837 research outputs found
Semi-classical limit and minimum decoherence in the Conditional Probability Interpretation of Quantum Mechanics
The Conditional Probability Interpretation of Quantum Mechanics replaces the
abstract notion of time used in standard Quantum Mechanics by the time that can
be read off from a physical clock. The use of physical clocks leads to apparent
non-unitary and decoherence. Here we show that a close approximation to
standard Quantum Mechanics can be recovered from conditional Quantum Mechanics
for semi-classical clocks, and we use these clocks to compute the minimum
decoherence predicted by the Conditional Probability Interpretation.Comment: 8 pages, references adde
Lattice knot theory and quantum gravity in the loop representation
We present an implementation of the loop representation of quantum gravity on
a square lattice. Instead of starting from a classical lattice theory,
quantizing and introducing loops, we proceed backwards, setting up constraints
in the lattice loop representation and showing that they have appropriate
(singular) continuum limits and algebras. The diffeomorphism constraint
reproduces the classical algebra in the continuum and has as solutions lattice
analogues of usual knot invariants. We discuss some of the invariants stemming
from Chern--Simons theory in the lattice context, including the issue of
framing. We also present a regularization of the Hamiltonian constraint. We
show that two knot invariants from Chern--Simons theory are annihilated by the
Hamiltonian constraint through the use of their skein relations, including
intersections. We also discuss the issue of intersections with kinks. This
paper is the first step towards setting up the loop representation in a
rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi
Loop Quantization of Maxwell Theory and Electric Charge Quantization
We consider the loop quantization of Maxwell theory. A quantization of this
type leads to a quantum theory in which the fundamental excitations are
loop-like rather than particle-like. Each such loop plays the role of a
quantized Faraday's line of electric flux. We find that the quantization
depends on an arbitrary choice of a parameter e that carries the dimension of
electric charge. For each value of e an electric charge that can be contained
inside a bounded spatial region is automatically quantized in units of
hbar/4*pi*e. The requirement of consistency with the quantization of electric
charge observed in our Universe fixes a value of the, so far arbitrary,
parameter e of the theory. Finally, we compare the ambiguity in the choice of
parameter e with the beta-ambiguity that, as pointed by Immirzi, arises in the
loop quantization of general relativity, and comment on a possible way this
ambiguity can be fixed.Comment: 7 pages, Revtex, no figures, typos corrected and one reference adde
Classical and quantum general relativity: a new paradigm
We argue that recent developments in discretizations of classical and quantum
gravity imply a new paradigm for doing research in these areas. The paradigm
consists in discretizing the theory in such a way that the resulting discrete
theory has no constraints. This solves many of the hard conceptual problems of
quantum gravity. It also appears as a useful tool in some numerical simulations
of interest in classical relativity. We outline some of the salient aspects and
results of this new framework.Comment: 8 pages, one figure, fifth prize of the Gravity Research Foundation
2005 essay competitio
Consistent discretizations: the Gowdy spacetimes
We apply the consistent discretization scheme to general relativity
particularized to the Gowdy space-times. This is the first time the framework
has been applied in detail in a non-linear generally-covariant gravitational
situation with local degrees of freedom. We show that the scheme can be
correctly used to numerically evolve the space-times. We show that the
resulting numerical schemes are convergent and preserve approximately the
constraints as expected.Comment: 10 pages, 8 figure
Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra
In a companion paper we introduced a kinematical arena for the discussion of
the constraints of canonical quantum gravity in the spin network representation
based on Vassiliev invariants. In this paper we introduce the Hamiltonian
constraint, extend the space of states to non-diffeomorphism invariant
``habitats'' and check that the off-shell quantum constraint commutator algebra
reproduces the classical Poisson algebra of constraints of general relativity
without anomalies. One can therefore consider the resulting set of constraints
and space of states as a consistent theory of canonical quantum gravity.Comment: 20 Pages, RevTex, many figures included with psfi
Finite, diffeomorphism invariant observables in quantum gravity
Two sets of spatially diffeomorphism invariant operators are constructed in
the loop representation formulation of quantum gravity. This is done by
coupling general relativity to an anti- symmetric tensor gauge field and using
that field to pick out sets of surfaces, with boundaries, in the spatial three
manifold. The two sets of observables then measure the areas of these surfaces
and the Wilson loops for the self-dual connection around their boundaries. The
operators that represent these observables are finite and background
independent when constructed through a proper regularization procedure.
Furthermore, the spectra of the area operators are discrete so that the
possible values that one can obtain by a measurement of the area of a physical
surface in quantum gravity are valued in a discrete set that includes integral
multiples of half the Planck area. These results make possible the construction
of a correspondence between any three geometry whose curvature is small in
Planck units and a diffeomorphism invariant state of the gravitational and
matter fields. This correspondence relies on the approximation of the classical
geometry by a piecewise flat Regge manifold, which is then put in
correspondence with a diffeomorphism invariant state of the gravity-matter
system in which the matter fields specify the faces of the triangulation and
the gravitational field is in an eigenstate of the operators that measure their
areas.Comment: Latex, no figures, 30 pages, SU-GP-93/1-
A realist interpretation of quantum mechanics based on undecidability due to gravity
We summarize several recent developments suggesting that solving the problem
of time in quantum gravity leads to a solution of the measurement problem in
quantum mechanics. This approach has been informally called "the Montevideo
interpretation". In particular we discuss why definitions in this approach are
not "for all practical purposes" (fapp) and how the problem of outcomes is
resolved.Comment: 7 pages, IOPAMS style, no figures, contributed to the proceedings of
DICE 2010, Castiglioncello, slightly improved versio
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