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 ${\ensuremath{\rho}}_{0}$ with Lorentz-invariant spectrum which persists at the absolute zero of temperature, and a temperature-dependent energy density ${\ensuremath{\rho}}_{T}$ which satisfies the laws of statistical mechanics. The mean-square fluctuation $〈{(\ensuremath{\delta}{\ensuremath{\rho}}_{T})}^{2}〉$ of ${\ensuremath{\rho}}_{T}$ is calculated from classical electromagnetic theory and is shown to depend explicitly on $〈{\ensuremath{\rho}}_{0}〉$. Classical statistical mechanics leads then uniquely from $〈{(\ensuremath{\delta}{\ensuremath{\rho}}_{T})}^{2}〉$ to $〈{\ensuremath{\rho}}_{T}〉$, which turns out to satisfy Planck's formula.