Abstract

It’s 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 don’t follow trajectories because a particle in our world is a set of _elemental_ particles following different trajectories, each in a thread. The “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. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition.