  The problem of defining the boundary conditions for the universe is
considered here in the framework of a classical dynamical theory, pointing out
that a measure on boundary conditions must be included in the theory in order
to explain the statistical regularities of evolution. It is then suggested that
quantum statistical regularities also could derive from this measure. An
explicit definition of such a measure is proposed, using both a simplified
model of the universe based on classical mechanics and the non-relativistic
quantum mechanics formalism. The peculiarity of such a measure is that it does
not apply to the initial conditions of the universe, i.e. to the initial
positions and momenta of particles, but to their initial and final positions,
from which the path is derived by means of the least action principle. This
formulation of the problem is crucial and it is supported by the observation
that it is incorrect to liken the determination of the boundary conditions of
the universe to the preparation of a laboratory system, in which the initial
conditions of the system are obviously determined. Some possible objections to
this theory are then discussed. Specifically, the EPR paradox is discussed, and
it is explained by showing that, in general, a measure on the boundary
conditions of the universe generates preinteractive correlations, and that in
the presence of such correlations Bell's inequality can no longer be proven
true. Finally, it is shown that if one broadens the dynamical scheme of the
theory to encompass phenomena such as particle decay and annihilation, the
least action principle allows for an indeterministic evolution of the system.
