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EPR CORRELATIONS, BELL INEQUALITIES AND COMMON CAUSE SYSTEMS

Gábor Hofer‐Szabó

Published Mar 5, 2014• 1 citation
Publisher

Abstract

Standard common causal explanations of the EPR situation assume a so-called joint common cause system that is a common cause for all correlations. However, the assumption of a joint common cause system together with some other physically motivated assumptions concerning locality and no-conspiracy results in various Bell inequalities. Since Bell inequalities are violated for appropriate measurement settings, a local, non-conspiratorial joint common causal explanation of the EPR situation is ruled out. But why do we assume that a common causal explanation of a set of correlation consists in finding a joint common cause system for all correlations and not just in finding separate common cause systems for the different correlations? What are the \nperspectives of a local, non-conspiratorial separate common causal explanation for the EPR scenario? And finally, how do Bell inequalities relate to the weaker assumption of separate common cause systems? \n

DOI
10.1142/9789814596299_0013

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Standard common causal explanations of the EPR situation assume a so-called joint common cause system that is a common cause for all correlations. However, the assumption of a joint common cause system together with some other physically motivated assumptions concerning locality and no-conspiracy results in various Bell inequalities. Since Bell inequalities are violated for appropriate measurement settings, a local, non-conspiratorial joint common causal explanation of the EPR situation is ruled out. But why do we assume that a common causal explanation of a set of correlation consists in finding a joint common cause system for all correlations and not just in finding separate common cause systems for the different correlations? What are the \nperspectives of a local, non-conspiratorial separate common causal explanation for the EPR scenario? And finally, how do Bell inequalities relate to the weaker assumption of separate common cause systems? \n
In this paper I assess the adequacy of no-conspiracy conditions present in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these can not be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. Violations of measurement independence thus need not entail any kind of conspiracy (nor backwards in time causation). This new reading of measurement dependence provides the grounds for an explicitly non-factorizable (in the sense of Bell’s factorizability) common cause model for EPR. 1
One diagnosis of Bell's theorem is that its premise of Outcome Independence is unreasonably strong, as it postulates one common screener system that purports to explain all the correlations involved. This poses a challenge of constructing a model for quantum correlations that is local, non-conspiratorial, and has many separate screener systems rather than one common screener system. In particular, the assumptions of such models should not entail Bell's inequalities. We prove that the models described do not exist, and hence, the diagnosis above is incorrect.
In the paper we compare three principles accounting for correlations, namely Reichenbach's Common Cause Principle, Bell's Local Causality Principle, and Einstein's Reality Criterion and relate them to the Bell inequalities. We show that there are two routes connecting the principles to the Bell inequalities. In case of Reichenbach's Common Cause Principle and Bell's Local Causality Principle one assumes a non-conspiratorial joint common cause for a set of correlations. In case of Einstein's Reality Criterion one assumes strongly non-conspiratorial separate common causes for a set of perfect correlations. Strongly non-conspiratorial separate common causes for perfect correlations, however, form a non-conspiratorial joint common cause. Hence the two routes leading the Bell inequalities meet.
Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a 'common causal justification' of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities.
It is well known that correlations produced by common causes in the past cannot violate Bell's inequalities. This was emphasized by Bell in his celebrated example of Bertlmann's socks. However, if common causes are induced by the very measurement process i.e., actualized at each run of a joint measurement, in a way that depends on the type of joint measurement that is being executed (hence, the common causes are contextually actualized), the resulting correlations are able to violate Bell's inequalities, thus providing a simple and general explanation for the origin of quantum correlations. We illustrate this mechanism by revisiting Bertlmann's socks example. In doing so, we also emphasize that Bell's inequalities, in their essence, are about demarcating 'non-induced by measurements' (non-contextual) from 'induced by measurements' (contextual) common causes, where the latter would operate at a non-spatial level of our physical reality, when the jointly measured entangled entities are microscopic in nature.
According to a conventional view, there exists no common-cause model of quantum correlations satisfying locality requirements. In fact, Bell's inequality is derived from some locality conditions and the assumption that the common cause exists, and the violation of the inequality has been experimentally verified. On the other hand, some researchers argue that in the derivation of the inequality the existence of a common common-cause for multiple correlations is implicitly assumed and that the assumption is unreasonably strong. According to their idea, what is necessary for explaining the quantum correlation is a common cause for each correlation. However, in this paper, we will show that in almost all entangled states we can not construct a local model that is consistent with quantum mechanical prediction even when we require only the existence of a common cause of each correlation.