (Lo) would like to thank Eric J. Weinberg for his demand that leads to new discovery.

8) 7Misner et al. [23; p. 841] point out that M is the total mass as measured by a distant observer using the Keplerian orbits

of electrically neutral particles. In other words, for an electron, the constant M is m 0 , the accelerated mass of the elec-

tron.

9) According to m = E/c2, the mass increment of a charged capacitor is negligible. For a capacitor of 200F charged to

1000 volt, the related mass increment would be about 10-12 gram.

10) Some related experiments can be stated in the Biefeld–Brown effect , http://en.wikipedia.org/wiki/Biefeld–Brown_effect

11) For instance, just as Pauli [46], ‘t Hooft [44], Misner et al. [23] etc., due to inadequate background in pure mathematics

[47], failed in understanding Einstein’s equivalence principle. ‘t Hooft also did not see that the operation of linearization

to obtain an approximate solution may be invalid. However, he does understand the need of a bounded solution. Ein -

stein, Infeld, & Hoffman [57] did not even recognize the need for proving the boundedness of a solution. Currently,

when knowledge in pure mathematics is required, some physicists make mistakes inadvertently, although they are very

good otherwise. For example, Pauli was a bright theoretical physicist, and ‘t Hooft is an excellent applied mathemati -

cian. Nevertheless, they both failed to understand Einstein’s equivalence principle (see Appendix A).

12) The Nobel Laureates are selected by a Nobel Committee that consists of five members elected by The Royal Swedish

Academy of Sciences. In its first stage, several thousand people are asked to nominate candidates. These names are scru-

tinized and discussed by experts until only the winners remain. The nomination and selection process for the Nobel Prize

in Physics is usually long and rigorous. This is a key reason why these Nobel Prizes have grown in importance over the

years to become the most important prizes in Physics. On the other hand, any error of the Nobel Committee in physics is

almost certainly an error of those considered to be experts in the field.

References:

1. A. Einstein, H. A. Lorentz, H. Minkowski, H. Weyl, The Principle of Relativity (Dover, New York, 1952).

2. A. Einstein, The Meaning of Relativity (1922) (Princeton Univ. Press, 1974); Einstein added Appendix II in 1950.

3. A. N. Whitehead, The Principle of Relativity (Cambridge Univ. Press, Cambridge, 1922).

4. A. S. Eddington, The Mathematical Theory of Relativity (1923) (Chelsea, New York, 1975), p. 10.

5. C. Y. Lo, Astrophys. J. 455, 421-428 (Dec. 20, 1995); Editor S. Chandrasekhar, a Nobel Laureate, suggests and approves

the Appendix: The Gravitational Energy-Stress Tensor for the necessity of modifying Einstein equation.

6. C. Y. Lo, On Gauge Invariance in Physics & Einstein’s Covariance Principle, Phys. Essays, 23 (3), (Sept. 2010). Bulletin

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(2010).Phys. Essays 18 (1), 547-560 (December, 2005).

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ences, 25D (1), 41- 47 (2006).

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32. C. Y. Lo, Chinese J. of Phys., Vol. 41, No. 4, 332-342 (2003).

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38. W. Q. Liu (http://www.cqfyl.com) got certified results of lighter capacitors after charged in a Chinese Laboratory of the

Academy of Science. Also, his weighting of magnets is consistent with the claim of J. A. Wheeler [27, p. 263] (private

communication, August 2007).

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Mixing, 2, 1-22, 2004. living@doylebuehler.com.

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42. http://news.softpedia.com/news/The-First-Test-That-Proves-General-Theory-of-Relativity-Wrong-20259.shtml

43. C. Y. Lo, Bulletin of Pure and Applied Sciences, 27D (2), 149-170 (2008); at the request of ‘t Hooft, his article on gravita-

tional waves is attached as the Appendix B. The Appendix A is on Einstein’s Principle of Equivalence.

44. G. ‘t Hooft, “Strange Misconceptions of General Relativity”, (there are other problems beyond those addressed in [43])

http://www.phys.uu.nl/~thooft/gravitating_misconceptions.html

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50. C. Y. Lo, Bulletin of Pure and Applied Sciences, 26D (2), 73-88 (2007).

51. H. C. Ohanian & R. Ruffini, Gravitation and Spacetime (Norton, New York, 1994).

52. H. C. Ohanian, “Einstein's Mistakes: The Human Failings of Genius (Norton, New York, 2008).

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54. D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space (Princeton Mathematical

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56. Volker Perlick (republished with an editorial note), Gen. Relat. Grav. 32(4), 761-763 (2000).

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