arXiv:0712.1634

Quantum Observables and a Model of Noncommutativity

Tung Ten Yong

Published Dec 11, 2007• 0 citations

Abstract

This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically. Unlike quantum systems, the basic entities in this model have definite properties. Relations with no-go theorems and other hidden variable theories are also discussed.

DOI: 10.48550/arxiv.0712.1634

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The article gives an introductory summary of our recent results from the perspective of the new conceptual notion of noncommutative values of quantum observables, where basic quantum mechanics is seen a theory of particle dynamics that is intrinsically noncommutative.Real numbers as an algebra is really an abstract mathematical model for the description of values of physical quantities.Quantum mechanics illustrates the limitation of that perspective.The noncommutative values preserve the algebraic relations among the observables in their values.Such a value contains the complete information the theory presents for an observable on a given state.All physical quantities, including coordinates of the physical space for describing the location of a particle take definite noncommutative values.

AAPPS bulletinFeb 8, 20220 citations

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