Interpretation of quantum theory: the quantum "grue-bleen" problem

Abstract: We present a critique of the many-world interpretation of quantum mechanics, based on different pictures'' that describe the time evolution of an isolated quantum system. Without an externally imposed frame to restrict these possible pictures, the theory cannot yield non-trivial interpretational statements. This is analogous to Goodman's famousgrue-bleen'' problem of language and induction. Using a general framework applicable to many kinds of dynamical theories, we try to identify the kind of additional structure (if any) required for the meaningful interpretation of a theory. We find that the ``grue-bleen'' problem is not restricted to quantum mechanics, but also affects other theories including classical Hamiltonian mechanics. For all such theories, absent external frame information, an isolated system has no interpretation.