Abstract
In the first part of this paper it is shown how EPR-situations are correlated with von Neumann's standard form of quantum mechanical states describing a system consisting of two dynamical independent subsystems. These standard forms are the mathematical tools for a proof of a conjecture of E. Scheibe: If the 4 selfadjoint operators in Bell's — inequality are pairwise EPR — related, then this inequality is valid in the strong form (with the same upper bound as in statistical mechanics). In the last section the question is discussed whether observations made on the two subsystems together with EPR-relations between them, determine the state of the composed system.
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Short notation according to the Gedanken-Experiment of Einstein, Podolsky and Rosen
von Neumann, J. Mathematische Grundlagen der Quantenmeckanik VI, 2
Scheibe, E.: Von Neumann's und Bell's Theorem. Ein Vergleich. Philosophia naturalis, Band28 (1991), Heft 1, p. 35
Scheibe, E.: EPR-situation and Bell's inequality. In: Existence and Explanation. Spohn, W. et al. (eds.) Dordrecht, 1991, pp. 115–129
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Communicated by H. Araki
Retired, however for a time back at
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Schlieder, S. EPR-relations, von Neumann's standard forms and a proof concerning a conjecture of E. Scheibe. Commun.Math. Phys. 169, 589–596 (1995). https://doi.org/10.1007/BF02099313
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DOI: https://doi.org/10.1007/BF02099313