Physics-Special Relatvity-Twin Paradox

Twin Paradox

Data Does Not Match Special Relativity Time Dilation
Open Letter On Twin Paradox
Open Letter On Special Relativity
Sign Open Letter
Survey Questionnaire
Mainstream Response
Debate Methodology
Can't Be Due To Relative Velocity
Can't Be Due To Turnaround Acceleration
Time Difference Accumulation Is Not Indeterminate
Dingle's Question
Blog Discussion
Two Step Argument
Three Step Argument
Two Step Argument #2

Top Divider




1a) Einstein's Changing Views
Einstein’s 1905 paper1 defined the basis for Special Relativity. In that paper, Einstein derived the symmetric time dilation equation which applies equally to all inertial observers. Then he wrote, “From this", referring to the time dilation equation, “the following peculiar consequence follows" that if a clock takes a round trip, it will lose time versus a stay-at-home clock.

Einstein's claim seemed to many to be unjustified and, hence, not just counter-intuitive but also counter-logical. Hence, Einstein's claim initiated what was first called the Clock Paradox as many asked, in essence, “How can a symmetric effect, time dilation, cause an asymmetric result, namely, a net proper time difference (NPTD)?" The critics said that the time dilation equation could not be interpreted as describing physical time dilation as that would mean that all the clocks in inertial frame A run faster than all the clocks in inertial frame B AND all the clocks in inertial frame B run faster than all the clocks in inertial frame A! Furthermore, even if one accepted the apparently self contradictory interpretation of the time dilation equation that Einstein's claim implied, it must be as true for the traveling twin as for the stay-at-home twin as relativity claims that all inertial frames are equal. Hence, by applying Einstein's logic consistently from the traveling twin's frame(s), one would conclude that it was not the traveling clock that accumulated less time but rather the stay-at-home clock.

The relativists tried to counter this problem by claiming that because the traveling twin accelerated, special relativity could not be used from his frames. This did indeed identify a bona fide asymmetry between the twins. However, if this criterion were to be applied consistently, then this cure would be worse than the original illness as it would rule out virtually any practical application of Special Relativity. Furthermore, the claim seemed rather specious as the traveling twin would be in an inertial frame for the constant velocity segments which could be made to be an arbitrarily high percentage (e.g., 99.99999%) of the round trip and adding proper times from different frames has always been allowed.

These problems clearly troubled Einstein throughout his life. Einstein published a number of differing versions of Special Relativity (1905, 1907, 1910, 1911, 1912 and 19162) with some specifying that time dilation was apparent and not physical. Mendel Sachs reviewed many Einstein papers and presentations and wrote3, "I will quote some of his comments that were made during his life, that convince me that Einstein did not believe, after all, that the kinematic relations, such as the Lorentz transformations of special relativity, or the space-time transformations between accelerated frames (of general relativity), can indeed induce relative 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, in 1921, he said the following:

"Geometry predicates nothing about relations of real things, but only geometry together with the purport of physical laws can do so... The idea of 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 real world. It is also clear that the solid body and the clock do not in the conceptual edifice of physics play the part of irreducible elements, but that 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 the foregoing comment, we should temporarily support the use of the length and time transformations as though they were physically real, because "we are still far from possessing such certain knowledge of theoretical principles 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 admitted that one must not, in principle, interpret the theory of relativity to imply that similar physical entities age differently by virtue of their relative motion. But, on the other hand, he said that we should nevertheless assume (for the time being!) that there is such a physical correlation between 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 exact way, when taking account of the measuring rods and clocks that are used to verify these laws."

In 1911, Einstein was shifting focus on the Twin Paradox solution to spacetime diagrams and the invariance of the interval4. Also, in 1911, Max von Laue made a similar shift5. (Incidentally, Paul Langevin, also in 1911, popularized the issue by focusing on the differential aging of a pair of twins rather than on a pair of clocks and the Clock Paradox was renamed the Twin Paradox6.) In 1916, Einstein while working on General Relativity, sharpened his focus on spacetime diagrams and the invariance of the interval7. In 1918, Einstein articulated the so called General Relativity Explanation of the Twin Paradox. That explanation contended that the turnaround acceleration creates an (artificial/virtual) gravitational field and the difference in gravitational potential between the accelerating twin and the stay-at-home twin causes the net proper time difference. The net proper time difference accumulates during the turnaround acceleration.

The General Relativity Explanation of the Twin Paradox gained some adherents such as Max Born8. However, one objection to that approach was that the same acceleration parameters (i.e., same time, place and amount of acceleration) were claimed to produce hugely differing amounts of time dilation. There were several other unanswerable objections.

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 Paradox problems. Regarding the above cited reference, C. S. Unnikrishnan wrote10 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 was necessary 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 on Special Relativity, at least until he raised questions about the Twin Paradox., He was one of the founders of the British Society for the History of Science, and served as President from 1955 to 1957. Dingle founded what later became the British Society for the Philosophy of Science as well as its attendant journal, the British Journal for The Philosophy of Science. He was elected a Fellow of the Royal Astronomical Society in 1922 and served as president of the society from 1951 to 1953. Dingle was a professor in physics departments at prestigious British colleges and headed those departments at times. Dingle wrote 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 and concluded that Einstein's claim and its implications were clearly false. Initially, Dingle asserted that Special Relativity did NOT predict a difference between the twins' aging and that Einstein original description of Special Relativity had made a regrettable error by including the Clock Paradox claim. After much discussion with his peers, he changed his view and concluded that the currently accepted interpretation of Special Relativity was compatible with Einstein's claim and was, hence, clearly inconsistent. 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's 1972 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 most publicized of such debates. Relativists claimed that Dingle was defeated and 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 concluded that Dingle’s opponents had NOT addressed the arguments he raised. (Chang made great efforts to be fair and objective and at the end of the paper Chang added that he disagreed with Dingle’s asking for "physical explanations", however, many of Dingle’s arguments were aimed at inherent 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 twenty years, namely, that Einstein's Special Relativity lead to contradictions and was untenable. Beginning on page 27 of "Science At The Crossroads", Dingle lays out one of several such arguments. In brief, he asks if we consider two non-accelerated clocks, in deep space, moving at constant relative velocity with respect to each other, which one, according to Special Relativity, is running slow? No one could answer that question. One could claim that Special Relativity was just about what was observed and, hence, did not address differences in clock rates. However, Dingle showed that approach was at odds with Einstein's 1905 paper and at odds with Special Relativity professors' views in that era. Further, if one took the "just observed" approach, then much of the experimental evidence that was alleged to support Special Relativity would clearly not apply to Special Relativity and no experiment has confirmed symmetric "time dilation" observations.

1c) Other Views

The Twin Paradox Debate has raged unabated, even when censored, for more 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 high degree mutually exclusive solutions to the Twin Paradox have been published by mainstream physicists in mainline journals. From 1905 through about 1920, there was vigorous and open debate about the Twin Paradox and Special Relativity. Then, after Eddington's solar eclipse experiments seemed to confirm General Relativity, strong support for relativity coalesced the physics community and dissent started a sharp downward trend despite earlier criticism having never been addressed. In the mid to late 1950s, the Dingle debates again stirred up some interest and controversy, but, afterward, dissent seemed to be cast as quackery and was even less tolerated.

One such school of thought is worth noting here. Geoffrey Builder, who incidentally wrote a well known paper trying to reconcile the Twin Paradox with Special Relativity, contended that Special Relativity implied a special physics frame and that Special Relativity and Lorentz Aether Theory were equivalent theories. Simon Prokhovnik and others from the "Australian School" agreed.

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

In the latter half of the 20th century, mainline journals increasingly rejected papers questioning Twin Paradox resolutions without reviewing them.

This seemingly extreme reaction is probably because rebuttals to Twin Paradox resolutions were seen to be either explicit or implicit attacks on Special Relativity and Special Relativity is held to be one of the foundation blocks of modern physics. However, as discussed below, this rationale is based on a faulty assumption as a proper understanding of the Twin Paradox could save Special Relativity by leading to a more tenable interpretation. Furthermore, the rest of modern physics is not built on Special Relativity per se, but rather on specific characteristics of Special Relativity which can also be found in alternative variations and in other theories.

2) Experiment Results

Many think that experiment results have confirmed the NPTD prediction and, hence, the Twin Paradox is a dead issue. However, this is an erroneous conclusion.

A wide variety of mutually exclusive explanations for the Twin Paradox have been put forward. The experiment results are alleged to be consistent with all these explanations, but not all can be correct. So we see that just being in mathematical agreement with the experiment data does NOT prove that the explicit or implicit physics explanation is correct. Only one explanation, or set of equivalent explanations, can be correct. It’s also possible that an explanation that’s not been put forward by the mainstream is the correct explanation and that that explanation not only matches the experiment data, but is also free of any logic problems or paradoxes and gives a coherent description of the physics involved.

Furthermore, experiment data for clock rate dependence on velocity clearly disagrees with Special Relativity's symmetric time dilation equation. For accelerators and for cosmic rays entering the atmosphere, it's clear that the evidence supports asymmetric "time dilation". The internal "clocks" of particles moving with respect to the earth centered frame have a slower rate than clocks at rest in that frame and the reverse is not true as a consistent application of Special Relativity's symmetric time dilation equation would suggest. This is also seen in GPS even though 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. Clocks that 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 the clocks in the satellites and on earth bring in sync (We'll ignore other fine tuning adjustments here.) It's clear that if the satellite clocks were only adjusted for a difference in gravitational potential and not adjusted for velocity with respect to the ECI frame, they would lose proper time when compared to clocks at rest on earth. That's because their clock rates would have 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 slower than for clocks in the satellites and note that all clocks would have been accelerating 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 transforms that are preferred frame based match the data better than Special Relativity's Lorentz Transformations13.

[Note: Some have said that Special Relativity's time dilation and General Relativity's clock rate dependence on gravitational potential are linked by the Principle of Equivalence. However, the one is not a good analogy for the other. Special Relativity's time dilation equation is symmetric whereas General Relativity's is asymmetric. A better match for General Relativity would be with asymmetric clock retardation as a function of velocity with respect to a special frame. Data from NASA, GPS, VBLI and other sources suggest a hierarchy of special frames (e.g., planet centered 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 paradox and that anyone who so argues is a quack. However, there have been and still are a wide range of Twin Paradox reconciliation arguments – many of which are mutually exclusive. All these conflicting arguments are published in the main physics journals and none have been proclaimed incorrect although some have been quietly abandoned.

As noted above, Einstein initially held that the cause of the NPTD was time dilation as a function of relative velocity. However, Einstein himself changed his position several times and in 1918 published an explanation based on General Relativity. Nevertheless, explaining the NPTD by time dilation remained the de facto standard explanation for many decades and still has its adherents today.

Many papers giving reconciliation arguments have been published in the following 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 constant velocity 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 small acceleration)

III) Nature of Spacetime/Gestalt/Other

IIIa) Nature of or kinematics of Spacetime (Vague but probably true. 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 how the NPTD occurs to confused and/or skeptical students than at giving a physical cause. However, if, for example, time dilation was not an inherently paradoxical explanation, then using totally different constructs would 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 mutually exclusive cause. Similarly, professors who teach Twin Paradox using one physical cause for the NPTD are implicitly/explicitly rejecting any mutually exclusive cause. Hence, all causes for the NPTD have been implicitly/explicitly rejected by a significant number of the most knowledgeable professors.

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

"Although it has even been experimentally confirmed that the twin who travels away and comes back will age less, a conceptually very convincing theoretical treatment of the problem is still awaited." - A Simple Solution of the Twin Paradox Also Shows Anomalous Behaviour of Rigidly Connected Distant Clocks by Vidwan Singh Soni (2002 Eur. J. Phys. 23 225)


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 be erroneous) 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 have students being confused and taught contradictory physics lessons. This is made all the worse as the different causes imply contradictory concepts about the underlying theory – Special Relativity

4) Important Implications

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

a) Einstein, Dingle and many other prominent physicists have seen that trying 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 Special Relativity’s time dilation equation can NOT be interpreted as describing a physical change in proper time accumulation without leading to contradictions. Since Special Relativity’s time dilation and length contraction equations were derived in tandem using analogous logic, it follows that length contraction also can NOT be interpreted as describing a physical change in proper length. Further, to be consistent, this implies that, in general, Special Relativity is not describing the physical world directly, but rather is describing how each inertial observer observes the world. These descriptions of observations can be very useful, but their limitations should also be candidly stated. (Remember that while Special Relativity can NOT be describing a physical change in proper time accumulation, 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 Special Relativity such as astronomy and especially cosmology. The relativistic Doppler effect is currently thought of in terms of relative velocity. This can be misleading as it’s difficult to know the meaning of relative velocity of 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 effect with its dependence on the observer’s and the source’s speed with respect to the wave’s carrier medium can be transformed into the relativistic Doppler effect. In other words, the physical model underlying the relativistic Doppler effect may employ the observer’s and the source’s speed with respect to the wave’s carrier (local) medium.

c) Some have claimed that relativity has become more philosophy/ideology/religion than science. For example, Dr. Peter Hayes, using the Twin Paradox as a prime example, writes15 that ignoring considerable 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.

5) A Great Opportunity And A Major Obstacle

The Twin Paradox seems to be a loose end in current theory. Many times in the past when a loose end appeared in physics and one pulled on that loose end, current paradigms came apart at the seams and new paradigms were 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 a replacement theory

- A clearer, more accurate view of Special Relativity where ambiguities and 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 expands the domain of currently accepted physics.

As a first step toward a serious analysis of the Twin Paradox, we asked the core of the mainstream, those who control what's published and funded, etc., what the generally accepted Twin Paradox reconciliation argument was. If the Twin Paradox was well understood and not a paradox/problem, this should have been a very easy task. Our original Report tried to make the case for serious examination in a most tactful way and called for a cooperative, harmonious analysis. However, the paucity of responses and the actual responses seems to indicate that the Twin Paradox is known to be a real problem, but one that should be kept hidden. 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 position on the Twin Paradox and describe, as best they can, how the NPTD accumulates. If all one gets is silence, then the core of the mainstream is confirming the above.

Depending on the nature of the generally accepted Twin Paradox reconciliation argument, we may wish to ask some questions to test the 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 German government 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

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 Paradox using currently accepted theory, no reply will be given.


1) A. Einstein, "On the Electrodynamics of Moving Bodies", Annalen der Physik 17 891 (1905)
2) A. Einstein,"Relativity: The Special and General Theory", Springery (1916)
3) M. Sachs, "On Einstein's Later View of the Twin Paradox", Foundations of Physics, Vol. 15, No.9, 1985
4) A. Einstein, "Die Relativitäts-Theorie". Naturforschende Gesellschaft, Zürich, Vierteljahresschrift 56: 1–14 (1911)
5) M. von Laue "Two Objections Against the Theory of Relativity and their Refutation", Physikalische Zeitschrift 13: 118–120 (1911)
6) P. Langevin "The Evolution of Space and Time". 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 against the theory of relativity", Die Naturwissenschaften 48, pp. 697-702 (29 November 1918)
10) C. S. Unnikrishnan, Current Science, Vol. 89, No. 12, p. 2008 (2005) – see
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) P. Hayes, Social Epistemology, 23, 57 (2009).


I) Causes - Arguments trying to explain the Twin Paradox in terms of currently accepted physics

A. Einstein, Ann. der Phys. 17, 891 (1905).

A. Einstein, Naturwissenschaften, 6, 697 (1918).

H. Thirring, Naturwissenschaften, 9, 209 (1921).

E. B. McGilvary, Phil. Rev., 40, 375 (1931)

F. I. Mikhail, Proc. Camb. Phil. Soc., 48 608 (1952)

W.H. McCrea, Nature 167, 680 (1951).

W.H. McCrea, Nature 179, 909 (1957).

W.H. McCrea, Nature 216, 122 (1967).

R. C. Tolman, Relativity, Thermodynamics and Cosmology, (Oxford, 1934) pp. 194-197

E. L. Hill, Phys. Rev, (2) 72 236 (1947)

R. Dugas, Histoire de la Méecanique, (Neuchâtel, 1950) pp.481-482

H. Törnebohm, A Logical Analysis of the Theory of Relativity, (Göteborg, 1952) p. 41-42

A. Grünbaum, Phil. Sci. 21, 249 (Jul., 1954)

A. d'Abro, The Evolution of Scientific Thought (Dover, 1927), p. 223.

M. Born, Einstein's Theory of Relativity (Dover, 1965), p. 261, p. 355.

D.W. Sciama, The Unity of the Universe (Doubleday, 1959), p. 151.

W. Cochran, Vistas 3 78 (1960)

J.L. Martin, General Relativity: A Guide to its Consequences for Gravity and

Cosmology (John Wiley & Sons, 1980), p. 12.

E.F. Taylor and J.A. Wheeler, Spacetime Physics (W. H. Freeman and Co., 1963), p. 92.

J.S. Prokhovnik, Found. Phys. 19, 541 (1989).

H. Bondi, Relativity and Common Sense (Dover, 1964), p. 147.

D.J. Larson, Phys. Essays, 5, 545 (1992).

F.L. Markley, Am. J.Phys. 41, 1246 (1973).

D.E. Hall, Am. J.Phys. 44, 1204 (1976).

L. Marder, Time and the Space Traveler (U. Pennsylvania P., 1971), p.11.

W.G. Unruh, Am. J. Phys. 49, 589 (1981).

G. Builder, Aust. J. Phys. 10: 246 (1957).

G. Builder, Am. J. Phys. 27, 656 (1959).

G. Builder, Phil. Sci. 26, 135 (1959).

C. Møller, The Theory of Relativity (Clarendon Press, 1972), p. 292.

J.T.Y Chou and S. Bradbury, Nature 179, 1242 (1957).

J. Terrell, R.K. Adair, R.W. Williams, F. C. Michel, D. A. Ljung, D. Greenberger, J.P. Matthesen, V. Korenman, T.W. Noonan, Phys. Today, 9, (January 1972).

V. S. Soni, Eur. J. Phys. 23 225 (2002).

D. J. Miller, Am. J. Phys. 78 (6) 633 (June 2010).

T Muller, A. King, D. Adis, Am. J. Phys.76 (4&5) 360 (April/May 2008).

D. Styer, Am. J. Phys. 75 (9) 805 (September 2007).

E. Rebhan, Eur. J. Phys. 6 197 (1985).

C. Leubnert, K. Aufingert and P. Krumm, Eur. J. Phys. 13 170 (1992).

J. Jones, Phys. Educ. 7 48 (1972).

Y. Shamdi, Phys. Educ. January 20 33 (1985).

P. F. Broadfoot, Phys Educ 20 203 (1985).

J. O. Linton, Phys. Educ. 32 308 (1997).

H. Helm and J. Gilbert, Phys. Educ. 20 124 (1985).

R. de Abreu, eprint arXiv:physics/0203025 (March 2002 ).

Ø Grøn, Eur. J. Phys. 27 885 (2006).

L. Iorio, Eur. J. Phys. 26 535 (2005).

P. Pesic, Eur. J. Phys. 24 585 (2003). [Argues for Einstein 1905 and against Einstein 1918]

E. Sheldon, Eur. J. Phys. 24 91 (2003).

J. Uzan, J. Luminet, R. Lehoucq and P. Peter, Eur. J. Phys. 23 277 (2002).

D. Dieks, Eur. J. Phys. 12 253 (1991).

A. Harpaz, Eur. J. Phys. 11 82 (1990).

S. Kak, Int'l. J. Th. Phys. 5 (46) 1424 (2007).

Paradoxes In The Theory Of Relativity by Yakov Terletskii.

Electromagnetism And Relativity by E. G. Cullwick

Introduction To The Theory Of Relativity by F. W. Sears and R. W. Brehme

Basic Concepts Of Relativity by R. H. Good

The Natural Philosophy Of Time by G. J. Whitrow

A First Course In General Relativity by B. F. Schultz

Special Relativity by A. P. French 

Theory Of Relativity by W. Pauli

On Time by M. Shallis

The Special Theory Of Relativity by H. Muirhead

The Riddle Of Gravitation by P. G. Bergmann

The Special Theory Of Relativity for Mathematics Students by P. Lorimer

Relativity and Geometry by R. Torretti

II) Rebuttals to arguments trying to reconcile the Twin Paradox with currently accepted theory

H. A. Lorentz, The Principle of Relativity for Uniform Translations, in: Lectures on Theoretical Physics (1910–1912), Vol. 3 (Macmillan, London, 1931)

P. Langevin, Scientia 10, 31 (1911).

A. Lovejoy, Philos.Rev. 40, 48 (1931).

A. Lovejoy, Philos.Rev. 40, 152 (1931).

A. Lovejoy, Philos.Rev. 40, 549 (1931).

A. Lovejoy, Philos.Rev. 41, 498 (1932).

H.E. Ives, J. Opt. Soc. Am. 27, 177 (1937).

H.E. Ives, J. Opt. Soc. Am. 27, 263 (1937).

H.E. Ives, J. Opt. Soc. Am. 27, 305 (1937).

H.E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938).

H.E. Ives, Science 91, 79 (1940).

H.E. Ives and G.R. Stilwell, J. Opt. Soc. Am. 31, 369 (1941).

H.E. Ives and G.R. Stilwell, J. Opt. Soc. Am. 32, 25 (1942).

H.E. Ives, Philos. Mag. 36, 392 (1945).

H.E. Ives, J. Opt. Soc. Am. 38, 879 (1948).

H.E. Ives, J. Opt. Soc. Am. 39, 757 (1949).

H.E. Ives, Proc. Am. Philos. Soc. 95, 125 (1951).

H.E. Ives, Scient. Proc. R.D.S. 26, 9 (1952).

H.E. Ives, J. Opt. Soc. Am. 42, 540 (1952).

H.E. Ives, J. Opt. Soc. Am. 43, 217 (1952).

H. Jeffreys, Am. J. Phys. 11, 583 (1958).

H. Dingle, Aust. J. Phys. 10, 418 (1957).

H. Dingle, Nature 179, 865 (1957).

H. Dingle, Science 127, 158 (1958).

H. Dingle, Nature 195, 985 (1962).

H. Dingle, Nature 197, 1248 (1963).

H. Dingle, Science at the Crossroads (Martin Brian & O'Keeffe, 1972), p. 129. Downloadable from the CNPS Data Base - Click Here

E. G. Cullwick, Bull. Inst. Phys. 10 52 (1959).

D. H. Frisch and J. A. Smith, Amer. J. Phys., 31, 342 (1963)

J. D. Edmonds, JR., SST 1(1), 21 (1978)

S.J. Prokhovnik, Speculat. Sci. Technol. 2, 225 (1979).

S.J Prokhovnik, The Logic of Special Relativity (Cambridge U. P., 1967), p1, 17, 56, 108.

M. Sachs, Phys. Today, 23 (September 1971)

M. Harada, M. Sachs, Phys. Essays 11, 521 (1998).

C.H. Brans, D.R. Stewart, Phys. Rev. D, 8, 1662 (1973).

D. Turner, R. Hazelett, “The Einstein Myth and the Ives Papers", (Devin-Adair) p 34-75.

I. McCausland, Phys. Essays 3(2), 176 (1990)

I. McCausland, Phys. Essays 6(2), 127 (1993)

I. McCausland, Phys. Essays 9(3), 484 (1996)

I. McCausland, Phys. Essays 12(3), 438 (1999)

I. McCausland, Phys. Essays 18(4), 550 (2005)

I. McCausland, Phys. Essays 22(2), 81 (2009)

S. Brown, Phys. Essays, 4, 42 (1991).

P. Hayes, Studies in History and Philosophy of Modern Physics, 41, 354 (2010).

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]

T. E. Phipps, Jr., Old Physics For New (Aperion, 2006), pp. 42-43, 123-148, 155, 161, 167, 169, 175, 180, 199, 206-7, 225, 234, 237, 244

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

H. B. Tilton & F. Smarandache, Begin The Adventure, Pima College Press (2010) – 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)

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 online - it issues a similar challenge to the mainstream to what's shown above

G.O Mueller, 95 Years of Criticism of the Special Theory of Relativity (1908-2003); AVAILABLE ON LINE:
- English Translation

- English Version of Catalogue of Errors for Both Theories of Relativity (Translator Rothwell Bronrowan)

- Absolute Magnitude of the Special Theory of Relativity Chapter 9 – The Thought Experiment (Translator Rothwell Bronrowan)

- International Reception of GOM Project

- Original German Version

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).
I. McCausland, A Scientific Adventure: Reflections on the Riddle of Relativity (Aperion 2011)

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