Time in Quantum Geometrodynamics

Kheyfets, Arkady; Miller, Warner A.

doi:10.1142/s0217751x00001361

Cited by 3 publications

(5 citation statements)

References 6 publications

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“…York's "extrinsic time" [10] is amongst potential candidates for such a treatment. In this respect it is of interest to compare with the approach by [11]. The progress of these further researches will be reported elsewhere.…”

Section: Discussionmentioning

confidence: 95%

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A nonlinear quantum model of the Friedmann universe

Wang¹

2003

Class. Quantum Grav.

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A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrödinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantisation of a Friedmann universe with a massive scalar field whose dynamical behaviour is investigated numerically.

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Section: Discussionmentioning

confidence: 95%

“…for a wavefunction ψ(q a , t) of weight 1 2 with respect to the metric γ ab (q a , τ (t)). Nonetheless, like (11), the inner product of two wavefunctions ψ 1 and ψ 2 can be defined to be…”

Section: Classical and Quantum Dynamics Of A Non-relativistic Particlementioning

confidence: 99%

A nonlinear quantum model of the Friedmann universe

Wang¹

2003

Class. Quantum Grav.

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“…On the practical side, the theory consists of a Schrödinger equation coupled to the first-order differential expectation valued equation. This system of equations can be successfully solved numerically, which was done in the case of various cosmologies including the Bianchi IX cosmology [5,6]. It was originally expected that one might find effects different from the predictions of the classical theory for the highly non-classical states, for example accelerated expansion of the universe.…”

Section: Discussionmentioning

confidence: 99%

“…In this article we apply the formalism of Quantum Geometrodynamics (QG) [4,5,6,7] to the anisotropic homogeneous Bianchi type IX cosmological model. Because of its structure, it can be parameterized with only few degrees of freedom instead of the infinity of degrees of freedom of the field in the general case.…”

Section: Introductionmentioning

confidence: 99%

Quantum geometrodynamics of the Bianchi IX cosmological model

Kheyfets¹,

Miller²,

Vaulin³

2006

Class. Quantum Grav.

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The canonical quantum theory of gravity -Quantum Geometrodynamics (QG) is applied to the homogeneous Bianchi type IX cosmological model. As a result, the framework for the quantum theory of homogeneous cosmologies is developed. We show that the theory is internally consistent, and prove that it possesses the correct classical limit (the theory of general relativity). To emphasize the special role that the constraints play in this new theory we, compare it to the traditional ADM square-root and Wheeler-DeWitt quantization schemes. We show that, unlike the traditional approaches, QG leads to a well-defined Schrödinger equation for the wave-function of the universe that is inherently coupled to the expectation value of the constraint equations. This coupling to the constraints is responsible for the appearance of a coherent spacetime picture. Thus, the physical meaning of the constraints of the theory is quite different from Dirac's interpretation. In light of this distinctive feature of the theory, we readdress the question of the dark energy effects in the Bianchi IX cosmological model for highly non-classical quantum states. We show that, at least for this model, for any choice of the initial wave function, the quantum corrections will not produce the accelerated expansion of the universe.

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“…A somewhat related approach which also gives cosmic time dependence for averages of certain dynamical variables in the presence of anisotropy was developed by Kheyfets and Miller in Ref. [5]. For the generalization of this approach see Ref.…”

Section: Introductionmentioning

confidence: 99%

Counter-Example Where Cosmic Time Keeps Its Original Role in Quantum Cosmology

Guendelman

Kaganovich

2006

Time and Matter

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In the minisuperspace models of quantum cosmology, the absence of time in the Wheeler-DeWitt (constraint) equation, is the main point leading to the generally accepted conclusion that in the quantum cosmology there is no possibility to describe the evolution of the universe procceding in the cosmic time (the time usually used in classical cosmology). We show that in spite of the constraint, under the specific circumstances, the averaging of some of the Heisenberg equations can give nontrivial additional information about explicit time dependence of the expectation values of certain dynamical variables in quantum cosmology. This idea is realized explicitly in a higher dimensional model with a negative cosmological constant and dust as the sources of gravity. When there is an anisotropy in the evolution of the universe, the above phenomenon (i.e. explicit cosmic time dependence of certain expectation values) appears and we find the new quantum effect which consists in "quantum * The talk presented to International colloquium on the science of time "Time and Matter" at Venice International University, Italy, August 11-17, 2002 † guendel@bgumail.bgu.ac.il ‡ alexk@bgumail.bgu.ac.il 1 inflationary phase" for some dimensions and simultaneous "quantum deflationary contraction" for the remaining dimensions. The expectation value of the "volume" of the universe remains constant during this quantum "inflationdeflation"process.2

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Time in Quantum Geometrodynamics

Cited by 3 publications

References 6 publications

A nonlinear quantum model of the Friedmann universe

A nonlinear quantum model of the Friedmann universe

Quantum geometrodynamics of the Bianchi IX cosmological model

Counter-Example Where Cosmic Time Keeps Its Original Role in Quantum Cosmology

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