zaybu wrote:The FSC is not dependent on the inertial frame of the observer, as far as I know. It arises in electromagnetism, which is itself a Lorentz invariant theory. The explanation as to why there are variations in the FSC would have to come from somewhere else. However, the article is not striding to give an explanation of this variation, but it does claim there are variations, and if this is true, it is quite outstanding.
You can define the FSC in terms of either the electric or magnetic constant, where the speed of light itself is the inverse of the square root of the electric times the magnetic constant, c = 1/(sqrt(u*e)). Thus the vacuum permeability and permittivity must covary in the same way space and time do under relativity. If they didn't, the speed of light wouldn't remain constant.
Given the inverse relation between space and time, any time dilation corresponds to a space dilation in another frame, such that the interval remains the same. General Relativity is a little different in the way this symmetry is expressed. Unlike Special Relativity, all observers agree that a clock on the ceiling is going faster than a clock on the floor. They just don't always agree how fast that is, or how big the difference is. Now, if your instruments are sensitive enough, and you fail to account for the gravitation variation, certain measurements of the emitter on the floor being measured at the ceiling will falsely indicate that the spacetime interval is variant, when it shouldn't be.
The only remaining question is, in what way can the observational effects be affected by the distance of the object. One of the big ones is the Hubble expansion. Can we assign the difference of frames as solely the result of the recessional velocity, or does the fact that in the interim between emission and detection the Universe expanded also contain a time dependent gravitational increase of depth, lead to clocks slow with expansion. What about dark energy and dark matter. If we are not properly accounting for the physics behind a constant spacetime interval, then that interval will not appear constant, even if the correct laws of physics says it should.
I'm not trying to make specific claims, though that is my rough guess based on what I do know. If I could prove it, that would be far more impressive. But for now we simply can't say with any significant certainty. There is big game at the foundations of physics, regardless of how that ends up working out.