We develop a rigorous treatment of discontinuous stochastic unitary ev
olution for a system of quantum particles that interacts singularly wi
th quantum ''bubbles'' in a cloud chamber at random instants of time.
This model allows us to observe and track quantum particle trajectorie
s as in a cloud chamber by sequential unsharp localization of spontane
ous scatterings of the bubbles. Thus, the continuous reduction and spo
ntaneous localization theory is obtained as the result of quantum filt
ering theory, a theory describing the conditioning of the a priori qua
ntum state by the measurement data. We show that in the case of indist
inguishable particles, the a posteriori dynamics is a mixing dynamics,
giving rise to an irreversible Boltzmannian reduction equation. The l
atter coincides with the nonstochastic Schrodinger equation only in th
e mean field approximation, whereas the central limit yields Gaussian
mixing fluctuations described by stochastic reduction equations of dif
fusive type.