A Survey of Hidden-Variables Theories by F. J. Belinfante

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By F. J. Belinfante

A Survey of Hidden-Variables Theories is a three-part booklet at the hidden-variable theories, referred during this ebook as ""theories of the 1st kind"". half I experiences the causes in constructing varieties of hidden-variables theories. the search for determinism ended in theories of the 1st sort; the hunt for theories that seem like causal theories while utilized to spatially separated structures that interacted long ago ended in theories of the second one sort. components II and III additional describe the theories of the 1st variety and moment style, respectively.
This e-book is written to make the literature on hidden variables understandable to those that are careworn through the unique papers with their controversies, and to commonplace reader of physics papers.

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Therefore only As can contribute to the sum in the last member of (39). It follows that all V]f> are zero with N the exception of V%>. Then £ Vft = <1>V^ = 1 gives ( 41 ) VÌP = V £ } = ônIfN = 2, the matrix V(ip, ξ)Φ then for ψ = φ± and for all ξ reduces to where νχ2 = ^i2(l) is a function of the hidden variables which is not yet determined by (41). Then, with the Tik of (34) given by (35), eq. (36) gives Vg> = c2+cs (vl2+ v*12\ Vg> = s2-cs (v12+ v*12\ (43) and (Β)ψ,ξ = %BkVif= B1 c2+B2s2+(B1-B2) cs (v12+v*12).

From V$ 3= 0 it then follows that we must have I »ia(D I = 0, (48) so that (42) simplifies for ψ = φι and for all ξ to vr-(l l)· m This gives Vop the eigenvalues 1 and 0 for the eigenfunctions φι and φι. op considered before. Keeping the old notation (42) for Vjf\ we then from (44) find that 2Re {#12} = tan Θ or —cot Θ, as in (46a, b). The direct contradiction between this result and (48) then shows that our assumption of existence of Vop satisfying (23) for all observables must have been wrong.

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. In fact, the inequality (29) expresses the absence of such relations for measurements on a single system.

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