Gravity, Geometry and the Quantum

After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic cosmology. Quantum geometry effects are shown to replace the big bang by a big bounce. Thus, quantum physics does not stop at the big-bang singularity. Rather there is a pre-big-bang branch joined to the current post-big-bang branch by a `quantum bridge'. Furthermore, thanks to the background independence of loop quantum gravity, evolution is deterministic across the bridge.Comment: Minor typos corrected, including a factor of $\pi$ in the expression of the critical density. 16 pages, 2 figures. To appear in the Proceedings of the `Einstein Century' Conference, 15-22 July, Paris, edited by J-M Alimi et al (American Institute of Physics

Quantum Geometry and Gravity: Recent Advances

Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as well as cosmological horizons; a natural resolution of the big-bang singularity; the development of spin-foam models which provide background independent path integral formulations of quantum gravity and `finiteness proofs' of some of these models; and, the introduction of semi-classical techniques to make contact between the background independent, non-perturbative theory and the perturbative, low energy physics in Minkowski space. These developments spring from a detailed quantum theory of geometry that was systematically developed in the mid-nineties and have added a great deal of optimism and intellectual excitement to the field. The goal of this article is to communicate these advances in general physical terms, accessible to researchers in all areas of gravitational physics represented in this conference.Comment: 24 pages, 2 figures; report of the plenary talk at the 16th International Conference on General Relativity and Gravitation, held at Durban, S. Africa in July 200

Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence

We develop first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates. Following an exact renormalization-group approach pioneered by Onsager, we demonstrate the existence of a "collisionless range" of scales (lengths and velocities) in 1-particle phase space where the ideal Vlasov-Maxwell equations are satisfied in a "coarse-grained sense". Entropy conservation may nevertheless be violated in that range by a "dissipative anomaly" due to nonlinear entropy cascade. We derive "4/5th-law" type expressions for the entropy flux, which allow us to characterize the singularities (structure-function scaling exponents) required for its non-vanishing. Conservation laws of mass, momentum and energy are not afflicted with anomalous transfers in the collisionless limit. In a subsequent limit of small gyroradii, however, anomalous contributions to inertial-range energy balance may appear due both to cascade of bulk energy and to turbulent redistribution of internal energy in phase space. In that same limit the "generalized Ohm's law" derived from the particle momentum balances reduces to an "ideal Ohm's law", but only in a coarse-grained sense that does not imply magnetic flux-freezing and that permits magnetic reconnection at all inertial-range scales. We compare our results with prior theory based on the gyrokinetic (high gyro-frequency) limit, with numerical simulations, and with spacecraft measurements of the solar wind and terrestrial magnetosphere.Comment: Several additions have been made that were requested by the referees of the PRX submission. In particular, discussion previously relegated to Supplemental Materials are now included in the main text as appendice

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.Comment: 75 pages, 8 figures, style file included, some comments and references adde

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many non-linear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.Comment: 109 pages, 1 figure; this version is an update of the Living Review article originally published in 2002; available on-line at http://www.livingreviews.org

Electromagnetism as an emergent phenomenon: a step-by-step guide

We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two scenarios that, although qualitatively different, share some important features, with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwell's mechanical model for electrodynamics, where Maxwell's equations appear as dynamical consistency conditions. We next take a superfluid $^3$He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and that it is only in the low-energy regime that this physical reality is blurred in favour of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance.Comment: 41 pages, 4 figures; v2: references added, version accepted for publicatio

Invisibility and Inverse Problems

This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.Comment: 68 pages, 12 figures. To appear in the Bulletin of the AM

GRAND UNIFIED FIELD THEORY-A PREDATOR PREY APPROACH: CORROBORATION- DISSIPATION MODELS:PART ONE

A system of EMF (ELECTROMAGNETIC FOR FIELD) decelerating the dissipation coefficient of GF (GRAVITATIONAL FIELD) and parallel system of GF that contribute to the dissipation of the velocity of production of EMF in an accelerated sense is investigated. It is shown that the time independence of the contributions portrays another system by itself and constitutes the equilibrium solution of the original time independent system. With the methodology reinforced with the explanations, we write, parri passu the governing equations with the nomenclature for the systems in the foregoing, including those of SNF AND WNF system. Further papers extensively draw inferences upon such concatenation process, ipso facto fait accompli. A final Grand Unified Theory is proposed and the   equations are given in the annexure, Which can be solved by the same methodology of the present paper mutatis mutandis. Gravitation is considered the weakest, but at Planck’s length it becomes extremely powerful, so powerful as to punch the holes, We discuss all the aspects of Cosmology and Quantum Mechanics and arrive at a reconciliatory solution after a lengthy discussion which seemed inevitable and necessary to put the theory on terra firma.. The forces of gravity and electromagnetism are familiar in everyday life. Two new forces are introduced when discussing nuclear phenomena: the strong and weak interactions. When two protons encounter each other, they experience all four of the fundamental forces of nature simultaneously. The weak force governs beta decay and neutrino interactions with nuclei. The strong force, which we generally call the nuclear force, is actually the force that binds quarks together to form baryons (3 quarks) and mesons (a quark and an anti-quark). The nucleons of everyday matter, neutrons and protons, consist of the quark combinations uud and udd, respectively. The symbol u represents a single up quark, while the symbol d represents a single down quark. The force that holds nucleons together to form an atomic nucleus can be thought to be a residual interaction between quarks inside each individual nucleon. This is analogous to what happens in a molecule. The electrons in an atom are bound to its nucleus by electromagnetism: when two atoms are relatively near, there is a residual interaction between the electron clouds that can form a covalent bond. The nucleus can thus be thought of as a "strong force molecule.