Relativity and Current in Wire
The question here, (which wasn't answered properly) asks why the electron density of a current carrying wire does not increase. If it does, why is there no force on the charge? My heuristic estimate of Lorentz transformations says that the electric field of the electrons should also increase.
Extensive online research has led me to only two legitimate answers to the question posted in the link. The first is simply to state the fact that electrons and protons have the same density throughout the wire as a definition. The second is to say that since electrons are free to move, any electric field in the lab frame can easily be cancelled out by the freely moving electrons if they move apart (becoming more spaced out). In this case, there is no disagreement between Maxwell's equations and the Lorentz transformed Maxwell's equations.
But surely we can just engineer a wire in which the electrons are not free to change their spacing, but only move in the forward direction? Then the Lorentz transformed solution for the acceleration of the particle disagrees with the classical results? I was not satisfied by the explanations given as they were not fundamental enough. How do we resolve this?
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