114 research outputs found
Dust as a Standard of Space and Time in Canonical Quantum Gravity
The coupling of the metric to an incoherent dust introduces into spacetime a
privileged dynamical reference frame and time foliation. The comoving
coordinates of the dust particles and the proper time along the dust worldlines
become canonical coordinates in the phase space of the system. The Hamiltonian
constraint can be resolved with respect to the momentum that is canonically
conjugate to the dust time. Imposition of the resolved constraint as an
operator restriction on the quantum states yields a functional Schr\"{o}dinger
equation. The ensuing Hamiltonian density has an extraordinary feature: it
depends only on the geometric variables, not on the dust coordinates or time.
This has three important consequences. First, the functional Schr\"{o}dinger
equation can be solved by separating the dust time from the geometric
variables. Second, the Hamiltonian densities strongly commute and therefore can
be simultaneously defined by spectral analysis. Third, the standard constraint
system of vacuum gravity is cast into a form in which it generates a true Lie
algebra. The particles of dust introduce into space a privileged system of
coordinates that allows the supermomentum constraint to be solved explicitly.
The Schr\"{o}dinger equation yields a conserved inner product that can be
written in terms of either the instantaneous state functionals or the solutions
of constraints. Examples of gravitational observables are given, though neither
the intrinsic metric nor the extrinsic curvature are observables. Disregarding
factor--ordering difficulties, the introduction of dust provides a satisfactory
phenomenological approach to the problem of time in canonical quantum gravity.Comment: 56 pages (REVTEX file + 3 postscipt figure files
Covariant perturbations of domain walls in curved spacetime
A manifestly covariant equation is derived to describe the perturbations in a
domain wall on a given background spacetime. This generalizes recent work on
domain walls in Minkowski space and introduces a framework for examining the
stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0
Jacobi's Principle and the Disappearance of Time
Jacobi's action principle is known to lead to a problem of time. For example,
the timelessness of the Wheeler-DeWitt equation can be seen as resulting from
using Jacobi's principle to define the dynamics of 3-geometries through
superspace. In addition, using Jacobi's principle for non-relativistic
particles is equivalent classically to Newton's theory but leads to a
time-independent Schrodinger equation upon Dirac quantization. In this paper,
we study the mechanism for the disappearance of time as a result of using
Jacobi's principle in these simple particle models. We find that the path
integral quantization very clearly elucidates the physical mechanism for the
timeless of the quantum theory as well as the emergence of duration at the
classical level. Physically, this is the result of a superposition of clocks
which occurs in the quantum theory due to a sum over all histories.
Mathematically, the timelessness is related to how the gauge fixing functions
impose the boundary conditions in the path integral.Comment: Published version. Significant amendments to presentation. 27 page
Perturbations of a topological defect as a theory of scalar fields interacting with an external vector potential
This is a revised version of gr-qc/930403
Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
I apply the preceding paper's semiclassical treatment to geometrodynamics.
The analogy between the two papers is quite useful at the level of the
quadratic constraints, while I document the differences between the two due to
the underlying differences in their linear constraints. I provide a specific
minisuperspace example for my emergent semiclassical time scheme and compare it
with the hidden York time scheme. Overall, interesting connections are shown
between Newtonian, Leibniz--Mach--Barbour, WKB and cosmic times, while the
Euler and York hidden dilational times are argued to be somewhat different from
these.Comment: References Update
Graphical Evolution of Spin Network States
The evolution of spin network states in loop quantum gravity can be described
by introducing a time variable, defined by the surfaces of constant value of an
auxiliary scalar field. We regulate the Hamiltonian, generating such an
evolution, and evaluate its action both on edges and on vertices of the spin
network states. The analytical computations are carried out completely to yield
a finite, diffeomorphism invariant result. We use techniques from the
recoupling theory of colored graphs with trivalent vertices to evaluate the
graphical part of the Hamiltonian action. We show that the action on edges is
equivalent to a diffeomorphism transformation, while the action on vertices
adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections
in the final formula in the main body of the paper and in the formula for the
Tetrahedral net in the Appendi
Large quantum gravity effects: Unexpected limitations of the classical theory
3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly
soluble under the assumption of axi-symmetry. The solution is used to probe
several quantum gravity issues. In particular, it is shown that the quantum
fluctuations in the geometry are large unless the number and frequency of
photons satisfy the inequality . Thus, even when
there is a single photon of Planckian frequency, the quantum uncertainties in
the metric are significant. Results hold also for a sector of the 4-dimensional
theory (consisting of Einstein Rosen gravitational waves).Comment: 8 pages, No figures, ReVTe
Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
Strategies intended to resolve the problem of time in quantum gravity by
means of emergent or hidden timefunctions are considered in the arena of
relational particle toy models. In situations with `heavy' and `light' degrees
of freedom, two notions of emergent semiclassical WKB time emerge; these are
furthermore equivalent to two notions of emergent classical
`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,
in a geometric phase formalism, extended to include linear constraints, and
with particular care to make explicit those approximations and assumptions
used. I propose a new iterative scheme for this in the cosmologically-motivated
case with one heavy degree of freedom. I find that the usual semiclassical
quantum cosmology emergence of time comes hand in hand with the emergence of
other qualitatively significant terms, including back-reactions on the heavy
subsystem and second time derivatives. I illustrate my analysis by taking it
further for relational particle models with linearly-coupled harmonic
oscillator potentials. As these examples are exactly soluble by means outside
the semiclassical approach, they are additionally useful for testing the
justifiability of some of the approximations and assumptions habitually made in
the semiclassical approach to quantum cosmology. Finally, I contrast the
emergent semiclassical timefunction with its hidden dilational Euler time
counterpart.Comment: References Update
Quantization of a generally covariant gauge system with two super Hamiltonian constraints
The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a
finite-dimensional gauge system featuring two quadratic super Hamiltonian and m
linear supermomentum constraints is studied as a model for quantizing generally
covariant gauge theories. The proposed model ``completely'' mimics the
constraint algebra of General Relativity. The Dirac constraint operators are
identified by realizing the BRST generator of the system as a Hermitian
nilpotent operator, and a physical inner product is introduced to complete a
consistent quantization procedure.Comment: 17 pages. Latex file. Minor changes, two references adde
The Quantum States and the Statistical Entropy of the Charged Black Hole
We quantize the Reissner-Nordstr\"om black hole using an adaptation of
Kucha\v{r}'s canonical decomposition of the Kruskal extension of the
Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional
Schroedinger equation in Gaussian time by coupling the gravitational field to a
reference fluid or dust. The physical phase space of the theory is spanned by
the mass, , the charge, , the physical radius, , the dust proper time,
, and their canonical momenta. The exact solutions of the functional
Schroedinger equation imply that the difference in the areas of the outer and
inner horizons is quantized in integer units. This agrees in spirit, but not
precisely, with Bekenstein's proposal on the discrete horizon area spectrum of
black holes. We also compute the entropy in the microcanonical ensemble and
show that the entropy of the Reissner-Nordstr\"om black hole is proportional to
this quantized difference in horizon areas.Comment: 31 pages, 3 figures, PHYZZX macros. Comments on the wave-functional
in the interior and one reference added. To appear in Phys. Rev.
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