How much impact would it make in science if the speed of light is discovered to be variable?

Question

So if such a thing happens, how would it alter current physics?

Answer 1

There are a few results of variable speed of light:

Ellis claimed that any varying c theory

1. must redefine distance measurements
2. must provide an alternative expression for the metric tensor in general relativity
3. might contradict Lorentz invariance
4. must modify Maxwell's equations
5. must be done consistently with respect to all other physical theories