I was recently reading this short article: http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html It explains how magnetic and electric fields are related because in one frame of reference where there's a net magnetic force and no net electric force, there may be another frame of reference where there is no magnetic fforce but only an electric effect with the same result.
However, I'm not sure why the increase in charge density isn't symmetric between the two frames they examine. If in the frame of the lone proton, we get Lorentz length contraction that leads to an increased density of positive charge in the wire, why do we not in the frame of the wire see Lorentz contraction with the moving electrons leading to higher density of negative electric charge that would cancel out the forces we'd expect from the magnetic fields?
Why are they able to fiat that the moving electrons are uniformly distributed, but when we move to another frame of reference where the protons in the wire are the ones that appear to be moving that they are not?
Is it really just a fiat? What would happen if we started out with the wire having no current in it with the electrons initially uniformly distributed and then induced the current in the wire, would we then symmetrically see Lorentz contraction in both frames?
I'm thinking my issue is not fully understanding Lorentz contraction and its effect when acceleration is involved. For example, it also confuses me why it is both the case that the string should break between two rockets tied together with string and that if I got in a rocket and accelerated up to near the speed of light headed towards Alpha Centauri that the distance to Alpha Centauri would appear to shrink. Do empty spaces between objects get contracted, or don't they? Does it have something to do with which objects are the ones doing the accelerating to achieve the relative velocities?