I recently stumbled upon a video (1) which explained that what is assumed to be the speed of light is actually the two-way speed of light.
As explained in the video, hypothetically the speed of light varies across different directions of spacetime. If this is the case, then how is it possible that the average of such (ie: two-way speed of light) fits so perfectly in Einstein's mass-energy equivalence? I cannot wrap my head around whether this means anything physically, or whether it is merely a coincidence that the constant in that equation is exactly equal to the two-way speed of light.
Alternatively, I also wonder; why is the mass-energy equation valid if we don't actually know the one-way speed of light?
Any clarification would be greatly appreciated.
Best Answer
The video comes close to acknowledging the following, but doesn't quite explicit state it: this is merely a matter of coordinate system. The fact that there is no physical experiment that can distinguish between an isotropic speed of light and an anisotropic one means that it is not a matter of physical phenomenon, it is purely a matter of how you model the world. The statement "hypothetically the speed of light varies across different directions of spacetime" doesn't refer to anything meaningful.
The essential postulate of relativity is that physics works the same in all inertial reference frames (hence the name: the numerical representations of physics are relative to the reference frame). It follows that the two-way speed of light is invariant (in the context of relativity, "invariant" is understood to mean "invariant with respect to Lorentz transformations").
A velocity is distance divided by time, and time is simply one coordinate of a 4-vector. How much of that vector is "time" and how much is "space" is a matter of coordinate system, not of physical reality, and so the one way speed of light is not a matter of physical reality. It is only the two way speed of light that has a real physical effect on the universe. This two way speed is intertwined with many other constants, such as electromagnetic constants. It is tied to the rest of physics, and not just a coincidence. These ties appear regardless of your coordinate system; converting to an anisotropic coordinate system will alter all the numbers in a way that preserves the essential relationships.