Special relativity does not reject the possibility of an aether.It merely has no use for an aether.Consider the difference between Einstein’s approach to explaining length contraction and time dilation, versus Lorentz’s approach.Hendrik Lorentz believed in a dynamical interpretation of the transformation that bears his name. In other words, Lorentz believed that passage through an aether resulted in an actual physical contraction of all the atoms making up an object.A comoving observer would not be able to measure any length change in the object, because his rulers would be subject to exactly the same length contraction effect.On the other hand, because Lorentz believed that a moving object experienced a bona fide physical contraction, it should be possible to detect the physical results of the object undergoing strain as a result of its shape changes.For example, a charged capacitor would experience a torque as it moved through the aether.
This was the theoretical justification for the Trouton–Noble experiment:Source: Drawing the line between kinematics and dynamics in special relativityLikewise, if the object were transparent, compressive stresses would result in the observation of birefringence in the moving object. This was the theoretical justification for the Experiments of Rayleigh and Brace. Strain in an object could be detected through the use of polarized light.Source: Make Pictures With Polarized Light From an LCDIn contrast, Einstein approached his analysis through a careful analysis of what it actually means to measure time and length. He was careful not to blithely assume that, say, two clocks could be synchronized, but rather, he insisted that the precise operational steps required to perform such a synchronization be specified.Through his careful analysis, he was able to point out fundamental shortcomings in the intuitive understanding that people had concerning what it means for two events to be simultaneous. Starting from relativity of simultaneity, Einstein extended his kinematic analysis to encompass all of the other effects that special relativity is famous for.
Aether had absolutely no role to play in this analysis. Einstein’s development of special relativity began with a fundamental analysis of the meaning of measurement, and he explored the logical consequences of his discoveries into the realm of kinematics and electrodynamics.Later, Hermann Minkowski was to reinterpret Einstein’s kinematic analysis in favor of a geometric approach.Further reading: Spacetime – WikipediaIn a comment, Mark Barton noted that “there isn’t any actual difference between Lorentz and Einstein on the physicality of length contraction.”I’ve moved my response to him from the comments section to here:Response to Mark: Lorentz’s views evolved over the years.
The mantra expressed by current advocates of Lorentz Ether Theory (i.e. LET), that LET and SR are supposedly indistinguishable in their predictions, is an interpretation of Lorentz’s views only after an exchange of letters between 1904–1905 with Poincare, who pointed out, among other things, the group nature of his transforms. LET advocates ignore the entire historical development of Lorentz’s views prior to 1905.For example, in Lorentz’s 1904 Weiterbildung der Maxwellschen Theorie, Lorentz considered the Trouton-Noble and the Rayleigh experiments as presenting a problem that resisted solution because “the motion of molecules is ignored…consequently the removal of this defect seems to be a pressing task,” which Lorentz addressed by proposing another conjecture, “the theory of the electromagnetic mass” whereby Lorentz proposed to transfer the the hypothesis of the change of dimensions from bulk matter to the constituent molecules.
“Perhaps the dimensions of the individual electrons become changed by translation.”A.I. Miller, in his Albert Einstein’s Special Theory of Relativity, covers the historical development of Lorentz’ theory of the electron in Chapter 1, pp 11–113, and it is impossible for me to summarize adequately all the twists and turns in Lorentz’ thought.
To me, the most important point is that even after Poincare demonstrated the group nature of Lorentz’s transforms and deduced the correct value of l on page 79 of Miller, and even after Einstein entered into the picture, Lorentz’s theory remained a theory of the deformable electron. A 1906 statement by Poincare is enlightening:”If the electron’s inertia is exclusively of electromagnetic origin, if it is subjected to no forces other than those of electromagnetic origin, or to the forces due to the supplementary potential L^c, then no experiment can detect evidence of absolute motion.”In other words, to Poincare and to Lorentz, the inability to detect absolute motion was a consequence of the balancing of dynamical effects rather than a fundamental principle in itself.