Editing Michelson–Morley experiment (section)

=== Special relativity ===
[[Albert Einstein]] formulated the theory of [[special relativity]] by 1905, deriving the Lorentz transformation and thus length contraction and time dilation from the relativity postulate and the constancy of the speed of light, thus removing the ''ad hoc'' character from the contraction hypothesis. Einstein emphasized the [[Kinematics|kinematic]] foundation of the theory and the modification of the notion of space and time, with the stationary aether no longer playing any role in his theory. He also pointed out the group character of the transformation. Einstein was motivated by [[Maxwell's theory of electromagnetism]] (in the form as it was given by Lorentz in 1895) and the lack of evidence for the [[luminiferous aether]].<ref group=A name=einstein />

This allows a more elegant and intuitive explanation of the Michelson–Morley null result. In a comoving frame the null result is self-evident, since the apparatus can be considered as at rest in accordance with the relativity principle, thus the beam travel times are the same. In a frame relative to which the apparatus is moving, the same reasoning applies as described above in "Length contraction and Lorentz transformation", except the word "aether" has to be replaced by "non-comoving inertial frame". Einstein wrote in 1916:<ref group=A name=einstein2 />

{{Quote|Although the estimated difference between these two times is exceedingly small, Michelson and Morley performed an experiment involving interference in which this difference should have been clearly detectable. But the experiment gave a negative result — a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the æther produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the difference in time mentioned above. Comparison with the discussion in Section 11 shows that also from the standpoint of the theory of relativity this solution of the difficulty was the right one. But on the basis of the theory of relativity the method of interpretation is incomparably more satisfactory. According to this theory there is no such thing as a "specially favoured" (unique) co-ordinate system to occasion the introduction of the æther-idea, and hence there can be no æther-drift, nor any experiment with which to demonstrate it. Here the contraction of moving bodies follows from the two fundamental principles of the theory, without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun.}}

The extent to which the null result of the Michelson–Morley experiment influenced Einstein is disputed. Alluding to some statements of Einstein, many historians argue that it played no significant role in his path to special relativity,<ref group=A name=stachel /><ref group=A name=Polanyi /> while other statements of Einstein probably suggest that he was influenced by it.<ref group=A name=dongen /> In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.<ref group=A name=stachel />

It was later shown by [[Howard Percy Robertson]] (1949) and others<ref name=rob group=A /><ref name=sexl group=A /> (see [[Test theories of special relativity|Robertson–Mansouri–Sexl test theory]]), that it is possible to derive the Lorentz transformation entirely from the combination of three experiments. First, the Michelson–Morley experiment showed that the speed of light is independent of the ''orientation'' of the apparatus, establishing the relationship between longitudinal (β) and transverse (δ) lengths. Then in 1932, Roy Kennedy and Edward Thorndike modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short.<ref name=KennedyThorndike/> The [[Kennedy–Thorndike experiment]] took place for many months as the Earth moved around the Sun. Their negative result showed that the speed of light is independent of the ''velocity'' of the apparatus in different inertial frames. In addition it established that besides length changes, corresponding time changes must also occur, i.e., it established the relationship between longitudinal lengths (β) and time changes (α). So both experiments do not provide the individual values of these quantities. This uncertainty corresponds to the undefined factor <math display="inline">\varphi</math> as described above. It was clear due to theoretical reasons (the [[Lorentz group|group character]] of the Lorentz transformation as required by the relativity principle) that the individual values of length contraction and time dilation must assume their exact relativistic form. But a direct measurement of one of these quantities was still desirable to confirm the theoretical results. This was achieved by the [[Ives–Stilwell experiment]] (1938), measuring α in accordance with time dilation. Combining this value for α with the Kennedy–Thorndike null result shows that ''β'' must assume the value of relativistic length contraction. Combining ''β'' with the Michelson–Morley null result shows that ''δ'' must be zero. Therefore, the Lorentz transformation with <math display="inline">\varphi=1</math> is an unavoidable consequence of the combination of these three experiments.<ref name=rob group=A />

Special relativity is generally considered the solution to all negative aether drift (or [[isotropy]] of the speed of light) measurements, including the Michelson–Morley null result. Many high precision measurements have been conducted as tests of special relativity and [[modern searches for Lorentz violation]] in the [[photon]], [[electron]], [[nucleon]], or [[neutrino]] sector, all of them confirming relativity.