THE MICHELSON-MORLEY EXPERIMENT

By the late 1880s the question was no longer whether light was a wave — Maxwell's equations had decided that — but what it was a wave in. Sound waves are oscillations of air. Water waves are oscillations of water. Light waves were assumed to be oscillations of the luminiferous aether, a medium so subtle it pervaded all space and yet so rigid that transverse oscillations could rip through it at three hundred million metres a second. Maxwell's 1865 wave equation contains a constant $c = 1/\sqrt{\mu_0 \varepsilon_0}$ but says nothing about which frame to measure that $c$ in. The natural answer, compatible with Galilean intuition, was a privileged frame — the rest-frame of the aether — in which Maxwell's equations held cleanly. In every other frame, Galilean velocity addition should kick in and a moving observer should see light at $c \pm v$ depending on direction.

If that picture is right, the Earth — orbiting the Sun at about thirty kilometres per second — must be sailing through an aether wind. A laboratory bolted to the spinning rock should feel that wind the way a cyclist feels still air on a fast road. The wind is real, the prediction goes, so the wind is measurable. The instrument that measures it is the interferometer, and the man who built the most sensitive one of his century was .

The trick, in one sentence: split a beam of monochromatic light into two perpendicular paths of equal length, bounce each half off an end-mirror, recombine them, and look at the interference fringes. If both paths take the same time, the fringes sit still; if one path takes longer than the other by even a small fraction of a wavelength, the fringes shift by a corresponding fraction of a fringe-width.

The aether-wind prediction is straightforward. Let arm length be $L$, source wavelength be $\lambda$, apparatus speed through the aether be $v$. The arm pointing along the wind sees light fight upstream then sail downstream; the arm perpendicular to the wind sees light traverse a slight diagonal in both directions. Working out the round-trip times to first order in $\beta = v/c$ and converting the time difference into a fringe count gives

That is the peak shift, achieved when the apparatus is aligned with the wind. As the bench rotates by an angle $\theta$, the two arms exchange roles, and the shift relative to the $\theta = 0$ orientation traces a $\cos 2\theta$ — a $\pi$-periodic curve, two full peaks per rotation:

For the apparatus Michelson and Edward Morley assembled in the basement of Adelbert Hall at Case Western Reserve University in 1887 — a granite slab floating on a one-and-a-half-tonne pool of mercury, with mirrors folding the round-trip optical path eight times to give an effective $L \approx 11~\text{m}$, illuminated by a sodium D-line lamp at $\lambda = 589~\text{nm}$, riding the Earth's $v \approx 30~\text{km/s}$ orbital motion — the formula returns

$\Delta n \approx 0.37 \text{ fringes}.$

A third of a fringe-width. The eye can resolve a hundredth of a fringe-width on the same plate. The signal sits more than thirty times above the noise. If the aether is there, this experiment cannot miss.

What follows is the most famous null result in physics — and the cleanest way to see it is to plot prediction and observation on the same axes.

Read that figure carefully, because every word in §01.4 follows from it. The dashed curve is what nineteenth-century physics expected. It is not subtle. It oscillates between $+0.37$ and $-0.37$ fringes as the apparatus rotates, and at every angle except the four nodes its absolute value is more than ten times the noise floor. The solid curve is what the apparatus actually delivered. It hugs zero. It dips into the grey strip occasionally, the way any real instrument's output does, but it never climbs out of it. The two curves are not within the noise of each other. They are different by an order of magnitude.

Michelson and Morley repeated the experiment at midnight and noon, in spring and in autumn — different orientations of Earth's velocity vector — and got the same null. They published in the American Journal of Science, 34, 333 (1887), as "On the Relative Motion of the Earth and the Luminiferous Aether," and concluded that "the relative velocity of the Earth and the aether is probably less than one sixth" of the orbital speed. Subsequent repeats — Morley and Miller 1904, Joos 1930, modern laser-stabilised cavity tests — pushed the upper bound on the wind speed below $10^{-17}$. The wind is not slow. It is not there.

The cleanest way to internalise the result is to picture the apparatus moving through the wind it is supposed to be measuring.

Two escape routes from the null were tried. The first was an aether dragged along by the Earth, leaving the lab momentarily at rest in it; this was killed by Joos's 1929 repeat at different orbital phases and by Fizeau's 1851 experiment on light through moving water, which had already shown the aether is not substantially dragged by matter. The second — and the one that took root for nearly two decades — was material contraction.

In 1889 George FitzGerald proposed, and in 1892 independently and more rigorously argued, that an arm of the interferometer aligned with the aether wind physically shrinks by a factor of $\sqrt{1 - v^2/c^2}$ — a real material shortening, caused by molecular forces being electromagnetic in origin and therefore subject to the wind. A shrinkage of exactly that magnitude cancels the longer round-trip time and produces zero fringe shift. Lorentz developed the algebra into what we now call the Lorentz transformation, complete with a "local time" that ran differently in the moving frame. He believed the contraction was real. He believed the local time was a calculational fiction. He kept the aether.

The contraction hypothesis was not crazy. It saved the aether, predicted the null result, and matched every electromagnetic measurement of the 1890s. Lorentz's 1904 paper — eighteen years after Cleveland, one year before Einstein — contained the full Lorentz transformation, derived from the assumption of real material contraction in a real aether. The algebra was complete. What was missing was the geometry.

By the close of 1887 the experiment had killed three things and surfaced one. Killed: the dragged aether, the wind detectable to first order in $v/c$, and the privileged frame in which Maxwell's equations were supposed to hold. Surfaced: a mismatch between Maxwell's electromagnetism, which is not Galilean invariant, and the Galilean kinematics every nineteenth-century laboratory assumed. If light has a single speed and Galileo's transformation says it can't, one of the two is wrong.

The reader who has come this far through §01.1–§01.3 already has the assembly. Galileo gave us inertial frames and a velocity-addition rule. Maxwell gave us a wave equation with a fixed $c$. Michelson and Morley showed that no inertial frame moves with respect to the aether the way the Galilean rule says it must. Three propositions; at most two can be true. The next two topics — §01.4 einsteins-two-postulates and §01.5 relative-simultaneity — are about which two Einstein kept and what he was forced to give up. The price was Newtonian time.

Lorentz spent fifteen years saving the aether by adding contractions to it. Einstein, in 1905, looked at the same equations and asked a different question: what if there is no aether, and the contraction is not a property of matter but of how lengths transform between frames in spacetime? The algebra is identical. The physics is not. For this topic the clean takeaway is the figure above. Dashed amber, solid cyan, never meeting. An interferometer asked the wind which way it was blowing, and the answer came back: there is no wind.