  Non-relativistic quantum mechanics is shown to emerge from classical
mechanics through the requirement of a relativity principle based on special
transformations acting on position and momentum uncertainties. These
transformations keep the Heisenberg inequalities invariant and form a group.
They are related to dilatations of space variables provided the quantum
potential is added to the classical Hamiltonian functional. The Schr\"odinger
equation appears to have a nonunitary and nonlinear companion acting in another
time variable. Evolution in this time seems related to the state vector
reduction.
