John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions.

We argue against the common view that it is impossible to give a causal account of the distant correlations that are revealed in EPR-type experiments. We take a realistic attitude about quantum mechanics which implies a willingness to modify our familiar concepts according to its teachings. We object to the argument that the violation of factorizability in EPR rules out causal accounts, since such an argument is at best based on the desire to retain a classical description of nature that (...) consists of processes that are continuous in space and time. We also do not think special relativity prohibits the superluminal propagation of causes in EPR, for the phenomenon of quantum measurement may very well fall outside the domain of application of special relativity. It is possible to give causal accounts of EPR as long as we are willing to take quantum mechanics seriously, and we offer two such accounts. (shrink)

John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions. IntroductionThe EPR-Bohm experimentLocal causalityBell's inequality from separate common causes4.1 A weak screening-off principle4.2 Perfect correlation and ‘determinism’4.3 A minimal theory for spins4.4 No conspiracyDiscussion.

A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition (...) of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle. (shrink)

Nancy Cartwright believes that we live in a Dappled World– a world in which theories, principles, and methods applicable in one domain may be inapplicable in others; in which there are no universal principles. One of the targets of Cartwright’s arguments for this conclusion is the Causal Markov condition, a condition which has been proposed as a universal condition on causal structures.1 The Causal Markov condition, Cartwright argues, is applicable only in a limited domain of special cases, and thus cannot (...) be used as a universal principle in causal discovery. I have no dispute with any of these claims here. Rather, I wish to argue for a very limited thesis: that the Causal Markov condition is applicable in the specific domain of microscopic quantum mechanical systems; further, that the condition can fruitfully be applied to the much discussed EPR setup. This is perhaps a surprising conclusion, for it is precisely in this domain that Cartwright’s arguments against the Causal Markov condition have been considered to be the most successful. (shrink)

Reichenbach worked in an era when philosophers were hopeful about the unity of science, and particularly about unity of method. He looked for universal tests of causal connectedness that could be applied across disciplines and independently of specific modeling assumptions. The hunt for quantum causes reminds us that his hopes were too optimistic. The mark method is not even a starter in testing for causal links between outcomes in E.P.R., because our background hypotheses about these links are too thin to (...) supply the kind of information we need to put the method into play. When we turn to conventional statistical methods, we have seen that one test proposed — robustness of the conditional probabilities — can be conclusive only when we know that there are no other causal factors at work. In the particular case of E.P.R., it has often been assumed that this antecedent question can be settled by applying Reichenbach's conjunctive fork condition. But that application is in no way free of further modeling assumptions. Cartwright (1989) has shown that the conjunctive fork is only a necessary condition on a common cause under very limiting restrictions (restrictions that take one far from the case of maximal commonality); and she has argued that these special conditions are not satisfied in E.P.R.Finally, even given the assumption that there are no other causes at work, the significance of robustness for E.P.R. is unclear. We need a model which tells us how one outcome would influence the other; without that, there is no way of interpreting the results of the robustness test so that it is decisive. In each of the approaches we discussed, Reichenbach provided the crucial guiding ideas that underlay our construction of a causality test; but the articulation of a specific criterion depends on the other details of the model. What is a criterion for a specific kind of link in one model need not be in another. We have illustrated with robustness and E.P.R., but we take the point to be perfectly general: there are no tests of causality outside of models which already have significant causal structure built in. (shrink)

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it (...) which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbachs definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle. (shrink)

It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it (...) which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle. (shrink)

Two principles of locality used in discussions about quantum mechanics are distinguished. The intuitive no-action-at-a distance requirement is called physical locality. There is also a mathematical requirement of a kind of factorizability which is referred to as "locality". It is argued in this paper that factorizability is not necessary for physical locality. Ways of producing models that are physically local although not factorizable which are concerned with correlations between the behavior of pairs of particles are suggested. These models can account (...) for all the quantum mechanical single and joint probabilities. (shrink)