×

zbMATH — the first resource for mathematics

A histories approach to quantum mechanics. (English) Zbl 0935.81005
Summary: A histories approach to quantum mechanics is formulated without the consistency requirement. Plausible, physically motivated axioms for a history structure are presented. In this structure, the consistency requirement is unnecessary because the joint sequential distributions are already probability measures. It is shown that the logic of a history structure is a temporal effect algebra and conversely, any temporal effect algebra is isomorphic to the logic of a history structure. When this general framework is specialized to a Hilbert space context, it reduces to a previously studied formalism.

MSC:
81P05 General and philosophical questions in quantum theory
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1063/1.532348 · Zbl 0916.03042
[2] DOI: 10.1103/PhysRevD.47.3345
[3] DOI: 10.1119/1.14965
[4] DOI: 10.1119/1.14965
[5] DOI: 10.1119/1.14965
[6] DOI: 10.1063/1.530544 · Zbl 0814.03040
[7] DOI: 10.1063/1.531267 · Zbl 0882.46031
[8] DOI: 10.1063/1.531267 · Zbl 0882.46031
[9] DOI: 10.1016/0003-4916(90)90045-P
[10] DOI: 10.1016/0003-4916(90)90045-P
[11] DOI: 10.1016/0003-4916(90)90045-P
[12] DOI: 10.1016/0003-4916(90)90045-P
[13] DOI: 10.1016/0003-4916(90)90045-P
[14] DOI: 10.1016/0003-4916(90)90045-P
[15] DOI: 10.1063/1.531709 · Zbl 0861.03047
[16] DOI: 10.1063/1.531709 · Zbl 0861.03047
[17] DOI: 10.1007/BF00672802 · Zbl 0832.03029
[18] DOI: 10.1090/S0002-9947-1995-1249874-8
[19] DOI: 10.1007/BF00672820 · Zbl 0806.03040
[20] DOI: 10.1007/BF02283036 · Zbl 1213.06004
[21] DOI: 10.1007/BF02058635
[22] DOI: 10.1007/BF02058635
[23] Kôpka F., Tatra Mountain Math. Publ. 1 pp 83– (1992)
[24] Kôpka F., Math. Slovaca 44 pp 21– (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.