  We develop a rigorous treatment of discontinuous stochastic unitary evolution
for a system of quantum particles that interacts singularly with quantum
"bubbles" at random instants of time. This model of a "cloud chamber" allows to
watch and follow with a quantum particle along the trajectory in the cloud
chamber by sequential unsharp localization of spontaneous scatterings of the
bubbles. Thus, the continuous reduction and spontaneous localization theory is
obtained as the result of quantum filtering theory, i.e., a theory describing
the conditioning of the a priori quantum state by the measurement data. We show
that in the case of indistinguishable particles the a posteriori dynamics is
mixing, giving rise to an irreversible Boltzmann-type reduction equation. The
latter coincides with the nonstochastic Schroedinger equation only in the mean
field approximation, whereas the central limit yields Gaussian mixing
fluctuations described by stochastic reduction equations of diffusive type.
