Next Article in Journal
Visual Discrimination of the 17 Plane Symmetry Groups
Next Article in Special Issue
Is the Notion of Time Really Fundamental?
Previous Article in Journal
Facile and Convenient One-Pot Process for the Synthesis of Spirooxindole Derivatives in High Optical Purity Using (−)-(S)-Brevicolline as an Organocatalyst
Previous Article in Special Issue
Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?
Article Menu

Article Versions

Export Article

Open AccessArticle
Symmetry 2011, 3(2), 171-206; doi:10.3390/sym3020171

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

1
Department of Physics, University at Albany (SUNY), 1400 Washington Avenue, Albany, NY 12222, USA
2
Departments of Physics and Informatics, University at Albany (SUNY), 1400 Washington Avenue, Albany, NY 12222, USA
*
Author to whom correspondence should be addressed.
Received: 9 March 2011 / Revised: 6 April 2011 / Accepted: 12 April 2011 / Published: 27 April 2011
(This article belongs to the Special Issue Quantum Symmetry)
Download PDF [658 KB, 3 May 2011; original version 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 quantum theory; probability theory; foundations of quantum theory; foundations of probability theory
Figures

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

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.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top