Observation and superselection in quantum mechanics

TL;DR

This paper clarifies conceptual issues in quantum measurement approaches based on superselection rules, emphasizing environment coupling and proposing minimal observable attribution, challenging traditional assumptions about classical reality.

Contribution

It demonstrates the inadequacy of the prototype superselection approach and advocates for environment-based superselection rules, aligning with environmental decoherence solutions.

Findings

Prototype approach with superselection sectors in state space is untenable.

Coupling system and apparatus to environment supports consistent measurement models.

Only central observables are assigned properties, dropping the eigenvector-eigenvalue link.

Abstract

We attempt to clarify the main conceptual issues in approaches to `objectification' or `measurement' in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical `reality' relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (Hepp) where superselection sectors are assumed in the state space of the apparatus is shown to be untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way `environmental' solutions to the measurement problem (Zeh, Zurek) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor.