Grant R. Fowles - Introduction to Modern Optics

The famous Michelson-Morley experiment, performed in 1887, was designed to measure the absolute velocity of the earths motion in space by means of light waves.

A diagram of the optical arrangement is shown in . The apparatus is essentially an optical interferometer. A beam of light from a source S is split into two beams by a half-silvered mirror M. One beam is reflected to a mirror M 1, which in turn reflects the light directly back to M. The other beam is transmitted directly to the mirror M 2, which also reflects the light back to M. The two partial beams then unite at M, part of the combined light going to an observer O who sees an interference pattern of bright and dark fringes. The interference pattern can be made to shift by one fringe by displacing either of the two mirrors M 1 or M 2 a distance of wavelength.

. Simplified diagram of the Michelson-Morley experiment.

If mirrors M 1 and M 2 are both located at precisely the same distance from M and if the apparatus does not move during the time that light is reflected back and forth, then the two waves return to M at the same phase so that a bright fringe is seen at O . Suppose, however, that the whole apparatus is moving in the direction of the initial beam SM. The paths of the beams will then be as shown by the directed lines in the figure. The times taken by the two partial waves in their respective journeys are no longer the same if it is assumed that light travels with a constant speed c in some medium. The situation is analogous to the case of two swimmers in a stream, one swimmer going upstream and back, the other going across the stream and returning.

To analyze the situation quantitatively, let us suppose that the speed of the apparatus through the medium is u. Then the wave moving toward M 2 travels with a speed c u relative to the apparatus. On its return this wave travels with relative speed c + u. The total time for the round trip is therefore

in which d is the distance OM 2 . On the other hand, the wave reflected by M 1 travels along the path MM 1 O, as shown. If we call t 1 the total time for the round trip in this case, then the distance MM 1 is equal to . Thus

Solving for t 1, we get

The time difference t between the two paths is accordingly

This corresponds to a phase difference

where is the wavelength of the light.

In their experiment, Michelson and Morley obtained an effective distance d of 10 m by multiple reflections as indicated in .

. Actual light path in the Michelson-Morley experiment.

The experiment was performed by floating the entire apparatus in a pool of mercury and observing the fringes as the apparatus was rotated through an angle of 90 degrees. This would cause either of the two beams to be alternately parallel or perpendicular to the earths motion. In its orbital motion around the sun, the earths speed is about 104 c . The expected shift with yellow light, 5900 A, was about one third of a fringe. Actually there was no observable shift at all. This negative result came as a surprise to the scientific world. It was in contradiction to the (then) accepted idea concerning electromagnetic radiation, namely, that such radiation must have a medium for its transmission through space. This medium, called the ether, was supposed to be an all-pervading substance, and numerous calculations concerning its properties had been carried out, including some by Maxwell.

The Michelson-Morley experiment has been repeated many times by different observers with essentially the same negative results. There have been some reports of measurable fringe shifts, but none anywhere near as large as should be predicted by the orbital speed of the earth. This is actually a minimum speed since the speed of the whole solar system, due to rotation of our galaxy, is about ten times the earths orbital speed.

The idea of the ether had been so widely accepted that it was many years before it was finally abandoned. In fact two physicists, Fitzgerald and Lorentz, proposed to explain the null result of the Michelson-Morley experiment by suggesting that a body contracts in the direction of its motion through the ether in precisely the ratio . This amount of shortening, known as the Fitzgerald-Lorentz contraction, would just equalize the two light paths so that there would be no fringe shift. Now such an ad hoc explanation of the experiment is not very satisfactory, for the contraction is not capable of direct observation. Any attempt to measure it would fail, since the measuring apparatus contracts along with the object to be measured.