  We consider the hypothesis that quantum mechanics is an approximation to
another, cosmological theory, accurate only for the description of subsystems
of the universe. Quantum theory is then to be derived from the cosmological
theory by averaging over variables which are not internal to the subsystem,
which may be considered non-local hidden variables. We find conditions for
arriving at quantum mechanics through such a procedure. The key lesson is that
the effect of the coupling to the external degrees of freedom introduces noise
into the evolution of the system degrees of freedom, while preserving a notion
of averaged conserved energy and time reversal invariance.
  These conditions imply that the effective description of the subsystem is
Nelson's stochastic formulation of quantum theory. We show that Nelson's
formulation is not, by itself, a classical stochastic theory as the conserved
averaged energy is not a linear function of the probability density. We also
investigate an argument of Wallstrom posed against the equivalence of Nelson's
stochastic mechanics and quantum mechanics and show that, at least for a simple
case, it is in error.
