Wheeler-DeWitt quantization and singularities

Falciano, F. T.; Pinto-Neto, Nelson; Struyve, Ward

doi:10.1103/physrevd.91.043524

Cited by 29 publications

(37 citation statements)

References 34 publications

(123 reference statements)

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“…These are typically based on the Wheeler-DeWitt quantum equation. Relevant progresses in this directions can be found for example in [69][70][71][72], where conceptual features/differences characterizing the Bohmian approach to quantum gravity (in terms of trajectories) with respect to previous customary approaches were clearly stated. The GLP representation of CQG-theory proposed in the present paper shares the conceptual advantages of adopting a Bohmian approach to quantum physics.…”

Section: Quantum Gravity Theories and Bohmian Formulation In Literaturementioning

confidence: 99%

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Tessarotto

Cremaschini

2018

Entropy

104

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A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proven to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.

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Section: Quantum Gravity Theories and Bohmian Formulation In Literaturementioning

confidence: 99%

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Tessarotto

Cremaschini

2018

Entropy

104

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“…The Bohmian theory describes the evolution of an actual metric and hence there are singularities whenever this metric is singular, i.e., when a = 0. The question of singularities in the special case where V M = V G = 0 was considered in [32,41]. In this case, the Wheeler-DeWitt equation is…”

Section: Free Massless Scalar Fieldmentioning

confidence: 99%

Bohmian Quantum Gravity and Cosmology

Pinto-Neto¹,

Struyve²

2019

Applied Bohmian Mechanics

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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.

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“…Some cosmological applications of the Bohmian approach to quantum gravity are the explanation of the quantum-to-classical transition in inflation theory [22,23] and the study of space-time singularities [24][25][26].…”

Section: Quantum Gravitymentioning

confidence: 99%

Towards a Novel Approach to Semi-Classical Gravity

Struyve

2017

The Philosophy of Cosmology

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Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a space-time metric which satisfies Einstein's field equations. In the usual approach to semiclassical gravity, the matter source term in Einstein's field equations is given by the expectation value of the energy-momentum tensor operator. In this paper, we suggest an alternative approach based on Bohmian mechanics. In Bohmian mechanics, a quantum system is described by an actual configuration (e.g., an actual scalar field), which evolves under the influence of the wave function. The idea is to consider the actual energy-momentum tensor corresponding to this configuration as the matter source term in Einstein's field equations. This approach is expected to improve upon the usual approach.

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Wheeler-DeWitt quantization and singularities

Cited by 29 publications

References 34 publications

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Bohmian Quantum Gravity and Cosmology

Towards a Novel Approach to Semi-Classical Gravity

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