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A.T. said:You are contradicting yourself.
The MM-setup doesn't rely on clock synchronization or exact distance measurement, and would not give a null result in water with sound. I cannot follow your argument about the Doppler shift in the 90°-arm, that miraculously cancels out the expected phase shift. If I move trough a sound medium parallel to a wall and make a loud sound, I receive the echo without any Doppler shift. It doesn't even matter if the wall also moves with me or rests in the medium. This sound travels exactly the same way, it would in the 90°-arm of a sound-MM-setup.
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Let me handle the Doppler shift first. When you are moving through the water, the sound you emit into the water will have a Doppler shift depending on your velocity with respect to the water. Another object moving at the same velocity, will not detect this Doppler shift, as it will have the inverse shift when receiving. If I am wrong on this, Doppler shift has been redefined.
Secondly let me handle the 90°-arm. If I send out a sound wave at exactly 90° when moving through the water, I can not get the reflection back, as it will come back behind me.
The sound reflection I get back can only one that I have aimed slightly in front of me. As it therefore has a forward component, the wave in the water will have a Doppler shift component as explained before. This shift will be a function of v/c. If I am wrong on this, we have to re-evaluate basic physics or geometry, or we have assumed that sound travels balistically and its speed is dependent on its source.
You are right. The MM-setup doesn't rely on clock synchronization or exact distance measurement. It relies on waves interfering, with the presumption in the calculations that the wave traveling at 90° is interfering with the one at 0° with no Doppler effect in the waves. To presume the wave at 90° is interfering you have to assume that light travels ballistically. To presume no Doppler shift in either the arm or straight, you have to assume the "medium" traveling at the same speed as your system (i.e. no absolute medium).
I assume light does not travel ballistically (I think most scientists will agree). I assume there will be a Doppler effect to the vacuum (I think most scientists will disagree). We all know that the results did not tie up with what was expected from the calculations. So which of the assumptions are wrong?