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.
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 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 show that quantum nonequilibrium (or deviations from the Born rule) can propagate nonlocally across space. Such phenomena are allowed in the de Broglie–Bohm pilot-wave formulation of quantum mechanics. We show that an entangled state can act as a channel whereby quantum nonequilibrium can be transferred nonlocally from one region to another without any classical interaction. This suggests a novel mechanism whereby information can escape from behind the classical event horizon of an evaporating black hole.
We present arguments suggesting that deviations from the Born probability rule could be generated for trans-Planckian field modes during inflation. Such deviations are theoretically possible in the de Broglie-Bohm pilot-wave formulation of quantum mechanics, according to which the Born rule describes a state of statistical equilibrium. We suggest that a stable equilibrium state can exist only in restricted conditions: on a classical background spacetime that is globally hyperbolic or in a mild quantum-gravity regime in which there is an effective Schrödinger equation with a well-defined time parameter. These arguments suggest that quantum equilibrium will be unstable at the Planck scale. We construct a model in which quantum nonequilibrium is generated by a time-dependent regulator for pilot-wave dynamics, where the regulator is introduced to eliminate phase singularities. Applying our model to trans-Planckian modes that exit the Planck radius, we calculate the corrected primordial power spectrum and show that it displays a power excess (above a critical wavenumber). We briefly consider how our proposals could be tested by measurements of the cosmic microwave background.
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.
In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we develop field-theoretical models of quantum nonequilibrium systems which could exist today as relics from the very early Universe. We consider relic excited states generated by inflaton decay, as well as relic vacuum modes, for particle species that decoupled close to the Planck temperature. Simple estimates suggest that, at least in principle, quantum nonequilibrium could survive to the present day for some relic systems. The main focus of this paper is to describe the behavior of such systems in terms of field theory, with the aim of understanding how relic quantum nonequilibrium might manifest experimentally. We show by explicit calculation that simple perturbative couplings will transfer quantum nonequilibrium from one field to another (for example from the inflaton field to its decay products). We also show that fields in a state of quantum nonequilibrium will generate anomalous spectra for standard energy measurements. Possible connections to current astrophysical observations are briefly addressed.