Symmetries, superselection rules, and decoherence

TL;DR

This paper examines how symmetries and superselection rules influence decoherence, highlighting that certain superpositions become practically inaccessible despite existing theoretically, especially in the context of charges and masses.

Contribution

It clarifies the distinction between pure symmetries and redundancies, and analyzes how decoherence affects superpositions related to charges and masses.

Findings

Superpositions with different charges are theoretically possible but become inaccessible via decoherence.

Superpositions with different masses also become practically inaccessible through decoherence.

The distinction between symmetries and redundancies is crucial for understanding superselection rules.

Abstract

We discuss the applicability of the programme of decoherence -- emergence of approximate classical behaviour through interaction with the environment -- to cases where it was suggested that the presence of symmetries would lead to exact superselection rules. For this discussion it is useful to make a distinction between pure symmetries and redundancies, which results from an investigation into the constraint equations of the corresponding theories. We discuss, in particular, superpositions of states with different charges, as well as with different masses, and suggest how the corresponding interference terms, although they exist in principle, become inaccessible through decoherence.