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 Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently approximative nature and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian, we are referring not only to Everett's own work, but also to versions of quantum theory that elaborate and refine his. The notion of relative states first appeared in Everett (Everett 1973 In The many worlds interpretation of quantum mechanics (eds BS DeWitt, N Graham)). We are proposing a formalism for relative states that is more detailed and more illuminating than Everett's.) 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 space–time.
Highlights
The dynamical evolution of all quantum systems is unitary at all times except—according to most traditional ‘interpretations’ of quantum theory—during measurements
Construction similar to ours was presented by Hewitt-Horsman & Vedral [12], in their Section V. They do not draw the conclusion that the Heisenberg relative states are states of fully quantum systems, with their own algebras of observables and with the identical structure to those of the original system; nor do they explain that these systems are always local in space and are, not literally universes
Translating between the Schrödinger and Heisenberg pictures is usually a straightforward process, doing so for the relative-state construction brings with it the conceptual difficulty of decomposing the Heisenberg descriptors into relative descriptors: q-numbers which, following a measurement, represent individual instances of a combined quantum system, and which should correspond to the Schrödinger-picture relative-state vectors
Summary
The dynamical evolution of all quantum systems is unitary at all times except—according to most traditional ‘interpretations’ of quantum theory—during measurements. As a consequence of that unitarity, when a measurer has measured an observable of another system, both the system and the measurer exist in multiple instances such that every possible measurement outcome is observed, but in autonomously evolving parts of reality, often called ‘parallel universes’.1. Everett formulated his construction in the Schrödinger picture, in which the parallel universes are described by autonomously evolving components of the universal state vector. The theory of relative states itself, whether by that name or not, is central to all versions of the quantum theory of measurement, for the relative states are where the outcomes of measurements appear explicitly
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