14 research outputs found
Realistic clocks, universal decoherence and the black hole information paradox
Ordinary quantum mechanics is formulated on the basis of the existence of an
ideal classical clock external to the system under study. This is clearly an
idealization. As emphasized originally by Salecker and Wigner and more recently
by other authors, there exist limits in nature to how ``classical'' even the
best possible clock can be. When one introduces realistic clocks, quantum
mechanics ceases to be unitary and a fundamental mechanism of decoherence of
quantum states arises. We estimate the rate of universal loss of unitarity
using optimal realistic clocks. In particular we observe that the rate is rapid
enough to eliminate the black hole information puzzle: all information is lost
through the fundamental decoherence before the black hole can evaporate. This
improves on a previous calculation we presented with a sub-optimal clock in
which only part of the information was lost by the time of evaporation.Comment: 3 Pages, RevTex, no figure
Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
General relativity is a deterministic theory with non-fixed causal structure.
Quantum theory is a probabilistic theory with fixed causal structure. In this
paper we build a framework for probabilistic theories with non-fixed causal
structure. This combines the radical elements of general relativity and quantum
theory. The key idea in the construction is physical compression. A physical
theory relates quantities. Thus, if we specify a sufficiently large set of
quantities (this is the compressed set), we can calculate all the others. We
apply three levels of physical compression. First, we apply it locally to
quantities (actually probabilities) that might be measured in a particular
region of spacetime. Then we consider composite regions. We find that there is
a second level of physical compression for the composite region over and above
the first level physical compression for the component regions. Each
application of first and second level physical compression is quantified by a
matrix. We find that these matrices themselves are related by the physical
theory and can therefore be subject to compression. This is the third level of
physical compression. This third level of physical compression gives rise to a
new mathematical object which we call the causaloid. From the causaloid for a
particular physical theory we can calculate verything the physical theory can
calculate. This approach allows us to set up a framework for calculating
probabilistic correlations in data without imposing a fixed causal structure
(such as a background time). We show how to put quantum theory in this
framework (thus providing a new formulation of this theory). We indicate how
general relativity might be put into this framework and how the framework might
be used to construct a theory of quantum gravity.Comment: 23 pages. For special issue of Journal of Physics A entitled "The
quantum universe" in honour of Giancarlo Ghirard
Loss of coherence from discrete quantum gravity
We show that a recent proposal for the quantization of gravity based on
discrete space-time implies a modification of standard quantum mechanics that
naturally leads to a loss of coherence in quantum states of the type discussed
by Milburn. The proposal overcomes the energy conservation problem of
previously proposed decoherence mechanisms stemming from quantum gravity.
Mesoscopic quantum systems (as Bose--Einstein condensates) appear as the most
promising testing grounds for an experimental verification of the mechanism.Comment: 4 pages, no figures, small final changes, to appear in Class. Quan.
Gra
The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
The Hamiltonian constraint remains the major unsolved problem in Loop Quantum
Gravity (LQG). Seven years ago a mathematically consistent candidate
Hamiltonian constraint has been proposed but there are still several unsettled
questions which concern the algebra of commutators among smeared Hamiltonian
constraints which must be faced in order to make progress. In this paper we
propose a solution to this set of problems based on the so-called {\bf Master
Constraint} which combines the smeared Hamiltonian constraints for all smearing
functions into a single constraint. If certain mathematical conditions, which
still have to be proved, hold, then not only the problems with the commutator
algebra could disappear, also chances are good that one can control the
solution space and the (quantum) Dirac observables of LQG. Even a decision on
whether the theory has the correct classical limit and a connection with the
path integral (or spin foam) formulation could be in reach. While these are
exciting possibilities, we should warn the reader from the outset that, since
the proposal is, to the best of our knowledge, completely new and has been
barely tested in solvable models, there might be caveats which we are presently
unaware of and render the whole {\bf Master Constraint Programme} obsolete.
Thus, this paper should really be viewed as a proposal only, rather than a
presentation of hard results, which however we intend to supply in future
submissions.Comment: LATEX, uses AMSTE
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ