Robert K. Clifton

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.

Relativity, Quantum Mechanics and EPR

The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete.

Locality, Lorentz invariance, and linear algebra: Hardy's theorem for two entangled spin-s particles

Abstract Hardys two recent arguments, one against local realism and the second against Lorentz invariant elements-of-reality, are generalized to the case of two entangled spin-s particles. However it is also argued that the second arguments does not have the significance Hardy claims for it.

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.

Hardy's nonlocality theorem for n spin-12 particles

Abstract Hardys recent proof of a contradiction between local realism and quantum predictions is extended to n spin- 1 2 particles. As expected, classical behaviour emerges discontinuously at the limit n =∞.

Determinism, realism, and Stapp's 1985 proof of nonlocality

Two recent criticisms of Stapps 1985 proof of an incompatibility between locality and quantum mechanics are clarified. One of these criticisms (charging that the proof requires determinism) is supported by a detailed logical analysis of the locality conditions in the proof. The other criticism (charging that the proof assumes realism) is shown to be based upon a misinterpretation of the rôle of counterfactuals in the proof. Further, Stapps own replies to these criticisms are shown to be inadequate.

The rastall model and Stapp's proof of nonlocality

Recently two distinct arguments have been given (by Stapp, and Bedford and Stapp) to prove that a model proposed by Rastall for the statistics of EPR-correlated spin-1/2 particles, which happens to violate the Bell inequality, conflicts with locality. Neither argument makes use of the fact that the Rastall model violates the Bell inequality; therefore both seem to provide independent support for a more general proof of Stapps, which allegedly establishes that any model violating this inequality, including quantum mechanics, must imply the existence of nonlocal influences. However, it is shown here that both of these arguments are invalid under an indeterministic interpretation of quantum mechanics, a conclusion which agrees with the same criticism made by other authors but directed against Stapps more general proof of nonlocality.