June 26, 2019
MMX, Michelson, Morley, Experiment, Derivation, velocity, celerity, speed, Relativity, Ether, Aether
This article deals critically with the relativistic derivation of the result of the Michelson and Morley experiment. This experience is at the source of the theory of Relativity.
There is a historical explanation, that of Albert Einstein, based on the failure of the hypothesis of the ether to explain the lack of phase shift whatever the frame is, except to consider in addition a contraction of the lengths in accordance with the Lorentz- FitzGerald’s hypothesis. But this remains an indirect explanation. It is pointed out here that it has not been found on the internet a direct mathematical derivation based on relativistic assumptions alone. And it is specified that a mathematical demonstration would remain incomplete if it only dealt with the particular case of the observer linked to the interferometer without taking care of the general case where the interferometer is in translation with respect to the observer (as it is also the case for the demonstration with the aether). The difficulty of this derivation comes in the way of reconciling the different distances traveled by the two light beams, the absence of fringe shift and the hypothesis made on the speed of light which is postulated (and not measured) constant according to the theory of Relativity. It is here considered the consequences of a variation of the velocity of light according to the reference frame. Specific experiments are proposed to validate or not this approach.