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Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry

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Author(s): Philip Goyal | Kevin H. Knuth

Journal: Symmetry
ISSN 2073-8994

Volume: 3;
Issue: 2;
Start page: 171;
Date: 2011;
Original page

Keywords: quantum theory | probability theory | foundations of quantum theory | foundations of probability theory

ABSTRACT
Quantum theory is a probabilistic calculus that enables the calculation of the probabilities of the possible outcomes of a measurement performed on a physical system. But what is the relationship between this probabilistic calculus and probability theory itself? Is quantum theory compatible with probability theory? If so, does it extend or generalize probability theory? In this paper, we answer these questions, and precisely determine the relationship between quantum theory and probability theory, by explicitly deriving both theories from first principles. In both cases, the derivation depends upon identifying and harnessing the appropriate symmetries that are operative in each domain. We prove, for example, that quantum theory is compatible with probability theory by explicitly deriving quantum theory on the assumption that probability theory is generally valid.
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