  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.
