Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

TL;DR

This paper examines Einstein's lesser-known 1924-1925 quantum theory of the monatomic ideal gas, highlighting its non-statistical approach and its significance in the development of quantum statistics, despite initial neglect.

Contribution

It presents a detailed analysis of Einstein's non-combinatorial approach to quantum gas theory, emphasizing its conceptual foundations and historical context.

Findings

Einstein's approach was based on thermodynamic analogies and adiabatic transformations.

The paper clarifies Einstein's motivations and the role of Ehrenfest in his development.

It highlights the conceptual ambiguities and the significance of Einstein's non-statistical arguments.

Abstract

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well-known to Einstein from earlier work on Wien's displacement law, Planck's radiation theory, and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.