The thought experiment of Einstein's train
The thought experiment of Einstein's train
<UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid referencebody (coordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: 

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. 

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the midpoint M of the length A —> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the midpoint 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 referencebody 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 referencebody (coordinate system) has its own particular time; unless we are told the referencebody 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)
(I have previously presented the following ideas, but I have discussed them in much greater detail in my latest book, "Paradox of the invariance of the speed of light." (Chapitre.com). These issues are of great importance because they are liable to result in a major change of approach to spacetime in the field of Physics. In this book, I have presented the reasons why the speed of light cannot be invariant in all possible cases in the framework of absolute simultaneity. I have attempted to answer the main criticisms liable to be put forward against my objection about the spaceship and the missile. The book also includes several spacetime diagrams, along with my explanations and comments. The Appendices include a circular letter to specialists in the field, as well an open letter to Lee Smolin, in which I express the hope that these ideas may open the way to developing a new conception of spacetime.)
(click on the title to see the book)
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 thirtysix 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 shuttke and the missile. 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 spacetime 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) (1). 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 Spacetime diagram of relativity does not correspond to what actually happens. This would also mean that the speed of light is not always invariant.
Objection of the shuttle and the missile
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’EspaceTemps" ("The Driving Principle of the Universe and SpaceTime"). 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 spacetime 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 spacetime 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 spacetime 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 spacetime 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.
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