Two Comments on the Common Cause Principle

Until the 1990’s philosophers took it almost for granted that the common cause principle is at odds with quantum theory. Roughly, they argued that a common cause explanation of correlations between four pairs of events leads inevitably to Bell inequalities, and since Bell inequalities are violated in quantum theory, there cannot be a common cause explanation of quantum correlations. Redei and his collaborators have made a two-fold effort in order to under-cut the implication from the assumption of common causes to Bell Inequalities. First, they claimed that it’s not the assumption of a common cause for each pair of correlated events that leads to the inequalities but the distinct assumption that there is a common cause for all four pairs of projection operators that are correlated; this is the common-common cause hypothesis to which I shall return below. The other important contribution is the formulation of the principle of common cause in algebraic quantum field theory and the proof of the existence of a common cause that explains quantum correlations which are prescribed by the violation of Bell inequalities for a state of the system. Hence, not only there is nothing odd in the common cause explanation of quantum correlations, but moreover, the violation of Bell inequalities for a pair of spacelike regions and for a state of the system is a sufficient condition for the existence of quantum correlations, that may be explainable in terms of common causes. In this talk, I shall present two relatively independent sets of remarks on common causes and the violation of Bell inequalities in algebraic quantum field theory. The first set of remarks concerns the possibility of reconciling Reichenbachian ideas on common causes with quantum field theory in the face of an already known difficulty: the event shown to satisfy statistical relations for being the common cause of two correlated events has been associated with the union, rather than the intersection, of the backward light cones of the correlated events. I explore a way of overcoming this difficulty by considering the common cause to be a conjunction of suitably located events. But I show that this line of thought too is beset with interpretational problems. My second set of remarks concerns the type of inequality one may