Vacuum Branching, Dark Energy, Dark Matter

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. In an earlier version of the present work, we proposed 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 the present article, we adapt the earlier version to quantum electrodynamics of electrons and protons on a lattice in Minkowski space. The earlier version, however, here is simplified by replacing a definition of complexity which takes the physical vacuum as 0 complexity starting point, with a definition which takes the bare vacuum as starting point. As a consequence of this replacement, the physical vacuum itself is expected to branch yielding branches with energy densities slightly larger than that of the unbranched vacuum. If the vacuum energy renormalization constant is chosen as usual to give 0 energy density to the unbranched vacuum, in an expanding universe vacuum branches will appear to have a combination of dark energy and dark matter densities. The hypothesis that vacuum branching is the origin of the observed dark energy and dark matter densities leads to an estimate of \(\mathcal {O}(10^{-18} {m}^3)\) for the parameter b which enters the complexity measure governing branch formation and sets the boundary between quantum and classical behavior.