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

Critique of the Papers of Fine and Suppes

Abner Shimony

Published Jan 1, 1980• 9 citations
Publisher

Abstract

‘Bell's Theorem’ is the collective name for a family of arguments, which more accurately should be referred to as ‘Theorems of Bell's Type’, all being variants of the remarkable argument given by J. S. Bell (1964). All of these arguments have the format E & H → I, where E is a description of a type of experimental setup involving pairs of particles emitted from a common source, H is a physical hypothesis which typically expresses some version of “realism” and some version of “locality”, and I is an inequality concerning correlations between particles of a pair. There are differences among theorems of Bell's type regarding the details of the inequality I , which are important in actually carrying out experimental tests. There are differences regarding the arrow—i.e., the procedure whereby I is inferred from E & H.

DOI
10.1086/psaprocbienmeetp.1980.2.192611

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‘Bell's Theorem’ is the collective name for a family of arguments, which more accurately should be referred to as ‘Theorems of Bell's Type’, all being variants of the remarkable argument given by J. S. Bell (1964). All of these arguments have the format E & H → I, where E is a description of a type of experimental setup involving pairs of particles emitted from a common source, H is a physical hypothesis which typically expresses some version of “realism” and some version of “locality”, and I is an inequality concerning correlations between particles of a pair. There are differences among theorems of Bell's type regarding the details of the inequality I , which are important in actually carrying out experimental tests. There are differences regarding the arrow—i.e., the procedure whereby I is inferred from E & H.
While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental facts from some list of assumptions, thus showing that at least one of the assumptions must be wrong; but there is disagreement about what the assumptions were that went into the argument. In this paper, I make a few points in order to help clarify the situation. Introduction Different authors have expressed very different views about what Bell's theorem shows about physics. The disagreement concerns particularly the question of which assumptions go into the argument. Since we have to give up one of the assumptions leading to the empirically violated Bell inequality, knowing what the assumptions were is crucial. For example, if author X believes that the argument requires only one assumption, A 1 , while author Y believes that it requires two, A 1 and A 2 , then X will conclude that A 1 ¬ must be abandoned, while Y will conclude that either A 1 or A 2 must abandoned, so A 1 may well be true in our world if A 2 is false. In this paper, I consider several assumptions that have been mentioned in connection with Bell's theorem, and I look into their roles in the proof of Bell's theorem. While I do not say anything here that has never been said before, I hope that my remarks can nevertheless be helpful to some readers. For the sake of definiteness, the version of the relevant experiment that I will consider involves two spin-1\2 particles, initially in the singlet spin state ψ = 2 −1/2 (|↑↓ ⟩ − |↓↑ ⟩). Two widely separated experimenters, Alice and Bob, have one particle transported to each of them. At spacelike separation, they each choose a direction in space, represented by the unit vectors a and b , and carry out a quantum measurement of the spin observable in this direction on their particle, ( a · σ ) ⊗ I and I ⊗ ( b · σ ), with I the 2 × 2 unit matrix and σ the triple of Paulimatrices. The possible outcomes, A and B , are±1 on each side. Bell's theorem is the statement that under the assumptions we are about to discuss, Bell's inequality holds; quantum theory predicts violations of Bell's inequality, and experiments have confirmed these predictions.
Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as `strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as `weakly objective,' that is, each correlation function pertains to a different set of particle pairs. It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).
As was remarked two years ago at a symposium of the PSA on locality and hidden variables (Shimony 1981), the Bell theorems together with experiments supporting the quantum correlations (violating the inequalities of the theorems) provide a rather remarkable opportunity for philosophy. Shimony summed this up in the nice phrase, “experimental metaphysics”. For, as he pointed out, arguments based on Bell-type theorems, concluding that certain experiments should exhibit correlations obeying a certain inequality, generally employ premises of a metaphysical character, e.g., that the systems in question are deterministic (in the experimental observables). If, in fact, the experimental predictions are violated, and if one has reason to believe any other premises involved, then one must give up the metaphysical hypothesis.
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.