We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional
Ψ, must be in quantum nonequilibrium with a probability distribution
P=∣Ψ∣2 (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions
ψ. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution
ρ=∣ψ∣2 at the beginning of the semiclassical regime, with quantum relaxation
ρ→∣ψ∣2 taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution
ρ=∣ψ∣2 can evolve to a final distribution
ρ=∣ψ∣2. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit
∼1/k3 in the primordial power spectrum at wavenumber
k, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.
We study incomplete relaxation to quantum equilibrium at long wavelengths, during a preinflationary phase, as a possible explanation for the reported large-scale anomalies in the cosmic microwave background. Our scenario makes use of the de Broglie--Bohm pilot-wave formulation of quantum theory, in which the Born probability rule has a dynamical origin. The large-scale power deficit could arise from incomplete relaxation for the amplitudes of the primordial perturbations. We show, by numerical simulations for a spectator scalar field, that if the preinflationary era is radiation dominated then the deficit in the emerging power spectrum will have a characteristic shape (an inverse-tangent dependence on wave number
k, with oscillations). It is found that our scenario is able to produce a power deficit in the observed region and of the observed (approximate) magnitude for an appropriate choice of cosmological parameters. We also discuss the large-scale anisotropy, which might arise from incomplete relaxation for the phases of the primordial perturbations. We present numerical simulations for phase relaxation, and we show how to define characteristic scales for amplitude and phase nonequilibrium. The extent to which the data might support our scenario is left as a question for future work. Our results suggest that we have a potentially viable model that might explain two apparently independent cosmic anomalies by means of a single mechanism.
Quantum mechanics is a highly successful fundamental theory which has passed every experimental test to date. Yet standard quantum mechanics fails to provide an adequate description of measurement processes, which has long been rationalized with operationalist and positivist philosophical arguments but is nevertheless a serious shortfall in a fundamental theory. In this dissertation we introduce quantum mechanics with a discussion of the measurement problem. We then review the de Broglie-Bohm pilot-wave formulation, a nonlocal hidden-variables theory where the state of a quantum system is described by a configuration (independent of measurements) in addition to the wave function, and we apply it to fundamental problems concerning black holes and the early universe.\nIn de Broglie-Bohm theory, general initial conditions allow for deviations from the statistical predictions of standard quantum mechanics. We review how the Born rule can be understood as the result of an equilibration process for systems with sufficient mixing before proceeding to study the implications of quantum nonequilibrium in various physical contexts.\nIn this work we show that small perturbations to a system are themselves insufficient to drive relaxation to quantum equilibrium even over very long timescales. This has implications for the potential survival of nonequilibrium in relic particles, and renders it unlikely that field perturbations can be driven to equilibrium by small corrections to the Bunch-Davies vacuum during inflation, allowing for the possible detection of imprints of nonequilibrium in the cosmic microwave background. Using a simple model we also demonstrate how quantum nonequilibrium can propagate nonlocally through entanglement, providing a mechanism for information flow from black holes. This opens up a possible path to the resolution of the black hole information paradox by allowing for information to be released in hidden variable degrees of freedom during black hole evaporation. Finally, we consider whether features in the angular power spectrum of temperature anisotropies in the cosmic microwave background radiation could arise from quantum nonequilibrium initial conditions. Preliminary results indicate that this approach can provide a natural explanation for the power deficit anomaly at large angular scales, as well as oscillatory features in the same regime.
Abstract We investigate the dynamical stability and relaxation of subquantum non-equilibrium states within the framework of De Broglie Bohm field theory during primordial inflation. By evaluating the quantum Hamilton-Jacobi formalism on a covariant Friedmann-Lemaître Robertson-Walker (FLRW) background, I demonstrate that non-linearities intrinsic to the field-theoretic quantum potential generate microscopic phase-space chaos. I solve the Jacobi deviation equation for coupled Fourier modes and extract the maximal Lyapunov exponent spectrum. I find that sub-horizon modes exhibit rapid exponential trajectory divergence driving coarse-grained subquantum entropy toward zero via Valentini's subquantum H-theorem. This dynamic phase-mixing enforces the Born rule well before horizon crossing, rendering anti-relaxation statistically prohibited for generic inflationary potentials. Finally, I map residual non-equilibrium corrections onto the Cosmic Microwave Background (CMB) power spectrum at low multipoles establishing current observational bounds from Planck 2018 data and providing forecasts for B-mode polarization measurements from LiteBIRD and CMB-S4.
We show that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances and at very early times. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with nonstandard field fluctuations (``quantum nonequilibrium''). We show that inflationary expansion can transfer microscopic nonequilibrium to macroscopic scales, resulting in anomalous power spectra for the cosmic microwave background. The conclusions depend only weakly on the details of the de Broglie-Bohm dynamics. We discuss, in particular, the nonequilibrium breaking of scale invariance for the primordial (scalar) power spectrum. We also show how nonequilibrium can generate primordial perturbations with nonrandom phases and intermode correlations (primordial non-Gaussianity). We address the possibility of a low-power anomaly at large angular scales, and show how it might arise from a nonequilibrium suppression of quantum noise. Recent observations are used to set an approximate bound on violations of quantum theory in the early Universe.
We show how pilot-wave theory points to new physics, beyond quantum mechanics, in three distinct ways. First, generalised cosmological initial conditions, departing from the Born rule, can lead to observable anomalies in the cosmic microwave background and in relic cosmological particles. Second, a breakdown of the Born rule in the deep quantum-gravity regime, with gravitational corrections that render the Born rule semiclassically unstable, can create anomalies in Hawking radiation from evaporating black holes. Third, a regularised equation of motion that remains finite at nodes of the wave function generates corrections to the Born rule at short distances, while a natural time-dependent generalisation implies an instability of quantum equilibrium at short times, effects which may be observable in high-energy collisions.