Not every charge, just the free electrons, because they can change their proper distances. Contracted repulsive fields are still repulsive. So why should the electrons move closer together?And please don't say, that since in a conductor, every charge wants to spread all over the volume and since the number of electrons are equal to the number of protons, so there is NO net charge due to Length contraction, because instead of contracting the inter gaps electrons tend to contract themselves at their previous spacing before the current.
This is incomprehensible. And using bold font doesn't give it any more sense.Because the ditto condition is always present for the regular Lorentz transform of a current.(i.e. a conductor.......same volume......same no. of charges......no net charge......) where you changed the nature of Length contraction in order to get all the observed facts correct.
If you wonder why atoms in a lattice behave differently than free electrons when they start moving in some frame, then consider the different interaction in the two cases: Lennard-Jones potential between atoms can be attractive or repulsive. Coulomb forces between electrons are always repulsive.
The cations are fixed in the lattice, so they cannot change their proper distance. The electrons are free to move, so they can change their proper distance, while keeping the distance in the wire frame constant.