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Michelson & Morley's experiment implies that either the aether does not exist OR that the Earth is stationary with respect to aether.

Now, one consequence of relativity is that we CAN physically regard the Earth as stationary, with all the universe moving with respect to it. So, we could say that in our Earth-stationary frame the aether is stationary as well.

This would mean that Michelson & Morley's experiment does not imply by itself the lorentz transfomation apparatus (since this experiment was performed on aether-stationary-earth).

It seems to me that some different experiment should be required in order to prove the Lorentz transformations, considering some reference frames IN MOTION with respect to Earth. Michelson & Morley's one is insufficient in this light.

Ok well, I'm pretty sure I have gone wrong conceptually in some statement, but I can't see where. Can you please correct me?

And moreover, can you please state any experiment which effectively tested relativistic effects (time dilation and length contraction) in reference frames in motion with respect to Earth?

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  • $\begingroup$ The muon decay in the atmosphere experiment shows time dilation and length contraction. $\endgroup$
    – user234190
    Commented Sep 13, 2019 at 22:58
  • $\begingroup$ @uder47014 thank you. What about my assumption about stationary aether with respect to earth? Is it plausible? If not why? $\endgroup$ Commented Sep 13, 2019 at 23:02
  • $\begingroup$ Einstein pointed out that there is no aether because there is no theoretical to believe there is one. $\endgroup$
    – user234190
    Commented Sep 13, 2019 at 23:07
  • $\begingroup$ I know what he pointed out, but that doesn't seem to falsify my assumption $\endgroup$ Commented Sep 13, 2019 at 23:10
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    $\begingroup$ Physicists stopped thinking that Earth was a special place in the universe a long time ago. $\endgroup$
    – G. Smith
    Commented Sep 13, 2019 at 23:38

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It seems to me that some different experiment should be required in order to prove the Lorentz transformations

Yes, you are completely correct. The Michelson and Morley experiment is insufficient by itself to experimentally deduce the Lorentz transform.

Robertson (Rev. of Mod. Phys. 21, pg 378, 1949) showed that you could deduce the Lorentz transform from the combination of the Michelson and Morley experiment, the Kennedy and Thorndike experiment, and the Ives and Stilwell experiment. When you do that you empirically obtain the Lorentz transform to within 0.1% without assuming the postulates of relativity. Of course, with more recent and more precise experiments, the accuracy is far better than 0.1% now.

If you are not looking for a quantitative measurement of the Lorentz transform, then qualitatively you can say the the Michelson Morley experiment is incompatible with a traditional rigid aether, and the Sagnac experiment is incompatible with a dragged aether. Only the Lorentz aether remains compatible with experiment since it is the only aether that is designed to be experimentally identical to there being no aether.

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  • $\begingroup$ Wikipedia has a decent page on the Lorentz Ether Theory. I am not sure why they used the spelling "ether" instead of "aether". $\endgroup$ Commented Sep 14, 2019 at 1:50
  • $\begingroup$ @StephenG That's how it's spelled in the country with the largest english speaking population as a native language. $\endgroup$
    – user234190
    Commented Sep 14, 2019 at 14:04
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    $\begingroup$ @user47014 "Aether" has a specific use in physics, and "ether" has multiple other uses. In this physics context I think that "aether" would be more appropriate to avoid ambiguity (however much it may tax this mysterious country you mention to use one additional letter :-) ). $\endgroup$ Commented Sep 14, 2019 at 14:51
  • $\begingroup$ @StephenG if you want to say the states is mysterious ok. It's spelled 'ether' in physics textbooks there. If you want to write the authors and tell them that that's cool. $\endgroup$
    – user234190
    Commented Sep 14, 2019 at 14:56

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