Henri Bergson: Half-relativity – Michelson-Morley experiment (3)

Here then is the explanation proposed by Lorentz, an explanation of which another physicist, Fitzgerald, also had the idea. The line OA would contract by the effect of its movement, so as to reestablish equality between the two double paths. If the length of OA, which was l at rest, becomes l√(1 – v²/c²) when this line moves with speed v, the path traveled by the ray in the ether will no longer be measured by 2l/(1 – v²/c²) , but by 2l/√(1 – v²/c²) and the two paths will be effectively equal. It will therefore be necessary to admit that any body moving with any speed v undergoes, in the direction of its movement, a contraction such that its new dimension is the old one in the ratio of √(1 – v²/c²) to unity. This contraction, naturally, also affects the rule with which we measure the object as well as the object itself. It thus escapes to the terrestrial observer. But we would notice it if we adopted an immobile observatory, the ether. (1)

More generally, let’s call S a system immobile in the ether, and S’ another example of this system, a double, which was first one with it and which then detaches itself in a straight line with the speed v. As soon as it leaves, S’ contracts in the direction of its movement. Anything that is not perpendicular to the direction of movement participates in the contraction. If S were a sphere, S’ will be an ellipsoid. This contraction explains why the Michelson-Morley experiment gives the same results as if light had a constant speed equal to c in all directions.

(1) It seems at first that instead of a longitudinal contraction we could also have assumed a transverse expansion, or even both at the same time, in the appropriate proportion. On this point, as on many others, we are obliged to leave aside the explanations given by the theory of relativity. We limit ourselves to what interests our present research.

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