On the analogy between stochastic electrodynamics and nonrelativistic quantum electrodynamics

TL;DR

This paper demonstrates a formal analogy between nonrelativistic quantum electrodynamics in the Weyl-Wigner representation and stochastic electrodynamics, explaining the conditions under which SED aligns with quantum theory.

Contribution

It reveals a first-order Planck constant approximation showing the formal analogy between quantum electrodynamics and stochastic electrodynamics, clarifying their similarities and limitations.

Findings

SED matches quantum theory for quadratic Hamiltonians

The analogy is valid to first order in Planck constant

SED fails for non-quadratic Hamiltonians

Abstract

I expose nonrelativistic quantum electrodynamics in the Weyl-Wigner representation. Hence I prove that an approximation to first order in Planck constant has formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.