Pilot-Wave Theory without Nonlocality

Abstract: It is generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a thread, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a set of threads locality can be recovered. Our world can be described by a many-threads theory, as defined by Jeffrey Barrett in the opening quote. Particles do not follow trajectories because a particle in our world is a set of elemental particles following different trajectories, each in a thread. The so-called elements of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wave function becomes a three-dimensional density distribution of a particle's subset measures, the stuff of an electron probability cloud. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles, approximated by Many Interacting Worlds theory. EPR-Bell non-locality does not apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition.