Eli5: If accelerating charges produce electromagnetic waves, what happens if we are accelerating with the charge? Can there be light in one frame and not in another?

Question

Eli5: If accelerating charges produce electromagnetic waves, what happens if we are accelerating with the charge? Can there be light in one frame and not in another?

In: Physics

Answer 1

The question you asked is what caused us to throw out Galilean Relativity because if you take Maxwell’s equations at face value they don’t make sense in the exact way you’ve just pointed out.

What you have to do is take relativity into account. The photons are still going to go away from you (and the moving charge) at the speed of light, your clock is just going to go slower than a stationary observer. The electromagnetic force remains constant (the Lorentz force) and you use a Lorentz transformation to jump between reference frames. These transformations take into account the finite and invariant speed of light when jumping between reference frames.