Paradox of the invariance of the speed of light

By Philippe de Bellescize

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.

• Language: English
• Publisher: Les Editions Chapitre.com
• Release date: Feb 9, 2021
• ISBN: 9791029011351

Book preview

cover.jpg

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