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While initial versions of Bell's theorem captured the notion of locality withthe assumption of factorizability, in later presentations, Bell argued thatfactorizability could be derived from the more fundamental principle of localcausality. Here we show that, contrary to what is commonly assumed, in order toderive factorizability from the principle of local causality, a non-trivialassumption, similar but strictly independent of settings independence, isrequired. Loosely speaking, such an extra assumption demands independencebetween the states of the measurement apparatuses. We conclude that it ispossible to construct a model, satisfying both the principle of local causalityand settings independence, but that, in virtue of violating this additionalassumption--and thus factorizability--is able to break Bell's inequality.

From locality to factorizability: a novel escape from Bell's theorem