In order to explain how the Michelson experiment worked, I switch from ether to air, and discuss an unorthodox airspeed meter before returning to the “etherspeed” meter.
Airspeed
Imagine a rather unusual airspeed indicator mounted on an airplane. It consists of a sound generator—a drum would do—and a sound receiver such as a microphone mounted on top of the plane amidships, and small plates to reflect sound, one attached to the tail and one to a wingtip, equidistant from the sound generator-receiver combination, as shown schematically in the figure.
Unusual airspeed indicator. Sound waves start from point A and return to point A after reflecting from the equidistant plates M1 and M2. The time difference between the returning echoes provides a measure of the airspeed.
A noise is created, some time elapses, and echoes return from the tail and the wingtip. If the plane is in motion, the wingtip echo will arrive slightly sooner than the tail echo, and the time difference of the echoes could be displayed in the cockpit to let the captain know how fast the plane is moving. Suppose, for instance, that the speed of the plane is 150 m/s, or about 340 mph, half the speed of sound, and that the reflecting plates are 30 m from the source of sound. The sound wave traveling to the tail would have a speed with respect to the airplane of 50 percent more than the speed of sound, that is, 450 m/s. Its journey to the tail would therefore require 0.067 s. On its return trip, it would be making good a speed with respect to the plane of only 150 m/s, and would require three times as long to get back, 0.2 s. Altogether 0.267 s would elapse before the echo from the tail returned. We can express this algebraically. The outbound time from the source A to the tail reflector M1, a distance L away, is
where va is the speed of the airplane and vs is the speed of sound. The sum vs + va in the denominator is the speed of the backward-propagating sound wave relative to the airplane. The time for the echo to return is
The round-trip time for the tail echo is the sum of these two expressions,
Analysis of the trip to the wingtip and back is slightly more complicated, requiring use of the Pythagorean theorem. The result is
The important point is that this latter time is shorter, 0.231 s in our example. Both echoes are delayed by the motion, but the tail echo is delayed more than the wingtip echo, and the difference is easily interpreted in terms of the speed of the airplane.
Etherspeed
Michelsons experiment used an “etherspeed indicator” exactly like the unorthodox airspeed indicator described above—except that light replaced sound as the wave being transmitted and the ether replaced the air as the supposed medium of transmission. Light is sent simultaneously in two perpendicular directions and then reflected back. The source of light and the apparatus are fixed with respect to the Earth, and are therefore being carried through the ether by the Earth (if there is an ether). The time difference between the two reflected light signals is too small to measure directly, but it is inferred from the interference of the two waves. The design of the experiment is shown in the figure below.
Schematic arrangement of Michaelson-Morley experiment.
A light wave arriving from the left is split by a lightly silvered glass plate into two waves, one running upward to mirror M1 and the other continuing on to mirror M2. This wave-splitting action ensures that the two waves get underway at exactly the same instant. Some of the light returning from mirror M1 passes through the plate and some returning from M2 is reflected from the plate to the eye of the observer or, better, to a light-sensitive device more accurate than the eye. If the mirrors M1 and M2 are exactly the same distance from the glass plate (this is not necessary, but it simplifies the discussion), and if the apparatus is at rest with respect to the ether, the two waves arriving at the observer will be exactly in phase and will reinforce each other to give a bright light. If instead the apparatus is moving through the ether, for example in the upward direction in the diagram, the light from M1 will be slightly more delayed in its round trip than the light from M2, and the two waves will no longer be exactly in phase. There will be partial interference of the two waves, and the light seen by the observer will be less bright.
Of course the Earth cannot be stopped and started at will to look for a change of light intensity. But what is simple and just as effective is to change the orientation of the apparatus. Michelson rotated the whole apparatus through 90 degrees so that the path to M1, if initially upwind and downwind, became cross-wind. A change in intensity should have been observed as the rotation proceeded. Michelson and Morley repeated the experiment at various times of the year to catch the Earths motion in various directions through space (through the ether) as the Earth swung around the Sun.
The magnitude of the effect that Michelson hoped to observe is extremely small, because of the leisurely pace of the Earth round the Sun, and it is small wonder that the Berlin traffic, even in 1881, was sufficient to disturb his experiments. The orbital speed of the Earth is about 30,000 m/s (67,000 mph), which is one ten-thousandth of the speed of light. We may suppose, as Michelson did, that the Earth also moves through the ether at this speed. A typical distance from the lightly silvered plate to the reflecting mirrors in his apparatus was 1.2 m. If you use these numbers in our airspeed-indicator equations above, you find that the upwind-downwind beam should have been retarded with respect to the crosswind beam by about 4 x 10-17 s. In this exceedingly short time light travels 12 nm, or 1.2 x 10-8 m . A single wavelength of visible light is about fifty times greater, or 600 nm. Therefore as the apparatus is rotated, the shift of the two waves with respect to each other is much less than the 300 nm that would be required to convert bright constructive interference into dark destructive interference. Nevertheless, a slight change of intensity should occur, and Michelson felt confident that he could observe this tiny effect of the ether without difficulty.
No matter what the time of day or time of year, no matter what source of light was employed, a rotation of the apparatus never produced any observable change of light intensity. The Michelson-Morley etherspeed indicator always gave a reading of zero, indicating no motion of the Earth through the ether. Since the Earth is rotating about its own axis and traveling about the Sun, it seems inconceivable that the ether should execute such gyrations as to remain always at rest with respect to the Earth. It is easier even to give up the ether than to imagine this.1
1 Nevertheless, some scientists embraced the “ether drag” hypothesis, that ether close to the Earth is dragged along with the Earth, assuring that in Berlin or Cleveland, Michelson’s apparatus was at rest relative to the ether.