George Francis FitzGerald and H.A. Lorentz offered a solution of sorts:
in drifting through the æther, "solid" bodies
were not perfectly unaffected by it but in fact suffered
a common "drag" in the direction of motion that caused
all the yardsticks to be "squashed" in that direction,
so that the apparatus seemed to be unaffected
only because the apparatus and the yardstick and the
experimenters' eyeballs were all contracted
by exactly the same multiplicative factor!
They showed by simple arguments that said factor was
in fact
where
-- i.e. exactly the factor defined earlier in the
LORENTZ TRANSFORMATIONS, so named after one of their
originators!23.3
Their equations were right, but their explanation
(though no more outlandish than what we now believe to be correct)
was wrong.
For one thing, these famous " LORENTZ CONTRACTIONS" of the lengths of meter or yardsticks were not accompanied (in their model) by any change in the relative lengths of time intervals -- how could they be? Such an idea makes no sense! But this leads to qualitative inconsistencies in the descriptions of sequences of events as described by different observers, which also makes no sense. Physics was cornered, with no way out.
Ernst Mach, who had a notorious distaste for "fake" paradigms (he believed that Physics had no business talking about things that couldn't be experimented upon),23.4 proposed that Physics had created its own dilemma by inventing a nonexistent "æther" in the first place, and we would do well to forget it! He was right, in this case, but it took a less crusty and more optimistic genius to see how such a dismissal could be used to explain all the results at once.