In a true classical model, light always travels at c relative to the source. In any other frame, that moves relative to the source, light cannot be at c in that frame.
In rotating frames light also travels at c relative to the source. This is observed to happen in the Michelson Morley experiment. Where the lab rotates around the earths axis but light is observed to travel at c on both arms.
Of course relativists will argue that light actually is variant in the lab frame to counter the classical assumption it isn't. This however is unsubstantiated. To date no variance has been observed in any MMX style experiments.
In the Sagnac experiment relativists have long argued that classical theory cannot explain the fringe shift observed in the rotating setup. They do so by erroneously assuming classical theory predicts light will be at a constant speed in the lab. That is at c+-v in the lab. This is a ridiculous claim as even relativists admit classical theory predicates that light must always propagate away from a source at c in the *source frame*. But this is an impossible calculation as a constant speed in a rotating source frame will not, by a Galilean transformation, lead to a constant speed in the lab frame.
It is a mathematical impossibility for an object to travel the same distance in a straight line every second, away from a rotating object. This is the mistake relativists make when trying erroneously to discredit a classical model
In Sagnac there are three separate frames to consider.
1)The lab frame, where the source and mirrors rotate. This is the traditional frame used by relativists to describe both classical and SR. In this frame light travels at variable speeds in a classical model. (As it has to travel at constant speeds away from the rotating source.)
2)The rotating setup frame where the lab and the universe rotate around the setup but the source and mirrors don't move. In this frame the light travels at a constant speed relative to the source. But because the setup itself rotates and the light beam has to travel in the same direction in the universal frame (for instance due west), the light beam curves in this frame, always propagating in a specific universal direction. (This frame is similar to the MMX source frame where light is also at a constant speed but curves on each path).
To explain in detail, think of it like this. If you shine a beam of light into space in one direction (west) and then swivel the beam to another direction (north west) Does the beam that initially left in a westerly direction from your source also move or get dragged north? No. This is never observed. So if a single point of the light beam from the Sagnac source left the source when it pointed west it will continue travelling west at c away from the source. Which is why if you are in a rotating frame with the source rotating in a circle then the beam will curve away from the source in this frame until it hits the first mirror. Then it will curve in that direction etc..
https://youtube.com/watch?v=qGQil7I0ixg
3)And thirdly, the rotating source frame where the source and the mirrors rotate around a point centred on the source. But the rest of the background universe including the lab only move slightly back and forth on the spot.
This is the true source frame as in this frame the light is at constant speeds and in straight lines.
This is the frame in which one can easiest calculate the path difference for classical theory. Because the light travels at the same speed in straight lines and one only has to calculate where and when the mirrors are for each reflection. It is this frame in which the path differences become obvious. Note how one light path chases the mirrors around,as they move away from the direction of beam travel, leading to a longer path length than the light beam travelling in the same direction as the mirrors rotation.
https://youtube.com/watch?v=7X8wlbXFaMo
