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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 booklet as ""theories of the 1st kind"". half I studies the factors in constructing kinds of hidden-variables theories. the hunt for determinism resulted in theories of the 1st style; the search for theories that seem like causal theories whilst utilized to spatially separated structures that interacted long ago ended in theories of the second one variety. elements II and III extra describe the theories of the 1st sort and moment style, respectively.
This ebook is written to make the literature on hidden variables understandable to people who are careworn by way of the unique papers with their controversies, and to usual reader of physics papers.

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2 that we could define V(ip, £)op if we would relax our requirement of the validity of (23) for all observables, and would require its validity for not more than two noncommutative observables in a two-dimensional Hilbert space, provided we also relin­ quish the nonnegative definitiness of Vop. Let us see what happens to the resolution of Uop by (53) in this "mutilated" case. 2 in a two-dimensional Hilbert space. We show in Appendix A that, with (23) valid only for the observables A and B considered in eqs.

32 A SURVEY OF HIDDEN-VARIABLES THEORIES so that apparently at least one of the assumptions under which he derived this theorem 18 must be violated in our case. It is easily seen (Appendix A) that a condition here violated is von Neumann's requirement that Vop should be nonnegative definite. 2)op here violate this condition. 2, by a different choice of Vop we made Vop nonnegative definite. For this purpose we had to drop the requirement of validity of (23) for any observable B of which ψ is not an eigenfunction.

By (10), this is ina theory of the first kind the probability pp with which the ξ(β) occur in an equilibrium distribution. Thus, instead of (52), we shall try whether we can write Uop in the form £/(V)op = fpPV(ip9$e>U· iß) (53) This improvement, of course, does not make it possible to write Uop really as a super­ position of density matrices for dispersionfree states (i/;, £) of which each could be used to calculate expectation values of all observables in such a dispersionfree state. The reason for the impossibility of making this work, however, is not the reason given by von Neumann.

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