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Logic, Probability, and Quantum Theory

Published online by Cambridge University Press:  14 March 2022

Arthur I. Fine
Arthur I. Fine*
Affiliation:
Cornell University
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Abstract

The aim of this paper is to present and discuss a probabilistic framework that is adequate for the formulation of quantum theory and faithful to its applications. Contrary to claims, which are examined and rebutted, that quantum theory employs a nonclassical probability theory based on a nonclassical “logic,” the probabilistic framework set out here is entirely classical and the “logic” used is Boolean. The framework consists of a set of states and a set of quantities that are interrelated in a specified manner. Each state induces a classical probability space on the values of each quantity. The quantities, so considered, become statistical variables (not random variables). Such variables need not have a “joint distribution.” For the quantum theoretic application, there is a uniform procedure that defines and determines the existence of such “joint distributions” for statistical variables. A general rule is provided and it is shown to lead to the usual compatibility-commutivity requirements of quantum theory. The paper concludes with a brief discussion of interference and the misunderstandings that are involved in the false move from interference to nonclassical probability.

Type
Research Article
Information
Philosophy of Science , Volume 35 , Issue 2 , June 1968 , pp. 101 - 111
Copyright
Copyright © 1968 The Philosophy of Science Association

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