Recently Bell has conjectured that, with “epsilonics,” one should be able to argue, à la EPR, from “almost ideal correlations” (in parallel Bohm-Bell pair experiments) to “almost determinism,” and that this should suffice to derive an approximate Bell-type inequality. Here we prove that this is indeed the case. Such an inequality—in principle testable—is derived employing only weak locality conditions, imperfect correlation, and a propensity interpretation of certain conditional probabilities. Outcome-independence (Jarrett's “completeness” condition), hence “factorability” of joint probabilities, is not assumed, (...) but rather an approximate form of this is derived. An alternative proof to the original one of Bell [1971] constraining stochastic, contextual hidden-variables theories is thus provided. (shrink)

We will formulate two Bell arguments. Together they show that if the probabilities given by quantum mechanics are approximately correct, then the properties exhibited by certain physical systems must be nontrivially dependent on thetypes of measurements performedand eithernonlocally connected orholistically related to distant events. Although a number of related arguments have appeared since John Bell's original paper (1964), they tend to be either highly technical or to lack full generality. The following arguments depend on the weakest of premises, and the (...) structure of the arguments is simpler than most (without any loss of rigor or generality). The technical simplicity is due in part to a novel version of the generalized Bell inequality. The arguments are self contained and presuppose no knowledge of quantum mechanics. We will also offer a Dutch Book argument for measurement type dependence. (shrink)

We present an exegesis of the Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics, and defend it against the critique in Fine. (1) We contend,contra Fine, that it compares favorably with an argument reconstructed by him from a letter by Einstein to Schrödinger; and also with one given by Einstein in a letter to Popper. All three arguments turn on a dubious assumption of “separability,” which accords separate elements of reality to space-like separated systems. We discuss how this assumption figures (...) in the literature spawned by the Bell inequalities. (shrink)

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)

The properties of classical and quantum systems are characterized by different algebraic structures. We know that the properties of a quantum mechanical system form a partial Boolean algebra not embeddable into a Boolean algebra, and so cannot all be co-determinate. We also know that maximal Boolean subalgebras of properties can be (separately) co-determinate. Are there larger subsets of properties that can be co-determinate without contradiction? Following an analysis of Bohrs response to the Einstein-Podolsky-Rosen objection to the complementarity interpretation of quantum (...) mechanics, a principled argument is developed justifying the selection of particular subsets of properties as co-determinate for a quantum system in particular physical contexts. These subsets are generated by sets of maximal Boolean subalgebras, defined in each case by the relation between the quantum state and a measurement (possibly, but not necessarily, the measurement in terms of which we seek to establish whether or not a particular property of the system in question obtains). If we are required to interpret quantum mechanics in this way, then predication for quantum systems is quite unlike the corresponding notion for classical systems. (shrink)

I show that locality, as it occurs in EPR arguments for the incompleteness of quantum mechanics, can be construed as causal independence understood in terms of Lewis’ counterfactual analysis of causation. This construal has two benefits. It supplements recent analyses, which have not treated locality in detail. And it clarifies the relation between two EPR arguments that have recently been distinguished. It shows that the simpler of the two is more complex than has been thought; and that the other argument (...) does not need ‘counterfactual definiteness’.I aim to show that in the EPR argument (Einstein et al. 1935) for the incompleteness of quantum mechanics (QM), locality can be taken as causal independence, understood in terms of Lewis’ counterfactual analysis of causation.Recent analyses of the EPR argument makes this construal of locality timely, for two reasons. First, these analyses typically say little about locality. (shrink)

It has been suggested that the measuring apparatus used to measure quantum systems ought to be idealized as consisting of an infinite number of quantum systems. Let us call this the infinity assumption. The suggestion that we ought to make the infinity assumption has been made in connection with two closely related but distinct problems. One is the problem of determining the importance of the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. The other is the measurement (...) problem. These problems are not internal to the quantum mechanical formalism. They arise when we obtain particular formal results in applying the quantum mechanical formalism to measurement interactions. The formal results are problematic because they resist explanation. Various authors have claimed that by making the infinity assumption we can neglect the limitations on measurement. Bub (1988) and (1989) claims it allows us to solve the measurement problem. I will argue that both claims are unjustified. (shrink)