Quantum theory and probability theory: Their relationship and origin in symmetry
type: Item
instance of: scholarly article
title: Quantum theory and probability theory: Their relationship and origin in symmetry
zbMATH Open document ID: 1360.81048
author: Philip Goyal
author: Kevin H. Knuth
published in: Symmetry
publication date: 2017-05-12T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 81P16
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 6714440
zbMATH Keywords: quantum theory
zbMATH Keywords: probability theory
zbMATH Keywords: foundations of quantum theory
zbMATH Keywords: foundations of probability theory
MaRDI profile type: Publication
full work available at URL: sym3020171
OpenAlex ID: W2110163460
Wikidata QID: Q59943788
DBLP publication ID: journals/symmetry/GoyalK11
DOI: 10.3390/SYM3020171
description: scientific article; zbMATH DE number 6714440