Einstein and quanta of light: A difficult road to discovery

Abstract

Einstein’s fundamental work “On a Heuristic Viewpoint Concerning the Production and Transformation of Light” (1905) contains a quantum explanation of the processes of interaction between the radiation field and the substance. These processes of “transformation” (i. e., photoluminescence, photoelectric effect and photo-ionisation) are examined in the last three paragraphs. In the preceding six paragraphs Einstein compares thermodynamic properties of the balanced thermal radiation with properties of the ideal gas. Based on the analogy between the first and the second, he makes the conclusion about discrete properties of the electromagnetic radiation. In 2005 M.Nauenberg noticed a “gap” in this explanation. In order to check its mathematical correctness, V.M. Babich (2014) suggested to verify the exact differential condition for the presumed differential of entropy. It was found that this condition is satisfied for the radiation on the whole (including all frequencies). However, it is not valid for the part of the radiation in the small spectral interval. The aim of this article is to explain the details of this verification and to discuss the meaning of the difference in properties of radiation on the whole and in the small spectral interval.