Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

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 Redhead's ([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 proof's 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 Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's 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 2's proof (3). *Portions of this paper were presented by R. K. Clifton to the 1988 British Society for the Philosophy of Science Conference at the University of Southampton. R. K. Clifton wishes to thank the Natural Sciences and Engineering Research Council of Canada, the Royal Commission for the Exhibition of 1851, and the Governing Body of Peterhouse at Cambridge University for support during this work. (shrink)

The Einstein-Podolsky-Rosen (EPR) paradox and the correlated states it introduced comprise one of the central interpretive problems of quantum mechanics. Because of the apparent nonlocal character of this paradox, it should be given a relativistic treatment. The purpose of this paper is to provide such a treatment.