Einstein’s quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics |
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Authors: | Enric Pérez Tilman Sauer |
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Institution: | 1. Departament de Física Fonamental, Universitat de Barcelona, c. Martí i Franquès 1, 08028, Barcelona, Spain 2. Einstein Papers Projects, Caltech 20-7, Pasadena, CA, 91125, USA
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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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