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 $$P\ne \left| \Psi \right| ^{2}$$ . Dynamical relaxation to the Born rule can occur only after the early universe has emerged into a semiclassical or Schrödinger 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 $$\left| \psi \right| ^{2}$$ (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 Schrödinger approximation allow quantum nonequilibrium $$\rho \ne \left| \psi \right| ^{2}$$ to be created from a prior equilibrium ( $$\rho =\left| \psi \right| ^{2}$$ ) state. Such effects are very tiny and difficult to observe in practice.