What is the medium that affects the speed of light in the Fizeau Experiment?

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Nice link - it'll take me weeks to go through it all, but I really need to...
 
The Fizeau Experiment
Fizeau measured the speed of light in moving mediums, most notably moving water. Fresnel proposed a "drag coefficient" which putatively described how strongly a moving material medium "dragged" the ether. SR predicts no ether but does predict that the speed of light in a moving medium differs from the speed in the medium at rest, by an amount consistent (to within experimental resolutions) with these experiments and with the Fresnel drag coefficient.
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according to this, light speed is different in a moving medium,
and i think its is relative to the theory of "frame dragging", if
that is correct what is the medium that is in motion?
 
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So, to calculate a proper time of a worldline in SR using an inertial frame is quite easy. But I struggled a bit using a "rotating frame metric" and now I'm not sure whether I'll do it right. Couls someone point me in the right direction? "What have you tried?" Well, trying to help truly absolute layppl with some variation of a "Circular Twin Paradox" not using an inertial frame of reference for whatevere reason. I thought it would be a bit of a challenge so I made a derivation or...

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