  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.
