It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. This paper presents a stronger Bell argument which even forbids certain non-local theories. The conclusion of the stronger Bell argument presented here provably is the strongest possible consequence from the violation of Bell inequalities on a qualitative probabilistic level. Since among the excluded non-local theories are those whose only non-local probabilistic connection is a dependence between the space-like separated measurement outcomes of EPR/B experiments, (...) outcome dependence cannot be the crucial dependence for explaining a violation of Bell inequalities. Rather, the remaining non-local theories, which can violate Bell inequalities, are characterized by the fact that at least one of the measurement outcomes in some sense probabilistically depends both on its local as well as on its distant measurement setting. While this is not to say that what is usually called parameter dependence has to hold, some kind of dependence on the distant parameter cannot be avoided. Against the received view, established by Jarrett and Shimony, that on a probabilistic level quantum non-locality amounts to outcome dependence, this result confirms and makes precise Maudlin's claim that some kind of parameter dependence is required. (shrink)

It is a well known fact that a common common causal explanation of the EPR scenario which consists in providing a local, non-conspiratorial common common cause system for a set of EPR correlations is excluded by various Bell inequalities. But what if we replace the assumption of a common common cause system by the requirement that each correlation of the set has a local, non-conspiratorial separate common cause system? In the paper we show that this move does not yield a (...) solution by providing a general recipe how to derive any Bell(δ) inequality—that is an inequality differing from some Bell inequality in a term of order of δ—from the assumption that an appropriate set of almost perfect anticorrelations has a separate common causal explanation. (shrink)

It is often argued that no local common cause models of EPR correlation exist. However, Szabó and Rédei pointed out that such arguments have the tacit assumption that plural correlations have the same common causes. Furthermore, Szabó showed that for EPR correlation a local common cause model in his sense exists. One of his requirements is that common cause events are statistically independent of apparatus settings on each side. However, as Szabó knows, to meet this requirement does not entail that (...) different combinations of common cause events (e.g. meet and join in lattice-theoretic terminology) are statistically independent of measurement settings. This further condition is formulated in two ways. First, the apparatus settings are completely independent of such combinations. Second, the apparatus settings on each side are independent of such combinations. Does a common cause model which meets the former and the latter respectively exist? This problem is considered. In particular, the latter version is Szabó’s and Rédei’s open problem. Negative answers are given to both versions. (shrink)

Some researchers argued that in the non-existence proof of hidden variables, the existence of a common common-cause of multiple correlations is tacitly assumed and that the assumption is unreasonably strong. According to their idea, it is sufficient if the separate common-cause of each correlation exists. However, for such an idea, various no-go results are already known. Recently, Higashi showed that there exists no local separate common-cause model for the correlations that appear in Hardy’s famous argument. In this paper, I give (...) another simple and suggestive proof of the same content. First, I will show that there exists no local common common-cause model of the correlations that appear in Hardy’s argument. Second, taking the proof as a hint, following almost the same steps, I will show the non-existence of a local separate common-cause model for those correlations. Finally, based on the argument in the previous sections, I will discuss what we can conclude about the issue of reducibility from a separate common-cause model to a common common-cause model. It will be concluded that it is “irreducible” at least by a usual method. (shrink)

A probability space is common cause closed if it contains a Reichenbachian common cause of every correlation in it and common cause incomplete otherwise. It is shown that a probability space is common cause incomplete if and only if it contains more than one atom and that every space is common cause completable. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the principle is only falsifiable if conditions on the common cause (...) are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause. (shrink)

In the paper the relation between the standard probabilistic characterization of the common cause and Bell's notion of local causality will be investigated. It will be shown that the probabilistic common cause follows from local causality if one accepts, as Bell did, two assumptions concerning the common cause: first, the common cause is localized in the intersection of the past of the correlating events; second, it provides a complete specification of the `beables' of this intersection. However, neither assumptions are a (...) priori requirements. In the paper the logical role of these assumptions will be studied and it will be shown that only the second assumption is necessary for the derivation of the probabilistic common cause from local causality. (shrink)

We examine possible causal structures of experiments with entangled quantum objects. Previously, these structures have been obscured by assuming a misleading probabilistic analysis of quantum non locality as 'Outcome Dependence or Parameter Dependence' and by directly associating these correlations with influences. Here we try to overcome these shortcomings: we proceed from a recent stronger Bell argument, which provides an appropriate probabilistic description, and apply the rigorous methods of causal graph theory. Against the standard view that there is only an influence (...) between the measurement outcomes, we show that there must be an influence from one setting to its distant outcome: EPR correlations can only come about if one of the outcomes is a common effect of both settings. Our discussion makes explicit under which assumptions similar conclusions from information theoretic considerations can be interpreted causally. (shrink)

It is widely accepted that the violation of Bell inequalities excludes local theories of the quantum realm. In this paper I present a stronger Bell argument which even forbids certain non-local theories. The remaining non-local theories, which can violate Bell inequalities, are characterised by the fact that at least one of the outcomes in some sense probabilistically depends both on its distant as well as on its local parameter. While this is not to say that parameter dependence in the usual (...) sense necessarily holds, it shows that the received analysis of quantum non-locality as “outcome dependence or parameter dependence” is deeply misleading about what the violation of Bell inequalities implies. (shrink)

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most likely experimentally falsified, (...) the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both. (shrink)