Einstein, Equipartition, Fluctuations, and Quanta

Abstract

After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for non‐localized quantized wave modes. Although nobody noticed this flaw in Einstein’s reasoning at the time, his fluctuation argument, and several others like it, failed to convince anybody of the reality of light quanta. Even Millikan’s verification of Einstein formula for the photoelectric effect only led to the acceptance of the formula, not of the theory behind it. Einstein’s quantization of matter was better received, especially his simple model of a solid consisting of quantized oscillators. This model could explain why the specific heats of solids fall off sharply as the temperature is lowered instead of remaining constant as it should according to the well‐known Dulong‐Petit law, which is a direct consequence of the equipartition theorem. The confirmation of Einstein’s theory of specific heats by Nernst and his associates was an important milestone in the development of quantum theory and a central topic at the first Solvay conference of 1911, which brought the fledgling theory to the attention of a larger segment of the physics community. Returning to the quantum theory after spending a few years on the development of general relativity, Einstein combined his light‐quantum hypothesis with elements of Bohr’s model of the atom in a new quantum radiation theory.