Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

TL;DR

This paper explores the scaling symmetries of classical zero-point radiation by analyzing charged particles in circular orbits, finding that only Coulomb potentials produce a unique, scale-invariant radiation spectrum, implying non-electromagnetic potentials are unsuitable for classical radiation equilibrium.

Contribution

It demonstrates that only Coulomb potentials yield a scale-invariant radiation spectrum in classical systems, highlighting the special role of electromagnetic interactions in radiation equilibrium.

Findings

Coulomb potential (n=1) produces a unique, scale-invariant radiation spectrum.

Scaling symmetries are present in systems with potentials V(r)=-k/r^n.

Non-electromagnetic potentials do not support stable radiation equilibrium.

Abstract

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.