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PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association

Causal Analysis of Hidden Variables

Patrick Suppes

Published Jan 1, 1980• 0 citations

Abstract

My contribution to this symposium is focused on the retreat from strong conditions of causality that have been forced upon us by quantum mechanics. My intent is to describe in more or less successive stages the retreat from the paradise of deteministic causation. This retreat has taken place through a thicket of quantum-nechanical details. It is ny intention to describe the general principles involved but to refer to the literature for proofs and full technical elaboration, even of matters that are crucial to the conceptual development. The history of the efforts to prove or disprove the possibility of hidden variables begins at least with von Neumann and includes important work by Kochen and Specker and others, but much of the recent analysis has centered around Bell's inequality and related results. In spite of its importance and significance I shall ignore this earlier history and begin with these recent discussions.

DOI: 10.1086/psaprocbienmeetp.1980.2.192610

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My contribution to this symposium is focused on the retreat from strong conditions of causality that have been forced upon us by quantum mechanics. My intent is to describe in more or less successive stages the retreat from the paradise of deteministic causation. This retreat has taken place through a thicket of quantum-nechanical details. It is ny intention to describe the general principles involved but to refer to the literature for proofs and full technical elaboration, even of matters that are crucial to the conceptual development. The history of the efforts to prove or disprove the possibility of hidden variables begins at least with von Neumann and includes important work by Kochen and Specker and others, but much of the recent analysis has centered around Bell's inequality and related results. In spite of its importance and significance I shall ignore this earlier history and begin with these recent discussions.

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familiar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem," thereby clarifying the conceptual link between these two results of Bell.

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.

For almost three decades in the twentieth century, the physics community believed that John von Neumann had proved the impossibility of completing quantum mechanics by a local realist, hidden-variables theory. Although Grete Hermann had raised strong objections to von Neumann's proof, she was largely ignored. This situation lasted, until John Bell rediscovered that von Neumann's proof was flawed: a \emph{sufficient} condition for local realism had been taken as a \emph{necessary} one. Bell subsequently established various constraints on hidden-variables theories, in the form of inequalities that can be submitted to experimental test. All performed tests to date have opened some loopholes. The quest to close them motivated great technical achievements and ongoing efforts to improve what has already been reached. There is, however, a rather ironic twist concerning Bell inequalities. On deriving them, Bell also took a sufficient condition for local-realism, as if it were a necessary one. As a consequence, even completely loophole-free Bell inequality violations would not disprove local realism. We argue that Bell inequalities cannot follow from local-realism alone. The proof is given by constructing three local-realist models that entail Bell inequality violations.

We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.