The Sagnac effect is where light is sent both ways around a loop (fibre optic cable loop/coil or an arrangement of mirrors) and the time it takes light to complete the loop is increased in one direction and decreased in the other from the rotation, in other words one trip would be seen to exceed C and the other to be less than C.
But this is explained as accepted under Special Relativity by the sudden inclusion of a preferred frame with proper time etc.... And the insistence that if we measured the speed of light in a portion of the Loop, we would still detect light moving at C in that portion. This is a real effect that is used as an optical gyroscope in guidance systems, so there is no debate IF the trip time varies, it really is accepted and considered Ok with Special Relativity. Now what if we rotated the loop at near the speed of light? Now if we looked at the time it takes for light to go one direction it would act like the trip was about half the length due to addition of C and almost C. In the other direction it would be lengthened hugely since it would be C minus almost C. Now in one direction the same photon could do many laps in the time the other completes a tine portion. Can the speed of light be measured in a portion to be C in both directions when one photon moves though many times (and the rest) while the other photon is struggling to do it once? NO! And if this obvious truth is accepted, then we must ask, could not any curved path be a portion of a large circle, hence act as if it were a portion of a very large rotating frame even if the circle would be trillions of times larger than the galaxy? This then means that in practice all motion would not be perfectly linear due to influences of gravity and all would have relativistic light speed differences! The speed of light being C is actually not indicated by most experiments to measure the speed of light as C under all conditions, rather confirmation bias and stilted interpretations of results are used to keep the theory alive. John