On the Classical Theory of Equilibrium Between Matter and Radiation

The problem of establishing the Rayleigh-Jeans law for equilibrium electromagnetic radiation in a cavity is studied without making the customary simplifying assumptions. By using a Hamiltonian formalism analogous to that introduced by Fermi for quantum electrodynamics the analysis is simplified, general expressions for absorption and emission are obtained, and the correspondence with the quantum mechanical treatment is established. The model considered consists of a cavity which contains classical charged particles which move in an arbitrary potential while interacting with electromagnetic radiation. The work covers much the same ground as the fundamental but neglected work of McLaren, though the methods used are simpler and more direct. The applications are to those parts of radio astronomy where the wavelengths are sufficiently large to allow a classical description. In particular, Twiss's analysis of stimulated emission at radio wavelengths is incorporated in the analysis.