  We give a counter example to show that determinism as such is in
contradiction to quantum mechanics. More precisely, we consider a simple
quantum system and its environment, including the measurement device, and make
the assumption that the time evolution of the global system, the quantum system
plus this environment, is deterministic, i. e., the time evolution is given by
a dynamical trajectory from some initial conditions. From this, we prove a type
of Bell inequalities which are violated by quantum mechanics, reaching the
conclusion that our quantum system evolves in a non deterministic way. In order
to seize the interest of this conclusion, one must realize that it cannot be
reached from the present experimental violation of Bell inequalities predicted
by quantum mechanics, since this violation is compatible with non-local
realism.
