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By F. J. Belinfante

A Survey of Hidden-Variables Theories is a three-part publication at the hidden-variable theories, referred during this publication as ""theories of the 1st kind"". half I studies the explanations in constructing forms of hidden-variables theories. the search for determinism ended in theories of the 1st sort; the hunt for theories that appear like causal theories whilst utilized to spatially separated platforms that interacted long ago ended in theories of the second one style. elements II and III extra describe the theories of the 1st style and moment type, respectively.
This booklet is written to make the literature on hidden variables understandable to people who are pressured via the unique papers with their controversies, and to usual reader of physics papers.

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59). In terms of the K/5 this paradox amounted to the following. In a three-dimensional space (N = 3) for a given hidden-variables state (tp, I), let a function v(h) of the variable unit vector h be given with the following properties : (a) Every v(h) is either 1 or 0; (b) For any orthogonal set {w(/>}, with 1 <: i ^ N9 let £ Ü(Ä<'>) = 1, (61a) (61b) so that for N = 3 for each triad {h{i)} one of the three v(h{i)) will be = 1, and the other two v(h(i)) will be zero. 3 that it is impossible that v will depend on n only.

For which ν(φη) = 0, there must exist other φ for which this function has values between 0 and 1. This contradicts our initial assumption that ν(φη) would be a truth value always equal to 0 or 1. This suffices to prove the impossibility of defining, in a Hilbert space of three or more dimensions, any truth values ν(φη) independent of the {φ^ that would satisfy (61a, b). In other words, we have here another proof of the Kochen-Specker paradox. As Gleason's proof of his lemma (70) is somewhat messy, we do not give it here.

Our first and least fundamental objection against von Neumann's presentation is that he simply tries to put Uop equal to the sum of density operators for the ensembles of hiddenvariables states that together are supposed to make op Εψ. This inconsistency is easily reme­ died. , we should remember that all density operators are normalized, in order that by (20) or possibly (23) they may provide averages. Therefore, before they are added, each V(\p, l) op should be multiplied by the probability wß with which the eigenvalues of observables described by l0^ occur in the ensemble^ described by ϋ(ψ)ορ.

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