A while back (thread) you guys helped me understand why [itex]\tilde{F}=m\frac{d\gamma\tilde{v}}{dt}[/itex] (3-vectors) as it follows from [itex]\bar{F}=q\Psi\bar{v}[/itex] (4-vectors) and [itex]\tilde{F}=q(\tilde{E}+\tilde{v}\times \tilde{B})[/itex] (3-vectors). However, I had the impression that one also uses [itex]\tilde{F}=m\frac{d\gamma\tilde{v}}{dt}[/itex] in relativistic mechanics, making abstracting of the nature of the force and therefore not necessarily being electromagnetic as in its derivation. Is that true?(adsbygoogle = window.adsbygoogle || []).push({});

Secondly, there appears to be a chicken-egg problem here. Where does [itex]\bar{F}=q\Psi\bar{v}[/itex] come from? I assume it follows from the classical Lorentz force, but what are the extra's? [itex]\tilde{F}=m\frac{d\gamma\tilde{v}}{dt}[/itex] can't be part of it because then we do have a chicken-egg problem. I've been trying to find some comprehensive reference that builds this up from classical electrodynamics and the properties of Minkowski space, but without success.

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# Relativistic force and electromagnetic tensor follow up

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