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As we know, the revolutionizing step of the Special Relativity was, to solve the contradiction between electromagnetism and the Newtonian mechanics, not the Electromagnetism should be altered (which, as a new thing, had been the "natural" option), but the Newtonian mechanics.

But the problems leading to that existed long before (f.e., but not exclusively, the Michelson-Morley experiment).

Does any concurrent theory existed at the time, which was also based on this surprising idea?

Did any of them had signs, with time it could have developed into a Special Relativity, if Einstein didn't exist?

P.s. Aether and aether-dragging theories are not okay - they tried to solve the contradictions not by changing the classical mechanics. They suspected a new form of matter, which has uncommon properties, but behaved on the classical mechanics.

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To answer the question: "if Einstein did not exist": the special relativity was gradually developing independently of Einstein (by Lorentz and Poincare). If Einstein did not exist it would be developed at approximately the same time by the others. By the way, in the book of Whittaker, History of theories of electricity and magnetism, the chapter on special relativity is called "Relativity theory of Lorentz and Poincare", and Einstein does not play a very prominent role. But of course this is not a "concurrent theory", but the same theory. Special relativity is a logical conclusion from the theory of electromagnetism.

(With General relativity, it is different: there were no important experiments or observations that required it, and the idea is completely due to Einstein).

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  • $\begingroup$ If "aether and aether-dragging theories are not okay" then Lorentz-Poincare theory is excluded. It misses a key ingredient of special relativity, namely relativity, there is an absolute frame attached to ether, and at the fundamental level geometry is Euclidean and mechanics is Newtonian. Electromagnetic interactions force matter to conspire in a very clever way to create an illusion which turns out to be mathematically equivalent to SR for macroscopic objects. Lorentz himself said in 1927 that he couldn't have invented relativity $\endgroup$
    – Conifold
    Commented Feb 11, 2015 at 20:09
  • $\begingroup$ If Lorentz-Poincare theory stayed in place there would have been very serious problems in trying to come up not only with a consistent theory of gravitation but also of quantum field theory (quantum mechanics is non-relativistic) since they are fundamental theories, and Lorentz's theory does not extend the new mechanics beyond the electromagnetic forces. $\endgroup$
    – Conifold
    Commented Feb 11, 2015 at 20:14
  • $\begingroup$ @Conifold: it does. For example the decrease of length in the direction of the motion is a phenomenon of mechanics, not electrodynamics. Whatever Lorenz himself said, I believe special relativity would be completely understood within few years, without Einstein's contribution. $\endgroup$
    – Alexandre Eremenko
    Commented Feb 12, 2015 at 0:27
  • $\begingroup$ @AlexandreEremenko I assume you meant Lorentz (of e.g. 'Lorentz transformation' fame), not Lorenz (known from the 'Lorenz gauge' in electromagnetism)? The distinction matters ;) $\endgroup$
    – Danu ♦
    Commented Mar 1, 2015 at 14:01

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