Signal-Locality in Hidden-Variables Theories

We prove that all deterministic hidden-variables theories, that reproduce quantum theory for an ‘equilibrium’ distribution of hidden variables, give instantaneous signals at the statistical level for hypothetical ‘nonequilibrium ensembles’. This generalises another property of de Broglie-Bohm theory. Assuming a certain symmetry, we derive a lower bound on the (equilibrium) fraction of outcomes at one wing of an EPR-experiment that change in response to a shift in the distant angular setting. We argue that the universe is in a special state of statistical equilibrium that hides nonlocality.