• Which was Michelson's aim? To measure the motion of the earth with respect to the luminiferous ether (i.e. the isotropic propagation of light)!

• How did he perform it? Construct propagation time-differences longitudinal and transversal to the streaming of the ether.

• What did he really find? The ether is not all-pervading, but confined in the cellar like the air and in relative rest to it.

• Why did one need a luminiferous ether at all? Because Galileo's postulate of relativity had to be saved!

• The velocity of light is a scalar: It is the relation between electrostatic and magnetostatic Gaussian units

• Einstein's axiom: The speed of light is not changed in composition with other velocities
(Invariance of the wave equation, implying the Lorentz group; the concept of an material luminiferous ether becomes dispensable)

• From the position of SRT, the result of Michelson's experiment is trivial. Again from the position of SRT, the result backs the Einstein axiom at a very fundamental level.

• Michelson did not agree with this point of view. He always understood his result as backing the hypothesis of a material ether, dragged along with the earth and confined in the cellar.

• Theory, Explanation, Proof

• Why did one need a luminiferous ether at all? Because Galileo's postulate of relativity had to be saved!

• Does the earth really move instead of the sun? First argument: the order in the retrograde motion of planets!

• Second argument (2000 years later): The aberration of star light. The motion of the earth and Newton's emanation hypothesis for light back each other. The velocity of light is composed with that of the earth by simple (vectorial) addition as well.

• Only when light is a wave, interference can be understood. However, wave fronts do not show aberration.

• Wave groups may show aberration, if the motion with respect to the reference of isotropic propagation can be measured also without any looking outside. Galileo's principle of relativity is disproven, exept when the isotropic propagation is mediated by some material substance (the ether) which pervades all matter without being disturbed (Fresnel's excuse).

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• It is general use to say that the result of the Michelson experiment would prove the constancy of the velocity of light. This, however, was always denied by Michelson. Michelsons intent was to test whether the isotropy of the propagation of light would be disturbed by moving objects or not. He found that the isotropy is disturbed in such a way that it cannot be used to measure a relative velocity. Light propagates in some real substance which is confined in the cellar like air and is at rest in the cellar.

• What is wrong with this interpretation? It contradicts a small effect, namely the aberration of the light of stars. This effect was found in 1729 and was hailed as proof of the Copernican heliocentric theory of the solar system in connection with Newton's emanation theory of light.
However, only a wave theory can explain the mysterious interference patterns. As we learned at school, reflection and refraction can easily be explained. We hear nothing, regrettably, about that wave fronts do not show any aberration in a Galilean theory (where all velocities are to be composed additively). Fresnel called this problem the most difficult one of the wave theory. Fresnel found an excuse in the telescopes, which cut out by their aperture lens a wave group that moved again like a particle. However, this excuse required that material objects would not disturb the isotropy of the propagation of light. Thus, it seemed possible to measure motion against the isotropy system inside a closed laboratory in contrast to the expectation expressed by Galileo (the Galileo relativity principle). To save the principle, the isotropy system had to have a material carrier, the ether, and this ether had to be all-pervading. Fresnel decided for this hypothesis in order to be able to explain the aberration. This ether replaces speed trap and alley tree as outer reference for velocity. Reluctantly, the hypothesis was accepted.

Michelson's experiment showed that the ether cannot be all-pervading, but is confined in closed rooms and is dragged along with the earth - just as one would expect from a material substance. The question of the aberration is open again. Fresnel's explanation collapsed.

The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.
This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest.

Lorentz and Drude could show, that the admission of a motion-dependent form of simultaneity helps to construct an aberration for wave fronts.

• The experiment was first performed in 1881 in a cellar of the Astrophysical Observatory Potsdam. It was improved many times, in particular by Michelson. His interferometer made a triumphal procession through the physical technology.

• By use of the interference figure of two light waves, relative changes in the length of its two paths can be followed down to parts of the wave-length. One wave passes a path transversal to the motion of the earth through the ether (back and forth), the other wave a longitudinal one, returning back. To this end, a light ray is divided by a half-transparent mirror. The two parts of the ray are reflected by mirrors in definite distance so that they can be brought to interfere.
We now assume that the apparatus moves with some velocity v (30 km/s is the velocity of the earth on its orbit around the sun) againt the ether. The speed of light is denoted by c (30000 km/s). When the ray transversal to the direction of motion aerrives at its mirror, it has passes also the distance which the apparatus has made in the ether, in total c2ttransv2 = Ltransv2 + v2ttransv2. The longitudinal ray moved ctforth = Llong + vtforth, and then ctback = Llong - vtback.

It yields
ttransv2 = Ltransv2 / (c2 - v2),    tforth = Llong/(c-v) and    tback = Llong/(c+v).
The difference is
cttransv - ctforth - ctback = 2Ltransv/sqrt(1-(v/c)2) - Llong/(1-v/c) - Llong/(1+v/c)
approx 2Ltransv(1+(1/2)(v/c)2) - 2Llong(1+(v/c)2)
When the apapratus is reoriented by 90 degrees, the paths change correspondingly and the difference changes its sign. The interference figure should show this, but the interference figure does not change.

• Einstein's theory of relativity solved this problem on a purely geometric way without referring to the properties of the ether and the ether in general, with the relativity of simultaneity. The requirement that the aberration of particles coincides with the aberration of wave fronts yields the relativity of simultaneity and SRT in consequence.

• The motion of the ether was not the only problem of the theory of light and of electrodynamics in general. Einstein became convinced by heuristic (not stringent) reasons that the velocity of light cannot be composed with other velocities in the usual additive way. He stated the principle of the light velocity being constant, which meant that the speed of light, in composition with other velocities, can only yield the speed of light again. The speed of light is an invariant scalar as suspected, for instance, since its identification in the relation between electrostatic and magnetostatic units.

• Einstein saw independently of peculiar experiments that Galilean Relativity had to be restored to its universal validity and that this can be done when one chooses the principle (axiom) that there exists a velocity (the velocity of light in vacuo) which remain unchanged in composition with other velocities. From the point of SRT, the result of the Michelson experiment appears as a fundamental argument for adopting this axiom, and it helped to surmount the conservative resistance against the new picture of space and time. Michelson, however, always objected the

• Therefore, Einstein was not particularly aware of the Michelson experiment. However, from the point of the theory of relativity, Michelson's result found an equally simple explanation. The propagation of light is isotropic for any body independent of its motion, and the concept of the ether becomes dispensable. It was now acknowledged by Einstein, and when Michelson won the Nobel price for his technics, the experiment was tightly bound to the foundation of the theory. It helped decisively to overcome the conservative resistance against the new concepts of space and time. relativistic interpretation.

• Of course, the Michelson experiment does not prove any theory, just as no particular experiment or particular observation can prove a theory. A theory can be backed at best, and disproven in the negative case. A theory cannot be deduced from experiment or observation, it must be seen, be found. The best backing is the technical use of a theory. Our confidence in SRT is backed best by the prediction of antiparticles and the explanation of the spin. These are structural issues, not depending on small effects. Prescise measurements of the properties of light propagation may find small discrepancies, which would then show that the Maxwell equation have to be corrected.

Handouts

References

Michelson,A.A.: The relative motion of the Earth and the luminiferous ether, The American Journal of Science 22 (1881), 120-129.

Michelson,A.A.: Die Relativbewegung der Erde gegen den Lichtäther, Deutsche Übersetzung mit einem Vorwort von A.H.Compton und einem Nachwort von M.v.Laue, Die Naturwissenschaften 19 (1931, Heft 38), 777-784.

Bleyer,U., Gottlöber,S., Haubold,H.-J., Hempelmann,A., Mücket,J.-P., Müller,V., Stoll,D.: Zur Geschichte der Lichtausbreitung, Die Sterne 55(1979), 24-40.

Aberration:

P.Brosche, D.-E.Liebscher: Aberration and Relativity

P.Brosche, D.-E.Liebscher: Fallstricke der Aberration

Modern developments:
Modern Michelson-Morley Experiment using Cryogenic Optical Resonators
What is the experimental basis of Special Relativity?