Abstract
The Rayleigh-Jeans law and the J\"uttner (relativistic Maxwell-Boltzmann) distribution are shown to be compatible in equilibrium, to order ${\ensuremath{\beta}}^{2}$=(v/c${)}^{2}$, for the case of the Einstein-Hopf oscillator. The derivation of the matter distribution from the radiation law is thus consistent with the well-defined formulation of relativistic theories of interacting particles, in this approximation. One may formally define a temperature transformation law (admissible according to general Lorentz transformation requirements) such that the Rayleigh-Jeans law holds; however, a consistent classical relativistic statistical mechanics, and hence relativistic thermodynamics, of interacting particles is presently lacking.
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