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

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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 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.

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Abbreviations

AEA:

Albert Einstein Archives, The Hebrew University of Jerusalem, Israel Unpublished correspondence quoted by permission

AHQP:

Archive for History of Quantum Physics For a catalogue, see Kuhn et al. (1967)

EHA:

Ehrenfest Archive, Rijksarchief voor de Geschiedenis van de Natuurwetenschappen en van Geneeskunde, Leiden, Netherlands For a catalogue, see Wheaton (1977) We quote from the microfilm version included in the AHQP

HPE:

Huisbibliotheek van Paul Ehrenfest, Institut Lorentz, Leiden, Netherlands

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  1. Departament de Física Fonamental, Universitat de Barcelona, c. Martí i Franquès 1, 08028, Barcelona, Spain

    Enric Pérez

  2. Einstein Papers Projects, Caltech 20-7, Pasadena, CA, 91125, USA

    Tilman Sauer

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Pérez, E., Sauer, T. Einstein’s quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics. Arch. Hist. Exact Sci. 64, 561–612 (2010). https://doi.org/10.1007/s00407-010-0066-x

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