Relativity and Aether Theory, a Crucial Distinction

We study the case of two rockets which meet at a point O of an "inertial" co-ordinate system S, and move symmetrically toward two targets A and B placed at equal distances of point O. At the instant they meet, the clocks inside the rockets are synchronized. This question which was tackled in ref [1] is studied here in depth. Assuming the existence of a preferred aether frame S0 and the anisotropy of the one-way speed of light in the other frames, we show that if the speed of the rockets is determined exactly, the clocks inside the rockets will display different readings when they reach points A and B in contradiction with the relativity principle. Conversely, if the determination of the speed of the rockets is made with clocks placed at A and B synchronized by means of the Einstein-Poincare procedure, the clocks inside the rockets will display the same reading, a fact which seems in agreement with the relativity principle. But this synchronization procedure presupposes the invariance of the one-way speed of light, in contradiction with the assumptions made, and, therefore, introduces an error in the measurements. This demonstrates that if we assume the existence of an aether frame, the relativity principle is not a fundamental principle; it depends on an arbitrary synchronization procedure. In any case, this is an example of an experimental measurement which can be explained by aether theory without the assumption of the invariance of the one-way speed of light in all inertial frames