Beyond the Born rule in quantum gravity

TL;DR

This paper proposes a new understanding of probability in quantum gravity using the de Broglie-Bohm formulation, suggesting the universe is in quantum nonequilibrium at fundamental levels, with relaxation to the Born rule occurring after the early universe.

Contribution

It introduces a framework where the Born rule does not hold at the fundamental quantum gravity level and explains how relaxation to it occurs in the semiclassical regime.

Findings

No Born rule at the fundamental quantum gravity level.

Quantum nonequilibrium can be generated by quantum-gravitational effects.

Relaxation to the Born rule occurs after the early universe in a semiclassical regime.

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.