How does one go about rigorously deriving special relativistic dynamics (both relativistic mechanics and electrodynamics) from quantum electrodynamics? Is this even possible from the mathematical structure of QED?

  • $\begingroup$ What would you consider rigorous? $\endgroup$ – jacob1729 Jun 24 at 22:00
  • $\begingroup$ What would you consider to be a derivation of special relativistic dynamics? Since QED uses relativistic mechanics already, is it sufficient to derive Maxwell's equations? If not, what are the necessary features of a derivation of "relativistic mechanics"? $\endgroup$ – probably_someone Jun 24 at 23:05
  • $\begingroup$ So QED itself doesn’t admit a rigorous formulation, not sure how you want to derive its classical limit rigorously.. $\endgroup$ – Prof. Legolasov Jun 24 at 23:58
  • $\begingroup$ What I require are clear mathematical derivations (or rather, just a justification to whether or not it is possible to do so) of the dynamical equations in relativistic mechanics and electrodynamics from the formulation of quantum electrodynamics. Something along the lines of Ehrenfest's Theorem in the non relativistic case, but of course reproducing Maxwell's Equations as well. $\endgroup$ – DaRkSw0rD Jun 25 at 4:30

In a comment you clarify

but of course reproducing Maxwell's Equations as well"

The way mainstream physics sees this is that the classical level is emergent from the quantum level. To desire the exact equations for classical to come from the equations of quantum is like asking for the exact equations of thermodynamics to come out of statistical mechanics.

In this blog article by Motl, "How classical fields, particles emerge from quantum theory " the method is described, how to go from QED to classical light.

It is the data and the observables predicted that have to be consistent, not the mathematics, imo.

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  • 1
    $\begingroup$ Tysm! This article pretty much contains what I've been searching for. As I mentioned, I was looking for something along the lines of Ehrenfest's Theorem. The word "emergent" escaped me at the time I commented. $\endgroup$ – DaRkSw0rD Jun 25 at 11:16

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