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43 pages

English

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This book revisits Einstein’s postulate of the invariance of the speed of light, focusing on the corresponding train thought experiment. It shows how a close analysis of the supposed relativity of the simultaneity of light beam emissions brings us to the principle of the relativity of simultaneity at the physical level. However, in the objection about a spacecraft and a missile presented here, this principle turns out to be self-contradictory. The present logical and mathematical considerations are liable to challenge the validity of the second postulate of Special Relativity. Recognition of the results of this analysis could revolutionize our conception of spacetime.

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Publié par	Les Editions Chapitre.com
Date de parution	09 février 2021
Nombre de lectures	0
EAN13	9791029011351
Langue	English

Informations légales : prix de location à la page 0,0012€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

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Paradox of the invariance of the speed of light
Philippe de Bellescize
Paradox of the invariance of the speed of light
Les Éditions Chapitre.com
31, rue du Val de Marne 75013 Paris
© Les Éditions Chapitre.com, 2021
ISBN : 979-10-290-1135-1
Acknowledgements
The author would like to thank Dr . Jessica Blanc for her help with rewriting the Abstract and Gilles Plante for his contribution to Appendix 2. I am most grateful to all those whose comments and encouragements have helped me to develop my work on this subject.
English translation from the French by Dr. Jessica Blanc.
The photographic assembly on the cover was carried out by the Graphic Designer Frédéric Marin.
The images on the cover were provided by Fotolia. com and Shutterstock.
Introduction
The author describes how the invariance of the speed of light necessarily entails that the relativity of simultaneity at the physical level holds true in the case of two different inertial reference frames. The relativity of simultaneity at the physical level is a metaphysical principle which is implicitly used in the theory of Special Relativity, a theory which gave rise to a particular conception of spacetime {1} . This principle will be presented below, along with the reasons why it has to be differentiated from the simple relativity of the simultaneity of events perceived by two different observers. We will go on to see, however, that when an observer is accelerating, this principle can lead us to say one thing and the very opposite at the same time. Although this situation is nothing new, the formulae used so far to account for the Theory of Relativity do not express this contradiction. This is an important finding because it leads to the conclusion that the speed of light cannot be physically invariant {2} in all possible inertial situations, and it is therefore necessary to rethink how to present spacetime. It should also be possible to define those situations in which a difference in the speed of light can be actually measured, although this would first require further theoretical and technical investigations.
Is there some inaccurate reasoning at the root of special relativity?
It was once assumed that the speed of light was invariant with respect to the aether, and that it could therefore not be invariant with respect to the Earth . Although the aim of the Michelson - Morley experiment was to confirm this assumption, the results obtained in the latter experiment seem to show on the contrary that the speed of light is invariant with respect to the Earth . It was this finding that probably led Albert Einstein to adopt the following reasoning: if the speed of light is invariant with respect to the Earth , then since the Earth is a moving body, the speed of light must be invariant with respect to any body in a state of inertia. If we apply this reasoning to Einstein’s train thought experiment, this means that if the speed of light is invariant with respect to the station, then it must also be invariant with respect to the train, which is in constant motion with respect to the station. However , as I propose to establish here, this reasoning is not entirely accurate. As we will see, it is probably far more reasonable to expect the speed of light to constantly adapt to the current spatial configuration, although no proof of this hypothesis has been definitely established so far.
The invariance of the speed of light entails the principle of the relativity of simultaneity at the physical level
It is proposed in this section to comment on Einstein’s train thought experiment {3} , which was originally used to illustrate the concept of spacetime according to the theory of Special Relativity, whereas Einstein’s elevator thought experiment leads rather to the principle of equivalence he used to illustrate his theory of General Relativity. Einstein’s train thought experiment showed what effect the hypothetical invariance of the speed of light would have from the point of view of all inertial observers. The train thought experiment focuses on what two observers perceive while a train is moving through a station without stopping: the one observer (a passenger) is sitting in the middle of the train travelling at a constant speed through the station, and the second observer (the stationmaster) is standing motionless on the platform. At the instant when the two observers are crossing each other, two light sources are visible at equal distances from the stationmaster: one ahead of the train and the other, behind the train. In this situation, the two beams of light reach the stationmaster at the same time. Since they are emitted at equal distances from the stationmaster, he will conclude that both beams were emitted at the same instant because he assumes the speed of light to be invariant with respect to him. It is quite possible, however, that these two events did not actually occur simultaneously, but if the speed of light is assumed to be invariant with respect to the stationmaster and the distances between the stationmaster and the two beams of light are known, the two events will be taken by this observer to be simultaneous. In this context, we cannot therefore say that there is no simultaneity whatsoever, since the simultaneity of the two events perceived by the stationmaster is a logical conclusion based on the given premises {4} .
Generally speaking, two distant events that appear to be simultaneous from the point of view of a stationary observer will not be perceived as being simultaneous by a second observer who is constantly moving past the first observer unless both of them are in exactly the same place when observing or measuring these events. This could be called the relativity of the simultaneity of events perceived by two different observers. As we will see below, it is necessary to differentiate between this relativity of the simultaneity of events perceived by different observers at the time of measuring the events (that is to say during a measurement procedure) from the relativity of the simultaneity of the emission of beams of light {5} , as well as from the relativity of simultaneity at the physical level. One particular feature of this analysis of Einstein’s train thought experiment is that it shows that this supposed relativity of the simultaneity of light beam emission necessarily entails the relativity of simultaneity at the physical level. Let us now consider two different scenarios. First scenario: the two observers were both in the same place when the two beams reached the stationmaster (as in the version of the train thought experiment presented by Yann le Roux); second scenario: the two observers were both in the same place when the two beams were emitted, which corresponds to what was perceived by the stationmaster, assuming the speed of light to be invariant with respect to him (as in the version proposed by Albert Einstein).
In the first scenario, if we assume that the two rays were emitted simultaneously from the point of view of both observers (i. e. absolute simultaneity) and that the speed of light was invariant with respect to the stationmaster, then it follows that the speed of light cannot be invariant with respect to the observer in the train because in this scenario, at the instant when the two rays were emitted, the distances from the two light sources were not perceived as being the same by the passenger in the train travelling through the station. However, in the first scenario, the two rays both reach the passenger at the same time. Therefore, in this scenario, for the speed of light to also be invariant with respect to the passenger in the train, the two beams cannot have been taken by the latter to have been emitted simultaneously, although this was what the stationmaster perceived. Bearing this first conclusion in mind, we can now move on to the second scenario.
In the second scenario, we already know that the observer on the platform takes the two rays of light to have been emitted simultaneously, assuming the speed of light to be invariant with respect to him. However, as we saw in the previous paragraph, in order for the observer in the train to be able to conclude that the speed of light is invariant with respect to himself, then from his point of view, the two rays cannot have been emitted simultaneously: what has been said about the first scenario should presumably also be applicable to the second. The two scenarios are indeed fairly similar, except that the timing of the train is different. The passenger in the train will assume the beam of light occurring in front of the train to have been emitted before the two observers were aligned, and the second ray of light to have been emitted from behind the train after the two observers were aligned. We can therefore now define the metaphysical principle underlying the invariance of c between the point of origin of the beam of light and the point where the beam is perceived by the two inertial observers.
In the second scenario, at the instant when the two observers pass each other, the beam of light originating from the rear of the train is taken by the stationmaster, but not by the passenger in the train, to have been already emitted – i.e., to actually still exist at its point of origin. The passenger in the train will take the beam to exist only a short time later, when he is a little farther away from the stationmaster. For a body to be moving with respect to an observer, that body must be taken by that observer to exist. I propose to use the expression “to exist for” from now on because according to the latter principle, even though the two observers are in the same physical position, the beam of light originating from the rear of the train exists for the observer on the plat