  We discuss V.P. Belavkin's (2007) approach to the Schr\"odinger cat problem
and show its close relation to ideas based on superselection and interaction
with the environment developed by N.P. Landsman (1995). The purpose of the
paper is to explain these ideas in the most simple possible context, namely:
discrete time and separable Hilbert spaces, in order to make them accessible to
those coming from the philosophy of science and not too happy with
idiosyncratic notation and terminology and sophisticated mathematical tools.
Conventional elementary mathematical descriptions of quantum mechanics take
"measurement" to be a primitive concept. Paradoxes arise when we choose to
consider smaller or larger systems as measurement devices in their own right,
by making different and apparently arbitrary choices of location of the
"Heisenberg cut". Various quantum interpretations have different resolutions of
the paradox. In Belavkin's approach, the classical world around us does really
exist, and it evolves stochastically and dynamically in time according to
probability laws following from successive applications of the Born law. It is
a collapse theory, and necessarily it is non-local. The quantum/classical
distinction is determined by the arrow of time. The underlying unitary
evolution of the wave-function of the universe enables the designation of a
collection of beables which grows as time evolves, and which therefore can be
assigned random, classical trajectories. In a slogan: the past is particles,
the future is a wave. We, living in the now, are located on the cutting edge
between past and future.
