dorsal/arxiv
View SchemaConsistent Quantum Reasoning
| Authors | Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9505009 |
| URL | https://arxiv.org/abs/quant-ph/9505009 |
Abstract
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system involves a {\it framework}, often chosen implicitly, and a {\it statement} or assertion about the system which is either true or false within the framework with which it is associated. Quantum descriptions are no less ``objective'' than their classical counterparts, but differ from the latter in the following respects: (i) The framework employs a Hilbert space rather than a classical phase space. (ii) The rules for constructing meaningful statements require that the associated projectors commute with each other and, in the case of time-dependent quantum histories, that consistency conditions be satisfied. (iii) There are incompatible frameworks which cannot be combined, either in constructing descriptions or in making logical inferences about them, even though any one of these frameworks may be used separately for describing a particular physical system. A new type of ``generalized history'' is introduced which extends previous proposals by Omn\`es, and Gell-Mann and Hartle, and a corresponding consistency condition which does not involve density matrices or single out a direction of time. Applications which illustrate the formalism include: measurements of spin, two-slit diffraction, and the emergence of the classical world from a fully quantum description.
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"abstract": "Precise rules are developed in order to formalize the reasoning processes\ninvolved in standard non-relativistic quantum mechanics, with the help of\nanalogies from classical physics. A classical or quantum description of a\nmechanical system involves a {\\it framework}, often chosen implicitly, and a\n{\\it statement} or assertion about the system which is either true or false\nwithin the framework with which it is associated. Quantum descriptions are no\nless ``objective\u0027\u0027 than their classical counterparts, but differ from the\nlatter in the following respects: (i) The framework employs a Hilbert space\nrather than a classical phase space. (ii) The rules for constructing meaningful\nstatements require that the associated projectors commute with each other and,\nin the case of time-dependent quantum histories, that consistency conditions be\nsatisfied. (iii) There are incompatible frameworks which cannot be combined,\neither in constructing descriptions or in making logical inferences about them,\neven though any one of these frameworks may be used separately for describing a\nparticular physical system.\n A new type of ``generalized history\u0027\u0027 is introduced which extends previous\nproposals by Omn\\`es, and Gell-Mann and Hartle, and a corresponding consistency\ncondition which does not involve density matrices or single out a direction of\ntime. Applications which illustrate the formalism include: measurements of\nspin, two-slit diffraction, and the emergence of the classical world from a\nfully quantum description.",
"arxiv_id": "quant-ph/9505009",
"authors": [
"Robert B. Griffiths"
],
"categories": [
"quant-ph"
],
"title": "Consistent Quantum Reasoning",
"url": "https://arxiv.org/abs/quant-ph/9505009"
},
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