Horvat's "Probabilistic Locality" principle is logically independent of Bell's "Local Causality" criterion

physicsphysics.hist-phquant-phquantum-foundationsbell-theoremlocalityprobabilityarxiv

Sebastian Horvat (University of Vienna) defines a new constraint on probabilistic physical theories, "Probabilistic Locality": the probability distribution of what can happen at a spacetime point y is entirely determined by (supervenes on) the probability distribution of what can happen in y's immediate causal past. This differs in form from Bell's own criterion of "Local Causality" (Bell's theorem's underlying locality condition), which conditions a single probability distribution on events in the causal past and screens off correlations to spacelike-separated events — a constraint on one distribution rather than a relation between distributions across different possible initial conditions. Horvat proves the two criteria are logically independent of each other — neither implies the other — via two constructed counterexample theories (the paper's Principle 2, the Local Causality principle, and Proposition 2).