Logique quantique
Pour les articles homonymes, voir Logique (homonymie) et Quantique.
La logique quantique est la base de raisonnements et conclusions en accord avec les postulats de la mécanique quantique. En particulier, les observables n'étant pas forcément commutatives, le théorème d'Heisenberg (cf. principe d'incertitude) entraîne la notion d'intricats, notion purement quantique comme l'illustre le célèbre paradoxe du chat de Schrödinger.
John von Neumann a montré, en réfléchissant aux fondations de la mécanique quantique, que la logique d'Aristote (cf. Organon) était en contradiction avec la logique quantique. En particulier, la notion du tiers exclu n'existe pas en logique quantique. George Mackey, puis Veeraualli Seshadri Varadarajan ont développé ces réflexions.
Voir aussi
Bibliographie
- John von Neumann : mathematical foundations of Q M ; Princeton, 1955.
- Mackey : idem ; Benjamn, 1963.
- Varadarajan : geometry of Q theory. van Nostrand, 1968.
- Kitaev : classical & quantum computation ; AMS47, 2002.
- Hirvensalo : Q computing, springerV, 2001.
- Alain Connes : non-commutative geometry, springerV1831, 2004.
- G. Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, vol 37, 1936.
- D. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer-Verlag, 1989. This is a thorough but elementary and well-illustrated introduction, suitable for advanced undergraduates.
- D. Finkelstein, Matter, Space and Logic, Boston Studies in the Philosophy of Science vol V, 1969
- A. Gleason, Measures on the Closed Subspaces of a Hilbert Space, Journal of Mathematics and Mechanics, 1957.
- R. Kadison, Isometries of Operator Algebras, Annals of Mathematics, vol 54 pp 325-338, 1951
- G. Ludwig, Mathematical Foundations of Quantum Mechanics, Springer-Verlag, 1983.
- G. Mackey, Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, 1963 (paperback reprint by Dover 2004).
- J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955. Reprinted in paperback form.
- R. Omnès, Understanding Quantum Mechanics, Princeton University Press, 1999. An extraordinarily lucid discussion of some logical and philosophical issues of quantum mechanics, with careful attention to the history of the subject. Also discusses consistent histories.
- C. Piron, Foundations of Quantum Physics, W. A. Benjamin, 1976.
- H. Putnam, Is Logic Empirical, Boston Studies in the Philosophy of Science vol. V, 1969
- Hermann Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications, 1950.
Liens externes
- Ressources relatives à la recherche :
- Notice dans un dictionnaire ou une encyclopédie généraliste :
Notes et références
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