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.
Projection Operator Quantum Correlation Correlate Event Light Cone Bell Inequality
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I want to thank A. Arageorgis for his substantial help in this paper and A. Spanou for the final “word-haircut”.
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