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Cahill Analysis of Interferometer Experiments, Input?


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So i've been arguing with someone on ResearchGate regarding Special Relativity and other caveats related to his own pet Aether theory. He is, as many of these non-mainstream critics of Special Relativity are, a big fan of specific interferometer results from the late nineteenth or early twentieth century as he supports his theory on the back of a re-analysis of previous results. He claims that any vacuum interferometer will give a null result and that interferometers with a medium for the light beams would then give a non-null result. Something that was analyzed in this paper here: https://arxiv.org/pdf/physics/0205070.pdf. I'm curious about what your perspectives on it are given the derivations from their initial assumptions seemed to check out. 

If you could find a resource(s) for Lorentz Violating experiments conducted in a medium i'd heavily appreciate that. I had found a few that I thought had a relation to this such as https://arxiv.org/abs/0706.2031v1

His own paper is given here: https://www.researchgate.net/publication/350770907_MM-Cahill

The key idea is that this analysis combines both Lorentz contraction and the idea of light having a different speed in a chosen medium of 

\[ V = \frac{c}{n} .\]

You basically then perform the same analysis to determine the time difference between a path in the direction of motion and the path of the interferometer arm perpendicular to that. Which comes out to be 

398089640_ScreenShot2021-04-09at5_24_57PM.png.e0e1d8f7cc854a8784ccc50c3c197ace.png

Compared to it without the Lorentz contraction taken into account 

325342025_ScreenShot2021-04-09at5_25_30PM.png.ed6f7fc393c20f4c39f08d813ecda220.png

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