Derivation of the Blackbody Radiation Spectrum by Classical Statistical Mechanics

Abstract

It is assumed that the fluctuating radiation energy density in a blackbody cavity is the sum of two stochastically independent terms: a zero-point energy density ${\rho }_0$ with Lorentz-invariant spectrum which persists at the absolute zero of temperature, and a temperature-dependent energy density ${\rho }_T$ which satisfies the laws of statistical mechanics. The mean-square fluctuation $〈{\left(\delta {\rho }_T\right)}^2〉$ of ${\rho }_T$ is calculated from classical electromagnetic theory and is shown to depend explicitly on $〈{\rho }_0〉$. Classical statistical mechanics leads then uniquely from $〈{\left(\delta {\rho }_T\right)}^2〉$ to $〈{\rho }_T〉$, which turns out to satisfy Planck's formula.