Consistent histories and quantum reasoning

Robert B. Griffiths
Phys. Rev. A 54, 2759 – Published 1 October 1996
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Abstract

A system of quantum reasoning for a closed system is developed by treating nonrelativistic 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 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. Logical reasoning is a special case of probabilistic reasoning in which (conditional) probabilities are 1 (true) or 0 (false). As probabilities are only meaningful relative to some framework, the same is true of the truth or falsity of a quantum description. The formalism is illustrated using simple examples, and the physical considerations which determine the choice of a framework are discussed. © 1996 The American Physical Society.

  • Received 12 June 1996

DOI:https://doi.org/10.1103/PhysRevA.54.2759

©1996 American Physical Society

Authors & Affiliations

Robert B. Griffiths

  • Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

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Issue

Vol. 54, Iss. 4 — October 1996

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