Two Comments on the Common Cause Principle in Algebraic Quantum Field Theory

Abstract

Until the 1990s 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 a common cause (henceforth, CC) to Bell Inequalities. First, they claimed that it’s not the assumption of a CC for each pair of correlated events that leads to the inequalities but the distinct assumption that there is a CC 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 CC in algebraic quantum field theory (henceforth, AQFT) and the proof of the existence of a CC 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 CC 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 CCs.