Beyond the Born rule in quantum gravity

Abstract: We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we argue that there is no Born rule at the fundamental level of quantum gravity with a non-normalisable Wheeler-DeWitt wave functional $\Psi$. Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density $P\neq\left\vert \Psi\right\vert ^{2}$. Dynamical relaxation to the Born rule can occur only after the early universe has emerged into a semiclassical or Schr\"{o}dinger approximation, with a time-dependent and normalisable wave functional $\psi$, for non-gravitational systems on a classical spacetime background. In that regime the probability density $\rho$ can relax towards $\left\vert \psi\right\vert ^{2}$ (on a coarse-grained level). Thus the pilot-wave theory of gravitation supports the hypothesis of primordial quantum nonequilibrium, with relaxation to the Born rule taking place soon after the big bang. We also show that quantum-gravitational corrections to the Schr\"{o}dinger approximation allow quantum nonequilibrium $\rho\neq\left\vert \psi\right\vert ^{2}$ to be created from a prior equilibrium ($\rho=\left\vert \psi\right\vert ^{2}$) state. Such effects are very tiny and difficult to observe in practice.