  We provide a mechanism by which, from a background independent model with no
quantum mechanics, quantum theory arises in the same limit in which spatial
properties appear. Starting with an arbitrary abstract graph as the microscopic
model of spacetime, our ansatz is that the microscopic dynamics can be chosen
so that 1) the model has a low low energy limit which reproduces the
non-relativistic classical dynamics of a system of N particles in flat
spacetime, 2) there is a minimum length, and 3) some of the particles are in a
thermal bath or otherwise evolve stochastically. We then construct simple
functions of the degrees of freedom of the theory and show that their
probability distributions evolve according to the Schroedinger equation. The
non-local hidden variables required to satisfy the conditions of Bell's theorem
are the links in the fundamental graph that connect nodes adjacent in the graph
but distant in the approximate metric of the low energy limit. In the presence
of these links, distant stochastic fluctuations are transferred into universal
quantum fluctuations.
