Time and quantum theory: A history and a prospectus
The historical part of this paper analyzes in detail how ideas and expectations regarding the role of time in quantum theory arose and evolved in the early years of quantum mechanics (from 1925 to 1927). The general theme is that expectations which seemed reasonable from the point of view of matrix...
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| Published in | Studies in History and Philosophy of Modern Physics Vol. 52; pp. 24 - 38 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.11.2015
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| Online Access | Get full text |
| ISSN | 1355-2198 1879-2502 |
| DOI | 10.1016/j.shpsb.2015.03.002 |
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| Abstract | The historical part of this paper analyzes in detail how ideas and expectations regarding the role of time in quantum theory arose and evolved in the early years of quantum mechanics (from 1925 to 1927). The general theme is that expectations which seemed reasonable from the point of view of matrix mechanics and Dirac׳s q-number formalism became implausible in light of Dirac–Jordan transformation theory, and were dashed by von Neumann׳s Hilbert space formalism which came to replace it. Nonetheless, I will identify two concerns that remain relevant today, and which blunt the force of Hilgevoord׳s (2005) claim that the demand that time feature as an observable arose as the result of a simple conceptual error. First, I advocate the need for event time observables, which provide a temporal probability distribution for the occurrence of a particular event. Second, I claim that Dirac׳s use of the extended phase space to define time and (minus the) energy as conjugates is not subject to ‘Pauli׳s Theorem,’ the result that rules out time observables in von Neumann׳s formalism. I also claim that the need to define these event time observables leads to a novel motivation for considering Dirac׳s extended state space. |
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| AbstractList | The historical part of this paper analyzes in detail how ideas and expectations regarding the role of time in quantum theory arose and evolved in the early years of quantum mechanics (from 1925 to 1927). The general theme is that expectations which seemed reasonable from the point of view of matrix mechanics and Dirac׳s q-number formalism became implausible in light of Dirac–Jordan transformation theory, and were dashed by von Neumann׳s Hilbert space formalism which came to replace it. Nonetheless, I will identify two concerns that remain relevant today, and which blunt the force of Hilgevoord׳s (2005) claim that the demand that time feature as an observable arose as the result of a simple conceptual error. First, I advocate the need for event time observables, which provide a temporal probability distribution for the occurrence of a particular event. Second, I claim that Dirac׳s use of the extended phase space to define time and (minus the) energy as conjugates is not subject to ‘Pauli׳s Theorem,’ the result that rules out time observables in von Neumann׳s formalism. I also claim that the need to define these event time observables leads to a novel motivation for considering Dirac׳s extended state space. |
| Author | Pashby, Thomas |
| Author_xml | – sequence: 1 givenname: Thomas surname: Pashby fullname: Pashby, Thomas email: pashby@usc.edu, tom.pashby@gmail.com organization: School of Philosophy, University of Southern California, Mudd Hall of Philosophy, 3709 Trousdale Parkway, Los Angeles CA 90089-0451, United States |
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| CitedBy_id | crossref_primary_10_1103_PhysRevA_95_042108 crossref_primary_10_1515_phys_2019_0045 crossref_primary_10_1016_j_shpsb_2019_10_002 crossref_primary_10_1063_1_5051800 |
| Cites_doi | 10.1007/BF01328531 10.1007/s10701-009-9400-z 10.1016/j.shpsb.2009.06.007 10.1007/BF02435757 10.1103/PhysRevA.61.012104 10.1103/PhysRev.139.B684 10.1140/epjh/e2012-30024-5 10.1016/0920-5632(89)90447-7 10.1016/0003-4916(69)90251-6 10.1098/rspa.1927.0012 10.1088/1751-8113/43/50/505303 10.1007/BF01328377 10.1103/PhysRev.122.1649 10.1063/1.527184 10.1103/RevModPhys.34.845 10.1016/S0370-1573(00)00047-8 10.1016/j.shpsb.2004.10.002 10.1098/rspa.1926.0074 10.1007/BF01379806 10.1098/rspa.2001.0874 10.1098/rspa.1925.0150 10.1103/PhysRevD.40.2598 10.3367/UFNe.0181.201108d.0859 10.1119/1.18410 10.1063/1.1665388 10.1007/BF01397280 10.1007/BF00400979 10.1119/1.1430697 10.1016/S0034-4877(74)80004-2 10.1007/s00016-006-0276-4 10.1063/1.533050 10.1007/BF02848181 10.1098/rspa.1926.0133 10.1103/PhysRevA.66.044101 |
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