Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applications of Mathematics

On generalized localizability

Václav Alda

Published Jan 1, 1973• 14 citations
Publisher

Abstract

It is shown that the definition of generalized localizability, as given by Jauch and Piron, can be justified by direct arguments. A theorem, similar to that of Neumark on representation of POV - measures, is demonstrated for classical systems.
DOI
10.21136/am.1973.103445

Related papers

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

Zbigniew Banach, S?awomir Piekarski

International Journal of Theoretical Physics•Jan 1, 1993•1 citation

Localizability in the Hamiltonian formalism and in quantum-mechanics

R. D. Grigore

Unknow•Jan 1, 1989•0 citations

On the Localizability of Quantum Mechanical Systems

Arthur S. Wightman

From the very beginning of quantum mechanics, the notion of the position of a particle has been much discussed. In the nonrelativistic case, the proof of the equivalence of matrix and wave mechanics, the discovery of the uncertainty relations, and the development of the statistical interpretation of the theory led to an understanding which, within the inevitable limitations of the nonrelativistic theory, may be regarded as completely satisfactory.

Reviews of Modern Physics•Oct 1, 1962•417 citations

Neumark operators and sharp reconstructions: The finite dimensional case

Roberto Beneduci

A commutative positive operator valued (POV) measure F with real spectrum is characterized by the existence of a projection valued measure E (the sharp reconstruction of F) with real spectrum such that F can be interpreted as a randomization of E. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark’s extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of F and the sharp reconstruction of F. The relevance of this result to the theory of nonideal quantum measurement and to the definition of unsharpness is analyzed.

arXiv:1005.2955•Journal of Mathematical Physics•Feb 1, 2007•15 citations

A Refutation of the Proof by Jauch and Piron that Hidden Variables Can be Excluded in Quantum Mechanics

David Böhm, Jeffrey Bub

In this paper, we examine an argument of Jauch and Piron, which aims to prove the impossibility of hidden variables underlying the quantum theory, on the basis of certain assumptions that are weaker than those used by von Neumann for the same purpose. We show that, while the assumptions of Jauch and Piron are in fact weaker than those of von Neumann, the net result is that they actually prove nothing new at all. The conclusions of Jauch and Piron concerning the nonexistence of hidden variables are indeed seen to follow from a false assumption; i.e., that the impossibility of propositions that describe simultaneously the results of measurements of two noncommuting observables is an "empirical fact." Actually, it is shown that this assumption follows if and only if one first assumes what the authors set out to prove; i.e., that the current linguistic structure of quantum mechanics is the only one that can be used correctly to describe the empirical facts underlying the theory.

Reviews of Modern Physics•Jul 1, 1966•89 citations

The Generalized Representation of Particle Localization in Quantum Mechanics

G.F. Melloy

Foundations of Physics•Apr 1, 2002•4 citations
A commutative positive operator valued (POV) measure F with real spectrum is characterized by the existence of a projection valued measure E (the sharp reconstruction of F) with real spectrum such that F can be interpreted as a randomization of E. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark’s extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of F and the sharp reconstruction of F. The relevance of this result to the theory of nonideal quantum measurement and to the definition of unsharpness is analyzed.
In this paper, we examine an argument of Jauch and Piron, which aims to prove the impossibility of hidden variables underlying the quantum theory, on the basis of certain assumptions that are weaker than those used by von Neumann for the same purpose. We show that, while the assumptions of Jauch and Piron are in fact weaker than those of von Neumann, the net result is that they actually prove nothing new at all. The conclusions of Jauch and Piron concerning the nonexistence of hidden variables are indeed seen to follow from a false assumption; i.e., that the impossibility of propositions that describe simultaneously the results of measurements of two noncommuting observables is an "empirical fact." Actually, it is shown that this assumption follows if and only if one first assumes what the authors set out to prove; i.e., that the current linguistic structure of quantum mechanics is the only one that can be used correctly to describe the empirical facts underlying the theory.