David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy of Science 35 (2):101-111 (1968)
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
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Citations of this work BETA
Arthur Fine (1974). On the Completeness of Quantum Theory. Synthese 29 (1-4):257 - 289.
Soazig Le Bihan (2009). Fine's Ways to Fail to Secure Local Realism. Studies in the History and Philosophy of Modern Physics 40 (2):142-150.
Richard Schlegel (1970). Statistical Explanation in Physics: The Copenhagen Interpretation. Synthese 21 (1):65 - 82.
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