Chambers, Robert (UK) wrote:
http://www.physicsinsights.org/sagnac_1.html
You might also be interested in
http://www.atomicprecision.com/new/a45thpaper.pdf
which describes the Sagnac effect in terms of general, rather than special,
relativity. Special relativity is not applicable because it is not concerned
with acceleration.
This is a common misconception, but it's wrong.
With "classical" special relativity, such as Einstein laid out in his
1905 Electrodynamics paper, one must explicitly add the "clocks
hypothesis", which states that clocks are unaffected by acceleration.
Once you've done that, however, you can analyze acceleration with no
further problems. (The "clocks hypothesis" has also been experimentally
verified, by the way.)
In "modern" special relativity, which uses pseudo-Riemannian geometry
but restricts it to coordinate systems in which the metric is
Minkowski's, the "clocks hypothesis" is already built in and there are
no problems at all handling acceleration.
In fact, in many (or most) cases of simple accelerated motion it's
simplest to analyze the situation by using "flat" coordinates, and if
you want to answer certain questions involving simultaneity it's the
only way to do it.
Gravitation, on the other hand, cannot be handled by special relativity,
because it requires the treatment of curvature. In particular, if one
were to place a gravitating planet in the middle of the rotating disk,
then one would be unable to provide a full solution of the Sagnac effect
in that situation using only SR.
