On the preferred-basis problem and its possible solutions

Abstract

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.