A realistic model, where the apparatus simulates
a magnetic dot and where the tested system is a spin, is exactly solved.
Several time scales are exhibited, characterizing the establishment and
disappearance of correlations and the registration.  As in the solution of
the irreversibility paradox in statistical mechanics, the irreversibility of
the measurement emerges from the Schrödinger dynamics, through statistical
arguments based on the large number of degrees of freedom of the apparatus
and on the time scales of the process. The reduction of the state, as well
as the possibility of interpreting the quantum measurement process in terms
of classical probabilities and classical correlations, emerge likewise from
the general laws of quantum mechanics.