Bell's go theorem: regaining local causality with a new notion of realism

Abstract

Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. Realism is here formalized by the ontological models framework, where elements of reality are points of a measurable space and probabilities obey the Kolmogorov axioms. In the Bell scenario, locally causal ontological models posit a common cause supporting a global valuation, a joint assignment of outcomes to all measurements at once, across incompatible contexts. Within this notion of realism, Bell's theorem makes any realist explanation of the quantum predictions conspiratorial: any mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest operationally. We redefine realism through a new ontological framework that generalizes the standard one. The elements of reality, which we call records, are no longer points but relational parts of a point-free generalization of a topological space (sublocales of a locale). A record shared by two incompatible contexts establishes the sameness of a measurement across them, without such pairwise identities composing into a global valuation, and the common cause is then a web of such records. Within this framework, Bell's no-go theorem becomes a go theorem: local causality, restated for records, is no longer at odds with the quantum statistics. This is possible because modularity, the inclusion-exclusion law of classical probability, fails across incompatible contexts, so that the probability theory generalizes Kolmogorov's. We exhibit explicit models reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell-CHSH value up to the algebraic maximum. A realist explanation of the quantum predictions need not be conspiratorial; every causal influence posited by these models is reflected in the operational predictions.