3,960 research outputs found
Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory
We investigate the possibility of assigning consistent probabilities to sets
of histories characterized by whether they enter a particular subspace of the
Hilbert space of a closed system during a given time interval. In particular we
investigate the case that this subspace is a region of the configuration space.
This corresponds to a particular class of coarse grainings of spacetime
regions. We consider the arrival time problem and the problem of time in
reparametrization invariant theories as for example in canonical quantum
gravity. Decoherence conditions and probabilities for those application are
derived. The resulting decoherence condition does not depend on the explicit
form of the restricted propagator that was problematic for generalizations such
as application in quantum cosmology. Closely related is the problem of
tunnelling time as well as the quantum Zeno effect. Some interpretational
comments conclude, and we discuss the applicability of this formalism to deal
with the arrival time problem.Comment: 23 pages, Few changes and added references in v
Quantum cosmology of 5D non-compactified Kaluza-Klein theory
We study the quantum cosmology of a five dimensional non-compactified
Kaluza-Klein theory where the 4D metric depends on the fifth coordinate,
. This model is effectively equivalent to a 4D non-minimally
coupled dilaton field in addition to matter generated on hypersurfaces
l=constant by the extra coordinate dependence in the four-dimensional metric.
We show that the Vilenkin wave function of the universe is more convenient for
this model as it predicts a new-born 4D universe on the constant
hypersurface.Comment: 14 pages, LaTe
Decoherent histories analysis of the relativistic particle
The Klein-Gordon equation is a useful test arena for quantum cosmological
models described by the Wheeler-DeWitt equation. We use the decoherent
histories approach to quantum theory to obtain the probability that a free
relativistic particle crosses a section of spacelike surface. The decoherence
functional is constructed using path integral methods with initial states
attached using the (positive definite) ``induced'' inner product between
solutions to the constraint equation. The notion of crossing a spacelike
surface requires some attention, given that the paths in the path integral may
cross such a surface many times, but we show that first and last crossings are
in essence the only useful possibilities. Different possible results for the
probabilities are obtained, depending on how the relativistic particle is
quantized (using the Klein-Gordon equation, or its square root, with the
associated Newton-Wigner states). In the Klein-Gordon quantization, the
decoherence is only approximate, due to the fact that the paths in the path
integral may go backwards and forwards in time. We compare with the results
obtained using operators which commute with the constraint (the ``evolving
constants'' method).Comment: 51 pages, plain Te
Half Quantization
A general dynamical system composed by two coupled sectors is considered. The
initial time configuration of one of these sectors is described by a set of
classical data while the other is described by standard quantum data. These
dynamical systems will be named half quantum. The aim of this paper is to
derive the dynamical evolution of a general half quantum system from its full
quantum formulation. The standard approach would be to use quantum mechanics to
make predictions for the time evolution of the half quantum initial data. The
main problem is how can quantum mechanics be applied to a dynamical system
whose initial time configuration is not described by a set of fully quantum
data. A solution to this problem is presented and used, as a guideline to
obtain a general formulation of coupled classical-quantum dynamics. Finally, a
quantization prescription mapping a given classical theory to the correspondent
half quantum one is presented.Comment: 20 pages, LaTex file, Substantially revised versio
Effective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem
We use the decoherent histories approach to quantum theory to derive the form
of an effective theory describing the coupling of classical and quantum
variables. The derivation is carried out for a system consisting of a large
particle coupled to a small particle with the important additional feature that
the large particle is also coupled to a thermal environment producing the
decoherence necessary for classicality. The effective theory is obtained by
tracing out both the environment and the small particle variables. It consists
of a formula for the probabilities of a set of histories of the large particle,
and depends on the dynamics and initial quantum state of the small particle. It
has the form of an almost classical particle coupled to a stochastic variable
whose probabilities are determined by a formula very similar to that given by
quantum measurement theory for continuous measurements of the small particle's
position. The effective theory gives intuitively sensible answers when the
small particle is in a superposition of localized states.Comment: 27 pages, plain Te
Representations of Spacetime Alternatives and Their Classical Limits
Different quantum mechanical operators can correspond to the same classical
quantity. Hermitian operators differing only by operator ordering of the
canonical coordinates and momenta at one moment of time are the most familiar
example. Classical spacetime alternatives that extend over time can also be
represented by different quantum operators. For example, operators representing
a particular value of the time average of a dynamical variable can be
constructed in two ways: First, as the projection onto the value of the time
averaged Heisenberg picture operator for the dynamical variable. Second, as the
class operator defined by a sum over those histories of the dynamical variable
that have the specified time-averaged value. We show both by explicit example
and general argument that the predictions of these different representations
agree in the classical limit and that sets of histories represented by them
decohere in that limit.Comment: 11 pages, 10 figures, Revtex4, minor correction
Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory
This paper explores the possibility that an exactly decoherent set of
histories may be constructed from an approximately decoherent set by small
distortions of the operators characterizing the histories. In particular, for
the case of histories of positions and momenta, this is achieved by doubling
the set of operators and then finding, amongst this enlarged set, new position
and momentum operators which commute, so decohere exactly, and which are
``close'' to the original operators. The enlarged, exactly decoherent, theory
has the same classical dynamics as the original one, and coincides with the
so-called deterministic quantum theories of the type recently studied by 't
Hooft. These results suggest that the comparison of standard and deterministic
quantum theories may provide an alternative method of characterizing emergent
classicality. A side-product is the surprising result that histories of momenta
in the quantum Brownian motion model (for the free particle in the
high-temperature limit) are exactly decoherent.Comment: 41 pages, plain Te
Spacetime states and covariant quantum theory
In it's usual presentation, classical mechanics appears to give time a very
special role. But it is well known that mechanics can be formulated so as to
treat the time variable on the same footing as the other variables in the
extended configuration space. Such covariant formulations are natural for
relativistic gravitational systems, where general covariance conflicts with the
notion of a preferred physical-time variable. The standard presentation of
quantum mechanics, in turns, gives again time a very special role, raising well
known difficulties for quantum gravity. Is there a covariant form of
(canonical) quantum mechanics? We observe that the preferred role of time in
quantum theory is the consequence of an idealization: that measurements are
instantaneous. Canonical quantum theory can be given a covariant form by
dropping this idealization. States prepared by non-instantaneous measurements
are described by "spacetime smeared states". The theory can be formulated in
terms of these states, without making any reference to a special time variable.
The quantum dynamics is expressed in terms of the propagator, an object
covariantly defined on the extended configuration space.Comment: 20 pages, no figures. Revision: minor corrections and references
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