Classical Physics of Thermal Scalar Radiation in Two Spacetime Dimensions

TL;DR

This paper explores classical scalar radiation in two-dimensional spacetime, deriving spectra and laws in inertial and accelerated frames, revealing how thermal radiation transforms under relativistic conditions and reproduces the Planck spectrum.

Contribution

It provides a classical physics derivation of thermal radiation spectra and laws in both inertial and accelerated frames, connecting zero-point radiation with the Planck spectrum.

Findings

Derivation of Stefan-Boltzmann and Wien's laws in a relativistic classical context.

Transformation of zero-point radiation between inertial and Rindler frames.

Recovery of the Planck spectrum from classical zero-point radiation in accelerated frames.

Abstract

Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also Wien's derivation of the displacement theorem using the scaling of relativitic radiation theory. Next the spectrum of classical scalar zero-point radiation in an inertial frame is derived both from scale invariance and from Lorentz invariance. Part II involves the behavior of thermal radiation in a coordinate frame undergoing (relativistic) constant acceleration, a Rindler frame. The radiation normal modes in a Rindler frame are obtained. The classical zero-point radiation of inertial frames is transformed over to the coordinates of a Rindler frame. Although for zero-point radiation the two-field correlation function at different spatial points at a single time is the same between inertial and Rindler frames, the correlation function at two different times at a single Rindler spatial coordinate is different, and has a natural extension to non-zero temperature. The thermal spectrum in the Rindler frame is then transferred back to an inertial frame, giving the familar Planck spectrum.