Fizeau forgot to switch his light bulb on
Fizeau discovered the Doppler-Fizeau effect i.e. that the observed wavelength changes for light waves, well before Einstein was in diapers, and his effect has absolutelly nothing relativistic in it. He basically used the same equations that Doppler used for sound in air, and aplied them to light in aether.
But he forgot to multiply them, because if he did he would have discovered the invariance also before Einstein or the MM experiment. And Einstein would have been left without a job, since the invariance comes directly from classical wave physics, and does not require any length contraction/time dilation whatsoever. Or better said, Lorentz would have been left without a job, because he invented those ad-hoc gimicks in order to ‘save the aether’. But the aether did not need them, cause you can clearly see why.
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