A Stronger Bell Argument for (Some Kind of) Parameter Dependence
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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 (given usual background assumptions). 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 (a subset of outcome dependent theories), 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 (among them quantum theory), are characterized by the fact that at least one of the measurement outcomes in some sense (which is made precise) 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.