Michael Redhead

Particles, particle labels, and quanta : the toll of unacknowledged metaphysics

The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle indistinguishability, create the need for symmetrization or antisymmetrization (or, in principle, higher-order symmetries), which in turn results in “surplus formal structure” in the formalism, formal structure which corresponds to nothing in the real world. We argue that these facts show quanta to be unindividuatable entities, things in principle incapable of supporting labels, and so things which support no factual difference_if two of them are thought of as being switched. When thinking of the metaphysics of quanta, we should eschew the misleading labels of the tensor product Hilbert space formalism and prefer the ontologically more faithful description of the Fock space formalism. This conception eliminates puzzles about the quantum statistics of bosons.

More ado about nothing

In this paper questions about vacuum fluctuations in local measurements, and the correlations between such fluctuations, are discussed. It is shown that maximal correlations always exist between suitably chosen local projection operators associated with spacelike separated regions of space-time, however far apart these regions may be. The connection of this result with the well-known Fregenhagen bound showing exponential decay of correlations with distance is explained, and the relevance of the discussion to the question “What do particle detectors detect?” is addressed.

Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZs proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZs argument be modified in order to produce a valid proof. Finally, we motivate our more general proofs assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZs proof along these lines, we then consider the analogue, for our proof, of Bohrs reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bells. Nevertheless, we point out some new advantages of our proof over Bells, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bells, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell

The breakdown of quantum non-locality in the classical limit

Abstract We show how Mermins algebraic proof of non-locality can be extended to the N -particle case and discuss the discontinuous transition to classical behaviour that occurs in the physically unrealisable limit of an infinite number of particles.

Nonlocal Influences and Possible Worlds—A Stapp in the Wrong Direction

Stapp ([1971], [1977], [1985a], henceforth Stapp 1) claims to give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redheads ([1987], pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp [1989] (henceforth Stapp 2), has revised the logical structure of his proof including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proofs significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redheads criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proofs validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2s proof (3).

The compatibility of correlated CP violating systems with statistical locality

Abstract A recent claim that correlated pairs of CP violating neutral pseudo-scalar mesons have measurement properties incompatible with statistical locality is shown to be based upon an incorrect application of standard quantum measurement theory to superpositions of nonorthogonal states.

The Relativistic EPR Argument

At first glance, the realist interpretations of quantum mechanics such as Bohm’s offer many advantages over standard interpretations of the theory. In particular, they give a clear, intuitive picture of many potentially paradoxical physical situations, such as the two-slit experiment and the phenomenon of barrier penetration. At the same time, their chief drawback — a form of nonlocality that seems to conflict with the constraints of relativity theory — is apparently shared by the standard, “antirealist” interpretations that reject hidden variables and assume completeness, as was demonstrated by the original Einstein-Podolsky-Rosen argument. However, while the Bell argument that establishes nonlocality for realistic interpretations such as Bohm’s has been formulated in a relativistic context (Landau, 1987; Summers and Werner, 1985), there is no well-established relativistic formulation of the EPR argument. hi the absence of such a formulation, it seems hasty to conclude that the tension between the standard interpretations and relativity theory is just as great as that between Bohmian interpretations and relativity. Clearly, if a relativistic formulation of EPR could be given that did not entail nonlocality, antirealist interpretations would have an advantage over the Bohmian interpretation.

Unified Treatment of EPR and Bell Arguments in Algebraic Quantum Field Theory

A conjecture concerning vacuum correlations in axiomatic quantum field theory is proved. It is shown that this result can be applied both in the context of EPR-type experiments and Bell-type experiments.

A second look at a recent algebraic proof of nonlocality

We reply to M. Jones criticisms of our proof that factorable stochastic hidden-variable theories are inconsistent with GHZ-style strict correlations predicted by quantum mechanics. We endorse Jones clarifications of our definitions of the setsM and ΛTF. And we reply to his main criticism by invoking one additional locality-motivated assumption. Further, we show how this additional assumption can be weakened while preserving our proofs validity.

Propensities, correlations, and metaphysics

An attempt is made to defend realism and the absence of space-like causation in quantum mechanics, by invoking indeterminism and a new necessary condition for stochastic causality, we term robustness. This condition is defended against recent critical attacks by Cartwright and Jones, and by Healey, and the violation of the robustness condition in Bell-type correlation experiments is shown to follow if an appropriate interpretation of the state vector is employed.