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According to Wikipedia's Voigt transformation:

Lorentz did not adopt this transformation, as he found in 1904 that only the Lorentz contraction corresponds to the principle of relativity. Since Voigt's transformation preserves the speed of light in all frames, the Michelson–Morley experiment and the Kennedy–Thorndike experiment can not distinguish between the two transformations. The crucial question is the issue of time dilation. The experimental measurement of time dilation by Ives and Stillwell (1938) and others settled the issue in favor of the Lorentz transformation.

Einstein derived the Lorentz transformation using the two postulates, see Einstein’s Postulates and the Lorentz Transformations by Terletskii. Einstein also derived the equations for transverse and longitudinal mass and in the derivation time dilation equation was used. I'm a beginner and just trying to understand the relativity at basic level.

If both Einstein's and Lorentz's derivations were the same then wouldn't it mean that Voigt's time dilation equation had more chance of being wrong? If it was not decided until the experiment of Ives and Stillwell that which version of time dilation equation was right then it would also mean that though Einstein postulates were correct but still until 1938 there was still some doubt regarding some quantitative results derived by Einstein. In other words, if Voigt's time dilation was found correct, how would it have affected the other quantitative results or formulas?

I'd really appreciate if you could help me with it. I'm posting it here because IMHO it has more to do with the history.

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If Einstein's postulates are correct then Voigt's transformation is incorrect. Einstein showed in his 1905 paper that the Lorentz transformations were the only ones consistent with two postulates: invariance of the speed of light in all inertial frames and form-invariance of the laws of physics in all inertial frames (principle of relativity). His mathematics was checked by many prominent mathematicians, including Hilbert and Minkowski, so there were no doubts about his derivations long before 1938.

But invariance of the speed of light by itself is not enough. If Voigt's transformation turned out to be correct it would have meant that the principle of relativity is false, and the frame of ether can be detected after all, albeit not by Michelson–Morley or Kennedy–Thorndike type measurements.

However, special relativity had so many indirect confirmations by the end of 1910s (electrodynamic effects) that the Nobel committee felt comfortable enough to consider awarding Nobel prize for it (it was not awarded for political reasons), and Miller's seeming detection of the ether wind in 1920s was not taken seriously (his measurement errors were not explained until 1950s). Even general relativity, based on a more sweeping relativity principle, was confirmed by Eddington's observations of the 1919 eclipse (gravitational bending of light). So the Ives–Stilwell experiment of 1938 was more about crossing the t's and dotting the i's by a direct test of time dilation than any real doubts. Various high precision tests of special relativity are performed to this day, see experimental basis of Special Relativity bibliography.

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  • $\begingroup$ Thank you! I understand that I'm reading too much into the Voigt but I'm just curious to know that if it had the ingredients to become SR. "But invariance of the speed of light by itself is not enough." I believe that what you mean here is that the definition of simultaneity and proper method of clock synchronization are equally important along with the first postulate of SR. The first postulates of special theory of relativity is, from 1905 paper, "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations Cont'd $\endgroup$
    – PG1995
    Apr 10, 2020 at 8:39
  • $\begingroup$ of mechanics hold good", or in other words, the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. The second postulate is, the speed of light c is a constant, independent of the relative motion of the source. A side note. The postulate of Galilean relativity that the laws of motion are the same in all inertial frames becomes a part of the first postulate of special relativity. Voigt used these postulates: universal speed of light (second postulate of SR) and the invariance of the wave equation in an Cont'd $\endgroup$
    – PG1995
    Apr 10, 2020 at 8:40
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    $\begingroup$ @PG1995 It is a nice paper. As the author points out on p.10, while the wave equation is invariant under the Voigt's transformations the d'Alembert operator ◻ is not, so they do break the principle of relativity. Form-invariance will not be preserved if we put something other than $0$ into the right hand side of the equation. Thus, Voigt's "second postulate" was weaker than Einstein's. It was known that Maxwell's electrodynamics was not form-invariant under Galilean transformations, but that was to be expected since the ether frame is privileged. $\endgroup$
    – Conifold
    Apr 10, 2020 at 9:01
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    $\begingroup$ @PG1995 Yes, Einstein's speed of light postulate follows from the general invariance postulate if we assume that Maxwell's equations in the ether frame are fundamental laws that fall under it (as Voigt did for the wave equation). Michelson was pursuing ether wind experiments since 1881, but there were technical issues with his early attempts, so most physicists did not pay attention until they were fixed in 1887. Apparently, Voigt did, and it was of interest to explore what should have been expected under various hypotheses about ether. $\endgroup$
    – Conifold
    Apr 11, 2020 at 9:35
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    $\begingroup$ @PG1995 They were incorrect because his transformations turned out to be incorrect. Optical Doppler effect was rather controversial in the 19th century, and it was Voigt's primary motivation, more specifically, Michelson-Morley 1886 measurements of the Fresnel drag coefficient in a modification of 1851 Fizeau experiment, see The fall and rise of the Doppler effect by Nolte. $\endgroup$
    – Conifold
    Apr 13, 2020 at 1:56

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