Paul Ehrenfest on the Necessity of Quanta (1911): Discontinuity, Quantization, Corpuscularity, and Adiabatic Invariance

Sauer

2010

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.

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Section: A Displacement Law For Gasesmentioning

confidence: 95%

“…xlii-xlvi).136 See section 5 above.137(Krutkow 1914a),(Krutkow 1914b). 138(Klein 1985),(Navarro andPérez 2004, Navarro andPérez 2006).…”

unclassified

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

Sauer

2010

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“…He was especially interested in searching for adiabatic invariants, that is, mechanical quantities in different mechanical systems that remain constant under an adiabatic transformation; he also frequently highlighted their possible relativistic invariance. 59 At the same time, it seems that EHRENFEST began to suspect that a theorem of SZILY might provide a new route to extend the quantum theory to more general systems than those that he had treated by a new and suitable use of adiabatic invariants. 60 EHRENFEST gave two different, but closely related applications of adiabatic transformations in his paper: the determination of the possible rotational motions of a dipole (mechanics) and that of the corresponding allowed regions in phase space (statistical mechanics).…”

Section: Toward An Adiabatic Hypothesismentioning

confidence: 99%

Paul Ehrenfest: The Genesis of the Adiabatic Hypothesis, 1911–1914

Navarro

2006

Self Cite

“…Ehrenfest (1913a). On Ehrenfest's adiabatic hypothesis seeKlein (1970),Navarro & Pérez (2004),Navarro & Pérez (2006),Pérez (2009).3Ehrenfest (1913b).4 Ehrenfest(1914, 1916). With 'Boltzmann's principle' we are referring to the known relation between entropy and probability postulated by Boltzmann.5 Ehrenfest toSommerfeld, April/May 1916.…”

mentioning

confidence: 99%

Ehrenfest’s adiabatic hypothesis and the old quantum theory, 1916–1918

2008