Causality from Indexed Information States: Screening, Intervention, and the Bell Obstruction

Abstract

Wood and Spekkens showed that classical causal explanations of Bell-inequality violations require fine-tuning, and the program they opened asks for a causal vocabulary that privileges no member of the classical triad, “A causes B,” “B causes A,” “a common cause produces both.” This paper extracts one from a framework of observer-indexed partial information states. Its contribution, stated once and held to throughout: it supplies an indexed representation of statistical dependence, proves its screening properties, and identifies the additional structures needed to recover interventions and counterfactuals; the account of causation as coupling in place of production is the philosophical interpretation of that construction and does not borrow the representation results’ certainty. Three things are established, kept distinct. For factorized observational states in the regime of mutually exclusive alternatives, a correlation forces connectivity through graded couplings, separating families screen, screening being pairwise composition, and every screener carries the whole covariance: the statistical content of Reichenbach’s principle, with the classical triad recovered as the narration inventory of its two horns, the horns themselves exhaustive by definition and the substance lying in the graphical sufficient conditions, the factorization equivalences and the covariance identities. For directed mechanism histories, settling is surgery, so the interventional calculus is inherited, and counterfactual evaluation coincides with the functional-model one where functional structure is supplied. In the agreeing regime the Bell-type deviations are located as the boundary of these results: no noncontextual, measurement-independent joint valuation reproduces the two-wing statistics, and the deflationary reparse fails there. A representation theorem shows that hard invalidity together with independent mechanism weights suffices to represent every exclusiveregime state, which is the framework’s re-rendition of the correlation–causation distinction in its defensible form; the representation carries no direction, which mechanism histories supply and the framework does not derive, and the classical conviction that causes precede their effects in proper time is itemized as further conventions on a substrate about jointness, the first of them temporal alignment, motivated by an entropic record asymmetry the framework holds to be statistical and observer-relative. The philosophical proposal, that causal production be replaced by indexed coupling structure, is stated as a proposal and distinct from the proved correspondences.