Einstein and the universe: A popular exposition of the famous theory

by Charles Nordmann

1. Observation of the stars proves that interplanetary space is not empty, but is filled with a special medium, ether, in which the waves of light travel.

2. The fact of aberration and other phenomena seems to prove that the ether is not displaced by the earth during its course round the sun.

3. Michelson’s experiment seems to prove, on the contrary, that the earth bears the ether with it in its movement.

This contradiction between facts of equal authority was for years the despair and the wonder of physicists. It was the Gordian knot of science. Long and fruitless efforts were made to untie it until at last Einstein cut it with a single blow of his remarkably acute intelligence.

In order to understand how that was done—which is the vital point of the whole system—we must retrace our steps a little and examine the precise conditions of Michelson’s famous experiment.

I pointed out in the [preceding chapter] that Michelson proposed to study the speed of a ray of light produced in the laboratory and directed either from east to west or west to east: that is to say, in the direction in which the earth itself moves, at a speed of about eighteen miles a second, as it travels round the sun, or in the opposite direction. As a matter of fact, Michelson’s experiment was rather more complicated than that, and we must return to it.

Four mirrors are placed at an equal distance from each other in the laboratory, in pairs which face each other. Two of the opposing mirrors are arranged in the direction east-west, the direction in which the earth moves in consequence of its revolution round the sun. The other two are arranged in a plane perpendicular to the preceding, the direction north-south. Two rays of light are then started in the respective directions of the two pairs of mirrors. The ray coming from the mirror to the east goes to the mirror in the west, is reflected therefrom, and returns to the first mirror. This ray is so arranged that it crosses the path of the light which goes from north to south and back. It interferes with the latter light, causing “fringes of interference” which, as I said, enable us to learn the exact distance traversed by the rays of light reflected between the pairs of mirrors. If anything brought about a difference between the length of the two distances, we should at once see the displacement of a certain number of interference-fringes, and this would give us the magnitude of the difference.

An analogy will help us to understand the matter. Suppose a violent steady east wind blew across London, and an aviator proposed to cross the city about twelve miles from extreme west to east and back: that is to say, going with the wind on his outward journey and against it on the return journey. Suppose another aviator, of equal speed, proposed at the same time to fly from the same starting-point to a point twelve miles to the north and back, the second aviator will fly both ways at right angles to the direction of the wind. If the two start at the same time, and are imagined as turning round instantaneously, will they both reach the starting-point together? And, if not, which of them will have completed his double journey first?

It is clear that if there were no wind, they would get back together, as we suppose that they both do twenty-four miles at the same speed, which we may roughly state to be 200 yards a second.

But it will be different if, as I postulated, there is a wind blowing from east to west. It is easy to see that in such circumstances the man who flies east to west will take longer to complete the journey. In order to get it quite clearly, let us suppose that the wind is travelling at the same speed as the aviator (200 yards a second). The man who flies at right angles to the wind will be blown twelve miles to the west while he is doing his twelve miles from south to north. He will therefore have traversed in the wind a real distance equal to the diagonal of a square measuring twelve miles on each side. Instead of flying twenty-four miles, he will really have flown thirty-four in the wind, the medium in relation to which he has any velocity.