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Bohmian Quantum Gravity and Cosmology

Nelson Pinto-Neto, Ward Struyve

Published May 24, 2019• 33 citations
Publisher

Abstract

This chapter focuses on canonical quantum gravity and discusses how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. It shows that a significant progress can be made by considering the canonical quantization of gravity from the Bohmian point of view. The chapter highlights some important properties that will also be used in the context of quantum gravity. It explores the conceptual problems that appear when trying to interpret the theory in the context of orthodox quantum theory. The chapter describes Bohmian quantum gravity and explains how it solves the conceptual problems and minisuperspace models. It also shows how the problem of the quantum-to-classical limit in inflationary and bouncing models is solved. The chapter provides a new approach to semiclassical gravity, which treats gravity classically and matter quantum mechanically, based on Bohmian mechanics.

DOI
10.1201/9780429294747-11

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This chapter focuses on canonical quantum gravity and discusses how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. It shows that a significant progress can be made by considering the canonical quantization of gravity from the Bohmian point of view. The chapter highlights some important properties that will also be used in the context of quantum gravity. It explores the conceptual problems that appear when trying to interpret the theory in the context of orthodox quantum theory. The chapter describes Bohmian quantum gravity and explains how it solves the conceptual problems and minisuperspace models. It also shows how the problem of the quantum-to-classical limit in inflationary and bouncing models is solved. The chapter provides a new approach to semiclassical gravity, which treats gravity classically and matter quantum mechanically, based on Bohmian mechanics.
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explains the historical development of Bohmian mechanics, Bohmian mechanics for single particle and for many particle systems. It discusses the dynamics of a single hydrogen atom interacting with a strong laser and presents a clear example on how a Bohmianthinking on superluminal velocities and nonlocal interactions helps in extending the quantum theory towards relativity and quantum field theory. The book also explains model nanoscale electron devices and their Bohmiancomputing development for knowing the ab initio quantum mechanical structure, energetics and thermodynamics of multiatoms systems. It deals with new cosmological models describing the accelerating universe in the spatially flat case. The book describes how many conceptual problems that appear in a description of gravity in quantum mechanical terms, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian perspective.
The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.
This final chapter starts with a brief review of quantum-gravity phenomenology. It then focuses on an important conceptual issue – the relevance of quantum gravity for the general interpretation of quantum theory. A central part is devoted to the discussion of the quantum-to-classical transition, with decoherence as its crucial mechanism. It is shown that the quantum states used in cosmology can be interpreted in a sensible way. The chapter also contains a discussion of the arrow of time in the light of quantum cosmology and ends with a brief outlook and reflections.
Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.