Einstein’s Misinterpretation

Chapter "Einstein’s Misinterpretation in his Train Thought Experiment" in the book “And He Was Hovering Over the Waters: Toward a New Vision of the Physical World” :

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 reference-body (co-ordinate 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 on 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 mid-point 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 mid-point of the distance A —> B on the travelling train. Just when the flashes  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:
"Two events (e.g., the two lightning strikes A and B) that are simultaneous with respect to the embankment, are they also simultaneous with respect to the train? We shall show shortly that the answer must be negative."
From "Relativity, the special and general theory", translated by Robert W. Lawson, Henry Holt, New York 1920

Einstein’s Misinterpretation

"Two events (e.g., the two lightning strikes A and B) that are simultaneous with respect to the embankment, are they also simultaneous with respect to the train? We shall show shortly that the answer must be negative."

Principle of the Relativity of Simultaneity at the Physical Level

Once we understand that the invariance of the speed of light implies the relativity of simultaneity at the physical level, everything else follows.

There is likely only one way to define this relativity: in Einstein’s train thought experiment, the two light rays are emitted simultaneously for the observer on the embankment, but not for the observer on the train (relativity of simultaneity as posed by Einstein).

For the observer on the embankment, the two light rays are emitted when the two observers are equidistant from the two light sources (that is, when they are directly facing each other).

For the observer on the train, the light ray at the front of the train is emitted before the light ray at the rear of the train.

When the two observers are equidistant from the two sources (directly facing each other), the light ray at the front has already been emitted, while the one at the rear will be emitted later, when the train observer has moved a bit further forward.

Thus, when the two observers are equidistant from the two sources (directly facing each other), the rear light ray is deemed to exist for the observer on the embankment but not for the observer on the train (this is the relativity of simultaneity at the physical level). It will exist for the train observer only when he has moved a little further, or even much further if the sources are very far apart.

This is what is implied by Einstein's train thought experiment, even though it is not explicitly formulated. One simply needs to follow the reasoning to understand it (passage from the idea of the relativity of simultaneity to the principle of the relativity of simultaneity at the physical level, implicitly implied).

Moreover, the observer on the embankment, after the light ray has been emitted for him, could accelerate and join the observer on the train before the light ray has been emitted for the latter. Thus, the light ray — which can be replaced by any body — that has existed for the observer on the embankment should later not yet have existed for that same observer. We then find ourselves in the case illustrated by the shuttle and missile objection. It clearly shows that it is impossible, provided we take into account the existence of the missile according to the space-time diagram. Of course, to make this contradiction very evident, the missile would have to be extremely far from the shuttle. The relativity of simultaneity at the physical level is a principle implied by Special Relativity. It has a metaphysical scope and is not immediately verifiable. However, it can be shown with certainty that it leads to contradictions. This means that there must be an absolute simultaneity at the physical level in the absence of third possibility. Absolute simultaneity at the physical level is itself a principle, with metaphysical scope, and is also not immediately verifiable. Indeed, one cannot determine with certainty whether two distant events are simultaneous or not. But once it is understood that there necessarily must be an absolute simultaneity at the physical level, it leads to a complete paradigm shift in the conceptual system of physics.

Shuttle and Missile Objection

If we take into account what is implied by the relativity of simultaneity at the physical level, we arrive at two contradictory calculations concerning the position of a missile relative to a shuttle that has accelerated. Let us imagine that the missile has already traveled 100 meters before the shuttle accelerates. The shuttle begins its first calculation of the missile’s trajectory starting from that point. Once it has accelerated, it observes the missile’s position on the space-time diagram and, in certain cases, may find that the missile has not yet even departed. It then begins a second calculation of the missile’s trajectory while the missile is still supposedly at its starting point. Clearly, the two calculations will not indicate the same time of arrival for the missile, since according to the first, the missile has traveled more than 100 meters, while according to the second, it has not yet even departed (both calculations being performed at the same moment from the shuttle’s perspective). This means that, if we follow what the space-time diagram illustrates and if we take into account the existence of the missile, in some scenarios, we can encounter two mathematically contradictory representations regarding the missile’s position. And the difference between the two calculations stems entirely from the belief in the relativity of simultaneity at the physical level, not from an inaccuracy in the trajectory calculation. Of course, for this to become evident as described, the missile would have to be located at a very great distance from the shuttle.

Conclusion

The relativity of simultaneity at the physical level is a principle implied by Special Relativity, with metaphysical implications. By taking into account the metaphysical aspect involved (considering the existence of the body according to what the space-time diagram shows), one reaches two contradictory calculations concerning the position of the missile. This illustrates, even from a mathematical point of view, that such a relativity of simultaneity is impossible. It therefore implies that there must exist an absolute simultaneity at the physical level, in the absence of third possibility (1). From there, it follows that the speed of light cannot be physically invariant in all cases. Thus, this leads to the idea that physics could undergo a major paradigm shift regarding its conceptual system.

Note 1: There is no third possibility because, once we consider that a body exists “relative to” A, either it also exists “relative to” B, or it does not.