Methodological notes

The tree of paradox

Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

The specific nature of the randomness arising when quantum subsystems interact (collide) is analyzed. It is shown that the Birkhoff–Khinchin ergodic theorem—the key theorem for classical statistics—or its analog is absent, in principle, in the quantum theory. Thus quantum probabilities cannot be defined within the ergodic concept. A metric definition of probability, based on von Neumann's theory of measurement, is proposed as a measure of comparison of a posteriori physical situation with the a priori situation. The workability of the adopted approach is demonstrated for random walk problems and the theory of thermal equilibrium.

PACS: 03.65.Ud, 03.65.Ta, 05.40.Fb (all)
DOI: 10.1070/PU1993v036n08ABEH002302
Citation: Mityugov V V "The tree of paradox" Phys. Usp. 36 (8) 744–753 (1993)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Митюгов В В «Дерево парадокса» УФН 163 (8) 103–114 (1993); DOI: 10.3367/UFNr.0163.199308d.0103

© 1918–2023 Uspekhi Fizicheskikh Nauk
Email: Editorial office contacts About the journal Terms and conditions