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

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We shall renumber the {$,·} so that we have j = 1, and ψ = φ±. Then for any ξ the measurement of A shall give Ai with φι, so that η(ψ, |, {φί}) = j = 1 for ψ = φχ = φι and for any ξ. (37) It then follows from (19) that, in this case, (Α)ψ9* = Λι. (38) On the other hand, if Vop would exist with the property (23), (A%,s = ZZAklVlk= ZAjVJf\ k I (39) 7= 1 where we used the fact that on the basis {φ{} the matrix of Aop is diagonal. Since As ^ each Ap and since the diagonal elements Vffl cannot be negative,15 eq.

1 , 2 , . . , N), (66) i=l where the Xj finally would be generalized to the complex elements of a unitary matrix. Again, it follows that it is impossible to satisfy the conditions (61a, b) if we maintain as in (64) that, for given ψ and £, ν(φη) shall depend on φη only. " Again, this "paradox" will disappear when we allow v to jump to and fro between 1 ("red") and 0 ("blue") for a fixed choice of φη9 when the complete orthonormal set {,} of which φη is part is unitarily transformed in such a way that φη is left invariant.

Von Neumann apparently copied (31) from the rule (aA +bB)v or mix = a(A) ψ or mix T υ{ΰ/φ or mix (32) valid for the ensembles describing pure or mixed quantum states. To hidden-variable theorists, the property (32) for averages over quantum states is a happenstance which is not at all a priori obvious because results of measurements of (aA + bB)9 and of A and of B, require in general entirely different apparatus when^4op and Bop do not commute, and there­ fore it is surprising that there should be any relation at all between results of these measure­ ments.

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