Criterion for the Thermal Radiation Spectrum in Classical Physics

TL;DR

This paper proposes criteria for relativistic wave spectra, showing zero-point and thermal radiation as conformal group representations, and derives the Planck spectrum within classical physics.

Contribution

It introduces criteria linking zero-point and thermal radiation spectra to conformal group representations and derives the Planck spectrum classically.

Findings

Zero-point radiation is the conformal group’s identity representation.

Thermal radiation corresponds to an irreducible conformal group representation with temperature.

The Planck spectrum is derived including zero-point radiation in classical theory.

Abstract

Two criteria for the spectra of relativistic waves are proposed. Zero-point radiation provides the identity representation of the conformal group in Minkowski spacetime. Thermal radiation provides the irreducible representation of the conformal group in Minkowski spacetime which involves exactly one scaling parameter (the temperature) which is also time-stationary in a Rindler frame. Zero-point radiation is the limit of thermal radiation as the temperature goes to zero. Crucially, both zero-point radiation and thermal radiation take basically the same functional form in a Rindler frame. For relativistic scalar waves, a full derivation of the Planck spectrum including zero-point radiation is obtained with the classical theory.