NPA Twin Paradox Report

8/2/2019 NPA Twin Paradox Report

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dilation was apparent and not physical. Mendel Sachs reviewed manyEinstein papers and presentations and wrote3, "I will quote some of hiscomments that were made during his life, that convince me that Einsteindid not believe, after all, that the kinematic relations, such as the Lorentz

transformations of special relativity, or the space-time transformationsbetween accelerated frames (of general relativity), can indeed inducerelative physical changes in the make-up of matter, such as the claim of the twin paradox.

"In a lecture that Einstein gave to the Prussian Academy of Sciences, in1921, he said the following:

"Geometry predicates nothing about relations of real things, but onlygeometry together with the purport of physical laws can do so... The ideaof the measuring rod and the idea of the clock coordinated with it in the

theory of relativity do not find their exact correspondence in the realworld . It is also clear that the solid body and the clock do not in theconceptual edifice of physics play the part of irreducible elements, butthat of composite structures, which may not play any independent part in

theoretical physics." (Sachs' italics.)

Sachs continued, "Einstein then went on to say that, in spite of theforegoing comment, we should temporarily support the use of the lengthand time transformations as though they were physically real, because"we are still far from possessing such certain knowledge of theoreticalprinciples as to be able to give exact theoretical constructions of solid

bodies and clocks.""

Sachs continued, "Thus we see that, on the one hand, Einstein admittedthat one must not, in principle, interpret the theory of relativity to implythat similar physical entities age differently by virtue of their relativemotion. But, on the other hand, he said that we should neverthelessassume (for the time being!) that there is such a physical correlationbetween the physical aging of material entities and their relative motion-because we haven't yet learned how to treat the laws of matter in an exactway, when taking account of the measuring rods and clocks that are usedto verify these laws."

In 1911, Einstein was shifting focus on the Twin Paradox solution tospacetime diagrams and the invariance of the interval4. Also, in 1911,Max von Laue made a similar shift5. (Incidentally, Paul Langevin, also in1911, popularized the issue by focusing on the differential aging of a pairof twins rather than on a pair of clocks and the Clock Paradox wasrenamed the Twin Paradox6.) In 1916, Einstein while working on General



Relativity, sharpened his focus on spacetime diagrams and the invarianceof the interval7. In 1918, Einstein articulated the so called GeneralRelativity Explanation of the Twin Paradox. That explanation contendedthat the turnaround acceleration creates an (artificial/virtual) gravitational

field and the difference in gravitational potential between the acceleratingtwin and the stay-at-home twin causes the net proper time difference. Thenet proper time difference accumulates during the turnaroundacceleration.

The General Relativity Explanation of the Twin Paradox gained someadherents such as Max Born8. However, one objection to that approachwas that the same acceleration parameters (i.e., same time, place andamount of acceleration) were claimed to produce hugely differingamounts of time dilation. There were several other unanswerableobjections.

In late 1918, Einstein treated an accelerationless Twin Paradox scenario9 but the lack of accelerations and the lack of an asymmetry eliminated the(relativist) rebuttals to the original Clock Paradox concerns and, hence,the discussion had gone full circle back to the original Clock Paradoxproblems. Regarding the above cited reference, C. S. Unnikrishnanwrote10 about Einstein's imaginary discussion with a critic, "Curiously,

the discussion starts with a complaint by the critic that none of the

relativists had adequately responded to the criticisms of relativity by

many in journals. In fact, the critic accuses relativists of ‘shirking’ the

issue. This certainly suggests that Einstein considered that none of the

earlier discussions adequately addressed the problem and that it wasnecessary to respond. Ironically, Einstein’s resolution goes against the

standard resolutions discussed in textbooks and in most other writings! As

the physical cause of the asymmetry he uses the pseudo-gravitational field

and the gravitational time dilation of general relativity, after admitting

that special relativity is not suitable for resolving the issue due to the fact

that one of the twins undergoes accelerations during his trip."

1b) Dingle's Changing Views and His Debates

Herbert Dingle had a most distinguished career as a highly respected

physics professor and was considered one of the world's experts onSpecial Relativity, at least until he raised questions about the TwinParadox., He was one of the founders of the British Society for theHistory of Science, and served as President from 1955 to 1957. Dinglefounded what later became the British Society for the Philosophy of Science as well as its attendant journal, the British Journal for ThePhilosophy of Science. He was elected a Fellow of the Royal



Astronomical Society in 1922 and served as president of the society from1951 to 1953. Dingle was a professor in physics departments atprestigious British colleges and headed those departments at times. Dinglewrote a popular book and also a short but very well received text book on

relativity.

After his retirement in 1955, Dingle studied the Twin Paradox andconcluded that Einstein's claim and its implications were clearly false.Initially, Dingle asserted that Special Relativity did NOT predict adifference between the twins' aging and that Einstein original descriptionof Special Relativity had made a regrettable error by including the Clock Paradox claim. After much discussion with his peers, he changed his viewand concluded that the currently accepted interpretation of SpecialRelativity was compatible with Einstein's claim and was, hence, clearlyinconsistent. As Dingle put it, "The theory [special relativity] unavoidably

requires that A works more slowly than B and B more slowly than A --which it requires no super-intelligence to see is impossible." In Dingle's1972 book, Science at the Crossroads, he wrote "a proof that Einstein's

special theory of relativity is false has been advanced; and ignored,

evaded, suppressed and, indeed, treated in every possible way except that

of answering it ...."

The debates triggered by Dingle's views were the most open and mostpublicized of such debates. Relativists claimed that Dingle was defeatedand a quack. However, as E. G. Cullwick put it, “On one thing Professor

Dingle’s critics are all agreed, that he is wrong. They do not all agree,

however, on the nature of his error ." Furthermore, Hasok Chang, then of Harvard, did a thorough review of the Dingle debates11 and concludedthat Dingle’s opponents had NOT addressed the arguments he raised.(Chang made great efforts to be fair and objective and at the end of thepaper Chang added that he disagreed with Dingle’s asking for "physicalexplanations", however, many of Dingle’s arguments were aimed atinherent problems in his opponents’ logic.)

While today most tend to associate Dingle with the Twin Paradox debate,that issue was just the first logic step to Dingle's main focus for twentyyears, namely, that Einstein's Special Relativity lead to contradictions andwas untenable. Beginning on page 27 of "Science At The Crossroads",Dingle lays out one of several such arguments. In brief, he asks if weconsider two non-accelerated clocks, in deep space, moving at constantrelative velocity with respect to each other, which one, according toSpecial Relativity, is running slow? No one could answer that question.One could claim that Special Relativity was just about what was observedand, hence, did not address differences in clock rates. However, Dingle



showed that approach was at odds with Einstein's 1905 paper and at oddswith Special Relativity professors' views in that era. Further, if one took the "just observed" approach, then much of the experimental evidence thatwas alleged to support Special Relativity would clearly not apply to

Special Relativity and no experiment has confirmed symmetric "timedilation" observations.

1c) Other Views

The Twin Paradox Debate has raged unabated, even when censored, formore than a century (1905 - 2011) - see long, partial list below at end of Report. During that time, a very wide range of different and to a highdegree mutually exclusive solutions to the Twin Paradox have beenpublished by mainstream physicists in mainline journals. From 1905through about 1920, there was vigorous and open debate about the Twin

Paradox and Special Relativity. Then, after Eddington's solar eclipseexperiments seemed to confirm General Relativity, strong support forrelativity coalesced the physics community and dissent started a sharpdownward trend despite earlier criticism having never been addressed. Inthe mid to late 1950s, the Dingle debates again stirred up some interestand controversy, but, afterward, dissent seemed to be cast as quackery andwas even less tolerated.

One such school of thought is worth noting here. Geoffrey Builder, whoincidentally wrote a well known paper trying to reconcile the TwinParadox with Special Relativity, contended that Special Relativity implied

a special physics frame and that Special Relativity and Lorentz AetherTheory were equivalent theories. Simon Prokhovnik and others from the"Australian School" agreed.

Many others from 1905 to the present have maintained that the TwinParadox is an unresolved paradox. Many of these (e.g., Dingle, Ives,Lovejoy, Cullwick, Jeffreys) have had fine reputations in academia beforequestioning Twin Paradox resolutions. However, those who maintainedthere was an unresolved paradox were subjected to much ridicule forthose views. It is ironic that while many of these critics' arguments appearto have been widely but tacitly accepted as physicists sought new

solutions, however, these critics are still objects of derision.

In the latter half of the 20th century, mainline journals increasinglyrejected papers questioning Twin Paradox resolutions without reviewingthem.

This seemingly extreme reaction is probably because rebuttals to Twin



Paradox resolutions were seen to be either explicit or implicit attacks onSpecial Relativity and Special Relativity is held to be one of thefoundation blocks of modern physics. However, as discussed below, thisrationale is based on a faulty assumption as a proper understanding of the

Twin Paradox could save Special Relativity by leading to a more tenableinterpretation. Furthermore, the rest of modern physics is not built onSpecial Relativity per se, but rather on specific characteristics of SpecialRelativity which can also be found in alternative variations and in othertheories.

2) Experiment Results

Many think that experiment results have confirmed the NPTD predictionand, hence, the Twin Paradox is a dead issue. However, this is anerroneous conclusion.

A wide variety of mutually exclusive explanations for the Twin Paradoxhave been put forward. The experiment results are alleged to be consistentwith all these explanations, but not all can be correct. So we see that justbeing in mathematical agreement with the experiment data does NOTprove that the explicit or implicit physics explanation is correct. Only oneexplanation, or set of equivalent explanations, can be correct. It’s alsopossible that an explanation that’s not been put forward by themainstream is the correct explanation and that that explanation not onlymatches the experiment data, but is also free of any logic problems orparadoxes and gives a coherent description of the physics involved.

Furthermore, experiment data for clock rate dependence on velocityclearly disagrees with Special Relativity's symmetric time dilationequation. For accelerators and for cosmic rays entering the atmosphere,it's clear that the evidence supports asymmetric "time dilation". Theinternal "clocks" of particles moving with respect to the earth centeredframe have a slower rate than clocks at rest in that frame and the reverseis not true as a consistent application of Special Relativity's symmetrictime dilation equation would suggest. This is also seen in GPS eventhough it is (erroneously) claimed to be built on Special (and General)Relativity. GPS works as follows (see T. Van Flandern's paper)12

The Earth Centered Inertial (ECI) frame is used as the base frame. Clocksthat are to be used in GPS satellites are adjusted for General Relativistic,asymmetric time dilation and for clock retardation as a function of velocity with respect to the ECI frame. To be brief, this results in all theclocks in the satellites and on earth bring in sync (We'll ignore other finetuning adjustments here.) It's clear that if the satellite clocks were only



adjusted for a difference in gravitational potential and not adjusted forvelocity with respect to the ECI frame, they would lose proper time whencompared to clocks at rest on earth. That's because their clock rates wouldhave been slower than clocks at rest on earth. It would NOT be equally

true that clock rates for clocks at rest on earth would have been slowerthan for clocks in the satellites and note that all clocks would have beenaccelerating continuously as the earth rotates and orbits the sun. Also,world class expert on navigational systems (26 patents related to GPS)Ron Hatch recently published a paper showing that a set of transformsthat are preferred frame based match the data better than SpecialRelativity's Lorentz Transformations13.

[Note: Some have said that Special Relativity'stime dilation and General Relativity's clock rate

dependence on gravitational potential are linkedby the Principle of Equivalence. However, theone is not a good analogy for the other. SpecialRelativity's time dilation equation is symmetricwhereas General Relativity's is asymmetric. Abetter match for General Relativity would bewith asymmetric clock retardation as a function

of velocity with respect to a special frame. Datafrom NASA, GPS, VBLI and other sourcessuggest a hierarchy of special frames (e.g., planetcentered inertial frame, solar barycentric frame,galactic frame, galactic group frame ... frame of the fixed stars.)]

3) Accepted Resolutions

On the one hand, the mainstream has maintained that there is no paradoxand that anyone who so argues is a quack. However, there have been andstill are a wide range of Twin Paradox reconciliation arguments – many of which are mutually exclusive. All these conflicting arguments arepublished in the main physics journals and none have been proclaimedincorrect.



As noted above, Einstein initially held that the cause of the NPTD wastime dilation as a function of relative velocity. However, Einstein himself changed his position several times and in 1918 published an explanationbased on General Relativity. Nevertheless, explaining the NPTD by time

dilation remained the de facto standard explanation for many decades andstill has its adherents today.

Many papers giving reconciliation arguments have been published in thefollowing categories using the following constructs:

I) Relative Velocity

Ia) Time Dilation

Ib) Length Contraction (measuring rod contracts).

Ic) Length Contraction (space contracts)

Id) Time Dilation and Length Contraction

Ie) Change in Relativistic Kinetic Energy

If) Relative Simultaneity (NPTD accumulates during constantvelocity legs)

Ig) Swinging Lines of Simultaneity (similar to If)

Ih) Lorentz Transformations

Ii) Minkowski Diagrams (usually equivalent to Ia)

Ij) Invariance of the Interval (usually equivalent to aspects of Ia,Id)

Ik) Tracking Light Signal Exchanges

Il) Relativistic Doppler Shift

II) Turnaround Acceleration

IIa) Turnaround Acceleration

IIb) Changing Frames of Reference (different than IIa)



IIb) General Relativistic Effects

IId) Virtual Gravitational Fields

IIe) Equivalence Principle

IIf) Relative Simultaneity (NPTD jumps during arbitrarily smallacceleration)

III) Nature of Spacetime/Gestalt/Other

IIIa) Nature of or kinematics of Spacetime (Vague but probablytrue. But which physical spacetime and what physical characteristic?)

IIIb) Swings and Roundabout Theorem – (Similar to IIIa)

IIIc) Kerr Metric

Clearly, the mainstream is not clear about the Twin Paradox. Admittedly,a few of the above (e.g., Ik, Il) are aimed more at trying to explain howthe NPTD occurs to confused and/or skeptical students than at giving aphysical cause. However, if, for example, time dilation was not aninherently paradoxical explanation, then using totally different constructswould not be needed to explain the topic - especially to students.

Professors who have analyzed the Twin Paradox deeply enough to publish

a paper on the cause of the NPTD are explicitly rejecting any mutuallyexclusive cause. Similarly, professors who teach Twin Paradox using onephysical cause for the NPTD are implicitly/explicitly rejecting anymutually exclusive cause. Hence, all causes for the NPTD have beenimplicitly/explicitly rejected by a significant number of the mostknowledgeable professors.

Many, many individual professors have rejected most/all of the causeslisted above. Examples:

" Although it has even been experimentally confirmed that the twin who

travels away and comes back will age less, a conceptually veryconvincing theoretical treatment of the problem is still awaited ." - ASimple Solution of the Twin Paradox Also Shows Anomalous Behaviour of Rigidly Connected Distant Clocks by Vidwan Singh Soni(2002 Eur. J. Phys. 23 225)



and

“ At the present time there are a few (there may be many, but only a few

have expressed the view in print) who insist that one of the predictions

[asymmetric aging] in EINSTEIN'S first paper on the subject must beerroneous) for if correct the result would be contrary to the principle of

relativity!" – The Clock Paradox by W. Cochran (1960 Vistas 3 78)

However, this sense of dissatisfaction gets lost – it’s not widely published,it’s not usually in the text books, it’s not widely taught in the classrooms.

Hence, in addition to having the professors being at odds, we havestudents being confused and taught contradictory physics lessons. This ismade all the worse as the different causes imply contradictory conceptsabout the underlying theory – Special Relativity

4) Important Implications

There seem to be some important implications from the Twin Paradoxthat are being ignored:

a) Einstein, Dingle and many other prominent physicists have seen thattrying to explain the NPTD in the Twin Paradox leads to contradictions.The physics community seems satisfied just saying “OK, we’ll find

another explanation.” However, the clear implication is that SpecialRelativity’s time dilation equation can NOT be interpreted as describing a

physical change in proper time accumulation without leading tocontradictions. Since Special Relativity’s time dilation and lengthcontraction equations were derived in tandem using analogous logic, itfollows that length contraction also can NOT be interpreted as describinga physical change in proper length. Further, to be consistent, this impliesthat, in general, Special Relativity is not describing the physical worlddirectly, but rather is describing how each inertial observer observes theworld. These descriptions of observations can be very useful, but theirlimitations should also be candidly stated. (Remember that while SpecialRelativity can NOT be describing a physical change in proper timeaccumulation, preferred frame theories do predict a physical, asymmetric

change without any paradoxes or problems.)

b) The above has implications for other fields in science that use SpecialRelativity such as astronomy and especially cosmology. The relativisticDoppler effect is currently thought of in terms of relative velocity. Thiscan be misleading as it’s difficult to know the meaning of relative velocityof two objects separated by billions of light years in space and billions of



years in time in an expanding universe. As Einstein stated, “ All physics is

local.” Prof. D.R. Frankl’s paper14 shows how the classical Doppler effectwith its dependence on the observer’s and the source’s speed with respectto the wave’s carrier medium can be transformed into the relativistic

Doppler effect. In other words, the physical model underlying therelativistic Doppler effect may employ the observer’s and the source’sspeed with respect to the wave’s carrier (local) medium. Also, Prof.Franco Selleri's book 15 discusses how the physics of cetain phenomena(e.g., the Twin Paradox, Sagnac Effect, aberration of starlight) is betterdescribed and how certain problems in cosmology can be solved.

c) Some have claimed that relativity has become morephilosophy/ideology/religion than science. For example, Dr. Peter Hayes,using the Twin Paradox as a prime example, writes16 that ignoringconsiderable evidence against the current interpretation of relativity

smacks of relativity having become an ideology. Once this mode of thinking becomes accepted, it can become insidiously pervasive. Forexample, when observations on galactic rotations and universe expansiondidn’t match predictions, by far the predominantly accepted solution wasto assume the existence of Dark Matter and Dark Energy, respectively. Inother words, there’s a strong bias away from analyzing whether themismatch between theory and data might be due to a problem with thetheory. The response to that might be that the data supports the existenceof Dark Matter and Dark Energy. However, if one invents fudge factors tosatisfy the data, then the data is going to support the fudge factors. Oneshould keep an open mind regarding currently accepted theory lest we

continue with a Dark Age of (spacetime) Physics.

5) A Great Opportunity And A Major Obstacle

The Twin Paradox seems to be a loose end in current theory. Many timesin the past when a loose end appeared in physics and one pulled on thatloose end, current paradigms came apart at the seams and new paradigmswere developed and great progress was made.

Careful analysis of the Twin Paradox could lead to:

- Discovery of a major deficiency in Special Relativity and the need for areplacement theory

- A clearer, more accurate view of Special Relativity where ambiguitiesand confusion are eliminated and/or corrections/modifications are made.

- The discovery that the physical cause of the NPTD lies outside currently



accepted theory and a new compatible construct is revealed that expandsthe domain of currently accepted physics.

As a first step toward a serious analysis of the Twin Paradox, the NPA

asked the core of the mainstream, those who control what's published andfunded, etc., what the generally accepted Twin Paradox reconciliationargument was. If the Twin Paradox was well understood and not aparadox/problem, this should have been a very easy task. Our originalReport tried to make the case for serious examination in a most tactfulway and called for a cooperative, harmonious analysis. However, thepaucity of responses and the actual responses seems to indicate that theTwin Paradox is known to be a real problem, but one that should be kepthidden. See the Mainstream Response page for a detailed analysis.

That just reinforces the need for a candid dialog on the Twin Paradox. We

simply ask that the core of the mainstream clearly specify their positionon the Twin Paradox and describe, as best they can, how the NPTDaccumulates. If all one gets is silence, then the core of the mainstream isconfirming the above.

Depending on the nature of the generally accepted Twin Paradoxreconciliation argument, the NPA may wish to ask some questions to testthe validity of that argument.

6) The Twin Paradox Challenge (December

11, 2011) We ask that a single spokesperson or group be

selected by a top physics organization, such as

the American Institute of Physics (AIP) or the

American Association for the Advancement of

Science (AAAS) to give the currently accepted

solution and respond to questions about that

solution. We note that the Germangovernment has specified that the Albert

Einstein Institute (AEI) is the officially

designated responder for questions about

relativity, and, hence, it is in their mission to



respond. We would welcome such a dialog

with the AEI. (Send input to us at

[email protected])

All exchanges will be promptly posted to this

web site for all to see.

If the mainstream felt confident in resolving

the Twin Paradox, an answer would be

readily given. Conversely, if they do not feel

comfortable explaining the Twin Paradoxusing currently accepted theory, no reply will

be given.

Citations

1) A. Einstein, "On the Electrodynamics of Moving Bodies", Annalen der Physik 17 891

(1905)2) A. Einstein,"Relativity: The Special andGeneral Theory", Springery (1916)3) M. Sachs, "On Einstein's Later View of theTwin Paradox", Foundations of Physics, Vol. 15,No.9, 19854) A. Einstein, "Die Relativitäts-Theorie".Naturforschende Gesellschaft, Zürich,

Vierteljahresschrift 56: 1–14 (1911)5) M. von Laue "Two Objections Against theTheory of Relativity and their Refutation",Physikalische Zeitschrift 13: 118–120 (1911)



6) P. Langevin "The Evolution of Space andTime". Scientia 10: 31–54 (1911)7) A. Einstein, "The Foundation of the General

Theory of Relativity" (1916)8) M. Born, Einstein's Theory of Relativity, p.261, p. 355 (Dover, 1965)9) A. Einstein, "dialog about objections againstthe theory of relativity", DieNaturwissenschaften 48, pp. 697-702 (29November 1918)

10) C. S. Unnikrishnan, Current Science, Vol.89, No. 12, p. 2008 (2005) – see article 11) H. Chang, Stud. Hist. Phil. Sci. 24(5), 741(1993).12) T. Van Flandern, Aperion, Vol. 10, No.1, 69(2003) - (see paper)13) R. Hatch, Phys. Es. Vol. 23 No. 4 p. 540

14) D. R. Frankl, Am. J. Phys. 52(4), 374 (1984)15) F. Selleri, LA RELATIVITA' DEBOLE La

fisica dello spazio e del tempo senza paradossi (Melquiades, Milano 2007-2010) [The onlineEnglish version, "Weak Relativity", is availablefor free.]16) P. Hayes, Social Epistemology, 23, 57(2009).

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J. N. Percival, Phys. Essays, 8(1), 29 (1995).

C. K. Whitney, Aperion, 4 #2-3, 104 (1997).

T. Van Flandern, Aperion, 10 #1, 69 (2003) - see paper

S. Dumitru, Progress In Physics, 2, 125 (2008)

I. McCausland, A Scientific Adventure: Reflections on the Riddle of

Relativity (Aperion 2011) [Contains the above McCausland references



and much additional material]

H. Nordenson, Relativity, Time and Reality, (

London: George Allen and Unwin, 1969)Chapter 5

P. Beckmann, Einstein Plus Two (Golden Press, 1987)

C. S. Unnikrishnan, Current Science, Vol. 89,No. 12, p. 2008 (2005) – see article

D. R. Frankl, Am. J. Phys. 52(4), 374 (1984)

F. Smarandache, Absolute Theory of Relativity& Parameterized Special Theory of Relativity &Noninertial Multirelativity, Somipress (1982) –see book

Marinela Preoteasa (editor), Romanul care l-a

contrazis pe Einstein (Culegere de eseuri), 2012(Romanian) – see book

H. R. Reichenbach, The Philosophy of Space and Time (Dover, New

York, 1958)

H. R. Reichenbach, Philosophie der Raum-Zeit-

Lehre, (Berlin, 1928) p. 224

M. Jammer, Concepts of Simultaneity (The John Hopkins University

Press, 2006)

M. Jammer. at pg 205 of G. Toraldo di Francia, ed., Problems i the



Foundations of Physics (Societa Italiana di Fisica, Bologna and North

Holland, Amsterdam, 1979)

F. Selleri, LA RELATIVITA' DEBOLE La fisica dello spazio e del tempo

senza paradossi (Melquiades, Milano 2007-2010) [The online English

version, "Weak Relativity", is available for free.]

R. Hatch, GPS Solutions 8 67 (2004)

R. Hatch, Phys. Es. Vol. 23 No. 4 p. 540

M. S. Khan, Indian J. of Sci. and Tech., 5 (3)(2012) See paper onlinbe - it issues a similarchallenge to the mainstream to what's shownabove

G.O Mueller, Max Planck und der Verrat an der Wissenschaft [In German

with computer translation available.]

L. Essen, Relativity- Joke or Swindle?

M. Allais, The biggest mystification in the history of science: the theory

of relativity

R. M. Santilli, Ethical Probe

B. G. Wallace, "Mathematical Magic"

E.Gehrcke, Relativity - Mass delusion [In German]

Of special interest due to their breadth and depth



are:P. Hayes, Social Epistemology, 23, 57 (2009).H. Chang, Stud. Hist. Phil. Sci. 24(5), 741

(1993). F. Selleri, LA RELATIVITA' DEBOLE La fisica

dello spazio e del tempo senza paradossi (Melquiades, Milano 2007-2010) [The onlineEnglish version, "Weak Relativity", is availablefor free.]I. McCausland, A Scientific Adventure:

Reflections on the Riddle of Relativity (Aperion2011)

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