arXiv subjects

John T. Whelan

Publications and source records attributed to John T. Whelan.

43 records · Page 3Linked to original sources

arXiv1999

Quasi-Stationary Binary Inspiral: Project Overview

I describe the current status of a collaboration with J.D. Romano, R.H. Price, and W. Krivan to model the geometry of and gravitational radiation emitted by a binary system of compact objects in the regime where non-perturbative gravitational effects exist, but the rate of inspiral is still small relative to the orbital frequency. The method of looking for a stationary spacetime which approximates the evolving solution is initially being tested on a simpler model with an additional translational symmetry. This report consists of a general description of the method, followed by summaries of three techniques in varying stages of development: the simplification of the Einstein equations in the presence of two commuting Killing vectors which form a non-orthogonally-transitive symmetry group, the boundary conditions appropriate to the balance of ingoing and outgoing radiation needed to reconcile a stationary radiating solution with conservation of energy, and the treatment of gravitational waves far from the sources as linearized perturbations to the Levi-Civita spacetime. The poster presentation with which this paper is associated is available on line at http://www-itp.unibe.ch/~whelan/poster.ps.gz and the current status of the project is described at http://www-itp.unibe.ch/~whelan/qsbi.html

gr-qc↗

arXiv1998

Modeling the decoherence of spacetime

The question of whether unobserved short-wavelength modes of the gravitational field can induce decoherence in the long-wavelength modes (``the decoherence of spacetime'') is addressed using a simplified model of perturbative general relativity, related to the Nordstrom-Einstein-Fokker theory, where the metric is assumed to be conformally flat. For some long-wavelength coarse grainings, the Feynman-Vernon influence phase is found to be effective at suppressing the off-diagonal elements of the decoherence functional. The requirement that the short-wavelength modes be in a sufficiently high-temperature state places limits on the applicability of this perturbative approach.

gr-qc↗

arXiv1997

Skeletonizations of Phase Space Paths

Construction of skeletonized path integrals for a particle moving on a curved spatial manifold is considered. As shown by DeWitt, Kuchar and others, while the skeletonized configuration space action can be written unambiguously as a sum of Hamilton principal functions, different choices of the measure will lead to different Schrodinger equations. On the other hand, the Liouville measure provides a unique measure for a skeletonized phase space path integral, but there is a corresponding ambiguity in the skeletonization of a path through phase space. A family of skeletonization rules described by Kuchar and referred to here as geodesic interpolation is discussed, and shown to behave poorly under the involution process, wherein intermediate points are removed by extremization of the skeletonized action. A new skeletonization rule, tangent interpolation, is defined and shown to possess the desired involution properties.

gr-qc↗

arXiv1997

Propagator for a time-dependent harmonic oscillator

This paper has been withdrawn, as the explicit form of the propagator can be found in: V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3 V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Theor.Math.Phys. 24 (1975) 746, Sec.2 I am grateful to Professor Victor Dodonov for bringing this to my attention.

quant-ph↗

arXiv1997

Modelling the Decoherence of Spacetime (abridged)

The question of whether unobserved short-wavelength modes of the gravitational field can induce decoherence in the long-wavelength modes (``the decoherence of spacetime'') is addressed using a scalar field toy model with some features of perturbative general relativity. This is an abridged version of the author's paper gr-qc/9612028.

gr-qc↗

arXiv1995

Generalized quantum mechanics of nonabelian gauge theories

Hartle's generalized quantum mechanics in the sum-over-histories formalism is used to describe a nonabelian gauge theory. Predictions are made for certain alternatives, with particular attention given to coarse-grainings involving the constraint. In this way, the theory is compared to other quantum-mechanical descriptions of gauge theories in which the constraints are imposed by hand. The vanishing of the momentum space constraint is seen to hold, both through a simple formal argument and via a more careful description of the Lorentzian path integral as defined on a spacetime lattice. (Incidentally, the treatment of the time slicing in the path integral may be of general technical interest.) The configuration space realization of the constraint is shown to behave in a more complicated fashion. For some coarse grainings, we recover the known result from an abelian theory, that coarse grainings by values of the constraint either predict its vanishing or fail to decohere. However, sets of alternatives defined in terms of a more complicated quantity in the abelian case are exhibited where definite predictions can be made which disagree with the assumption that the constraints vanish. Finally, the configuration space sum-over-histories theory is exhibited in a manifestly Lorentz-invariant formulation.

hep-th↗

arXiv1994

Spacetime alternatives in relativistic particle motion

One of the reasons we expect a standard quantum mechanics, which predicts probabilities for alternatives defined on spacelike slices, to be inadequate for quantum gravity is that the notion of ``spacelike'' is ill-defined in a theory where the metric itself is behaving quantum-mechanically. Spacetime coarse grainings--sets of alternatives defined with respect to a region extended in time as well as space--have previously been considered in the quantum mechanics of a single nonrelativistic particle. This work examines spacetime coarse grainings in the quantum mechanics of a free *relativistic* particle, not as a theory for real particles (which are described by quantum field theory) but as a simple reparametrization-invariant theory which may model some features of quantum gravity. We use Hartle's sum-over-histories generalized quantum mechanics formalism, in which probabilities are assigned to a set of alternatives if they decohere, i.e., if the quantum-mechanical interference between their branches of the initial state is nearly zero. For one extremely simple set of alternatives, we calculate these branches. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities.

gr-qc↗