Relativistic Statistical Mechanics and Blackbody Radiation

Abstract

A manifestly Lorentz-invariant generalization of the Gibbs's canonical density operator is derived for the free fields of quantum electrodynamics from the maximum-entropy principle. Known results for the energy density, entropy, and other thermodynamic functions of blackbody radiation are very simply rederived. Use of the invariant density operator makes it clear that, contrary to recent assertions of Ott and others, it is not necessarily most natural to assume that temperature transforms like an energy. What is more to the point, it is shown that the concept of temperature in a moving system can be eliminated altogether if desired. Temperature may be conveniently considered as a purely rest-frame concept. The invariant density operator is then used to investigate the second-order two-point space-time correlation functions of the blackbody radiation field. The recent results of Mehta and Wolf and others are generalized to an arbitrary uniformly moving corodinate system, and the most interesting cases of pure temporal and spatial coherence are presented graphically. Two examples are given in which a moving observer measures a higher degree of coherence than he would in the rest system. Some remarks are made concerning the Gaussian nature of the phase-space distribution function, and the consequences for higher-order correlation functions in a moving frame are discussed briefly.