A Caltech Library Service

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

Pérez, Enric and Sauer, Tilman (2010) Einstein’s quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics. Archive for History of Exact Sciences, 64 (5). pp. 561-612. ISSN 0003-9519.

[img] PDF - Published Version
Restricted to Repository administrators only
See Usage Policy.


Use this Persistent URL to link to this item:


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 came 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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 2010 Springer-Verlag. Received: 30 April 2010; Published online: 16 July 2010. Communicated by Tilman Sauer. We thank Luis Navarro for reading an early version of the manuscript and making interesting comments on it. The focus of our attention on the third paper by Einstein on the quantum ideal gas, is due to his suggestion. Conversations with Pere Seglar have also helped very much in elucidating some statistical (and non-statistical) points discussed in this paper. T.S. thanks the Max Planck Institut for the History of Science and its history of quantum physics group for their hospitality in the summer 2009.
Issue or Number:5
Record Number:CaltechAUTHORS:20101108-100826026
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20711
Deposited By: Jason Perez
Deposited On:08 Nov 2010 21:35
Last Modified:03 Oct 2019 02:13

Repository Staff Only: item control page