Decoherence does not imply branching

Description

Title: Decoherence does not imply branching

Author: Ding Jia

Abstract: The Everettian interpretation posits that a quantum state evolving under the Schr{\”o}dinger equation provides a complete description of the universe. A crucial challenge is to explain how the time-oriented branching structure of the many-worlds emerges from the time-symmetric description. The branching-decoherence theorem for decoherent histories states that a set of histories is decoherent if it is branching, and conversely, a set of histories has a branching refinement if it is decoherent. This result has been employed to argue that decoherence implies branching.
The present work demonstrates that this perspective is untenable. Building on the branching-decoherence theorem, I establish a branching refinement-decoherence theorem, which states that a set of histories is decoherent if and only if it possesses a branching refinement. Having a branching refinement is a weaker condition than branching. Notably, this requirement can even be satisfied by a set of antibranching decoherent histories that branches in the opposite time direction. Such antibranching decoherent histories can be identified for all initial conditions. Consequently, decoherence alone is insufficient to imply the time-oriented branching structure, even when paired with a special choice of initial condition.

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• Original versions: Article v1.0