It's been quite a while since I thought about any of this carefully, so I could be off base here, but: lcamtuf is analyzing a somewhat odd scenario, and he see

It's been quite a while since I thought about any of this carefully, so I could be off base here, but: lcamtuf is analyzing a somewhat odd scenario, and he seems to have carefully omitted all the math. In the lab frame, there's a stationary test charge and an uncharged current-carrying wire. Ignoring relativity for a bit, the magnetic field around the wire is proportional to the current I (and I is proportional to v_drift/c). The Lorentz force [0] on the charge is q·v_charge·B, where v_charge is the velocity of the test charge, which is, drumroll please, exactly zero. There's no force, at least to first order! A current carrying wire does not attract charges of one particular charge, nor could it without rather odd symmetry violations. If you want to analyze this in a moving frame, even at first order in the boost velocity v_boost (the velocity of the moving frame, which does not need to equal v_drift), it gets more complicated: the test charge is moving, so it will experience a Lorentz force. But the fields themselves transform too, like this: https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity#Non-relativistic_approximations https://en.wikipedia.org/wiki/Classical_electromagnetism_and... And, of course, to first order everything will cancel out and there is still no force! (Otherwise there would be a massive inconsistency: a current-carrying wire would attract negative charges from the perspective of someone walking one way and would repel them from the perspective of someone walking the other way, and they would end up rather dramatically disagreeing with each other, and special relativity is not that weird.) The actual phenomenon that lcamtuf is talking about only shows up at higher order in the velocities involved, and one might argue that relativity does affect electromagnetic fields even at first order (see that link above!). FWIW, a useful heuristic for thinking about relativity is that the simultaneity-violating term in the Lorentz transformation (the -γβx term in t') implies that almost everyone's intuition for what's going on with multiple moving objects that are not in the same place (like multiple different electrons in a wire from the perspective of someone moving relative to the wire) is likely to be wrong. I haven't considered lcamtuf's explanation that carefully, and I'm not entirely convinced that it's right. But even that is a higher order effect, and lcamtuf's explanation seems like it has to be wrong even at first order! After all, at first order, there is no force on the test charge. But in a moving frame, as above, there is a Lorentz force on the charge unless the magnetic field disappears entirely, and v_drift is not going to be the boost velocity that makes the B field disappear. So I would apply large grains of salt to this model. [0] Wow, Lorentz got his last name all of this stuff!