Sound is a vibration of the air travelling as a wave. Ring a bell inside a glass jar with the air pumped out, and the sound does not get out.
Waves on water need water too. Whatever carries a wave is called its medium, and nineteenth century physics took it for granted that every wave has one.
Light reaches us from the Sun across empty space. So empty space too was supposed to be filled with a medium for light, and it was named the ether.
Light is a transverse wave and travels very fast. By the mechanics of the day, the ether had to behave like a solid far stiffer than steel, and yet offer no resistance at all to the motion of the planets.
If the ether exists, the Earth moves through it at km/s in its orbit. Seen from the Earth, the ether streams past at km/s the other way.
In this flow, take two beams of light that each go out and back over the same distance . Let the speed of the flow be , and write .
Light going along the flow moves at on the way out and on the way back. Its round-trip time is
The extra time lost on the slow leg is more than the time saved on the fast leg, so is longer than the it would take with no flow.
Light crossing the flow has to aim slightly upstream to cancel . By Pythagoras its speed across is , and the round trip takes .
Since is larger than , is shorter than , and the light that crossed the flow is back first.
For small , and . With these, the difference in path between the two beams, , comes to about .
For the Earth's orbit and . With arms m long the path difference is m, a time difference of only about seconds.
Instead of a clock, Michelson and Morley used the light waves themselves as the ruler. A half-silvered mirror splits one beam in two, the halves travel out and back along two arms at right angles, and then they are recombined.
The recombined light forms bright and dark fringes, and each time the path difference changes by one wavelength, the fringes shift sideways by one fringe.
The arms were folded back and forth with mirrors to a length of m. The path difference then comes to m, about a fifth of the wavelength of yellow light (around m).
The stone slab carrying the apparatus floated on mercury, and a light push kept it turning slowly. A quarter turn swaps the arm along the motion with the arm across it.
A quarter turn reverses the path difference, so with an ether the fringes should have moved by twice a fifth of a wavelength, of a fringe.
In the measurements, the shift that could be read was less than of a fringe, under a twentieth of the prediction. The paper adds that it was probably less than a fortieth.
The experiment was repeated afterwards in other seasons and other places. Experiments with optical resonators now show that any difference in the speed of light between directions is smaller than one part in .
If the Earth dragged the ether along with it, no flow would show up on the ground. But then aberration, the yearly shift in the directions of the stars that follows the Earth's orbit, could not be explained.
FitzGerald in and Lorentz in proposed that a body moving through the ether shrinks along its motion by a factor . Replace for the arm along the flow by , and becomes exactly equal to .
Why anything should shrink, though, remained a hypothesis: perhaps the forces between molecules change as they move through the ether.
In Einstein made the constancy of the speed of light in every frame a starting principle, instead of a result to be explained. The contraction became one of the consequences of that principle, and the ether was no longer needed.