Read the quote again. The electrons are moving through wires not freely in space.
There are a few things going on here. Misunderstandings....
First, in the OP the magnet, its magnetic field and the charged ball were all at rest in Sam's frame and Bob is moving.
Tach points out that since the magnet and the ball are not moving WRT eachother there is no Lorentz force between them in any frame.
Przyk, really said the same thing. He just said it differently. He said, that yes from Bob's frame the ball is moving but so is the magnet and its field. The ball and magnet are not moving WRT eachother in Bob's frame either.., they are moving together relative to Bob.
On the electron issue, the point was that two electrons moving parallel and "freely", is not the same as two electrons moving through either wires or a plasma. The initial problem with the electrons assumed they were moving relativistically. That only happens when they are moving freely. They move slowly through wires and/or a plasma. Only the potential or wave function moves relativistically through a wire. Put an electron in one end of a wire and at near c one (a different one) jumps off the other end (an analogy). The first electron does not move relativistically through the wire. Electron's are displaced from atom to atom in the wire from one end to the other, and this occurs at near relativistic velocity. Same thing in a plasma, since a plasma is generally composed of ions, the electron again moves from ion to ion. Not freely through space.
Electrons moving freely in space, are charged particles and likely do involved some Lorentz force, but from what I have read, to understand that, you would be getting into how an electron interacts with the ZPF not a wire or plasma. That would then involve QED or SED which is far beyond this discussion, although I have read some of that work, it is far beyond my comfort zone for comment. However, the Lorentz forces involved do seem to be linear in the direction of motion.
Przyk can correct me if I misunderstand what he intended, but I do not see that he was presenting anything different - generally - than Tach's basic arguement here.
As long as you remain with the OP from all frames of reference the magnet, its magnetic field and the charged ball are at rest relative to one another.., and no Lorentz force is involved. The charge has to be moving relative to the magnetic field (and in this case the magnet) for there to be any Lorentz force.., between them.
If Bob had his own charged ball and together he and his charged ball move throught the magnetic field, of Sam's magnet, then there would be a Lorentz force, but that was not what was set up in the OP.
