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 GHZ's 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 GHZ's argument be modified (...) in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's 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 Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, 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. (shrink)

In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=∞, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.

J. S. Bell's classic 1966 review paper on the foundations of quantum mechanics led directly to the Bell nonlocality theorem. It is not widely appreciated that the review paper contained the basic ingredients needed for a nonlocality result which holds in certain situations where the Bell inequality is not violated. We present in this paper a systematic formulation and evaluation of an argument due to Stairs in 1983, which establishes a nonlocality result based on the Bell-Kochen-Specker “paradox” in quantum mechanics.

We give a conceptually simple proof of nonlocality using only the perfect correlations between results of measurements on distant systems discussed by Einstein, Podolsky and Rosen—correlations that EPR thought proved the incompleteness of quantum mechanics. Our argument relies on an extension of EPR by Schrödinger. We also briefly discuss nonlocality and “hidden variables” within Bohmian mechanics.

In a recent paper, Conway and Kochen proposed what is now known as the “Free Will theorem” which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we (...) discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models. (shrink)

Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical (...) form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation. (shrink)