  The preferred basis problem is mentioned in the literature in connection with
the measurement problem and with the Many World Interpretation. It is argued
that this problem actually corresponds to two inequivalent problems: (i) the
preferred-decomposition problem, i.e., what singles out a preferred
decomposition of a suitable state vector of a system as the sum of a finite or
countable set of vectors?, and (ii) the preferred-representation problem, i.e.,
what singles out a preferred representation for the Hilbert space of a system?
In this paper the preferred-decomposition problem is addressed and two
processes, namely decoherence and permanent spatial decomposition (PSD), are
examined and compared as possible solutions to this problem. It is shown that,
perhaps contrary to common belief, in realistic situations decoherence is not
sufficient to solve the preferred-decomposition problem. PSD is the
(hypothesized) tendency of the wave function of the universe to decompose into
permanently non-overlapping wave packets. Three phases can be roughly
identified as composing PSD: Microscopic decomposition, amplification, and
interaction with the environment. Decoherence theory considers only the
interaction with the environment and ignores the first two phases. For this
reason PSD is fundamentally different from decoherence and, unlike decoherence,
provides a simple and non-elusive solution to the preferred-decomposition
problem.
