  The main distinction between classical mechanics and quantum mechanics is the
lack in the latter of a full mechanical determinism: different final states can
arise from the same physical state, after the measurement. No hidden variable
is supposed to exist, nothing can discriminate two apparently identical states
even if they give a different result. In this paper we try to put the basis for
a more fundamental theory that (approximately) coincides with quantum mechanics
when comparing statistics, but it is more fundamental, since it mathematically
describes measurement processes giving an explicit time evolution of the wave
function during the collapse. The theory is deterministic even if the
Heisenberg uncertainty principle is still valid. The theory distinguishes
physical states that collapse and physical states that do not collapse. The
theory can be made compatible with all experiments done in the past, but new
phenomena such as violations of the Born law or the superposition principle
could transpire. However, even if we have probably shown that it is possible to
build ad hoc a theory that can describe both the wave function collapse and the
Schroedinger linear evolution, a simple and unified construction is still
missing.
