Of velocity of light is constant we can't measure the velocity of earth compared to space.
It will be interesting to do an experiment with electrons. Make the two arms have electrons as particles, then use a quantum eraser to erase which arm the eleven came the use interference pattern to see the relative velocity. Light also can be used for this by put in measuring devices so that path information is present making photons behave like particles, then destroy the path information to get a diffraction pattern.
This is a good experiment to see special relativity applies to light waves but not photons when they behave like particles.
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