Classical statistical thermodynamics in the presence of electromagnetic radiation is reanalyzed, and is reformulated to give a natural classical description of the phenomena which originally led to the introduction of the idea of quanta. The traditional classical ideal gas fails to exist in principle for particles of finite mass which have electromagnetic interactions, and hence the classical proofs of energy equipartition are all erroneous. A consistently classical treatment of thermal radiation leads to the natural introduction of temperature-independent fluctuating radiation in the universe. The spectrum of this electromagnetic zero-point radiation may be obtained from the arguments for Wien's displacement law or from the requirement of Lorentz invariance of the radiation spectrum; this zero-point spectrum agrees with the $\frac{1}{2}\hslash \omega$ per normal mode familiar in quantum theory. The presence of temperature-independent disordered energy from zero-point radiation leads to a contribution to the entropy connected with thermodynamic probability distinct from the contribution of caloric entropy. The use of quanta in calculations of the thermodynamic probability is seen as a subterfuge to account for this mismatch between caloric entropy and probability. Several examples of statistical thermodynamics, which are generally regarded as having their explanation in terms of quanta, allow natural explanations within the context of classical theory with classical electromagnetic zero-point radiation.

• Received 5 June 1969

DOI:https://doi.org/10.1103/PhysRev.186.1304