Quantum spacetime without observers: Ontological clarity and the conceptual foundations of quantum gravity

Abstract

We explore the possibility of a Bohmian approach to the problem of finding a quantum theory incorporating gravitational phenomena. The major conceptual problems of canonical quantum gravity are the problem of time and the problem of diffeomorphism invariant observables. We find that these problems are artifacts of the subjectivity and vagueness inherent in the framework of orthodox quantum theory. When we insist upon ontological clarity-the distinguishing characteristic of a Bohmian approach-these conceptual problems vanish. We shall also discuss the implications of a Bohmian perspective for the significance of the wave function, concluding with unbridled speculation as to why the universe should be governed by laws so apparently bizarre as those of quantum mechanics.

The Ontology of Bohmian Mechanics

“…The relationship between the wavefunction and the motion of the particles is more appropriately conceived as a nomic one, rather than as a causal one in which one physical entity acts on the other. This leads us to the nomological interpretation of the wave-function, as suggested by Dü rr et al ([1997]), Goldstein and Teufel ([2001]) and Goldstein and Zanghì ([2013]). …”

“…The time-dependence of the effective wave-functions then comes only from the evolution of the spatial configuration, Y(t), of the particles that are not part of the described subsystem (see Goldstein and Teufel [2001] for details). In brief, the universal wave-function entering the guiding equation may well be a stationary solution of the universal Schrö dinger equation and still account for the usual quantum behaviour of subsystems as described by effective wave-functions and their Schrö dinger equations.…”

“…Furthermore, it is committed to a law of motion that describes how the positions of the particles develop in time. That's all (see, in particular, Dü rr et al [1997]; Goldstein and Teufel [2001]; Dü rr and Teufel [2009] for a textbook presentation). In particular, Newtonian concepts like acceleration and forces do not enter into the formulation of the theory, and velocities are not an additional independent parameter.…”

Reality and the Role of the Wave Function in Quantum Theory

“…For example, Stefan Teufel and one of us explored the possibility that a symmetry principle expressing a sort of quasi-4-diffeomorphism invariance would imply an evolution of 3-geometries governed by a universal wave function [19]. In technical terms, we demanded that the vector field on superspace defining the relevant motion form a representation of the "Dirac algebra" [8], a sort of algebra, sort of corresponding to 4-diffeomorphism invariance.…”

Solving the Measurement Problem: De Broglie--Bohm Loses Out to Everett

“…If we encountered objects like these, we would not deem them "immaterial" simply because they were made out of the wrong sort of field. 43 And let us not forget that the pure electromagnetic field is capable on its own of bending space-time-and that there is every reason to think that the wavefunction is too.…”