The Quest for Quantum Gravity
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The Future of Fundamental Physics
The Future of Fundamental Physics Nima Arkani-Hamed Abstract: Fundamental physics began the twentieth century with the twin revolutions of relativity and quantum mechanics, and much of the second half of the century was devoted to the con- struction of a theoretical structure unifying these radical ideas. But this foundation has also led us to a number of paradoxes in our understanding of nature. Attempts to make sense of quantum mechanics and gravity at the smallest distance scales lead inexorably to the conclusion that space- Downloaded from http://direct.mit.edu/daed/article-pdf/141/3/53/1830482/daed_a_00161.pdf by guest on 23 September 2021 time is an approximate notion that must emerge from more primitive building blocks. Further- more, violent short-distance quantum fluctuations in the vacuum seem to make the existence of a macroscopic world wildly implausible, and yet we live comfortably in a huge universe. What, if anything, tames these fluctuations? Why is there a macroscopic universe? These are two of the central theoretical challenges of fundamental physics in the twenty-½rst century. In this essay, I describe the circle of ideas surrounding these questions, as well as some of the theoretical and experimental fronts on which they are being attacked. Ever since Newton realized that the same force of gravity pulling down on an apple is also responsible for keeping the moon orbiting the Earth, funda- mental physics has been driven by the program of uni½cation: the realization that seemingly disparate phenomena are in fact different aspects of the same underlying cause. By the mid-1800s, electricity and magnetism were seen as different aspects of elec- tromagnetism, and a seemingly unrelated phenom- enon–light–was understood to be the undulation of electric and magnetic ½elds. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Conformal Symmetry in Field Theory and in Quantum Gravity
universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals). -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Gravity, Inertia, and Quantum Vacuum Zero Point Fields
Foundations of Physics, Vol.31,No. 5, 2001 Gravity, Inertia, and Quantum Vacuum Zero Point Fields James F. Woodward1 Received July 27, 2000 Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electri- cally charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reac- tion forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. 1. INTRODUCTION Several years ago Haisch, Rueda, and Puthoff (1) (hereafter, HRP) pub- lished a lengthy paper in which they claimed that a substantial part, indeed perhaps all of normal inertial reaction forces could be understood as the action of the electromagnetic zero-point field (EZPF), expected on the basis of quantum field theory, on electric charges of normal matter. In several subsequent papers Haisch and Rueda particularly have pressed this claim, making various modifications to the fundamental argument to try to deflect several criticisms. -
Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects
Advances in High Energy Physics Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Guest Editors: Emil T. Akhmedov, Stephen Minter, Piero Nicolini, and Douglas Singleton Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Advances in High Energy Physics Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects Guest Editors: Emil T. Akhmedov, Stephen Minter, Piero Nicolini, and Douglas Singleton Copyright © 2014 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in “Advances in High Energy Physics.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editorial Board Botio Betev, Switzerland Ian Jack, UK Neil Spooner, UK Duncan L. Carlsmith, USA Filipe R. Joaquim, Portugal Luca Stanco, Italy Kingman Cheung, Taiwan Piero Nicolini, Germany EliasC.Vagenas,Kuwait Shi-Hai Dong, Mexico Seog H. Oh, USA Nikos Varelas, USA Edmond C. Dukes, USA Sandip Pakvasa, USA Kadayam S. Viswanathan, Canada Amir H. Fatollahi, Iran Anastasios Petkou, Greece Yau W. Wah, USA Frank Filthaut, The Netherlands Alexey A. Petrov, USA Moran Wang, China Joseph Formaggio, USA Frederik Scholtz, South Africa Gongnan Xie, China Chao-Qiang Geng, Taiwan George Siopsis, USA Hong-Jian He, China Terry Sloan, UK Contents Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects,EmilT.Akhmedov, -
A Note on Conformally Compactified Connection Dynamics Tailored For
A note on conformally compactified connection dynamics tailored for anti-de Sitter space N. Bodendorfer∗ Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland October 9, 2018 Abstract A framework conceptually based on the conformal techniques employed to study the struc- ture of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions. 1 Introduction The study of asymptotic conditions on spacetimes has received wide interest within general relativity. Most notably, the concept of asymptotic flatness can serve as a model for isolated systems and one can, e.g., study a system’s total energy or the amount of gravitational ra- diation emitted [1]. More recently, with the discovery of the AdS/CFT correspondence [2], asymptotically anti de Sitter spacetimes have become a focus of interest. In a certain low en- ergy limit of the correspondence, computations on the gravitational side correspond to solving the Einstein equations with anti-de Sitter asymptotics. Within loop quantum gravity (LQG), the issue of non-compact spatial slices or asymptotic conditions on spacetimes has received only little attention so far due to a number of technical reasons. However, also given the recent interest in holography from a loop quantum gravity point of view [3, 4, 5], this question is important to address. -
Covariant Phase Space for Gravity with Boundaries: Metric Vs Tetrad Formulations
Covariant phase space for gravity with boundaries: metric vs tetrad formulations J. Fernando Barbero G.c,d Juan Margalef-Bentabola,c Valle Varob,c Eduardo J.S. Villaseñorb,c aInstitute for Gravitation and the Cosmos and Physics Department. Penn State University. PA 16802, USA. bDepartamento de Matemáticas, Universidad Carlos III de Madrid. Avda. de la Universidad 30, 28911 Leganés, Spain. cGrupo de Teorías de Campos y Física Estadística. Instituto Gregorio Millán (UC3M). Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Madrid, Spain. dInstituto de Estructura de la Materia, CSIC, Serrano 123, 28006, Madrid, Spain E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We use covariant phase space methods to study the metric and tetrad formula- tions of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting problem that we solve here by using the cohomological approach provided by the relative bicomplex framework. This setting provides a clean and ambiguity-free way to describe the solution spaces and associated symplectic structures. We also compute several relevant charges in both schemes and show that they are equivalent, as expected. arXiv:2103.06362v2 [gr-qc] 14 Jun 2021 Contents I Introduction1 II The geometric arena2 II.1 M as a space-time2 II.2 From M-vector fields to F-vector fields3 II.3 CPS-Algorithm4 IIIGeneral Relativity in terms of metrics5 IV General relativity in terms of tetrads8 V Metric vs Tetrad formulation 13 V.1 Space of solutions 13 V.2 Presymplectic structures 14 VI Conclusions 15 A Ancillary material 16 A.1 Mathematical background 16 A.2 Some computations in the metric case 19 A.3 Some tetrad computations 21 Bibliography 22 I Introduction Space-time boundaries play a prominent role in classical and quantum General Relativity (GR). -
Introduction to General Relativity
INTRODUCTION TO GENERAL RELATIVITY Gerard 't Hooft Institute for Theoretical Physics Utrecht University and Spinoza Institute Postbox 80.195 3508 TD Utrecht, the Netherlands e-mail: [email protected] internet: http://www.phys.uu.nl/~thooft/ Version November 2010 1 Prologue General relativity is a beautiful scheme for describing the gravitational ¯eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible the various ingredients that together give shape to this paradigm. After explaining the physical motivations we ¯rst introduce curved coordinates, then add to this the notion of an a±ne connection ¯eld and only as a later step add to that the metric ¯eld. One then sees clearly how space and time get more and more structure, until ¯nally all we have to do is deduce Einstein's ¯eld equations. These notes materialized when I was asked to present some lectures on General Rela- tivity. Small changes were made over the years. I decided to make them freely available on the web, via my home page. Some readers expressed their irritation over the fact that after 12 pages I switch notation: the i in the time components of vectors disappears, and the metric becomes the ¡ + + + metric. Why this \inconsistency" in the notation? There were two reasons for this. The transition is made where we proceed from special relativity to general relativity. -
Quantum Gravity from the QFT Perspective
Quantum Gravity from the QFT perspective Ilya L. Shapiro Universidade Federal de Juiz de Fora, MG, Brazil Partial support: CNPq, FAPEMIG ICTP-SAIFR/IFT-UNESP – 1-5 April, 2019 Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 Lecture 5. Advances topics in QG Induced gravity concept. • Effective QG: general idea. • Effective QG as effective QFT. • Where we are with QG?. • Bibliography S.L. Adler, Rev. Mod. Phys. 54 (1982) 729. S. Weinberg, Effective Field Theory, Past and Future. arXive:0908.1964[hep-th]; J.F. Donoghue, The effective field theory treatment of quantum gravity. arXive:1209.3511[gr-qc]; I.Sh., Polemic notes on IR perturbative quantum gravity. arXiv:0812.3521 [hep-th]. Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 I. Induced gravity. The idea of induced gravity is simple, while its realization may be quite non-trivial, depending on the theory. In any case, the induced gravity concept is something absolutely necessary if we consider an interaction of gravity with matter and quantum theory concepts. I. Induced gravity from cut-off Original simplest version. Ya.B. Zeldovich, Sov. Phys. Dokl. 6 (1967) 883. A.D. Sakharov, Sov. Phys. Dokl. 12 (1968) 1040. Strong version of induced gravity is like that: Suppose that the metric has no pre-determined equations of motion. These equations result from the interaction to matter. Main advantage: Since gravity is not fundamental, but induced interaction, there is no need to quantize metric. Ilya Shapiro, Quantum Gravity from the QFT perspective April - 2019 And we already know that the semiclassical approach has no problems with renormalizability! Suppose we have a theory of quantum matter fields Φ = (ϕ, ψ, Aµ) interacting to the metric gµν . -
Pos(Rio De Janeiro 2012)002 † ∗ [email protected] Speaker
Loop Quantum Gravity and the Very Early Universe PoS(Rio de Janeiro 2012)002 Abhay Ashtekar∗† Institute for Gravitational Physics and Geometry, Physics Department, Penn State, University Park, PA 16802, U.S.A. E-mail: [email protected] This brief overview is addressed to beginning researchers. It begins with a discussion of the distinguishing features of loop quantum gravity, then illustrates the type of issues that must be faced by any quantum gravity theory, and concludes with a brief summary of the status of these issues in loop quantum gravity. For concreteness the emphasis is on cosmology. Since several introductory as well as detailed reviews of loop quantum gravity are already available in the literature, the focus is on explaining the overall viewpoint and providing a short bibliography to introduce the interested reader to literature. 7th Conference Mathematical Methods in Physics - Londrina 2012, 16 to 20 April 2012 Rio de Janeiro, Brazil ∗Speaker. †A footnote may follow. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Loop Quantum Gravity Abhay Ashtekar Loop quantum gravity (LQG) is a non-perturbative approach aimed at unifying general rela- tivity and quantum physics. Its distinguishing features are: i) Background independence, and, ii) Underlying unity of the mathematical framework used to describe gravity and the other three basic forces of nature. It is background independent in the sense that there are no background fields, not even a space-time metric. All fields —whether they represent matter constituents, or gauge fields that mediate fundamental forces between them, or space- time geometry itself— are treated on the same footing. -
BEYOND SPACE and TIME the Secret Network of the Universe: How Quantum Geometry Might Complete Einstein’S Dream
BEYOND SPACE AND TIME The secret network of the universe: How quantum geometry might complete Einstein’s dream By Rüdiger Vaas With the help of a few innocuous - albeit subtle and potent - equations, Abhay Ashtekar can escape the realm of ordinary space and time. The mathematics developed specifically for this purpose makes it possible to look behind the scenes of the apparent stage of all events - or better yet: to shed light on the very foundation of reality. What sounds like black magic, is actually incredibly hard physics. Were Albert Einstein alive today, it would have given him great pleasure. For the goal is to fulfil the big dream of a unified theory of gravity and the quantum world. With the new branch of science of quantum geometry, also called loop quantum gravity, Ashtekar has come close to fulfilling this dream - and tries thereby, in addition, to answer the ultimate questions of physics: the mysteries of the big bang and black holes. "On the Planck scale there is a precise, rich, and discrete structure,” says Ashtekar, professor of physics and Director of the Center for Gravitational Physics and Geometry at Pennsylvania State University. The Planck scale is the smallest possible length scale with units of the order of 10-33 centimeters. That is 20 orders of magnitude smaller than what the world’s best particle accelerators can detect. At this scale, Einstein’s theory of general relativity fails. Its subject is the connection between space, time, matter and energy. But on the Planck scale it gives unreasonable values - absurd infinities and singularities.