Quantum Logic and Probability Theory
##plugins.themes.bootstrap3.article.sidebar##
Published:
05.10.2017
##plugins.themes.bootstrap3.article.main##
Abstract
The paper provides the review of the texts on quantum logic, the texts which are directly connected with the mathematical foundations of quantum mechanics. These are texts which discuss the theory of quantum probability. The development of the mathematical scheme of quantum mechanics is discussed along the following line: P.A.M. Dirack’s 1927 “The Principles of Quantum Mechanics”, J. von Neumann’s 1932 “Mathematische Grundlagen der Quantenmechanik”, G.Birkgoff-I.von Neumann’s 1936 “The logic of quantum mechanics”. It is shown that the further development of the mathematical foundations of quantum mechanics resulted in the construction of quantum theory of probability, the theory generalizing A.N.Kolmogorov’s classicalprobability and critically improving von Neumann’s 1932 mathematical scheme. DOI: 10.21146/2074-1472-2017-23-2-123-139
##plugins.generic.usageStats.downloads##
##plugins.generic.usageStats.noStats##
##plugins.themes.bootstrap3.article.details##
How to Cite
Pechenkin A. A. Quantum Logic and Probability Theory // Logicheskie Issledovaniya / Logical Investigations. 2017. VOL. 23. № 2. C. 123-139.
Issue
Section
Papers
References
Васюков В.Л. Квантовая логика. M.: ПЕР СЭ, 2005. 192 c.
Колмогоров А.Н. Основные понятия теории вероятностей. М.: ОНТИ, 1936. 120 c.
Гейзенберг В. Физика и философия. М.: Наука, 1963. 464 c.
Гнеденко В.Б. Курс теории вероятностей. М.: Наука, 1976. 448 с.
Дирак П.А.М Принципы квантовой механики. М.: Наука, 1979. 278 с.
фон Нейманн И. Математические основы квантовой механики. М.: Наука, 1964. 367 c.
Печенкин А.А. Обоснование научной теории: классика и современность. М.: Наука, 1991, 184 c.
Шредингер Э. Избранные труды по квантовой механике. М.: Мир, 1980, 420 с.
Birkhoff G., Neumann J. The Logic of Quantum Mechanics // Annals of Mathematics. 1936. Vol. 37. No. 4. P. 823–843.
van Fraassen B.C. The labyrinth of quantum logics // Boston Studies in the Philosophy of Science / R.S. Cohen and M.W. Vastovsky (eds.). Dordrehct: Reidel Publishing Company, 1972. Vol. 13. P. 224–254.
Hanson N.R. The concepr of positron. Сambridge: Cambr. Univ. Press, 1965. 236 p.
Hooker C. The logico-algebraic approach to quantum mechanics. Dordrehct: Reidel Publishing Company, 1975. 469 p.
Jammer M. The conceptual development of quantum mechanics. N. Y.: Wiley, 1966. 308 p.
Redei M. John von Neumann on mathematical and axiomatic physics // The role of mathematics in physical sciences / Ed by G.Boniolo et. al. Netherlands: Springer, 2005. P. 43–52.
Redei M. Von Neumann’s concept of quantum logic and quantum probability // John von Neumann and the Foundations of Quantum Physics / Ed. by M. Redei, M. Stotzner. Netherlands: Springer, 2001. 464 p.
Wilce A. Quantum logic and probability theory // Stanford encyclopedia of philosophy. 2002. Substantive revision – 2017. URL: https://plato.stanford.edu/entries/qt-quantlog (дата обращения: 30.08.2017).
Колмогоров А.Н. Основные понятия теории вероятностей. М.: ОНТИ, 1936. 120 c.
Гейзенберг В. Физика и философия. М.: Наука, 1963. 464 c.
Гнеденко В.Б. Курс теории вероятностей. М.: Наука, 1976. 448 с.
Дирак П.А.М Принципы квантовой механики. М.: Наука, 1979. 278 с.
фон Нейманн И. Математические основы квантовой механики. М.: Наука, 1964. 367 c.
Печенкин А.А. Обоснование научной теории: классика и современность. М.: Наука, 1991, 184 c.
Шредингер Э. Избранные труды по квантовой механике. М.: Мир, 1980, 420 с.
Birkhoff G., Neumann J. The Logic of Quantum Mechanics // Annals of Mathematics. 1936. Vol. 37. No. 4. P. 823–843.
van Fraassen B.C. The labyrinth of quantum logics // Boston Studies in the Philosophy of Science / R.S. Cohen and M.W. Vastovsky (eds.). Dordrehct: Reidel Publishing Company, 1972. Vol. 13. P. 224–254.
Hanson N.R. The concepr of positron. Сambridge: Cambr. Univ. Press, 1965. 236 p.
Hooker C. The logico-algebraic approach to quantum mechanics. Dordrehct: Reidel Publishing Company, 1975. 469 p.
Jammer M. The conceptual development of quantum mechanics. N. Y.: Wiley, 1966. 308 p.
Redei M. John von Neumann on mathematical and axiomatic physics // The role of mathematics in physical sciences / Ed by G.Boniolo et. al. Netherlands: Springer, 2005. P. 43–52.
Redei M. Von Neumann’s concept of quantum logic and quantum probability // John von Neumann and the Foundations of Quantum Physics / Ed. by M. Redei, M. Stotzner. Netherlands: Springer, 2001. 464 p.
Wilce A. Quantum logic and probability theory // Stanford encyclopedia of philosophy. 2002. Substantive revision – 2017. URL: https://plato.stanford.edu/entries/qt-quantlog (дата обращения: 30.08.2017).