The Michelson experiment of 1881 in Potsdam
DierckE.Liebscher, Potsdam, last change 2019, June 22
The questions
 Which was Michelson's aim?
To show that he is able to
measure the motion of the earth through its superposition on the velocity of light.
Such a superposition was known to take place since Bradley's observation of the
aberration of starlight (movie).
 How did he perform it?
He constucted his interferometer as a set of mirrors which produce two close images of a source.
The light from these apparent images could interfere (movie), and the interference pattern is extremely sensitive to
changes in distance of the apparent images. Such changes would be prodiced by the expected anisotropy of the velocity of light.
Apparently the motion of the earth does not show up in the room, just as Galilae expected.
Light could be suggested to propagate in some medium (which came into the name aether) contained in the room.
 What did he really find?
In his room, he did not find any anisotropy of the velocity of light.
Light could be suggested to propagate in some medium (which came into the name
aether) contained in the room like the air and in relative rest to it.
 What did he conclude?
1. The set is not good enough (it was good enough, after all).
2. The result of the experiment is at variance with the observation of aberration (movie),
as it was explained by addition of velocities.
In the end, this turned out to be a watertight proof of a contradiction.
It is the geometric clue after many attempts to explain the contradiction by the mechanics of light propagation
(properties of the aether which Michelson found contained).
 Where the rat was hidden?
In the elementary picture, wave fronts do not show aberration,
but it was sufficient for the time being to refer to wave crests which show the observed aberration.
If one accepts that the wave fronts too have to show the aberration (movie), one ends with the relativity of simultaneity.
The question how to control simultaneity led Einstein to start with the axiom that the speed of light
(the scalar value devoid of any direction) is not object of any composition with other velocities (movie).
In geometric terms: the speed of reflected light is independent on the motion of the mirror, in contrast
to tennis experience. This originates the Minkowski geometry on a registration strip (movie).
The errors
 The experiment does not prove Einstein's axiom that the speed of light does not change in superpositions.
Einstein's axiom is an axiom, not to be proven, but to be checked and backed in its consequences.
Its applicability could be disproven only, if one finds an essential conclusion to be wrong.
 The experiment does not prove that the velocity of light is isotropic everywhere,
or the same everywhere. "Always" and "everwhere" can never be proven, because we test only here and now.
"Alwas" and "everwhere" can be disproven, when our experiment here and now fails.
 The experiment proves nothing about the speed of light in the universe. In addition, we need an
etalon for velocity that far out. Using the Planck's constant combined with the elementary charge
as etalon, we actually find a constant speed through observation of the hyperfine structure of atomic spectra.
 The experiment does not disprove the existence of an aether. In its consequences, the aether only
reaffirms its uselessness for understanding the propagation of light.
 The experiment was sensitive enough when one considers our present knowledge of the motion
with respect to the cosmic radiation background (about 500 km/s).
The guiding thread
 Does the earth really move instead of the sun?
First argument: the order in the retrograde motion
of planets! (It is observed near opposition or inner conjunction only.)
 Second argument (2000 years later): The
aberration of star light. The motion of the earth and Newton's
emanation hypothesis for light support 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 in a Galilean theory
(where all velocities are to be composed additively). Fresnel called
this problem the most difficult problem of the wave theory.
 Fresnel argued for a
telescope, which cuts out by its aperture lens a
wave group that moved again like a particle. However, this excuse
required that material objects would not disturb the
propagation of light. Aberration seems 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 aether, and this aether had to be allpervading.
This aether replaces both speed trap and alley tree as outer
reference for velocity. Reluctantly, the hypothesis of an allpervading ("stationary") aether was accepted.
 Michelson found that  inside the room  the motion of the earth produces no anisotropy of the propagation.
When you expect an aether to determine the propagation, it must be contained in the room.
The aether cannot be
allpervading, but is confined and the more 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. Michelson's text:
The interpretation of these results is that
there is no displacement of the interference bands. The result of the
hypothesis of a stationary aether 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 aether, the latter
remaining at rest.
 The 19th century discussion clustered about the mechanics of wave propagation,
the properties of the aether. It ended in Lorentz' problematic
length contraction hypothesis, shown to be wrong by Einstein's theory.
 Galileo' principle of relativity appeared to be at stake because
it required first an allpervading aether to include aberration,
but second to be contained in rooms to answer Michelson's result.
It was discussed that Galieo's principle would be valid for mechanics only.

Lorentz and Drude finally admitted the geometric argument that wave fronts
itself must show aberration. The found the motiondependent form
of simultaneity.
The question of controlling simultaneity led Einstein to his findings.
 Einstein's theory of relativity solved the problem of simultaneity on a purely
geometric way without referring to any properties of the aether and the
aether in general. The requirement
that the aberration of particles coincides with the aberration of wave
fronts yields the relativity of simultaneity and SRT in consequence.
SRT reinstates Galiileo's principle.
Comments
 Einstein was not particularly aware of the Michelson experiment.
He intended to solve the problem of controlling simultaneity.
 From the
point of the resulting SRT, the result of Michelson's experiment is trivial. Again
from the point of SRT, the Michelson experiment 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 aether, dragged along with the earth and
confined in the basement.)
When Michelson won the Nobel price for his technics, the experiment became
tightly bound to the foundation of the theory. It helped decisively to
overcome the conservative resistance against the new concepts of space
and time.
 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.
 The Michelson 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.

The Wikipedia
article contains some questionable phrasing which reflects the many "didactic simplifications"
of the logical steps. For instance,

The Michelson–Morley experiment was not an attempt to detect the existence of aether,
but to demonstrate the superposition of the motion of the earth with the propagation of light,
in aether terms, of to demonstrate an allpervading aether.

The article does not make clear, that the consideration of aether properties
shifts the attention to mechanics, while the aberration poses a geometric
problem.

In the part about Length contraction and Lorentz transformation, the Lorentz contraction
and the relativistic length contraction are mixed. The difference is nowhere
explained. The Lorentz contraction is assumed to be a material effect of the aether wind.
The relativisitc length contraction is a purely geometic effect producedd by the relative
perspective of two observers
moving relative to each other. Both effects lead to the same formula (with different
velocities, however), therefore the confusion. The SRT shows, of course, that a Lorentz
contraction does not exist.

The Lorentz transformation is presented as arising by accounting for some time dilation
required by different experiments except aberration. Again, these experiments
refer
to the motion of the supposed aether, but never cite two observers in relative motion.
The LT were found through
accounting for aberration and the relativity of simultaneity. The relativistic time dilation
again is an affect of perspective between two observers in relative motion.
Handouts
References
Wikipedia, see Comments
Michelson,A.A.: The relative motion of the
Earth and the luminiferous ether, The American Journal of Science 22
(1881), 120129.
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), 777784.
Bleyer,U.,
Gottlöber,S., Haubold,H.J., Hempelmann,A., Mücket,J.P.,
Müller,V., Stoll,D.: Zur Geschichte der Lichtausbreitung, Die
Sterne 55(1979), 2440.
P.Brosche,
D.E.Liebscher: Aberration and Relativity