Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

TL;DR

This paper derives the classical Planck spectrum for scalar radiation using an accelerating frame, linking classical physics with relativistic effects and thermal equilibrium, and drawing analogies to quantum field theory phenomena.

Contribution

It presents a classical derivation of the Planck spectrum in an accelerating frame, incorporating zero-point radiation and relativistic physics, offering insights into thermal effects of acceleration.

Findings

Classical derivation of the Planck spectrum from an accelerating frame.

Connection between classical zero-point radiation and relativistic effects.

Analogies with thermal effects in relativistic quantum field theory.

Abstract

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.