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

TL;DR

This paper critiques the many-world interpretation of quantum mechanics, arguing that without external frames, theories like quantum and classical mechanics lack meaningful interpretation, similar to the 'grue-bleen' problem in language and induction.

Contribution

It generalizes the 'grue-bleen' problem to quantum and classical theories, highlighting the necessity of external structure for meaningful interpretation.

Findings

The 'grue-bleen' problem affects quantum and classical theories.

External frames are necessary for interpretability of isolated systems.

The problem is not unique to quantum mechanics but is more general.

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 famous ``grue-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.