Loop quantum gravity modification of the Compton effect

There are several approaches to quantum gravitational corrections of black hole thermodynamics. String theory and loop quantum gravity, by direct analysis on the basis of quantum properties of black holes, show that in the entropy–area relation the leading order correction should be of log-area type. On the other hand, generalized uncertainty principle (GUP) and modified dispersion relations (MDRs) provide perturbational framework for such modifications. Although both GUP and MDRs are common features of all quantum gravity scenarios, their functional forms are quantum gravity model dependent. Since both string theory and loop quantum gravity give more reliable solution of the black hole thermodynamics, one can use their results to test approximate results of GUP and MDRs. In this Letter, we find quantum corrected black hole thermodynamics in the framework of GUP and MDR and then we compare our results with string theory solutions. This comparison suggests severe constraints on the functional form of GUP and MDRs. These constraints may reflect characteristic features of ultimate quantum gravity theory.

There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay $\Delta t$ comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, $\Delta t$, and the relative change in the speed of muon neutrino $\Delta v$ in dependence on redshift $z$ turn to be wrong, we utilize its main features to estimate $\Delta v$. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, $\alpha$ that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.

The unification of quantum principles with Einstein's geometric conception of spacetime and gravity into a consistent theory of quantum gravity is one of the main open challenges at the foundations of modern theoretical physics. Among several approaches developed over the years, the two main candidates are string theory and loop quantum gravity (LQG). Both theories are characterized by their own achievements and open issues so that the solution to the problem of quantum gravity remains still elusive. In lack of experimental guidance, in order to make progress, it becomes important to single out common features shared by different approaches allowing to merge tools and ideas, thus providing indirect tests to potentially overcome current limitations. In this respect, one of the major recent developments is the so-called holographic principle and its string theory-based realization within the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, a conjectured duality between string theory in asymptotically AdS spacetime and a SU(N) gauge theory thought of as living on its conformal boundary. As such it provides a promising arena to look for possible connections between non-perturbative LQG and string theory non-perturbatively defined via its dual field theory. With this motivation in mind, in this thesis we focus on effective symmetry-reduced models for resolved cosmological and black hole singularities to which lot of effort has been devoted within the LQG community and their possible embedding within the AdS/CFT framework. First of all, we focus on the field theory signatures of the singularity resolution in the bulk of Kasner-AdS spacetimes and show via several examples of quantum corrected effective geometries that the finite-distance pole in the boundary two-point correlator previously interpreted as the holographic signature of the bulk singularity is smoothed out by quantum gravity effects. The time dependence of the boundary spacetime however prevents us from setting up an independent field theory computation to compare with the bulk gravity results. We move then to black hole (BH) singularities whose asymptotic boundary is Minkowski or AdS. Since no fully satisfactory effective LQG model is available already for the simplest static spherically symmetric case with zero cosmological constant, we consider the case of a 4-dimensional Schwarzschild BH as a necessary preparation for higher dimensional extensions to AdS BHs. New models based on new sets of canonical variables directly related to the Kretschmann scalar are thus introduced to take the onset of quantum effects under control, and the resulting quantum corrected spacetime structure is discussed in detail. A key ingredient of our analysis is the study of Dirac observables for the asymptotic ADM masses and their relation with admissible initial conditions for the effective dynamics compatibly with the requirement of a unique upper bound on curvature invariants resolving the central singularity. Finally, quantum corrections to thermodynamic quantities are also analyzed and, coming back to the original motivation of using LQG techniques for AdS/CFT, a possible extension to arbitrary dimensions and negative cosmological constant is sketched.

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we considered a covariant version of the GUP to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy–momentum dispersion relation was modified. Starting with the modified dispersion relation, the corrections to the wave function were obtained and the problems of the particle in a box and the hydrogen atom were revisited. Considering the minimal time may be an interesting new topic, which is not widely studied before. It may lead to new results that can open a new window into quantum gravity.

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational-wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.

Of the different approaches to quantum gravity, the best developed, from the point of view of addressing the key theoretical questions a quantum theory of gravity must answer, is loop quantum gravity. While string theory appears to better address the issue of unification, at least so far, it fails to provide a background independent approach to the quantum mechanics of spacetime geometry-a necessary condition for any quantum theory of gravity. Moreover, many key conjectures remain unproven, including perturbative finiteness and consistency, which have not been demonstrated for any string theory past second order in perturbation theory. By contrast, loop quantum gravity appears to provide a consistent and finite background independent approach to quantum gravity. There is recent progress on several issues, including accounting for the black hole entropy [8], and giving a precise quantum mechanical description of the earliest phases of the evolution of the universe [9, 10]. Furthermore, it gives unique predictions of novel quantum gravitational phenomena, such as the discreteness of area, volume and other observables. However, in this new era of quantum gravity phenomenology, a quantum theory of gravity must pass a stricter test to be taken as a serious candidate: it must make unambiguous predictions for the upcoming experiments which probe the Planck scale. One way such predictions may arise is by modifications of the energymomentum relations of low energy physics, of the form,

Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the latter is currently analyzed on the basis of the available observational data from gamma-ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.

Modern Canonical Quantum General Relativity

In many quantum gravity approaches, the cosmological constant is introduced by deforming the gauge group into a quantum group. In three dimensions, the quantization of the Chern-Simons formulation of gravity provided the first example of such a deformation. The Turaev-Viro model, which is an example of a spin-foam model, is also defined in terms of a quantum group. By extension, it is believed that in four dimensions, a quantum group structure could encode the presence of $\mathrm{\ensuremath{\Lambda}}\ensuremath{\ne}0$. In this article, we introduce by hand the quantum group ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$ into the loop quantum gravity (LQG) framework; that is, we deal with ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$-spin networks. We explore some of the consequences, focusing in particular on the structure of the observables. Our fundamental tools are tensor operators for ${\mathcal{U}}_{q}(\mathfrak{s}u(2))$. We review their properties and give an explicit realization of the spinorial and vectorial ones. We construct the generalization of the $\mathrm{U}(N)$ formalism in this deformed case, which is given by the quantum group ${\mathcal{U}}_{q}(\mathfrak{u}(N))$. We are then able to build geometrical observables, such as the length, area or angle operators, etc. We show that these operators characterize a quantum discrete hyperbolic geometry in the three-dimensional LQG case. Our results confirm that a quantum group structure in LQG can be a tool to introduce a nonzero cosmological constant into the theory. Our construction is both relevant for three-dimensional Euclidian quantum gravity with a negative cosmological constant and four-dimensional Lorentzian quantum gravity with a positive cosmological constant.

Possible corrections to the thermodynamic quantities of a 4D Schwarzschild–anti–de Sitter (SAdS) black hole are investigated by considering the generalized uncertainty principle (GUP) and the modified dispersion relation (MDR) separately. The quantum gravitational corrections to the Hawking temperature, energy and entropy of the black hole are calculated based on both the GUP and the MDR analysis. The explicit form of the corrections is worked out up to the sixth power of the Planck length. The quantum-corrected thermodynamic quantities due to GUP and MDR are used separately to obtain the quantum-gravitational corrections to the Cardy–Verlinde (C–V) formula. It is found that the C–V formula receives some new corrections in either of approaches. Through comparison of the corrections obtained from GUP and MDR approaches, it is shown that the results of these two alternative approaches should be identical if one uses the suitable expansion coefficients. Finally, the renormalized form of the C–V formula is introduced by redefining the Virasoro operator and the central charge within both the GUP and the MDR.

Lorentz invariance violation and the spectrum and source power of ultrahigh energy cosmic rays

The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounterbetween different approaches and different perspectives on the quantum-gravity problem. It contributedto a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program.There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed.In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field.Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics:• from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory,• from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime,• from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions.This volume provides an overview of these various topics, interesting for the specialist as well as accessibleto the newcomer. 4partially funded by CNRS PEPS /PTI ‘‘Metric aspect of noncommutative geometry: from Monge to Higgs’’

The holy grail of theoretical physics is to find the theory of everything that combines all the forces of nature, including gravity. This book addresses the question: how far are we from such discovery? Over the last few decades, multiple roads to finding a quantum theory of gravity have been proposed but no obvious description of nature has emerged in this domain. What is to be made of this situation? This volume probes the state-of-the art in this daunting quest of theoretical physics by collecting critical interviews with nearly forty leading theorists in this field. These broad-ranging conversations give important insights and candid opinions on the various approaches to quantum gravity, including string theory, loop quantum gravity, causal set theory and asymptotic safety. This unique, readable overview provides a gateway into cutting edge research for students and others who wish to engage with the open problem of quantum gravity.

The two fundamental pillars of physics for over 100 years have been quantum theory and general relativity, but their unification at short distances remains elusive, both technically and conceptually. This work is a philosophical investigation of the second kind of problem, and in particular of the striking fact that in many approaches to ‘quantum gravity’ classical spacetime structures are not merely quantized, but arguably absent—so that spacetime is not merely a classical limit, but ‘emergent’. This issue is not only central to the problem of quantum gravity, but of deep significance for our philosophical understanding of physical reality, promising a conceptual revolution at least as profound as Einstein’s. We give an introduction to the question of spacetime emergence in general, for philosophers of metaphysics and science, and argue that spacetime functionalism explains how something non-spatiotemporal could ever appear as space and time. More technical chapters investigate the issue in detail for causal set theory, loop quantum gravity, and string theory, and the book also serves as a philosophical introduction to those theories for philosophers of physics. Our results help physicists clarify what new conceptual framework—not resting on space and time—may be necessary to achieve a theory of quantum gravity; and show philosophers how the world may not be spatiotemporal at root, and what kind of a world we might then live in.

Loop quantum gravity is a physical theory that aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via quantisation. General relativity describes gravity in terms of geometry; therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well, thus, in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician’s point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three-dimensional case.