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Applications of Mathematics

On hidden variables

Václav Alda

Published Jan 1, 1972• 3 citations
Publisher

Abstract

The non-existence of hidden variables for the whole system in the formulation of Jauch and Piron can be easily deduced from the result of Zierler and Schlesinger. No further assumptions on the structure of yes - no experiments are needed.
DOI
10.21136/am.1972.103392

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The problem of hidden variables, purely conceptual at the start, has been early influenced by the practical aims of “causal theories” towards a mathematical scheme broader than the quantum formalism. Thus several authors have examined if a new formalism, built in the same spirit as that of quantum mechanics, however more general, might admit a determination by means of hidden parameters, and concluded negatively. In the present paper the two aspects (conceptual and practical) are considered separately. It first contains a study of the unrestricted proofs (Von Neumann, Jauch and Piron), given for the non-existence of hidden parameters. They are focussed on the dispersion-free states bound to them. Thus a preliminary stage consists in analyzing what properties these states should have. A method is given here for displaying these; they are shown to have an artificial character, which fits neither Von Neumann's proof nor that of Jauch and Piron and other authors (Misra). Thus, these proofs do not establish the inexistence of hidden variables, but only that of dispersion free states built more or less on the pattern of the quantum states. Suggestions are then proposed on the probable features of hidden parameters. They lead us to regard as improbable the hope of building a new deterministic scheme to be substituted for the quantum formalism. Thus, the determinism which can be maintained appears as purely conceptual. The question of a “deeper level” and the relation between determination and pictorial description are discussed briefly.