If an observer is stationary relative to a current-carrying wire in which electrons are moving, why does the observer measure the density of moving electrons to be the same as the density of electrons if there were no current in the wire?
I read the explanation of magnetic force as a consequence of special relativity. That is, when the observer moves with respect to a current carrying wire in the same direction as the flowing electrons, then s/he observes the density to decrease due to Lorentz expansion and observes the density of positive ions to increase due to Lorentz contraction. The imbalance of charges results in a force that can be explained by Coulomb's law.
That explanation mentions that when the observer is stationary, the density of positive ions and the density of electrons appears to be the same. That last point is what I am stuck on.
Why does the density of moving electrons appear to be the same as the density of stationary positive ions?
Clarification: I know that when the electrons are not moving, their charge density cancels out that of the stationary positive ions. When the electrons are moving, how could the charge density still cancel out that of the stationary positive ions?
Important: My assumption is that a current carrying wire will neither attract nor repel a charge that is stationary with respect to the wire. I am now not sure if that is right :-(