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

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.

Ladislas Natanson and Alfred Landé versus Planck’s law, the Boltzmann-Planck-Natanson statistics and the Bose statistics

“…Albert Einstein neither quoted Natanson's publications nor discussed them in his correspondence -see Einstein 1916;1917;1930;Einstein, Ehrenfest 1923;Einstein 1987Pérez, Sauer 2010. Nevertheless, Einstein had come across these publications by Natanson on at least two occasions: for the first time during or after the First Solvay Congress in 1911, as it was quoted by Planck 1912, p. 104, fn.…”

Indistinguishable elements in the origins of quantum statistics. The case of Fermi–Dirac statistics

“…Without a doubt, the scientific conditions in Leiden were very good, if we take into account that Fermi coincided with Einstein just when the famous physicist was finishing his paper on the quantum theory of the ideal gas [40]. It is hard to escape the idea that this might have influenced his subsequent contribution to statistics, despite the fact that it took more than a year until its publication.…”

“…That is, in general terms it was still being used as a visualizable and non-problematic notion. Moreover, just as there was an attempt-in Einstein's case-to find an explanation for the lack of statistical independence (in the form of the de Broglie hypothesis, for example [40]), Fermi did not seem to care at all. To broaden our study, we will also consider the first applications of Fermi statistics, to investigate the extent to which it was seen as a revolutionary or puzzling contribution, especially with regard to the individuality of particles.…”

Władysław Natanson i Alfred Landé a prawo Plancka, statystyka Boltzmanna-Plancka-Natansona oraz statystyka Bosego

“…Albert Einstein ani nie cytował publikacji Natansona, ani nie dyskutował ich w swojej korespondencji -zob. Einstein 1916;1917;1930;Einstein, Ehrenfest 1923;Einstein 1987Pérez, Sauer 2010. Tym niemniej Einstein miał co najmniej dwukrotnie okazję natknąć się na tę publikację Natansona: po raz pierwszy podczas lub po I Kongresie Solvaya w 1911 r., gdyż cytował ją Planck 1912, s. 104, fn.…”