Gravitational waves travel at the speed of light as well. So if the speed of light changes, so would the speed of gravity waves, presumably - otherwise, they would probably not be equal today (though of course it could always be a coincidence).
Gravitational waves and light travel at the same speed in a vacuum.
What if you took a very very very long piece of glass and sent both gravity waves and light waves through it?
The light will be slowed down. Google tells me that there is something analogous to the refractive index for gravity waves, so there should also be some slowing of the gravity waves, but would the optical refractive index and the gravitational refractive index be the same?
I'd expect that it would not be the same. The optical refractive index if I recall correctly doesn't depend on the masses of the particles that make up the medium it is traveling through. Just charge and arrangement.
Gravity waves should only depend on mass and arrangement.
The speed of light in a medium is always some constant specific to that medium times c. If c changes, the constant will not be affected. So I don't see how you could use the speed of light in a medium to deduce anything about c. The same logic applies to gravitational waves. And as long as the speed of gravitational waves is always equal to the speed of light, the relative values of the two will still not change.
Say old light speed in glass is k*c1, new speed is k*c2. Old gravity wave speed if n*c1, new is n*c2. How do you you use these numbers to find out if c1 == c2 or not?
