Sagnac and the absolute frame.
For such a simple experment the Sagnac effect has been the subject of much controversey with many different attempts to explain what is actually going on. I have been looking at the arguments on both sides. Some even claiming it is relativistic. Some say it is an artifact of rotation. That is the main one. Some say it is explainable by way of the shared frame that is the axis of motion. None of these stand up as far as I can tell. Rotation is only incidental. GPS uses one way Sagnac for corrections over distances that do not not circumnavigate the globe. Ives had also shown that the effect can also be translational.
I will give a brief summary of Sagnac and it's logical implications from one of the better and simpler explanations, found
here.
In the Sagnac experiment two photons are sent around the circumference of a disc in opposite directions to return to a detector where differences in the speed of light would be shown in a fringe pattern that can be measured. The source and detector are fixed to the disc.
If the disc is stationary the photons arrive at the detector at the same time. (Apparently). But If the disc is rotating one photon arrives earlier and one later.
Lets say we have two observers. Observer A who is positioned on the disc and rotating with it and observer B who is standing on the ground looking at the rotating disc.
Now depending on the frame of reference we have different points of view in regards to the speed of light. For a observer A on the disc, he would say that the speed of light is different, from his perspective he is stationary and the speed of light varies.
But for Observer B on the ground observing the disc it is a different story. He sees that the paths the light is taking is changing because of the rotation, one photon has a longer path because the detector is moving away in respect to it while moving towards the other photon making its path shorter. To this observer the speed of light seems constant only the distances are changing. But for observer A on the disc the distances are the same but the speed of light varies.
So which view is the correct one? The problem is according to Einstein there are no prefered frames of reference only relative frames of reference. So you can't say one is better than the other because the position of the observer is arbitrary. And if we say A is correct then we obviously undermine the second postulate of SR.
It gets more interesting. For Observer B on the ground the speed of light is not exactly constant either due to the much smaller disc and the observer rotating with the Earth on it's axis. Up to 15 degrees an hour. In fact a higher order sagnac effect.
Stepping up a level we can have the light path circle the Earth instead of the disc. Observer A is in the lab with the source and detector rotating along on the surface of the Earth. And Observer B is positioned stationary, not rotating, hovering above the pole of the Earth. Or you could say the ECI frame used in GPS.
The same is true here as in the smaller disc experiment. Observer A who's perspective is stationary but rotating with the Earth would say the speed of light is different, (if he did not know he was rotating.) But observer B at the pole would see the distances changing but would say the speed of light is the same. Is the speed of light truly isotropic in the ECI?
Apparently not, because the Earth is orbiting the Sun and that extra rotation, (another higher level sagnac effect) just as before gives a slight difference in the speed of light. GPS system use the ECI under the premise of the isotropic speed of light. But apparently the computations to adjust for the ECI have the sagnac corrections within them so for the system we have isotropic values.
You can step this up again, with the light path extending from the Earth and circling the sun along Earths orbital path. Observer A is on Earth and Observer B is stationary above the Sun. Again it is the same. And this time the tiny difference in the speed of light for observer B is from the motion of the solar system around the galactic center.
We can only conclude that there is but one true frame of reference where the speed of light is actually constant. The absolute frame of reference that is space itself as Newton first proposed. Or observer B hovering above the entire universe!
It was previously mentioned that Maxwells equations were hinting at the constancy of C. I remarked that Maxwells equations were founded on the assumption of an Aether. Both are true. Maxwell’s theories hold that the speed of light in the vacuum depends on the permittivity and permeability of the vacuum. Therefore the speed of light in vacuum is a property of the vacuum. Not from the metric properties of coordinate space. So the speed of light in vacuum can be an isotropic constant only with respect to a reference frame which is at rest or fixed in the physical space.
An absolute frame of reference.