Henri Bergson: Half-relativity – Michelson-Morley experiment (4)

But we should also know why we ourselves, in our turn, measuring the speed of light by terrestrial experiments such as those of Fizeau or Foucault, we always find the same number c, whatever the speed of the Earth relative to ether (1).

The motionless observer in the ether will explain it like this. In experiments of this kind, the ray of light always makes the double journey back and forth between the point and another point, A or B, on the Earth, as in the Michelson-Morley experiment. In the eyes of the observer who participates in the movement of the Earth, the length of this double path is therefore 2l.

Now, we say that it invariably finds the same speed c for light. It is therefore that invariably the clock consulted by the experimenter at the point indicates that the same interval t, equal to 2l/c, has elapsed between the departure and return of the ray.

But the spectator stationed in the ether, who follows with his eyes the path made in this medium by the ray, knows well that the distance traveled is in reality 2l/√(1 – v²/c²). He sees that the mobile clock, if he measured time like the motionless clock he keep next to him, would mark an interval 2l/c√(1 – v²/c²).

Since it nevertheless only marks 2l/c, it means that its time flows more slowly. If, in the same interval between two events, a clock counts a fewer number of seconds, each of them lasts longer.

The second of the clock attached to the moving Earth is therefore longer than that of the stationary clock in the immobile ether. Its duration is 1/√(1 – v²/c²).

But the inhabitant of the Earth knows nothing about it.

References

(1) It is indeed important to note (we have often neglected to do so) that this is not enough of the Lorentz contraction to establish, from the point of view of the ether, the complete theory of the Michelson-Morley experiment made on Earth. We must add the lengthening of time and the displacement of simultaneities, everything that we will find, after transposition, in Einstein’s theory. The point was well highlighted in an interesting article by C. D. Iiroad, Euclid, Newton and Einstein (Hibbert Journal, April 1920).