  The mechanism of the transition of a dynamical system from quantum to
classical mechanics is one of the remaining challenges of quantum theory.
Currently, it is considered to occur via decoherence caused by entanglement
and/or stochastic interaction with a quantum environment. Here we prove that,
in the absence of de-phasing environmental interaction, the asymptotic spatial
wave function of any quantum system, propagating over distances and times large
on an atomic scale but still microscopic, and subject to arbitrary
deterministic fields, becomes proportional to the initial momentum wave
function, \emph{where the particle positions and momenta are related by
classical mechanics.} This implies that detection of particle positions and
momenta at different times will yield results in accordance with classical
mechanics, without the need to postulate decoherence of the wave function.
