# The thought experiment of Einstein's train

The thought experiment of Einstein's train

 B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A —> B on the travelling train. Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.>

Relativity   the special and general theory, TRANSLATED BY ROBERT W. LAWSON, NEW YORK: HENRY HOLT, 1920

The error of interpretation of Einstein (explanation in a few words)

Why there can be no relativity of simultaneity at the physical level:

Once it is understood that the invariance of the speed of light implied the relativity of simultaneity at the physical level, everything else follows. There are not thirty-six ways to define the relativity of simultaneity at the physical level, there is undoubtedly only one: in the thought experience of the Einstein train, the two light rays are emitted at the same time for the observer at the railway station, and according to Einstein's interpretation, would not be emitted at the same time for the observer on the train.

For the observer at the railway station, the two light rays are emitted when the two observers are at the same distance from the two light sources (when the two observers are opposite each other).

For the observer on the train, the light ray at the front of the train would be emitted before the light ray at the back of the train. For the observer on the train, when the two observers are at the same distance from the two light sources (when the two observers are opposite each other), the light ray at the front of the train would already have been emitted, while the light ray at the back of the train would not have been emitted yet.  It will be emitted when the observer on the train is a little further away.

Therefore, when the two observers are at the same distance from the two light sources (when the two observers are opposite each other), the light ray at the back of the train appears to exist at the back of the train in relation to the observer at the railway station and does not appear to exist in relation to the observer on the train (this is the relativity of simultaneity at the physical level). In relation to the observer on the train, it will exist when the observer on the train is further away, and he can be much further away if the light sources are very distant. This is what is involved in the thought experiment of Einstein's train, even if it is not explicitly stated. Just follow the reasoning to understand this.

And once the light ray has been emitted for him, if the observer at the railway station speeds up and joins the observer on the train before the light ray is emitted for the observer on the train, we find ourselves in the case discussed in the objection of the shuttle and the missile (1). And we can see that it is impossible, as soon as we take into account the existence of the missile according to what is shown on the space-time diagram. Of course, to get to that case, we have to consider very large distances.

The relativity of simultaneity at the physical level is a principle implied by special relativity, it has a metaphysical range and it is not verifiable immediately. On the contrary, it can be shown with certainty that it leads to contradictions (see the objection of the shuttle and the missile). This means that there is in fact an absolute simultaneity at the physical level (2), because there is no third possibility (3). The absolute simultaneity at the physical level is also a principle having a metaphysical scope, and it is not verifiable immediately either. Indeed, it is not possible to know for sure whether two distant events are simultaneous or not. But once it is understood that there is necessarily an absolute simultaneity at the physical level, this leads to a complete paradigm shift with respect to the conceptual system of physics.

Objection of the shuttle and the missile

The Space-time diagram of relativity does not correspond to what actually happens. This would also mean that the speed of light is not always invariant.

href="https://youtu.be/6ZLSlDn4W_8

The diagram in the video is based on a ThM diagram (online physics forum http://www.forum2.math.ulg.ac.be/), expressing objection 2 of Chapter 1 from my book "Le Principe Moteur de l’Univers et l’Espace-Temps" ("The Driving Principle of the Universe and Space-Time"). I added this diagram in my new book "Et si Einstein s'était trompé sur un point capital dans son analyse aboutissant à la relativité restreinte?" ("What if Einstein was wrong about a crucial point in his analysis leading to the special relativity?")

If we take into account what is involved in the relativity of simultaneity at the physical level, we arrive at two contradictory calculations with regard to the position of the missile:

Let us imagine that the missile has already traveled 100 meters before the shuttle accelerates, the shuttle begins the first calculation of the trajectory of the missile from that point.

Once the shuttle has accelerated, it looks at the position of the missile on the space-time diagram and the missile has not left yet.  It starts the second calculation of the trajectory of the missile while the missile appears to be still at its starting point.

We can clearly see that the two calculations are not going to give the same moment of arrival of the missile, since according to the first calculation, the missile traveled more than 100 meters, whereas according to the second calculation, the missile has not left yet (these two calculations, at that moment, being made at the same time from the shuttle). This means that, if we follow what the space-time diagram says and if we take into account the existence of the missile, in some cases it is possible to have two contradictory mathematical representations with regard to the position of the missile. And the difference between the two calculations is due entirely to the belief in the relativity of simultaneity at the physical level, and is not due to inaccuracy in the calculation in relation to the trajectory. Of course, for this to be obvious as I have just described it, the missile would have to be hundreds of billions of kilometers away from the shuttle.

Conclusion

The relativity of simultaneity at the physical level is a principle implied by the special relativity, having a metaphysical scope. By taking into account the implicated metaphysical aspect (considering the existence of the body in accordance to what is shown on the space-time diagram), we reach two contradictory calculations concerning the position of the missile. This demonstrates, even from a mathematical point of view, that such a relativity of simultaneity is impossible. This means that there is an absolute simultaneity at the physical level in the absence of a third possibility (3). Therefore, the speed of light cannot be invariant in any case. From this point, it will be understood that this may lead the physics to an important paradigm shift with respect to its actual conceptual system.

Note 1: If the light source is very close to the rear of the train, the supposed difference in simultaneity would be slight, but if the light source is situated billions of billions of miles away, then the supposed difference in simultaneity could be very large, as this difference depends on the speed of the train and the distance of the light sources. And this difference in simultaneity may be sufficient to allow the observer standing on a platform, if he accelerates, to reach the observer inside the speeding train before the light beam at the rear of the train does not appear to exist in relation to the observer on the train. If this light beam were to be replaced by a missile, such a situation could exist where the missile would have already traveled 100 yards for the standing observer prior to starting to accelerate, and where the standing observer could reach the observer inside the train before the missile could be seen being launched by the observer inside the train. This is my reasoning for my objection of the shuttle and the missile without needing to make any equations or a space-time diagram.

Note 2 - Absolute simultaneity at the physical level: if the light flash exists for the observer standing on the station platform, then it must also exist for the observer inside the train, and vice versa. The mere fact that the light flash “exists” implies absolute simultaneity at the physical level, since, if a given body exists for one other body, then it necessarily exists for every other body in the physical world. This is one of the reasons why the universe has to have a present instant, except that this is not the case with the notion of time associated with restricted relativity.

Note 3: There is no third possibility, since, from the moment where we consider that such a body exists “to" A, either it exists also “to" B, or not.

Explanation: Why can't the speed of light be physically invariant with regard to absolute simultaneity at the physical level?

Let us consider Einstein’s train experiment taking the variant version put forward by Zefram Cochrane from the Futura-Sciences forum, whereby we consider that the light flashes reach the two observers simultaneously at the moment where the two observers are facing each other. Whereas, in Einstein's version, at that precise moment, the observer standing on the station measures the two flashes to be simultaneous.

Therefore, if we consider that both observers measure the two light flashes to be simultaneous, that would mean that this occurred for the observer inside the train before the train had actually arrived in the station. At that precise moment in time, the distance “between this observer and the light source at the front of the train” is not equal to the distance "between the same observer and the light source at the rear of the train”. Yet the two light flashes nevertheless reach this observer at the same time. In absolute simultaneity, the two light flashes travel two different distances at the same time, at least for one of the two observers, so the relative speed of the flashes for this observer is not the same. Consequently, this means that, in the context of absolute simultaneity at the physical level, the speed of light cannot be physically invariant with respect to the two observers. And it is for this reason that the physical invariance of the speed of light implies, at least theoretically, the relativity of simultaneity at the physical level (1). However, since the latter gives rise to two mathematically contradictory arguments, it is certain that the speed of light cannot be physically invariant with respect to all inertial frames of reference, and that it is also necessary to change the representation of space-time.

Note 1: After having demonstrated - by taking the variant version of the Train Thought Experiment put forward by Zefram Cochrane on the Futura-Science forum - that, in the context of absolute simultaneity at the physical level, the speed of light cannot be physically invariant, we can only go back and reconsider the initial version of Einstein’s experiment. Indeed, if we posit that the two light flashes are not measured to be simultaneous by both observers, we arrive at what I said in my commentary on the thought experiment of Einstein's train, and we see that invariance of the speed of light at the physical level implies the principle of relativity of simultaneity at the physical level.

Translated by Easy Translate

For further explanations:

Circular letter:

http://www.leprincipemoteurdelunivers.com/pages/circular-letter.html