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.

39 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

References in corpus (13)

• Primordial Black Holes as Dark Matter
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation
• On Galilean and Lorentz invariance in pilot-wave dynamics
• Astrophysical and Cosmological Tests of Quantum Theory
• De Broglie-Bohm Guidance Equations for Arbitrary Hamiltonians
• Signatures of Quantum Gravity in a Born-Oppenheimer Context
• Multiple-event probability in general-relativistic quantum mechanics
• The de Broglie-Bohm Quantum Theory and its Application to Quantum Cosmology
• Black Holes, Information Loss, and Hidden Variables
• De Broglie-Bohm Prediction of Quantum Violations for Cosmological Super-Hubble Modes
• Multiple-event probability in general-relativistic quantum mechanics: a discrete model
• Trans-Planckian fluctuations and the stability of quantum mechanics
• Quantum gravity and quantum probability

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