Hi Coordinate transforms based on Sagnac effect become somewhat different from the Lorentz-transformations.
Can you imagine how I have derived these? Primed (t', x', y', z') coordinates follows the rotation. Unprimed (t, x, y, z) are not rotating.) t' = t/(1-v^2/c^2) x' = x*(1+v^2/(c^2-v^2)) , whos' first Taylor term becomes = x*(1+v^2/c^2) y' = sqrt((v*y/c/2)^2+y^2) = y*sqrt(1+(v/c/2)^2), very similar to the Lorentz x' transform z' = should be similar to y (z' = sqrt((v*t/2)^2+z^2)) but somewhat more complex sin z is in radial direction. It becomes somewhat shorter towards the center compared to away from the centre. David
