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By F. J. Belinfante

A Survey of Hidden-Variables Theories is a three-part ebook at the hidden-variable theories, referred during this ebook as ""theories of the 1st kind"". half I stories the reasons in constructing sorts of hidden-variables theories. the search for determinism ended in theories of the 1st style; the search for theories that appear like causal theories whilst utilized to spatially separated structures that interacted long ago resulted in theories of the second one sort. components II and III additional describe the theories of the 1st type and moment variety, respectively.
This ebook is written to make the literature on hidden variables understandable to people who are careworn through the unique papers with their controversies, and to typical reader of physics papers.

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Extra resources for A Survey of Hidden-Variables Theories

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31), thus eliminating the contradiction between assumptions. As, instead, the postulate (6) with (19) is assumed, (54) reduces to the trivial relation (51). Then there is no longer any question of nonexistence of microstates (ψ, | ) that are dispersionfree in the sense of (54). Reason Three As a third reason for the nonexistence of hidden variables, von Neumann 19 alludes to the impossibility of a relation like (31) and to the validity of inequalities like (28) in hiddenvariables theory, which he considers to be in conflict with the relations (32) and (30) of 10 Von Neumann (1932), pages 171 ançl 167, or von Neumann (1955), pages 325 and 313-314, VON NEUMANN'S CLAIM OF IMPOSSIBILITY 33 quantum theory.

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. 3. 8 we alluded to confusion about the meaning of the expression "dispersionfree state" in some of the literature, due again to a failure to distinguish between the meaningful ensembles Εψ that represent a quantum-mechanical state, and the trivial and useless ensembles of identical copies of a single microstate that are needlessly forced upon the theory when one starts talking about the average value (Α)ψξ in a hidden-variables state which uniquely determines the value Αη(ν,ξ{φ{}) of A.

24) above, this cannot be a criterion by which to disqualify the theory, as the theory has neither need nor necessity for assuming relations like (53). See Appendix K for more on the Vop problem. Reason Two The second reason given by von Neumann 17 for the nonexistence of hidden-variables states is that they should be quantum-mechanical states represented by ensembles for which his axioms including our eq. (31) would be valid, and for which, additionally, for any observable A the postulate (Α>)ψ,ξ = ((Α)ψ,ξγ (54) would be valid.

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