Super-quantum Correlations in Local Systems With Incompatible Properties

Quantum theory predicts violations of Bell’s inequality. This implies a contradiction with at least one of three statistical conditions, known as “Realism” (joint distribution of relevant observables), “Locality” (conditional separability of pairwise observations, given a set of hidden variables), and “Free Will” (statistical independence between hidden variables and measurement settings). Here we describe a classical system with “clockwork” properties that is unquestionably local. It produces maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It contradicts every one of the three listed formal conditions. Nonetheless, it expresses the qualitative markers of ontological Realism, ontological Locality, and ontological Free Will, all at the same time. In other words, the three listed conditions do not correspond to the three ontological concepts with the same names. Therefore, there is no conflict between quantum theory and Local Realism.