I've heard that a changing magnetic field creates an electric field and vice versa. So if shoot an electron in a straight line, it would create a magnetic field in a circle around it. Let's say the electron is moving quickly down a road. But there is another particle moving exactly the same speed as the electron beside it. Relative to this particle, the electron is not moving at all, but relative to an observer on the road, it is moving very quickly. Would this not mean that from the particles perspective, there is no field being created, and the observer on the sidewalk experiences some sort of field?