Macroscopic Reality from Quantum Complexity

TL;DR

This paper proposes a novel approach to understanding macroscopic reality from quantum mechanics by decomposing quantum states into branches based on minimizing quantum complexity, with implications for the quantum-classical transition.

Contribution

It introduces a complexity-based branch decomposition method that unifies non-relativistic and Lorentz covariant formulations of quantum branching.

Findings

Branching occurs repeatedly over time in the non-relativistic case.

In the Lorentz covariant version, the real world is a single random branch at late times.

The complexity measure depends on a parameter that could be experimentally determined.

Abstract

Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. Here we propose a decomposition of a state vector into branches by finding the minimum of a measure of the mean squared quantum complexity of the branches in the branch decomposition. In a non-relativistic formulation of this proposal, branching occurs repeatedly over time, with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen randomly according to the Born rule. In a Lorentz covariant version, the real world is a single random draw from the set of branches at asymptotically late time, restored to finite time by sequentially retracing the set of branching events implied by the late time choice. The complexity measure depends on a parameter $b$ with units of volume which sets the boundary between quantum and classical behavior. The value of $b$ is, in principle, accessible to experiment.