  It is shown that the matrix models which give non-perturbative definitions of
string and M theory may be interpreted as non-local hidden variables theories
in which the quantum observables are the eigenvalues of the matrices while
their entries are the non-local hidden variables. This is shown by studying the
bosonic matrix model at finite temperature, with T taken to scale as 1/N. For
large N the eigenvalues of the matrices undergo Brownian motion due to the
interaction of the diagonal elements with the off diagonal elements, giving
rise to a diffusion constant that remains finite as N goes to infinity. The
resulting probability density and current for the eigenvalues are then found to
evolve in agreement with the Schroedinger equation, to leading order in 1/N.
The quantum fluctuations and uncertainties in the eigenvalues are then
consequences of ordinary statistical fluctuations in the values of the
off-diagonal matrix elements. This formulation of the quantum theory is
background independent, as the definition of the thermal ensemble makes no use
of a particular classical solution. The derivation relies on Nelson's
stochastic formulation of quantum theory, which is expressed in terms of a
variational principle.
