Beyond the Born rule in quantum gravity

Antony Valentini

doi:10.1007/s10701-022-00635-0

paper

Beyond the Born rule in quantum gravity

arXiv:2212.12175 · doi:10.1007/s10701-022-00635-0

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 $Ψ$ . Instead the universe is in a perpetual state of quantum nonequilibrium with a probability density $P \neq = ∣ Ψ ∣^{2}$ . 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 $ψ$ , for non-gravitational systems on a classical spacetime background. In that regime the probability density $ρ$ can relax towards $∣ ψ ∣^{2}$ (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 $ρ \neq = ∣ ψ ∣^{2}$ to be created from a prior equilibrium ( $ρ = ∣ ψ ∣^{2}$ ) state. Such effects are very tiny and difficult to observe in practice.

arXiv comment39 pages. For special issue of Foundations of Physics, 'Pilot-wave and beyond: Louis de Broglie and David Bohm's quest for a quantum ontology', ed. A. Drezet

Beyond the Born rule in quantum gravity

Abstract

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