#### Michelson-Morley Experiment

#### Sebastian DeLorenzo

Young’s diffraction experiment in 1801 corroborated the hypothesis that light was a wave. James Clerk Maxwell’s equations showed that light ought to be part of a family of electromagnetic (EM) waves, which included radio and gamma rays. At that time, it was known that all other waves vibrated in a certain medium: sound waves are the vibration of air molecules, waves far out at sea are the spiralling oscillation of water molecules. It was therefore theorised that light and other such EM waves were merely the vibration of an invisible ‘aether’ field permeating the universe. Since the speed at which waves propagate through a medium is proportional to the square root of its spring constant, and the aether’s resistance to motion had to be negligible to avoid it slowing down the planets, it was modelled as an invisible, incompressible, and frictionless fluid.

Maxwell’s equations include a factor of 1/c, where c is the speed of light. If we try to measure the speed of light by setting up light gates and sensitive clocks, we empirically obtain a value of 3*10^{8}. However, the earth is of course moving quickly around the sun, thus presumably changing the ‘true’ value as measured by a stationary observer. Perhaps you could measure the speed of light perpendicular to the earth’s velocity, but the whole solar system is also moving. Since the equations should work in all inertial frames of reference, c should be the speed of light relative to the aether, which should be the same for all observers who measure the speed of light and then add or subtract their own velocity relative to the aether. All that remained was to find the speed of earth relative to the aether. Previous attempts had all failed since it had been determined that it was necessary to detect second order (proportional to v^{2}/c^{2}) rather than first order (proportional to v/c) effects. However, in 1887 at Case Western Reserve University in Cleveland, Ohio, learning from their failed attempt in 1881, Michelson and Morley succeeded.

They set up a half-silvered mirror (A) which split a light beam into two beams, one travelling perpendicular to the earth’s movement and one parallel. Both beams hit a mirror a distance L from A and came back to A. They were then recombined and projected onto a screen. If the velocity of the earth relative to the aether was zero, both beams would travel the same distance and thus would have no phase difference. If the earth had a positive velocity, the distance travelled in the direction of the earth’s movement would be constant (since a distance vt is added during the outbound and subtracted during the rebound) while the distance travelled parallel would increase (since the beam now travels along a hypotenuse^{1}). There would therefore be a phase difference between the two beams, equal to L v^{2}/c^{2}, which could be determined from the screen’s interference pattern. However, when the experiment was conducted, there was no interference. This did not disprove the existence of the aether (as is commonly claimed), but showed that the speed of light is independent of the velocity of an observer (this has been confirmed on the 10^{-17} level^{2}). It is possible that the aether exists and that it speeds up to match the velocity of all matter which passes through it. However, since this implies there is no measurable difference between a universe with the aether and one without it, it is shaved off by Occam’s razor. An alternative explanation was that the earth happens not to move relative to the aether. This would mean that every single other planet and star moves relative to the aether, meaning the earth has a special place in the universe. This was too improbable to accept.

This remarkable result puzzled physics’ leading authorities. It was the great Hendrik Lorentz who proposed that two observers appear contracted to each other when they have a relative velocity. In order to preserve the fact that the speed of light is agreed upon by the two observers, time must contract by the same factor. This implies that the two observers agree on their own relative speed, v. This factor was 1/y where y = 1/sqrt(1-v^{2}/c^{2}) ^{3}. We can use this to derive the Lorentz transforms, according to which, if they start at the same place, the distances two observers measure towards an object are related by x’ = y(x-vt) and the times they measure are related by t’ = y(t-(xv/c^{2})) ^{4}.

His contemporaries scoffed at his equations since their implications (that length, time, and simultaneity are dependent on observers’ relative speeds) were counterintuitive and had seemingly been plucked out of thin air to conveniently corroborate this specific experiment without a sound underlying explanation. The true fault was assumed to lie within Maxwell’s equations, which were only twenty years old and rather incredible at the time. However, all attempts to replace them ended in failure as they predicted effects which could not be observed. Albert Einstein later developed his theory of general relativity, which explained how time and space were bent by mass, and from which Lorentz’s equations arose in the special case of constant speed in a straight line^{5}.

This, after it had been verified by experiments concerning the bending of light and expansion of the universe, provided the general framework physicists needed to accept the theory. In a way, Einstein’s work both redeemed and discredited Lorentz: he was a true believer in the aether, and his equations had been an attempt to save it. As with most physical theories, it has been reduced to a historical footnote.

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