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The British Journal for the Philosophy of Science

Einstein, Bell, and Nonseparable Realism

Federico Laudisa

Published Sep 1, 1995• 9 citations
Publisher

Abstract

In the context of stochastic hidden variable theories, Howard has argued that the role of separability—spatially separated systems possess distinct real states—has been underestimated. Howard claims that separability is equivalent to Jarrett‘s completeness: this equivalence should imply that the Bell theorem forces us to give up either separability or locality. Howard's claim, however, is shown to be ill founded since it is based on an implausible assumption. The necessity of sharply distinguishing separability and locality is emphasized: a quantitative formulation of separability, due to D'Espagnat, is reviewed and found unsatisfactory, in that it basically conflates separability and locality in a single notion. Finally, the possibility of an ‘Einsteinian’ nonseparable realism, envisaged by Shimony, is reviewed and found also to be implausible.

DOI
10.1093/bjps/46.3.309

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In the context of stochastic hidden variable theories, Howard has argued that the role of separability—spatially separated systems possess distinct real states—has been underestimated. Howard claims that separability is equivalent to Jarrett‘s completeness: this equivalence should imply that the Bell theorem forces us to give up either separability or locality. Howard's claim, however, is shown to be ill founded since it is based on an implausible assumption. The necessity of sharply distinguishing separability and locality is emphasized: a quantitative formulation of separability, due to D'Espagnat, is reviewed and found unsatisfactory, in that it basically conflates separability and locality in a single notion. Finally, the possibility of an ‘Einsteinian’ nonseparable realism, envisaged by Shimony, is reviewed and found also to be implausible.
We first examine Howard's analysis of the Bell factorizability condition in terms of ‘separability’ and ‘locality’ and then consider his claims that the violations of Bell's inequality by the statistical predictions of quantum mechanics should be interpreted in terms of ‘nonseparability’ rather than ‘nonlocality’ and that ‘nonseparability’ implies the failure of spacetime as a principle of individuation for quantum-mechanical systems. We will argue that his argument for the first claim is less than compelling and that any argument for the second claim will be interpretation-dependent and, hence, not generally valid.
Essay content differs substantially from presentation! In order to motivate his claim that the violation of the Bell inequalities forces us into a certain kind of holism, Howard (1985,1989,1992) develops a formal equivalence proof supposed to ground the stochastic “outcome independence” condition, the assumption of which is necessary for the derivation of the inequalities, in a physical principle, the separability principle. I will discuss several criticisms of Howard's equivalence proof that focus on the sufficiency of the separability principle for outcome independence. I will argue that, while none of these criticisms succeeds, they do constrain the possible form of Howard's argument.
Abstract. Bell's theorem refutes a conjunction of assumptions, and the disagreement of the last sixty years has been about which member to reject. This paper takes the horn Einstein himself identified: separability, the claim that the state of a composite system is fixed by the states of its parts together with their spatiotemporal relations. Following Howard, separability rather than locality is what gave Bell's factorization condition its warrant, and dropping it leaves operational locality and relativity untouched while removing the premise that reality decomposes into parts possessing states of their own. Separability licenses something else as well. Modelling presupposes a position exterior to what is modelled, and only separability makes such a position coherent. Gödel's incompleteness theorems show that a system required to account for itself from outside itself generates a process that does not terminate. Bell refutes the premise; Gödel refutes what the premise licenses. The paper's central claim is that these are one finding rather than two, and that they have not previously been read that way. A third claim follows and is weaker. The same assumption is argued to produce the observed failure of convergence in domains where the modeller is constitutive of what is modelled: the foundations of mathematics and of quantum mechanics do not converge, while astronomy and chemistry do. This is stated as a measurable prediction, nobody has measured it, and the paper identifies where the argument would fail if it is wrong.
Bell's theorem states that some quantum correlations can not be represented by classical correlations of separated random variables. It has been interpreted as incompatibility of the requirement of locality with quantum mechanics. We point out that in fact the space part of the wave function was neglected in the proof of Bell's theorem. However this space part is crucial for considerations of property of locality of quantum system. Actually the space part leads to an extra factor in quantum correlations and as a result the ordinary proof of Bell's theorem fails in this case. We present a criterium of locality in a realist theory of hidden variables. It is argued that predictions of quantum mechanics for Gaussian wave functions can be consistent with Bell's inequalities and hence Einstein's local realism is restored in this case.
J.S. Bell believed that his famous theorem entailed a deep and troubling conflict between the empirically verified predictions of quantum theory and the notion of local causality that is motivated by relativity theory. Yet many physicists continue to accept, usually on the reports of textbook writers and other commentators, that Bell's own view was wrong, and that, in fact, the theorem only brings out a conflict with determinism or the hidden-variables program or realism or some other such principle that (unlike local causality), allegedly, nobody should have believed anyway. (Moreover, typically such beliefs arise without the person in question even being aware that the view they are accepting differs so radically from Bell's own.) Here we try to shed some light on the situation by focusing on the concept of local causality that is the heart of Bell's theorem, and, in particular, by contrasting Bell's own understanding with the analysis of Jon Jarrett which has been the most influential source, in recent decades, for the kinds of claims mentioned previously. We point out a crucial difference between Jarrett's and Bell's own understanding of Bell's formulation of local causality, which turns out to be the basis for the erroneous claim, made by Jarrett and many others, that Bell misunderstood the implications of his own theorem.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.