Derivation of the Planck radiation spectrum as an interpolation formula in classical electrodynamics with classical electromagnetic zero-point radiation

Abstract

A closely argued derivation of Planck's spectrum for blackbody radiation is presented within classical electrodynamics with classical electromagnetic zero-point radiation. The presence of temperature-independent random classical radiation invalidates the ideas of traditional classical statistical mechanics which become valid only in the low-frequency or high-temperature limit where they lead to the Rayleigh-Jeans law for the thermal spectrum. The assumption of Lorentz invariance for the zero-point radiation determines the high-frequency part of the classical random radiation spectrum. The blackbody problem of classical physics with classical zero-point radiation as considered here is the derivation of an interpolation formula between these high- and low-frequency limits. Here we take advantage of the surprising diamagnetic behavior of a classical free point charge in zero-point radiation. This diamagnetic behavior is compared with the paramagnetic behavior of a magnetic dipole rotor of large moment of inertia, which behavior is derived from the low-frequency form of the radiation spectrum. If one requires the natural simple condition that the diamagnetic behavior as a function of temperature should differ only in the sign of the magnetic moment from the paramagnetic behavior as a function of temperature, then one is led uniquely to the Planck spectrum including zero-point radiation as the equilibrium spectrum for classical random radiation.