Reformulation of the Hidden Variable Problem Using Entropic Measure of Uncertainty

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()...

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Bibliographic Details
Published in:Synthese (Dordrecht) 1987-11, Vol.73 (2), p.371-379
Main Author: REDEI, M
Format: Article
Language:English
Subjects:
Algebra
Entropy
Epistemology. Philosophy of science. Theory of knowledge
Hidden variables
Homomorphisms
Linear transformations
Observational research
Philosophy
Physical theory
Physics
Quantum mechanics
Von Neumann algebra
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Summary:Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states φ ε E(A) the composite state φ ° L ε E() can be obtained as an average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of φ. It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L.
ISSN:0039-7857
1573-0964
DOI:10.1007/BF00484748