692 research outputs found
Bohmian Histories and Decoherent Histories
The predictions of the Bohmian and the decoherent (or consistent) histories
formulations of the quantum mechanics of a closed system are compared for
histories -- sequences of alternatives at a series of times. For certain kinds
of histories, Bohmian mechanics and decoherent histories may both be formulated
in the same mathematical framework within which they can be compared. In that
framework, Bohmian mechanics and decoherent histories represent a given history
by different operators. Their predictions for the probabilities of histories
therefore generally differ. However, in an idealized model of measurement, the
predictions of Bohmian mechanics and decoherent histories coincide for the
probabilities of records of measurement outcomes. The formulations are thus
difficult to distinguish experimentally. They may differ in their accounts of
the past history of the universe in quantum cosmology.Comment: 7 pages, 3 figures, Revtex, minor correction
Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of
matter fields to be formulated in terms of a unitarily evolving state vector
defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike
surfaces, as in the case of spacetimes with closed timelike curves, a more
general formulation of quantum mechanics is required. In such generalizations
the transition matrix between alternatives in regions of spacetime where states
{\it can} be defined may be non-unitary. This paper describes a generalized
quantum mechanics whose probabilities consistently obey the rules of
probability theory even in the presence of such non-unitarity. The usual notion
of state on a spacelike surface is lost in this generalization and familiar
notions of causality are modified. There is no signaling outside the light
cone, no non-conservation of energy, no ``Everett phones'', and probabilities
of present events do not depend on particular alternatives of the future.
However, the generalization is acausal in the sense that the existence of
non-chronal regions of spacetime in the future can affect the probabilities of
alternatives today. The detectability of non-unitary evolution and violations
of causality in measurement situations are briefly considered. The evolution of
information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0
An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold
It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an
appendix proving the semi-direct product structure of the MCG, corrected an
error in the characterization of the slide subgroup, reworded extensively.
All our analysis and conclusions remain as befor
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
Exponentially Large Probabilities in Quantum Gravity
The problem of topology change transitions in quantum gravity is investigated
from the Wheeler-de Witt wave function point of view. It is argued that for all
theories allowing wormhole effects the wave function of the universe is
exponentially large. If the wormhole action is positive, one can try to
overcome this difficulty by redefinition of the inner product, while for the
case of negative wormhole action the more serious problems arise.Comment: 9 pages in LaTeX, 4 figures in PostScript, the brief version of this
paper is to appear in Proceedings of the XXIV ITEP Winter School of Physic
On the variable-charged black holes embedded into de Sitter space: Hawking's radiation
In this paper we study the Hawking evaporation of masses of variable-charged
Reissner-Nordstrom and Kerr-Newman, black holes embedded into the de Sitter
universe by considering the charge to be function of radial coordinate of the
spherically symmetric metric.Comment: LaTex, p. 2
A Note on Hartle-Hawking Vacua
The purpose of this note is to establish the basic properties--- regularity
at the horizon, time independence, and thermality--- of the generalized
Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing
horizon admitting a regular Euclidean section. These states, for free or
interacting fields, are defined by a path integral on half the Euclidean
section. The emphasis is on generality and the arguments are simple but formal.Comment: 5 pages, LaTe
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Petrov types of slowly rotating fluid balls
Circularly rotating axisymmetric perfect fluid space-times are investigated
to second order in the small angular velocity. The conditions of various
special Petrov types are solved in a comoving tetrad formalism. A number of
theorems are stated on the possible Petrov types of various fluid models. It is
shown that Petrov type II solutions must reduce to the de Sitter spacetime in
the static limit. Two space-times with a physically satisfactory
energy-momentum tensor are investigated in detail. For the rotating
incompressible fluid, it is proven that the Petrov type cannot be D. The
equation of the rotation function can be solved for the Tolman type
IV fluid in terms of quadratures. It is also shown that the rotating version of
the Tolman IV space-time cannot be Petrov type D.Comment: 14 pages, version to appear in Gen. Rel. Gra
On the quantum origin of the seeds of cosmic structure
The current understanding of the quantum origin of cosmic structure is
discussed critically. We point out that in the existing treatments a transition
from a symmetric quantum state to an (essentially classical) non-symmetric
state is implicitly assumed, but not specified or analyzed in any detail. In
facing the issue we are led to conclude that new physics is required to explain
the apparent predictive power of the usual schemes. Furthermore we show that
the novel way of looking at the relevant issues opens new windows from where
relevant information might be extracted regarding cosmological issues and
perhaps even clues about aspects of quantum gravity.Comment: replacement with final version to appear in Classical and Quantum
Gravit
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