To be more precise: The MM-experiment should distinguisch between the stationary aether model of Fresnel and the dragged-along aether model of Stokes (see History of special relativity#The search for the ether. Michelson at first (1881) believed that Stokes model was confirmed, but in 1887 he already knew, that Stokes mode violates the law of aberration. That was the starting point for Lorentz, Poincare, etc. However, it was shown by Einstein, that all those develepments makes the ether and the classical concepts of space and time useless. (BTW: Maxwell's himself left only a few statements of the relative motion of aether and matter, see his article Ether from 1878).     