On the Law of Equipartition for Translational Motion of Excited Molecules in Equilibrium with Thermal Radiation

Abstract

Abstract Einstein’s radiation theory consists of two parts: the derivation of Planck's radiation law from a physical mechanism of absorption and emission of radiation by excited molecules that are in thermal equilibrium with the radiation field and a demonstration of the validity of the law of equipartition of energy for the translational motion of the molecules. Several incongruities are observed: Einstein could not have legitimately substituted back into his dynamical equilibrium condition, valid at any finite temperature, a limiting condition between the coefficients of absorption and stimulated emission that he obtained in the high temperature limit. His justification of the law of equipartition involves, on the one hand, treating the motion of the excited molecule as brownian motion while, on the other hand, employing special relativity to obtain an expression for the diffusion coefficient. In the former the velocity of the molecule is a stochastic variable while in the latter it is a uniform velocity. Hence equipartition does not hold for the translational motion.