  Non-relativistic quantum mechanics for a free particle is shown to emerge
from classical mechanics through an invariance principle under transformations
that preserve the Heisenberg position-momentum inequality. These
transformations are induced by isotropic space dilations. This invariance
imposes a change in the laws of classical mechanics that exactly corresponds to
the transition to quantum mechanics. The Schroedinger equation appears jointly
with a second nonlinear equation describing non-unitary processes. Unitary and
non-unitary evolutions are exclusive and appear sequentially in time. The
non-unitary equation admits solutions that seem to correspond to the collapse
of the wave function.
