dorsal/arxiv
View SchemaConsistent Histories and Quantum Reasoning
| Authors | Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9606004 |
| URL | https://arxiv.org/abs/quant-ph/9606004 |
| DOI | 10.1103/PhysRevA.54.2759 |
Abstract
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity operator on a Hilbert space of histories. Provided a consistency condition is satisfied, the corresponding Boolean algebra of histories, called a {\it framework}, can be assigned probabilities in the usual way, and within a single framework quantum reasoning is identical to ordinary probabilistic reasoning. A refinement rule, which allows a probability distribution to be extended from one framework to a larger (refined) framework, incorporates the dynamical laws of quantum theory. Two or more frameworks which are incompatible because they possess no common refinement cannot be simultaneously employed to describe a single physical system.
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"abstract": "A system of quantum reasoning for a closed system is developed by treating\nnon-relativistic quantum mechanics as a stochastic theory. The sample space\ncorresponds to a decomposition, as a sum of orthogonal projectors, of the\nidentity operator on a Hilbert space of histories. Provided a consistency\ncondition is satisfied, the corresponding Boolean algebra of histories, called\na {\\it framework}, can be assigned probabilities in the usual way, and within a\nsingle framework quantum reasoning is identical to ordinary probabilistic\nreasoning. A refinement rule, which allows a probability distribution to be\nextended from one framework to a larger (refined) framework, incorporates the\ndynamical laws of quantum theory. Two or more frameworks which are incompatible\nbecause they possess no common refinement cannot be simultaneously employed to\ndescribe a single physical system.",
"arxiv_id": "quant-ph/9606004",
"authors": [
"Robert B. Griffiths"
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"doi": "10.1103/PhysRevA.54.2759",
"title": "Consistent Histories and Quantum Reasoning",
"url": "https://arxiv.org/abs/quant-ph/9606004"
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