Quantum Gravity

I comment on rather significant recent developments that are relevant for proposals I had presented in previous PI seminars. The Fermi/GLAST space telescope has reported observations that would naturally fit previous formalizations of Planck-scale-induced in-vacuo dispersion (but also quite a few other things). And the unexplained excess noise found at the GEO600 interferometer is just of the type that had been previously described in terms of phenomenological models of spacetime foam (but may well be caused by quite a few other things). On the pure-theory side I can finally keep my promise to show that spacetime noncommutativity is a valuable tool of exploration of nonclassicality of spacetime, allowing the derivation of discretized spectra of distance, area, volume, and also providing a completely new overall geometric picture, in which amusingly the number Pi looses some of its privileges.

We derive geometric correlation functions in the new spinfoam model with coherent states techniques, making connection with quantum Regge calculus and perturbative quantum gravity. In particular we recover the expected scaling with distance for all components of the propagator. We expect the same technique to be well-suited for other spinfoam models.

In this talk I will review how ideas borrowed from perturbative Quantum Gravity and Effective Field Theory (EFT) in Particle Physics can be applied to problems in General Relativity (GR), such as calculating gravitational wave emission by inspiralling spinning binary systems, including finite size effects and absorption. I will discuss in somewhat more detail how to account for dissipative effects, where the GR/EFT duality is used to predict the power loss due to absorption in the dynamics of binary spinning Black Holes.

In this talk I will describe a topos formulation of consistent histories obtained using the topos reformulation of standard quantum mechanics put forward by Doering and Isham. Such a reformulation leads to a novel type of logic with which to represent propositions. In the first part of the talk I will introduce the topos reformulation of quantum mechanics. I will then explain how such a reformulation can be extended so as to include temporally-ordered collection of propositions as opposed to single time propositions. Finally I will show how such an extension will lead to the possibility of assigning truth values to temporal propositions.

The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework. I will also explain how this might be the ideal setting to attempt a proof of the Bousso entropy bound, or to incorporate the associated holographic principle in a quantization of gravity.

Using 2-dimensional CGHS black holes, I will argue that information is not lost in the Hawking evaporation because the quantum space-time is significantly larger than the classical one. I will begin with a discussion of the conceptual underpinnings of problem and then introduce a general, non-perturbative framework to describe quantum CGHS black holes. I will show that the Hawking effect emerges from it in the first approximation. Finally, I will introduce a mean field approximation to argue that, when the back reaction is included, future null infinity is `long enough\' to capture full information contained in pure states at past null infinity and that the S-matrix is unitary. There are no macroscopic remnants.

As well known, cosmic ray experiments can put strong constraints on possible Lorentz Invariance Violations. In particular, the presence of the so called GZK \'cut-off\' may indicate that protons do propagate in the Universe as expected from relativistic invariance. The presence of this feature in the spectrum has been convincingly indicated by the HiRes and Auger experiments, while the Auger Observatory has given indication on the correlation of Ultra High Energy Cosmic particles with nearby sources, as predicted by the GZK feature. I review the experimental results and discuss in particular both the theoretical and experimental intricacies and the limits on LIV parameters that can be deduced.

Motivated by the analogy proposed by Witten between Chern-Simons theories and CFT-Wess-Zumino-Witten models, we explore a new way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The results seem to indicate that this analogy can work in this particular case. This could be a good starting point for the search of a deeper connection between the description of black holes in LQG and a conformal field theory.

I discuss a class of compact objects (\'monsters\') with more entropy than a black hole of the same ADM mass. Such objects are problematic for AdS/CFT duality and the conventional interpretation of black hole entropy as counting of microstates. Nevertheless, monster initial data can be constructed in semi-classical general relativity without requiring large curvatures or energy densities.

The semiclassical-quantum correspondence (SQC) is a new principle which has enabled the explicit solution of the quantum constraints of GR in the full theory in the Ashtekar variables for gravity coupled to matter. The solutions, which constitute the physical space of states implementing the quantum dynamics of GR in the Dirac procedure, include a special class of states known as the generalized Kodama states (GKod). The GKodS can be seen as an analogue of the pure Kodama state (Kod) when quantum gravity (QGRA) is coupled to matter fields quantized on the same footing. The criterion for finiteness stems from a precise cancellation of the ultraviolet singularities stemming from the quantum Hamiltonian constraint, allowing for an exact solution. This signifies the following developments for 4D QGRA: (i) Equivalence among the Dirac, reduced phase, geometric and path integration approaches to quantization for GKods; (ii) A generalization of topological field theory to include matter fields via the instanton representation of GKod; (iii) A possible mechanism to establish 4D QGRA, via tree networks, as a renormalizable theory (iv) A direct link from QGRA to Minkoswki spacetime physics, which would enable tests of 4D QGRA without the necessity to access the Planck scale (v) A third-quantized analogy to second quantized spin network states implementing the quantum dynamics of GR. The aforementioned algorithm is designed to construct explicit solutions to the constraints of the full theory by inspection, while implementing any desired ‘boundary’ conditions on the states necessary to reduce to the appropriate semiclassical limit. Conversely, the finite states of 4D QGRA can place severe restrictions on phenomena occurring in the weak gravitational limit below the Planck scale. While we demonstrate this for the GKodS in this talk, the procedure can be applied to obtain a family of states labeled by two arbitrary functions of position, which possess the requisite Hilbert space structure in the limit where the matter fields are turned off. Remaining areas of research in progress include the illumination of the Hilbert space structure of the GKodS, analysis of various models for which the SQC can produce tractable solutions, in the full theory and in minisuperspace, and the addressal of any issues of interest regarding the mathematical rigor of the states.

We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An \'effective gravitational field\' dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the \'gravitational\' field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief introduction on this topic, we present our recent contributions to the field.

After reviewing Wilson\'s picture of renormalization, and the associated Exact Renormalization Group, I will show that no (physically acceptable) non-trivial fixed points exist for scalar field theory in D>=4. Consequently, an asymptotic safety scenario is ruled out, and the triviality of the theory is confirmed.