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Einstein-Podolsky-Rosen experiments: the structure of the probability space. I

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Foundations of Physics Letters

Abstract

Incompatibility of measurements, central to quantum mechanics, is captured in the formalism of empirical logic, which is based on a generalization of the notion of a sample space in Kolmogoroff's axiomatic theory of probability. In composite empirical systems of the kind considered in the Einstein-Podolsky-RosenGedankenexperiment, incompatibility gives rise to the notion of influence, which is closely related to stochastic independence.

These concepts are used to study the methodological structure of a large class of Einstein-Podolsky-Rosen type experiments, linking a series of much debated issues such as scientific Realism, ontological and epistemic uncertainty, determinism, locality, separability, factorizability, completeness, conservation, correlation, Bell-Clauser-Horne inequalities, and hidden-variables models to an axiomatic probability theory.

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Authors and Affiliations

  1. Institute for Mathematical Studies in the Social Sciences, Stanford University, 94305, Stanford, California, USA

    Matthias P. Kläy

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1. My translation. Fine infers a missing “not” in the first part of the sentence and translates “I can not reconcile myself to the following, that a manipulation undertaken on A has an influence on B...”. I do not dispute that Einstein could not reconcile himself with such a postulate of influence, and thus I agree with Fine's comments on this sentence. However, the German original needs no negation if one surmises that Einstein writes about the consequences of ahypothesis of influence.

2. The quasimanualAB consists of all subsets ofXY of the form ⋃ x∈E xF x, whereE ∈A andF x ∈B for allx ∈E can be chosen in all possible ways, together with the symmetrical subsets ofXY, where the rôle ofA andB is exchanged. See Refs. [22,43,55] for the technical details.

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Kläy, M.P. Einstein-Podolsky-Rosen experiments: the structure of the probability space. I. Found Phys Lett 1, 205–244 (1988). https://doi.org/10.1007/BF00690066

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