Heres the situation, I'm in a argument with a genuine geocentrist (yes, they still exist) who claims that Special relativity cannot be true because http://web.stcloudstate.edu/ruwang/PRL93.pdf this experiment proves it is wrong, he also sent me this handy video  . so i sent him http://www.mathpages.com/home/kmath169/kmath169.htm this paper showing him how it works. the problem arises when he responds again with this:

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The paper measures light speed relative to the wheel axes instead of relative to the observer that made the measurement.

"It only seems to be you who is making that conclusion"

No, there are many physicists who agree that that paper is wrong. I already debunked that paper; no amount of maths can change the fact that Special Relativity demands light travel at c relative to inertial frames, yet the inertial observer in the experiment measured light travel at other than c. Given these premises it necessarily follows that either the math is wrong or the math doesn't represent the results of the experiment, but I don't need to find out which is true to know the paper is incorrect.

UPDATE:

"Letting n denote the index of refraction of the fiber, the speed of light relative to the fiber at any point is c/n, and the speed of light relative to the fixed inertial coordinates of the roller axes is given by the relativistic speed composition formula (c/n ± v)/(1 ± v/nc)"

It is useless to speak of the fixed inertial coordinates of the roller axes, since the observer's frame is what is measuring the light speed and the observer's frame is not in the frame of either roller axis.

If the measurements were being made from the frame of the roller axes the author might have a point but as it is, his paper is ignoring a crucial fact.

This might be where his error lies, in that he's trying to calculate the speed of light relative to the axes' frame instead of the actual observer's frame which actually made the actual measurements ...

Because he is correct that the speed of light is c relative to an inertial frame centered on either roller axis.

But again, relative to the observer the speed of light is not c."

if someone could help me out that would be great.

Sounds like he is ignoring the changes in path length and the differences in rotational vs translational velocities under SR.

Did he strengthen his argument with actual counter mathematics?

All you provided is his statements. After all the first paper does not prove Sagnac wrong.  It is a highly cited paper that shows that linear motion does not affect the speed of light. For one thing light is only constant in a vacuum, this is a fibre optic cable so one should not expect constancy of c in the first place

 

Edited September 17, 20178 yr by Mordred