Suppose an electron is created somehow in the universe -- through particle-pair production or what have you. Suppose it is stationary so that electrodynamics (and specifically propagating electromagnetic waves) is unavailable for explanation. Certainly distance charges will feel Coulomb's force, but how quickly?
I'm wondering if, since electromagnetism is manifestly relativistic (Lorentz rather than Galilean invariant) we can use that to always move to a frame where the electron is travelling and then claim that there are in fact EM waves? I don't know.