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Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry
Department of Physics, University at Albany (SUNY), 1400 Washington Avenue, Albany, NY 12222, USA
Departments of Physics and Informatics, University at Albany (SUNY), 1400 Washington Avenue, Albany, NY 12222, USA
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Received: 9 March 2011; in revised form: 6 April 2011 / Accepted: 12 April 2011 / Published: 27 April 2011
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.
Keywords: quantum theory; probability theory; foundations of quantum theory; foundations of probability theory
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MDPI and ACS Style
Goyal, P.; Knuth, K.H. Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry. Symmetry 2011, 3, 171-206.
Goyal P, Knuth KH. Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry. Symmetry. 2011; 3(2):171-206.
Goyal, Philip; Knuth, Kevin H. 2011. "Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry." Symmetry 3, no. 2: 171-206.