Relativity and Aether Theory, a Crucial Distinction

Abstract

We study the case of two rockets which meet at a point O of an inertial co-ordinate system S, and are scheduled to move at constant speed, in opposite directions, toward two targets placed at equal distances from point O. At the instant they meet, the clocks inside the rockets are set to zero. When they reach the targets the rockets meet two clocks A and B whose reading is identical. This question which was tackled in ref [1] is studied here in depth. Assuming the existence of a preferred aether frame So in which the one-way speed of light is isotropic, and the anisotropy of this speed in the other frames, we show that, if the equal reading of the clocks A and B results from an exact synchronization, the clocks inside the rockets will display different readings when they reach A and B in contradiction with the relativity principle. Conversely, if the clocks A and B, which display an equal reading, have been synchronized by means of the Einstein-Poincare procedure, the inboard clocks will also display the same reading, a fact which seems in agreement with the relativity principle. But this synchronization method presupposes the invariance of the one-way speed of light, in contradiction with the assumptions made, and, therefore, introduces a measurement error. This demonstrates that if we assume the existence of an aether frame, the apparent relativity principle is not a fundamental principle; it depends on an arbitrary synchronization. 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.