  It is emphasized that a many-worlds interpretation of quantum theory exists
only to the extent that the associated basis problem is solved. The core basis
problem is that the robust enduring states specified by environmental
decoherence effects are essentially Gaussian wave packets that form continua of
non-orthogonal states. Hence they are not a discrete set of orthogonal basis
states to which finite probabilities can be assigned by the usual rules. The
natural way to get an orthogonal basis without going outside the Schroedinger
dynamics is to use the eigenstates of the reduced density matrix, and this idea
is the basis of some recent attempts by many-worlds proponents to solve the
basis problem. But these eigenstates do not enjoy the locality and
quasi-classicality properties of the states defined by environmental
decoherence effects, and hence are not satisfactory preferred basis states. The
basis problem needs to be addressed and resolved before a many-worlds-type
interpretation can be said to exist.
