The Twin Paradox describes a logical contradiction in special relativity when its “time dilation” construct is interpreted as causing a physical effect as opposed to a “just observed” effect.

## Origin

In 1905, Einstein published a paper1 which laid the basis for special relativity. After deriving the time dilation equations, he claimed that “From this …”1 (clearly referencing time dilation) it followed that if two clocks were at rest together in an inertial frame and then one clock made a round trip away from and back to the other clock, then the “traveling” clock would have accumulated less proper time than the “stationary” clock.

This claim caused many objections in the physics community of that timeframe. The problem was that special relativity’s time dilation is a function of relative velocity which requires that the time dilation effect of Clock A relative to Clock B has to be identical to the time dilation effect of Clock B relative to Clock A since the relative velocity between A and B is equal to the relative velocity between B and A. Hence, it was inherently contradictory to claim that special relativity’s time dilation would cause an asymmetric, physical effect (e.g., a net proper time difference (NPTD)). The above discussed controversy was called the Clock Paradox. However, in 1911 Paul Langevin2 discussed the problem in terms of twin humans rather than twin clocks and the paradox became known as the Twin Paradox, but the issues remained unchanged.

## Significance of the Twin Paradox

Per the above discussion, understanding the Clock Paradox/Twin Paradox seemed to show that one cannot logically interpret special relativity’s time dilation as describing an asymmetric physical change such as a clock rate change or a net proper time difference.

Of equal or greater importance, is that the history of the Twin Paradox has shown that physics academia chose, for more than a century, to ignore QED arguments on this topic simply because those arguments were at odds with currently accepted physics theory.

Thirdly, the study and analysis of the Twin Paradox is an excellent vehicle for learning how to think logically and scientifically.

## First Attempt At Reconciliation

Faced with the problem outlined in the 2nd paragraph of the Origin section above, relativists sought a rebuttal. They claimed that because the “traveling” twin accelerated or “changed frames”, the special relativistic calculation yielding the conclusion that the stay-at-home clock should have lost time, rather than the “traveling” twin, was invalidated. Obviously, the relativists had the analytical skills to realize that this was a bogus argument on many counts, however, it is not uncommon for one to be blind to evidence that one’s currently held belief system is false. There are several problems with the relativists’ claimed rebuttal, namely:

1. If special relativity can only be used by observers who remain stationary in an inertial frame, then that virtually precludes special relativity having any practical use as the earth is rotating and also orbiting around the sun and the sun and whole solar system is orbiting around the galactic center, etc., etc..
2. Further, if, per the relativists’ rebuttal, past and/or future acceleration precludes an observer from using special relativity, then that really precludes special relativity having any practical use.
3. There is no basis in the derivation of special relativity or in special relativity itself that supports the rebuttal premise.
4. If one changed the classic Twin Paradox scenario and had the stay-at-home clock mimic the turnaround acceleration, thus preserving complete symmetry, the special relativistic calculation for the time dilation effect would be, basically, unaffected, thus rebutting the rebuttal.

In addition to the logic flaws in the basic assumption upon which the Einstein’s original Twin Paradox claim rests, a massive amount of empirical evidence is at odds with the rebuttal argument. The data from GPS is particularly clear on this – for a more in depth discussion of the empirical data, see the article on “Time Dilation (Special Relativity)”. Most significantly, Einstein himself rejected his original Twin Paradox claim in 1916 and asserted the NPTD was due to the turnaround acceleration.3 In doing so, Einstein himself implied that special relativity’s time dilation is NOT the cause of the NPTD and does NOT cause clock rates to slow. [Note: Empirical evidence shows that increasing ABSOLUTE velocity causes atomic clocks to slow. Relativists erroneously claim that this supports Einstein’s original Twin Paradox claim and, hence, supports special relativity, whereas the empirical evidence actually refutes both as it shows the clock rate dependency is on absolute velocity as opposed to relative velocity - see Section 2 of the Home Page of http://twinparadox.net/ .]

## Relativists’ Reconciliation Arguments

As described above, early on many physicists criticized Einstein’s original Twin Paradox claim. Hence, relativists’ arguments trying to reconcile the apparent problems of the Twin Paradox claim with special relativity are called “reconciliation arguments”.

Note that the relativists tried to reconcile Einstein’s original Twin Paradox claim with special relativity even though straightforward analysis showed that the basic assumption that the claim was built on was false.

Relativists are in general agreement that the two can be reconciled. However, there is little agreement on which reconciliation argument is the correct argument. In fact, reconciliation arguments published in top physics journals give 21 different and distinct causes of the NPTD – all of which are mutually exclusive although some are partially overlapping. However, the top physics journals have NOT published rebuttals of any of these conflicting reconciliation arguments. (For more detail on the 21 reconciliation arguments, see Section 3 of the Report Page at TwinParadox.net.) Hence, it appears that relativists reject none of the reconciliation arguments – at least not explicitly. If a specific reconciliation argument was correct and correctly identified the cause of special relativity’s time dilation effects, then there would be no need for a 2nd, much less 20, additional reconciliation arguments and causes so there is at least a lot of implicit rejection of all of the reconciliation arguments within physics academia. All 21 of the reconciliation arguments are erroneous. However, it is beyond the scope of this article to discuss all 21 individually. Hence, below we give the conceptual rebuttals for the main categories of reconciliation arguments.

### The NPTD Accumulates Smoothly and Evenly As A Function Of Relative Velocity

The standard reconciliation argument claims that the relative velocity between two clocks causes a clock’s proper time accumulation rate to slow. The logic rebutting this argument/cause can be used for any argument that asserts that the net proper time difference (NPTD) accumulates smoothly and evenly during the constant velocity sections of the round trip Note that this category of reconciliation argument ignores the flaw in its tacit assumption as described in Section 3 “First Attempt At Reconciliation” above. In addition, it has another problem as discussed below.

If one just looks at a single Twin Paradox scenario and doesn’t really think about it, then all is well. All seems to be well because there is the tacit, unconscious assumption that the “stationary” or stay-at-home frame is a uniquely preferred frame. Once one realizes this, it’s easy to show this category of reconciliation arguments leads to a glaring contradiction. Hence, if one analyzes two overlapping Twin Paradox scenarios where, in the 2nd scenario, the stay-at-home frame of the 1st scenario changes roles and becomes the frame of the 2nd scenario’s “traveling” twin’s outbound journey and the 1st scenario’s “traveling” twin’s outbound journey frame becomes the 2nd scenario’s stay-at-home frame, then a contradiction is obvious. One is lead to the conclusion that the clocks in frame “A” are both faster and slower than the clocks in frame “B” which is impossible - especially, if one remembers that all clocks at rest in a frame accumulate proper time at the same rate. For a more detailed discussion, see the “Can't Be Due To Relative Velocity” page at TwinParadox.net.

This reconciliation argument has been espoused in physics academia (although admittedly by a shrinking number) for well over 100 years even though Einstein himself rejected it and shifted to accepting an argument in the category to be described next.3

As an aside, Herbert Dingle who was considered one of the foremost experts on special relativity of his day saw the obvious flaw in the constant-relative-velocity as cause reconciliation argument and this precipitated the famous Twin Paradox Debate. The establishment relativists basically tarred and feathered Dingle, labelled him a “quack” and drove him out of “respectable” physics. The establishment relativists worshipped Einstein and thought of Dingle as a heretic, but they overlooked that Einstein, much earlier than Dingle, had considered the logic discussed above and had recanted his claim that special relativity’s time dilation could cause an NPTD. For a more detailed discussion on Dingle’s views on the Twin Paradox, see the “Dingle’s Question” page at TwinParadox.net.

### NPTD Is Due To Turnaround Acceleration

This approach is mutually exclusive with the prior approach. Hence, it implicitly rejects Einstein’s assertion that special relativity’s time dilation, which is a function of relative velocity, is the cause of the NPTD. Thus, this approach doesn’t address the paradox aspect of the Twin Paradox at all.

Accordingly, we don’t really need to discuss this category of reconciliation argument at all – it does not argue for special relativity’s time dilation as a viable cause of the NPTD or as a possible cause of a physical effect. However, for those interested in doing critical thinking about this topic, we will briefly discuss some of the problems with this argument category.

1. If we change a classic Twin Paradox scenario so that the “stay-at-home” twin does exactly the same amount of accelerating as the “traveling” twin, he will end up back at his original position and if the calculation of the NPTD is done consistently, it will be virtually the same as for the classic Twin Paradox scenario – especially if it’s a long trip. Hence, in this modified Twin Paradox scenario both twins do the same amount of accelerating so, according to this argument, there should now be no NPTD. Yet the standard method of calculating the NPTD is virtually unaffected and produces virtually the same NPTD. For a more detailed discussion, see the “Can't Be Due To Turnaround Acceleration” page at TwinParadox.net.
2. Let us look at another flaw by analyzing two Twin Paradox scenarios where the relative velocities are the same and where the difference in duration is a factor of 100 and the turnaround accelerations are done in the same location. In other words, both sets of twins start in the same “stay-at-home” frame, but one traveling twin starts at a distance from the single turnaround acceleration area that is 100 times greater than the distance for the other twin. We arrange the start time of the two traveling twins so they will turnaround at the same location at the same time. Then, according to this category of reconciliation argument, we have accelerations whose parameters are identical in size, duration and location, but where one acceleration is alleged to have 100 times the effect on clocks as the other identical acceleration.
3. All the empirical data from accelerators agree that “time dilation” effects are NOT a function of acceleration per se, but rather are a function of velocity.

### NPTD IS Due To Relative Simultaneity Or Doppler Shift

This approach is mutually exclusive with the prior approaches. Hence, it implicitly rejects Einstein’s assertion that special relativity’s time dilation is the cause of the NPTD. Thus, this approach doesn’t address the paradox aspect of the Twin Paradox at all.

Accordingly, we don’t really need to discuss this category of reconciliation argument at all – it does not argue for special relativity’s time dilation as a viable cause of the NPTD or as a possible cause of a physical effect. However, for those interested in doing critical thinking about this topic, we will briefly discuss some of the problems with this argument category. Since both these arguments imply a physical model where the proper time difference accumulates smoothly and evenly as a function of relative velocity, they have the same general problems as described in section 4.1 above.

Unlike the acceleration argument, this type of argument does try reconcile the NPTD with special relativity. However, the problem is that both relative simultaneity and Doppler Shift are inherently “just observed” effects and do NOT describe proper time effects.

For example, when the “traveling twin” turns around and changes velocity from v to –v, what he observes regarding simultaneity will change. But that’s just an observed effect and neither his clock’s reading nor his twin’s clock’s reading will jump forward or backwards as a result. IF the traveling twin were to RESET his clock based on his changed view of simultaneity, then that would affect the clock’s reading, but the Twin Paradox is NOT about manually resetting the reading of one’s clock – it’s about proper time accumulation.

Regarding the Doppler Shift for light, this is a symmetric effect for light and, hence, is inherently a “just observed” effect. The frequency of emitted light does NOT change at the source when it is received by an observer in relative motion! [As an aside, note that the Doppler Shift for light can be explained in terms of the receiver’s and the sender’s velocities with respect to a single preferred frame4.]

### Intimidation And Bullying

As we’ve seen above, a great variety of different and conflicting reconciliation arguments and alleged causes of the Twin Paradox’s NPTD have been put forward. However, all are disputed with strong logic and ruled out by empirical data. Hence, the most common tactic employed by relativists discussing the Twin Paradox is to try to dissuade readers/students from questioning the relativist.

For example, Wikipedia’s article (date: 5/16/2017) on the Twin Paradox has as its 2nd sentence, before any discussion has been presented, “This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect[1][2] and naive[3][4].

Wikipedia is correct that “This result appears puzzling because … according to … time dilation and the principle of relativity, each should paradoxically find the other to have aged less”. Yes, that is the essence of the Twin Paradox as many distinguished physicists have articulated. Hence, Wikipedia simply tries to dismisses the essence of the Twin Paradox topic by proclaiming it to be “incorrect and naïve” and then goes on to discuss reconciliation arguments that contradict each other and where each is well known to be bogus.

Another example can be found in the Prof. Bernard Schultz of the Albert Einstein Institute in Germany textbook, “A first course in general relativity”. Schutz, regarding the Twin Paradox, writes, “Unfortunately, the careless student (or the attentive student of a careless teacher) often comes away with the idea that SR does in fact lead to paradoxes. This is pure nonsense.”

## A Compressed History of the Twin Paradox Debate From the Critical Thinker’s Perspective

Since most in physics academia react to the topic of the Twin Paradox dismissively and tend to think those who raise the topic are “quacks”, a little background may provide some balance. As discussed above, Einstein, in 1905, originally contended that the NPTD was caused by special relativity’s time dilation and that, hence, the NPTD accumulated smoothly during the constant velocity segments and was due to relative velocity with half the NPTD accumulating in the outbound segment and half in the inbound segment. There were a series of critics who showed that this contention lead to a contradiction. These critics were scorned, insulted and derided as quacks.

However, eventually, Einstein and many, many prominent physicists (e.g., Max Born) agreed that the critics had made a valid point and moved on to a variety of explanations focused on the turnaround acceleration. None of the relativists made any apologies to the above referenced critics and gave them no praise – curiously, the relativists still speak of them derisively.

Then there were a new series of critics who showed that this new turnaround acceleration contention lead to a number of contradictions. These critics were scorned, insulted and derided as quacks. However, eventually, many relativists (tacitly) agreed that this approach lead to contradictions and moved on to a variety of explanations based on relative simultaneity including “swinging lines of simultaneity” (e.g., “Spacetime Physics” by Archibald Wheeler and Edwin Taylor). None of the relativists made any apologies to the above referenced critics and gave them no praise – curiously, the relativists still speak of them derisively.

Then there were a new series of critics who showed that this relative simultaneity contention was invalid. These critics were scorned, insulted and derided as quacks. However, eventually, many relativists (tacitly) agreed that the critics were correct and moved on to a wide variety of explanations based on constructs from currently accepted theory. None of the relativists made any apologies to the above referenced critics and gave them no praise – curiously, the relativists still speak of them derisively.

Then there were a new series of critics who showed that these diverse contentions each individually lead to a number of fatal problems. These critics were scorned, insulted and derided as quacks. However, eventually, many relativists (tacitly) agreed that these approaches lead to contradictions and moved on to the position of the relativist responders discussed below. None of the relativists made any apologies to the above referenced critics and gave them no praise – curiously, the relativists still speak of them derisively.

To questions addressing , “How does the net proper time difference (NPTD) accumulate?”, most modern relativists shifted to answering that (using special relativity) one could not know. This is a significant change from the series of specific answers presented in prior decades. Their reasoning for this new agnosticism, aside from the failure of previous attempts at being specific, is as follows. Proper time is the time that accumulates on an observer's clock between two events on his worldline. That value is well defined and invariant (i.e., observer independent). The net proper time difference (NPTD) for the total round trip is well defined. The NPTD for the round trip is well defined because the start and end events are on the worldlines of both twins - in other words, the twins share the start event and end events so reading the clocks for each of those events is simultaneous for the twins - they are not separated so there's no issue of what time for the “traveling” twin is simultaneous with what time for the “stay-at-home” twin.

Conversely, when A and B are physically separated, relativist claim that special relativity’s construct of relative simultaneity prohibits determining a net proper time difference between A and B – i.e., using relativity, when A and B are separated, one cannot tell which events on A’s worldline are simultaneous with which events on B’s worldline and vice versa because observers in different frames have different views on which events are simultaneous with other events. This relativity based argument continues that if one cannot determine the net proper time difference (NPTD) between A and B, when A and B are physically separated, then one cannot describe or give a physical description of how the proper time difference accumulates. So this “we don’t know” argument would seem to save the day for the relativist’s goal of reconciling how the Twin Paradox NPTD accumulates with currently accepted theory. However, the “we don’t know” argument has the same problem as previous reconciliation arguments as it mixes proper time with observed time (relative simultaneity).

Simple logic shows that the proper time difference must accumulate in a specific way. For example, if special relativity’s time dilation is the cause, then the proper time difference must accumulate consistent with this claim, namely, as smoothly and evenly as the relative velocity. And we have seen that this claim leads to a logic contradiction. In addition, more generally, the relativists’ denying that half the NPTD accumulates during the outbound journey and half during the outbound journey even though the physics parameters of the inbound and outbound are identical for both segments except for direction, implies that the physics of the journey is direction dependent which is at odds with the Principle of Relativity.

Finally, around 2011 a group of critical thinkers asked the physics community about how many thought that the Twin Paradox articulated a real problem and should be given serious analysis – approximately 150 physicists worldwide heard about the open letter and signed it (see the “Open Letter on the Twin Paradox” page at TwinParadox.net for more information).

## The Future of the Twin Paradox

While literally thousands have written about the paradoxes and problems associated with the Twin Paradox and with interpreting special relativity’s time dilation with causing physical effects and with special relativity itself, physics academia remains unconvinced [5]. Hence, pursuing the path that the Twin Paradox points to should lead to significant progress in spacetime physics from younger, critical thinking physicists.

## References

1. Einstein, Ann. der Phys. 17, 891 (1905)
2. P. Langevin "The Evolution of Space and Time" ("L'évolution de l'espace et du temps"). Scientia 10: 31–54 (1911)
3. A. Einstein, "The Foundation of the General Theory of Relativity" (1916)
4. D.R. Frankl, Am. J. Phys. 52(4), 374 (1984) application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less” – giving no less than 4 references
5. G.O Mueller, 95 Years of Criticism of the Special Theory of Relativity (1908-2003); AVAILABLE ON LINE: - English Translation