Einstein's statistical quantum mechanics

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran +2 more

Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on the historical development of QM attributes the origin of quantum statistics, in particular, Bose-Einstein statistics, to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose-Einstein statistics in the combination of words in large texts, as a consequence of the entanglement created by the meaning carried by words when they combine in human language. Relying on this investigation, we put forward the hypothesis that entanglement, hence the lack of statistical independence, is due to a mechanism of contextual updating, which provides deeper reasons for the appearance of Bose-Einstein statistics in human language. However, this investigation also contributes to a better understanding of the origin of quantum mechanical statistics in physics. Finally, we provide new insights into the intrinsically random behaviour of microscopic entities that is generally assumed within classical statistical mechanics.

R. Shankar

Michael J. Creutz, Barry A. Freedman

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran +2 more

Abstract Identical systems, or ‘entities’, are ‘indistinguishable’ in quantum mechanics (QM), and the ‘symmetrization postulate’ rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis of the historical development of QM attributes the origin of quantum statistics, in particular, ‘Bose–Einstein statistics’, to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose–Einstein statistics in the combination of words in large texts, as a consequence of the ‘entanglement’ created by the meaning carried by words when they combine in human language. Relying on this investigation, we put forward the hypothesis that entanglement, hence the lack of statistical independence, is due to a ‘mechanism of contextual updating’, which provides deeper reasons for the appearance of Bose–Einstein statistics in human language. However, this investigation also contributes to a better understanding of the origin of quantum mechanical statistics in physics. Finally, we provide new insights into the ‘intrinsically random behaviour of microscopic entities’ that is generally assumed within classical statistical mechanics. This article is part of the theme issue ‘Newton, Principia, Newton Geneva Edition (17th–19th) and modern Newtonian mechanics: heritage, past & present’.

B. Freedman. Physics Department

Patrick H. Byrne

Summary Albert Einstein's attitude towards quantum mechanics—and statistical physics in general—was a puzzle to many of his contemporaries, and has remained a puzzle to the present. Though he made many significant contributions to statistical physics, he continually refused to regard that branch of science as fundamental. The present essay demonstrates that his attitude towards statistical physics was formed during his earliest investigations—between 1901 and 1903. In particular, it is shown that in Einstein's view, statistical laws are based upon non-statistical (causal) assumptions. This view influenced much of his later thinking. A few illustrations are offered, concluding with a discussion of his opposition to quantum mechanics.