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