The ether and the Michelson-Morley experiment

For over half a century the “convenient” solution was the ether: a hypothetical rigid, all-pervading medium in which electromagnetic waves propagated, just as sound propagates in air. Light would have velocity $c$ relative to the ether, and other observers would see different values. In this way both the Galilean transformations and the idea that $c$ was the speed of light in a single special frame — the one at rest in the ether — were saved together.

In 1887 Albert Michelson and Edward Morley built an interferometer of extraordinary precision to measure the Earth’s velocity relative to the ether. The idea was to split a beam of light in two using a half-silvered mirror, send each half along a different path — one parallel to the Earth’s motion, the other perpendicular — then recombine them and look for a shift in the interference fringes caused by the different travel times of the two beams.

Calculating the two times if the ether existed

Let $L$ be the length of each arm of the interferometer and $v$ the Earth’s velocity relative to the ether. For arm $A$, parallel to the motion, light travels outward against the “ether wind” (velocity $c-v$) and back with it (velocity $c+v$): $T_A = \frac{L}{c-v} + \frac{L}{c+v} = \frac{2L/c}{1 - v^2/c^2}$ For arm $B$, perpendicular to the motion, light must compensate for the Earth’s sideways displacement during the trip, and covers $2\sqrt{L^2 + (vT_B/2)^2}$ in a time: $T_B = \frac{2L/c}{\sqrt{1 - v^2/c^2}}$ The ratio of the two times is: $\frac{T_A}{T_B} = \frac{1}{\sqrt{1 - v^2/c^2}}$

Notice that the factor $1/\sqrt{1 - v^2/c^2}$ — the future Lorentz factor $\gamma$ — already appears here in 1887, well before Einstein formalised it. Michelson and Morley expected a fringe shift corresponding to this time difference… and instead found nothing.

The result was null: no shift in the interference fringes, no evidence of an “ether wind”. The experiment was repeated across different seasons (when the Earth moves in different directions around the Sun), but always with a null result. The consequences are decisive: if there is no ether wind, there is no privileged frame, and hypotheses I and II are ruled out. Only hypothesis III remains: the Galilean transformations must be abandoned.

The most famous experiment that found nothing

Michelson and Morley repeated the measurement across different seasons, thinking that at least in spring or autumn the Earth, moving in different directions around the Sun, would encounter distinguishable ether winds. Nothing. For almost 20 years physicists tried to save the ether with increasingly contrived hypotheses (Fitzgerald contraction, partial dragging, and so on). But the real problem was different: the ether does not exist. Einstein’s answer was, in essence, “it was never needed”.

Links

Topics: Special relativity Concepts: Einstein’s postulates Skills: Changing reference frame

Related exercises: Spacelike or timelike · Problem — Tunnel at 0.8c · Problem — A red traffic light seen as green