  An explicit dynamical model for non relativistic quantum mechanics with an
effective gravitational interaction is proposed, which, as being well defined,
allows in principle for the evaluation of every physical quantity. Its non
unitary dynamics results from a unitary one in a space with twice as many
degrees of freedom as the ordinary ones. It exhibits a threshold for the
emergence of classical behavior for bodies of ordinary density on rather long
times or instantaneously, respectively at around 10^11 or 10^20 proton masses.
