How can relativity explain the magnetic attraction of two electrons (or two electron beams) comoving in a vacuum at some certain constant velocity?
It is well known (https://acceleratorinstitute.web.cern.ch/acceleratorinstitute/ACINST89/Schindl_Space_Charge.pdf) that two parallel electrons or electron beams at the same velocity will experience an attractive Lorentz force that increases in magnitude and eventually equals the repulsive Coulomb force at the hypothetical velocity of c (if you could get to that velocity that is).
It seems that relativity would suggest that comoving electrons would of course view each other as being at rest and hence their Coulomb fields and forces would not be Lorentz contracted. In addition, they would not view any created magnetic fields and hence no Lorentz forces. This would seem to suggest that the electrons, from the comoving or proper frame of reference, would merely repel each other according to Coulomb's law. But, it is experimentally known that two parallel electrons or electron beams do in fact attract when moving at a given constant velocity.
When there is no wires involved, there seems no way to 'introduce' via length contraction, time dilation, or otherwise, a means via relativity to explain the attractive Lorentz force that negates and or counters the Coulomb force for these comoving electrons.
Please note, I am specifically NOT talking about wires, so I kindly request no references or explanations based on a Lorentz contraction of the positive atomic lattice in said wires as is generally done. By the way, I do not dispute the wire-based answers at all as they are entirely logically consistent.
The only things involved in the question, are the comoving parallel electrons or electrons beams and a vacuum through which they are moving at some constant velocity.