The Bohmian Model of Quantum Cosmology

Callender, Craig; Weingard, Robert

doi:10.1086/psaprocbienmeetp.1994.1.193027

Cited by 14 publications

(15 citation statements)

References 5 publications

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“…Bohmian mechanics has been also used as a realistic causal model for quantum cosmology [171][172][173] to address several open problems such as the still universe resulting from the fact that the Hamiltonian of classical general relativity equals zero, the so-called problem of time. Thus, even for a stationary wave function, the Bohmian formulation can provide a time evolution through the Bohmian trajectories.…”

Section: Beyond Spinless Nonrelativistic Scenariosmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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Abstract. Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

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Section: Beyond Spinless Nonrelativistic Scenariosmentioning

confidence: 99%

Applied Bohmian mechanics

et al. 2014

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“…One particularly interesting way to avoid ordering ambiguity, first proposed in Ref. [34,35], is to find the Lagrangian equivalent to (19), and then define q = f −1/2 (q)dq, so that we end up with the transformed Hamiltonian H = 1 2 p 2 , which has no ordering ambiguity. Now, the quantization of H leads unavoidably to the following rule, for the old variables q and p:…”

Section: The Ordering Problemmentioning

confidence: 99%

“…Ref.[13]. Lagrangian (1) is also related with effective string theory [7] and is also the Einstein frame version of several other scalar-tensor theories of gravity [5].The motivation for adopting an alternative interpretation of quantum mechanics in a cosmological setting comes from the fact that the exterior domain hypothesis [17], tacitly present in most standard interpretations of quantum mechanics, is considered by some authors as being a conceptual problem when the system under investigation is the universe [18][19][20]. Because of that, it has been proposed [20-23] to adopt in cosmology the Bohmian interpretation of quantum mechanics [24,25].…”

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confidence: 99%

Bouncing and cyclic quantum primordial universes and the ordering problem

Torres¹,

Fabris²,

Piattella³

2020

Class. Quantum Grav.

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In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-trivial case. Additionally, we show that the non-singular solutions already present in the trivial ordering formalism keep valid. * Bohmian) quantum cosmology. In Refs. [7-9], it is described how such an alternative interpretation can be generalized from quantum mechanics to cosmological models such as those of Eq. (1). In particular, even when V = 0 one is able to solve the singularity problem thanks to quantum corrections, which induce a bounce. The case of an exponential potential, related with a matter-dominated universe, was recently presented in Ref. [10].The Lagrangian (1) can also be seen as one of the simplest particular cases of Horndeski modified gravity theory [11], thus it is free of Ostrogradsky instability [12,13]. It is also in agreement with the recent constraints imposed by GW170817 and GRB170817A [14-16] on the velocity of gravitational waves. See e.g. Ref.[13]. Lagrangian (1) is also related with effective string theory [7] and is also the Einstein frame version of several other scalar-tensor theories of gravity [5].The motivation for adopting an alternative interpretation of quantum mechanics in a cosmological setting comes from the fact that the exterior domain hypothesis [17], tacitly present in most standard interpretations of quantum mechanics, is considered by some authors as being a conceptual problem when the system under investigation is the universe [18][19][20]. Because of that, it has been proposed [20-23] to adopt in cosmology the Bohmian interpretation of quantum mechanics [24,25]. Besides that, the Bohmian interpretation also solves the problem of time ambiguity in quantum cosmology and quantum gravity [26,27], thanks to the guidance equations. More about Bohm-de Broglie quantum mechanics can be found in Refs. [28][29][30][31][32][33].Another conceptual problem faced in the quantisation of a gravitational theory like (1) is the factor ordering ambiguity, a direct consequence of Dirac's quantisation rule. In Ref. [23], it is shown that the basic features of Bohmian quantum gravity do not really depend on the factor ordering, although some ordering must be chosen to actually apply quantisation. Basead on that argument, it is common to apply only the trivial ordering in the quantization of the constrained Hamiltonian, like it is done in Ref. [23]. But the factor ordering ambiguity remains, so that we can ask ourselves: if the general features of that theory are invariant under a change of ordering...

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“…It turns out, however, as a surprising consequence of the equations (4) and (5), that when a system has wave function Ψ, its configuration is typically random, with probability density ρ given by ρ = |Ψ| 2 , the quantum equilibrium distribution. In other words, it turns out that systems are somehow typically in quantum equilibrium.…”

Section: Bohmian Mechanicsmentioning

confidence: 99%

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

Teufel¹

2001

Physics Meets Philosophy at the Planck Scale

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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.

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The Bohmian Model of Quantum Cosmology

Cited by 14 publications

References 5 publications

Applied Bohmian mechanics

Applied Bohmian mechanics

Bouncing and cyclic quantum primordial universes and the ordering problem

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

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