Relativistic Waves are Required for the Planck Spectrum in Classical Physics

Abstract Although it is generally claimed that classical physics leads inevitably to the Rayleigh-Jeans law for thermal radiation, actually a completely relativistic physics is the required aspect. Here a derivation of the Planck spectrum for thermal radiation is given based upon wave uctuations within relativistic classical physics. In contrast to many earlier derivations, the analysis here in Minkowski spacetime depends upon relativistic waves alone, and does not require any interaction with charges or the use of an accelerated coordinate frame. The derivation depends crucially on thermal uctuations existing above the fundamental inertial-frame-independent uctuations of Lorentz-invariant classical zero-point radiation. Such frame-independent zero-point uctuations exist only in a relativistic wave theory and cannot exist in a nonrelativistic wave theory. Thus, such a classical derivation of the Planck spectrum exists in a Lorentz-covariant classical theory, such as classical electrodynamics, but not in a Galilean-covariant theory where all waves are based upon material media. Classical zero-point radiation provides a purely classical alternative to quanta in the analysis of the Planck spectrum.