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arXiv:1906.03670

Signatures of relic quantum nonequilibrium

Nicolas G. Underwood

Published Jun 9, 2019• 2 citations
arXivHTMLPDF

Abstract

[Shortened Abstract:] This thesis explores the possibility that quantum probabilities arose thermodynamically. A chief concern is the detection of primordial `quantum nonequilibrium', since this is observably distinct from textbook quantum physics. Chapters 2, 3, 4, and 5 are adaptations of references [1,2,3], and [4] respectively. Chapter 2 proposes (information) entropy conservation as a minimal requirement for a theory to feature classical-style thermodynamic relaxation. The resulting structure is dubbed `the iRelax framework'. Both classical mechanics and de Broglie-Bohm quantum theory are shown to be special cases. Indications for a possible extension or unification of de Broglie-Bohm theory are briefly highlighted. Chapter 3 examines ways in which quantum relaxation may be prevented. The method of the drift-field is introduced. A systematic treatment of nodes is given. A category of quantum states is found for which relaxation is significantly impeded, and may not complete at all. Chapters 4 and 5 consider the possibility that primordial quantum nonequilibrium may be conserved in the statistics of a species of relic cosmological particle. Necessary factors for this to be the case are discussed and illustrative scenarios are given both in terms of nonequilibrium particles created by inflaton decay, as well as relic vacuum modes for species that decoupled close to the Planck temperature. The search for so-called `smoking-gun' spectral lines created by dark matter decay or annihilation is argued to be a particularly promising setting for the detection of quantum nonequilibrium. Unintuitive spectral effects relating to the contextuality of quantum measurements are described. If such a suspected source of quantum nonequilibrium were found, its subjection to a specifically quantum mechanical test would confirm or deny the presence of the quantum nonequilibrium conclusively.

DOI
10.48550/arxiv.1906.03670

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[Shortened Abstract:] This thesis explores the possibility that quantum probabilities arose thermodynamically. A chief concern is the detection of primordial quantum nonequilibrium', since this is observably distinct from textbook quantum physics. Chapters 2, 3, 4, and 5 are adaptations of references [1,2,3], and [4] respectively. Chapter 2 proposes (information) entropy conservation as a minimal requirement for a theory to feature classical-style thermodynamic relaxation. The resulting structure is dubbed the iRelax framework'. Both classical mechanics and de Broglie-Bohm quantum theory are shown to be special cases. Indications for a possible extension or unification of de Broglie-Bohm theory are briefly highlighted. Chapter 3 examines ways in which quantum relaxation may be prevented. The method of the drift-field is introduced. A systematic treatment of nodes is given. A category of quantum states is found for which relaxation is significantly impeded, and may not complete at all. Chapters 4 and 5 consider the possibility that primordial quantum nonequilibrium may be conserved in the statistics of a species of relic cosmological particle. Necessary factors for this to be the case are discussed and illustrative scenarios are given both in terms of nonequilibrium particles created by inflaton decay, as well as relic vacuum modes for species that decoupled close to the Planck temperature. The search for so-called `smoking-gun' spectral lines created by dark matter decay or annihilation is argued to be a particularly promising setting for the detection of quantum nonequilibrium. Unintuitive spectral effects relating to the contextuality of quantum measurements are described. If such a suspected source of quantum nonequilibrium were found, its subjection to a specifically quantum mechanical test would confirm or deny the presence of the quantum nonequilibrium conclusively.
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.
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.
The hypothesis of quantum nonequilibrium at the big bang is shown to have observable consequences. For a scalar field on expanding space, we show that relaxation to quantum equilibrium (in de Broglie-Bohm theory) is suppressed for field modes whose quantum time evolution satisfies a certain inequality, resulting in a 'freezing' of early quantum nonequilibrium for these particular modes. For an early radiation-dominated expansion, the inequality implies a corresponding physical wavelength that is larger than the (instantaneous) Hubble radius. These results make it possible, for the first time, to make quantitative predictions for nonequilibrium deviations from quantum theory, in the context of specific cosmological models. We discuss some possible consequences: corrections to inflationary predictions for the cosmic microwave background, non-inflationary super-Hubble field correlations, and relic nonequilibrium particles.
We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of an equilibrium state. The proposed tests involve searching for nonequilibrium violations of quantum theory in: primordial inflaton fluctuations imprinted on the cosmic microwave background, relic cosmological particles, Hawking radiation, photons with entangled partners inside black holes, neutrino oscillations, and particles from very distant sources.
We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of an equilibrium state. The proposed tests involve searching for nonequilibrium violations of quantum theory in: primordial inflaton fluctuations imprinted on the cosmic microwave background, relic cosmological particles, Hawking radiation, photons with entangled partners inside black holes, neutrino oscillations and particles from very distant sources.
We extend de Broglie--Bohm (dBB) pilot-wave theory by introducing a complex source field into the Schrödinger equation and examining its effects on quantum equilibrium and nonequilibrium dynamics. In dBB theory, the physical particle distribution P, rather than the Born density ∣ψ∣2|ψ|^2∣ψ∣2, carries the ensemble probability, so a source term may modify the pilot wave without violating conservation of total particle probability. We derive the source-modified Hamilton--Jacobi and continuity equations, the transport equation for the nonequilibrium ratio f=P/∣ψ∣2f=P/|ψ|^2f=P/∣ψ∣2, and an exact entropy-production formula. Three applications follow. First, suitably designed sources can drive exponential relaxation toward quantum equilibrium. Second, the entropy-production rate admits a Prigogine-type bilinear form, providing a basis for a subquantum thermodynamics with entropy-producing and entropy-extracting regimes. Third, a tuned source can exactly cancel the Bohmian quantum potential, yielding classical particle trajectories while the guiding wave retains nontrivial structure and the nonequilibrium ratio remains conserved. The resulting framework provides a unified setting for studying source-driven quantum nonequilibrium, entropy exchange, and classicalization, and motivates further investigation of the physical and ontological status of the source field.