Everettian relative states in the Heisenberg picture

TL;DR

This paper develops a new formulation of Everett's relative states within the Heisenberg picture, clarifying the locality and nature of quantum multiplicity, and refining the concept of an Everett universe.

Contribution

It provides the first satisfactory Heisenberg-picture construction of Everett's relative states, highlighting locality and the role of entanglement in quantum multiplicity.

Findings

Makes manifest the locality of Everettian multiplicity

Defines a fully quantum Everett 'universe'

Connects Everettian decomposition with spacetime foliation

Abstract

Everett's relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schr\"odinger picture, makes manifest the locality of Everettian multiplicity, and its inherently approximative nature, and its origin in certain kinds of entanglement and locally inaccessible information. Our construction also allows us to give a more precise definition of an Everett 'universe', under which it is fully quantum, not quasi-classical, and we compare the Everettian decomposition of a quantum state with the foliation of a spacetime.