Conserved Quantities in Background Independent Theories

We discuss the difficulties that background independent theories based on quantum geometry encounter in deriving general relativity as the low energy limit. We follow a geometrogenesis scenario of a phase transition from a pre-geometric theory to a geometric phase which suggests that a first step towards the low energy limit is searching for the effective collective excitations that will characterize it. Using the correspondence between the pre-geometric background independent theory and a quantum information processor, we are able to use the method of noiseless subsystems to extract such coherent collective excitations. We illustrate this in the case of locally evolving graphs.Comment: 11 pages, 3 figure

Quantum gravity and the standard model

We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can be shown to be noiseless subsystems of the microscopic quantum dynamics. These are identified in terms of certain patterns of braiding of graphs, thus giving a quantum gravitational foundation for the topological preon model proposed by one of us. These results apply to a large class of theories in which the Hilbert space has a basis of states given by ribbon graphs embedded in a three-dimensional manifold up to diffeomorphisms, and the dynamics is given by local moves on the graphs, such as arise in the representation theory of quantum groups. For such models, matter appears to be already included in the microscopic kinematics and dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange

Quantum Histories and Quantum Gravity

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emergent geometry", are discussed.Comment: 35 pages (29 pages main body), two figure

Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure

A comment on black hole entropy or does Nature abhor a logarithm?

There has been substantial interest, as of late, in the quantum-corrected form of the Bekenstein-Hawking black hole entropy. The consensus viewpoint is that the leading-order correction should be a logarithm of the horizon area; however, the value of the logarithmic prefactor remains a point of notable controversy. Very recently, Hod has employed statistical arguments that constrain this prefactor to be a non-negative integer. In the current paper, we invoke some independent considerations to argue that the "best guess" for the prefactor might simply be zero. Significantly, this value complies with the prior prediction and, moreover, seems suggestive of some fundamental symmetry.Comment: 10 pages and Revtex; (v2) imperative title change and added one reference; (v3) minor content and style changes throughout; 7 new citations; (v4) 8 new citations, an addendum and other minor changes; (v5) yet more references, some points clarified, and a recent criticism is addressed (addendum 2

Relativistic Bose-Einstein Condensates: a New System for Analogue Models of Gravity

In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose-Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their non-relativistic counterpart. Relativistic condensates exhibit two (rather than one) quasi-particle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies