Bohmian Quantum Gravity and Cosmology

Abstract

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.

Against the disappearance of spacetime in quantum gravity

“…They are also available in the context of quantum gravity. For instance, a Bohmian primitive ontology for quantum gravity is pursued in Goldstein and Teufel (2001), Vassallo and Esfeld (2014) and Pinto-Neto and Struyve (2018). A primitive ontology of GRW flashes is pursued in Tilloy (2018) (see also Okon and Sudarsky 2014 for wave function collapse models in quantum gravity).…”

On the status of conservation laws in physics: Implications for semiclassical gravity

“…It is worth mentioning that the pilot-wave approach offers a natural path to deal with the full quantum gravity problem, in which both matter fields and the metric are treated quantum mechanically (see [35]). To do so, one again considers a globally hyperbolic spacetime with a preferred foliation, characterized by a lapse function N and a shift vector N i , together with a Hamiltonian characterization of the metric variables 20 .…”

Elimination of cosmological singularities in quantum cosmology by suitable operator orderings

“…with N as an arbitrary function of time [18]. This dynamics preserves the measure |ψ(a, T )| 2 a m+1 dadT (which is no probability measure).…”

“…is constant as a function of τ , i.e., ∂ τ φ 2 = 0. On the other hand, from the continuity equation (18) we have…”