DOCSLIB.ORG

Where Is H Hiding in Entropic Gravity?

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Where Is H Hiding in Entropic Gravity? SLAC-PUB-15931 Where is ~ Hiding in Entropic Gravity? Pisin Chen1;2;3;4∗ and Chiao-Hsuan Wang1;3y 1. Department of Physics, National Taiwan University, Taipei, Taiwan 10617 2. Graduate Institute of Astrophysics, National Taiwan University, Taipei, Taiwan 10617 3. Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, Taiwan 10617 4. Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, U.S.A. (Dated: December 15, 2011) The entropic gravity scenario recently proposed by Erik Verlinde reproduced the Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. This is atypical for emergent phenomena in physics, where the underlying, more fundamental physics often reveals itself as corrections to the leading classical behavior. So one naturally wonders: where is ~ hiding in entropic gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its variation law in order to obtain a self-consistent approach to the problem. Next we argue that when dealing with quantum gravity issues the generalized uncertainty principle (GUP) should be the more appropriate foundation. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime. In the weak gravity limit, such a GUP modified entropy exhibits a logarithmic correction term. When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on ~. Such deviation from the classical Newton's law may serve as a probe to the validity of the entropic gravity postulate. PACS numbers: 03.65.Ud, 04.50.Kd, 04.70.Dy, 89.70.Cf I. INTRODUCTION his perspective Einstein equations are now an equation of state rather than a fundamental theory. More ideas on emergent gravity have been recently proposed (See, for The issue of how gravity and thermodynamics are cor- example, [10{13]). related has been studied for decades, triggered by the seminal discovery by Bekenstein[1, 2] on the area-law of Similar to Jacobson's derivation of Einstein equa- black hole (BH) entropy and temperature. After Hawk- tions through thermodynamic, Verlinde treated gravity ing's discovery of the BH evaporation and the interpre- as an entropic force analogous to the restoring force of a tation of the its temperature as the thermal temperature stretched elastic polymer driven by the system's tendency of blackbody radiation[3], considerable efforts have been towards the maximization of entropy [13], and interest- made to find the statistical interpretation of the propor- ingly the Newton's law of gravitation was shown to arise. tionality of black hole entropy and its horizon area. See To arrive at the Newton's force law of gravity through [4] and [5], for example, for a review. By now a well- the first law of thermodynamic F dx = T dS, Verlinde accepted view is that the black hole entropy is associated first invoked the Compton wavelength of the test par- with the external thermal state perceived by an observer ticle to find the change of entropy with respect to its outside the event horizon who has no access to the BH displacement. He then invoked the holographic principle interior. Namely, the correlation between the degrees [14{16] and the equipartition theorem to define the tem- of freedom on opposite sides of the horizon results in a perature experienced by the test particle. One cannot mixed state for observation from the outside, i.e., the but notices that all these building blocks have quantum `entanglement entropy'[6, 7], which depends upon the mechanical origin, or more specifically the presence of ~. boundary properties and will be discussed more in the Yet all the ~'s just get subtly cancelled and at the end a later sections of this paper. purely classical Newton's law has emerged. This is rather atypical for emergent phenomena in physics, where the The inversion of the logic that describes gravity as an underlying, more fundamental physics often reveals itself emergent phenomenon was first proposed by Sakharov as corrections to the leading classical behavior. So one [8], who suggested that gravity is induced by quantum naturally wonders: where is hiding in entropic gravity? field fluctuations. Invoking the area scaling property of ~ entanglement entropy, Jacobson in 1995 [9] used basic There have been previous works aiming at finding the laws of thermodynamics to derive Einstein equations. In entropic corrections to Newton's law but however unsat- isfactory: Santos et al. [17] and Ghosh [18] suggested the corrected to Newton's grativy force law when the depen- dence on the uncertainty in position is included, which ∗Electronic address: [email protected] is bothersome; both Modesto [19] and Setare [20] sug- yElectronic address: [email protected] gested the sub-leading terms of force law rather than an Work supported by US Department of Energy under contract DE-AC02-76SF00515 and HEP. 2 exact form while the former considered only the correc- II. ENTROPIC GRAVITY tions to entropic variation without noting that the in- formation content and therefore the temperature is also A. Holographic principle and holographic affected, and the latter failed to introduce the right form entanglement entropy of GUP corrected entropy into consideration. We argue that when dealing with quantum gravity issues the gen- 1. Holographic principle eralized uncertainty principle (GUP) should be the more appropriate foundation. Indeed based on GUP it has Holographic principle [14, 15], which is developed from been demonstrated that the black hole Bekenstein en- black hole thermodynamics, plays a key role in Verlinde's tropy area law must be modified not only in the strong entropic interpretation of gravity. It dictates that the de- but also in the weak gravity regime [21]. In the weak grees of freedom in a d+2 dimensional quantum gravity gravity limit, such a GUP modified Bekenstein entropy system can be seen as encoded on its d+1dimensional exhibits a logarithmic correction. Such a log-correction boundary like a holographic image. This principle orig- is consistent with similar conclusions drawn from string inates from the Bekenstein-Hawking formula where the theory, AdS/CFT correspondence, and loop quantum BH entropy is proportional to the surface area of its event gravity considerations [22{25]. When applying it to the horizon: entropic derivations, we demonstrate that the resulting 2 2 3 entropic gravity does include sub-leading order correction 4πkBGM M kBc terms that depend on . SB = = 4π 2 = A: (1) ~ ~c Mp 4~G Here A is the surface area of black hole event horizon and p Mp = ~c=G is the Planck mass. For the second law of thermodynamics to hold, that is, the entropy in the universe to be non-decreasing, the holographic principle suggests that the information con- tent S of an enclosed spacetime region should be no larger than the Bekenstein-Hawking entropy defined by its sur- face area[2, 16]: k k c3 The organization of this paper is as follows. To address B B S ≤ 2 A = A = SB: (2) the question we posted, we first revisit the ideas of holo- 4Lp 4~G graphic screen as well as entropy and its variation law in p 3 order to obtain a self-consistent approach to the problem Here Lp = G~=c is the Planck length. This implies in section II. We set up the key ingredients of entropic that the number of fundamental degrees of freedom is gravity framework toward the derivation of weak-field- related to the surface area in spacetime. Note that the limit gravity force law. Holographic principle, which we black hole information paradox, that is, the information deem misapplied by Verlinde, is illustrated and the con- seems to be lost as all physical states evolve into the same cept of entanglement entropy is introduced to support final state of black hole, is also resolved by this principle. the validity of the derivation. We then revisit Verlinde's An extensive illustration of the holographic principle is previous work and make some elaboration for a more con- given by Bousso [16]. crete foundation of this entropic gravity, clarification of the idea of holographic screen and re-derivation of en- tropy variation law are made especially. In section III 2. Holographic entanglement entropy we bring in the generalized uncertainty principle, which leads to a corrected form of black hole temperature and In the derivation of the entropic gravity force law, entropy. The modification of the information content so the maximum value of the holographic entropy is used provided by GUP will result in the revision of the force rather than the inequality, which is unjustified. To treat law. In section IV we repeat the steps of Verlinde's, but the problem more properly, one should instead invoke with the entropy variation law and the temperature form the concept of entanglement entropy [26{30]. The en- redefined by the GUP corrected entropy. We arrive at tanglement entropy is a quantum mechanical quantity an exact force law of gravity at the end, and this exact that measures the correlation between a subsystem A force law recovers not only the classical Newton's law but and its complementary subsystem B. When the world also the sub-leading order quantum correction terms in is divided into two subsystems, the total Hilbert space the weak-field limit. In section V, conclusions and com- can be written as Htot = HA ⊗ HB. If an observer can ments are made about the implications of our findings.
Load more

Recommended publications
  • Inertial Mass of an Elementary Particle from the Holographic Scenario
    Document downloaded from: http://hdl.handle.net/10459.1/62944 The final publication is available at: https://doi.org/10.1142/S0217751X17500439 Copyright (c) World Scientific Publishing, 2017 Inertial mass of an elementary particle from the holographic scenario Jaume Gin´e Departament de Matem`atica, Universitat de Lleida, Catalonia, Spain. E{mail: [email protected] Abstract Various attempts have been made to fully explain the mechanism by which a body has inertial mass. Recently it has been proposed that this mechanism is as follows: when an object accelerates in one direction a dy- namical Rindler event horizon forms in the opposite direction, suppressing Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation in the other side is only slightly reduce by a Hubble-scale Casimir effect. This produces a net Unruh radiation pressure force that always op- poses the acceleration, just like inertia, although the masses predicted are twice those expected, see [17]. In a later work an error was corrected so that its prediction improves to within 26% of the Planck mass, see [10]. In this paper the expression of the inertial mass of a elementary particle is derived from the holographic scenario giving the exact value of the mass of a Planck particle when it is applied to a Planck particle. Keywords: inertial mass; Unruh radiation; holographic scenario, Dark matter, Dark energy, cosmology. PACS 98.80.-k - Cosmology PACS 04.62.+v - Quantum fields in curved spacetime PACS 06.30.Dr - Mass and density 1 Introduction The equivalence principle introduced by Einstein in 1907 assumes the com- plete local physical equivalence of a gravitational field and a corresponding non- inertial (accelerated) frame of reference (Einstein was thinking of his famous elevator experiment).
    [Show full text]
  • Quantization of Black Holes Is One of the Important Issues in Physics [1], and There Has Been No Satisfactory Solution Yet
    Quantization of Black Holes Xiao-Gang He1, 2, 3, 4, ∗ and Bo-Qiang Ma1, 2, 4, † 1School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871 2Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617 3Institute of Particle Physics and Cosmology, Department of Physics, Shanghai JiaoTong University, Shanghai 200240 4Center for High-Energy Physics, Peking University, Beijing 100871 Abstract We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr’s idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can be also derived from an Ansatz of quantized entropy ∆S = 4πk∆R/λ, which was suggested in a previous work to unify the black hole entropy formula and Verlinde’s conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors. PACS numbers: 04.70.Dy, 03.67.-a, 04.70.-s, 04.90.+e arXiv:1003.2510v3 [hep-th] 5 Apr 2010 ∗Electronic address: [email protected] †Electronic address: [email protected] 1 The quantization of black holes is one of the important issues in physics [1], and there has been no satisfactory solution yet.
    [Show full text]
  • Statistical Mechanics of Entropic Forces: Disassembling a Toy
    Home Search Collections Journals About Contact us My IOPscience Statistical mechanics of entropic forces: disassembling a toy This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 Eur. J. Phys. 31 1353 (http://iopscience.iop.org/0143-0807/31/6/005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 132.239.16.142 The article was downloaded on 06/12/2011 at 21:15 Please note that terms and conditions apply. IOP PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 31 (2010) 1353–1367 doi:10.1088/0143-0807/31/6/005 Statistical mechanics of entropic forces: disassembling a toy Igor M Sokolov Institut fur¨ Physik, Humboldt-Universitat¨ zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany E-mail: [email protected] Received 21 June 2010, in final form 9 August 2010 Published 23 September 2010 Online at stacks.iop.org/EJP/31/1353 Abstract The notion of entropic forces often stays mysterious to students, especially to ones coming from outside physics. Although thermodynamics works perfectly in all cases when the notion of entropic force is used, no effort is typically made to explain the mechanical nature of the forces. In this paper we discuss the nature of entropic forces as conditional means of constraint forces in systems where interactions are taken into account as mechanical constraints and discuss several examples of such forces. We moreover demonstrate how these forces appear within the standard formalism of statistical thermodynamics and within the mechanical approach based on the Pope–Ching equation, making evident their connection with the equipartition of energy.
    [Show full text]
  • Modified Newtonian Dynamics
    Faculty of Mathematics and Natural Sciences Bachelor Thesis University of Groningen Modified Newtonian Dynamics (MOND) and a Possible Microscopic Description Author: Supervisor: L.M. Mooiweer prof. dr. E. Pallante Abstract Nowadays, the mass discrepancy in the universe is often interpreted within the paradigm of Cold Dark Matter (CDM) while other possibilities are not excluded. The main idea of this thesis is to develop a better theoretical understanding of the hidden mass problem within the paradigm of Modified Newtonian Dynamics (MOND). Several phenomenological aspects of MOND will be discussed and we will consider a possible microscopic description based on quantum statistics on the holographic screen which can reproduce the MOND phenomenology. July 10, 2015 Contents 1 Introduction 3 1.1 The Problem of the Hidden Mass . .3 2 Modified Newtonian Dynamics6 2.1 The Acceleration Constant a0 .................................7 2.2 MOND Phenomenology . .8 2.2.1 The Tully-Fischer and Jackson-Faber relation . .9 2.2.2 The external field effect . 10 2.3 The Non-Relativistic Field Formulation . 11 2.3.1 Conservation of energy . 11 2.3.2 A quadratic Lagrangian formalism (AQUAL) . 12 2.4 The Relativistic Field Formulation . 13 2.5 MOND Difficulties . 13 3 A Possible Microscopic Description of MOND 16 3.1 The Holographic Principle . 16 3.2 Emergent Gravity as an Entropic Force . 16 3.2.1 The connection between the bulk and the surface . 18 3.3 Quantum Statistical Description on the Holographic Screen . 19 3.3.1 Two dimensional quantum gases . 19 3.3.2 The connection with the deep MOND limit .
    [Show full text]
  • Generalizing Entropic Force Formalism
    Yongpyung 2012, Greenpia Condo, Feb. 21st 2012 GENERALIZING ENTROPIC FORCE FORMALISM Jin-Ho Cho (Hanyang University) w/ Hosin Gong, Hyosung Kim (POSTECH) Motivation (for the entropic force) Quantum Gravity .....not successful so far the role of gravity in AdS/CFT tree level supergravity (closed string) / quantum SYM (open string) Fundamental or Emergent? Entropic Force rubber band tends to increase the entropy S : larger S : smaller [Halliday et al., Fundamentals of Physics] Verlinde’s Idea [Erik Verlinde, 1001.0785] entropic force : F x = T S 4 4 3 holographic principle : Ac /G~ = N E = NkBT/2 T = ~a/2πkBc entropy change : S =2πkB( x mc/~) 4 4 (for a screen shift x ) 4 Newtonian Physics Newton’s law : (a planar screen) T = ~a/2πckB S =2πkB( x mc/~) 4 4 F x = T S 4 4 ~a 2πkBmc x = 4 2πk c ✓ B ◆✓ ~ ◆ = ma x 4 3 Gravitational force : (a spherical screen) N = Ac /G~ 2 Mc = E = NkBT/2 1 Ac3 ~a r2c2 = = a 2 G 2πc ✓ ~ ◆✓ ◆ G Q1: Cosmological Constant ? g R ab R + ⇤g =8⇡GT ab − 2 ab ab 3 Ac /G~ = N F x = T S S =2πkB( x mc/~) 4 4 E = NkBT/2 4 4 T = ~a/2πkBc ‘Volume Energy’ NkBT E = Mc2 +↵V = 2 N~ a ~a = T = 4⇡c 2⇡ckB 2 Ac a 3 = N = Ac /G~ 4⇡G 4⇡GM 4⇡G↵V a = + A Ac2 Determination of ↵ spherically symmetric case GM 4⇡G↵r a = + = Φ r2 3c2 r GM c2⇤r = Newtonian limit of Einstein eq. r2 − 3 c4 ↵ = ⇤ −4⇡G Einstein equation 4 c NkBT E = Mc2 ⇤V = − 4⇡G 2 c4 k c3 Mc2 ⇤ dV = B TdN = adA − 4⇡G 2 4⇡G Z Z Z 1 a b 1 a b 2 T Tg n ⇠ dV ⇤gabn ⇠ dV ab − 2 ab −4⇡G Z⌃ ✓ ◆ Z⌃ 1 = R na⇠b dV 4⇡G ab Z⌃ Q2: Entropic Coulomb Force ? [JHC & Hyosung Kim, 2012 J.
    [Show full text]
  • Curriculum Vitae
    SEBASTIAN DE HARO Curriculum Vitae Assistant Professor in Philosophy of Science at the Institute for Logic, Language and Computation and the Institute of Physics of the University of Amsterdam 1. RESEARCH PROFILE Areas of specialisation: Philosophy of Science, History and Philosophy of Physics, Theoretical Physics Areas of competence: Epistemology, Metaphysics, Ethics, Philosophical and Social Aspects of Information, History of Science, History of Philosophy, Philosophy of Logic and Language, Philosophy of Mathematics 2. PREVIOUS POSITIONS • Lecturer (2009-2020), Amsterdam University College (AUC), University of Amsterdam. Tasks: teaching, curriculum development and evaluation, thesis supervision, member of the BSA committee. Between 2009-2015 I also had tutoring responsibilities. • Lecturer (2019-2020, fixed term), Department of Philosophy, Free University Amsterdam • Lecturer in theoretical physics (fixed term), Institute for Theoretical Physics, Faculty of Science, University of Amsterdam. Teaching, research, thesis supervision. 02/12 - 07/14. • Research associate. Managing editor of Foundations of Physics on behalf of Gerard ’t Hooft, Spinoza Institute/ITP, Utrecht University and Springer Verlag, 2008-2009. Research, managing editorial office, setting up new projects, contact Editorial Board. 3. PUBLICATIONS Total number of citations (all publications): 2,751. i10-index: 33. h-index: 22 Full list of publications and citation information via Google scholar profile: http://scholar.google.nl/citations?user=rmXDqN4AAAAJ&hl=nl&oi=ao Journal articles, book chapters, and book reviews General philosophy of science: journal articles (6) 1. ‘The Empirical Under-determination Argument Against Scientific Realism for Dual Theories’. Erkenntnis, 2021. https://link.springer.com/article/10.1007%2Fs10670-020-00342-0 2. ‘Science and Philosophy: A Love-Hate Relationship’.
    [Show full text]
  • Colloidal Matter: Packing, Geometry, and Entropy Vinothan N
    Colloidal matter: packing, geometry, and entropy Vinothan N. Manoharan Harvard John A. Paulson School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge MA 02138 USA This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science volume 349 on August 8, 2015. doi: 10.1126/science.1253751 The many dimensions of colloidal matter. The self-assembly of colloids can be controlled by changing the shape, topology, or patchiness of the particles, by introducing attractions between particles, or by constraining them to a curved surface. All of the assembly phenomena illustrated here can be understood from the interplay between entropy and geometrical constraints. Summary of this review article Background: Colloids consist of solid or liquid particles, each about a few hundred nanometers in size, dispersed in a fluid and kept suspended by thermal fluctuations. While natural colloids are the stuff of paint, milk, and glue, synthetic colloids with well-controlled size distributions and interactions are a model system for understanding phase transitions. These colloids can form crystals and other phases of matter seen in atomic and molecular systems, but because the particles are large enough to be seen under an optical microscope, the microscopic mechanisms of phase transitions can be directly observed. Furthermore, their ability to spontaneously form phases that are ordered on the scale of visible wavelengths makes colloids useful building blocks for optical materials such as photonic crystals. Because the interactions between particles can be altered and the effects on structure directly observed, experiments on colloids offer a controlled approach toward understanding and harnessing self-assembly, a fundamental topic in materials science, condensed matter physics, and biophysics.
    [Show full text]
  • Supersymmetry at Large Distance Scales
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server PUPT-1925 Supersymmetry at Large Distance Scales Herman Verlinde Physics Department, Princeton University, Princeton, NJ 08544 Abstract We propose that the UV/IR relation that underlies the AdS/CFT duality may provide a natural mechanism by which high energy supersymmetry can have large distance conse- quences. We motivate this idea via (a string realization of) the Randall-Sundrum scenario, in which the observable matter is localized on a matter brane separate from the Planck brane. As suggested via the holographic interpretation of this scenario, we argue that the local dynamics of the Planck brane – which determines the large scale 4-d geometry – is protected by the high energy supersymmetry of the dual 4-d theory. With this assumption, we show that the total vacuum energy naturally cancels in the effective 4-d Einstein equa- tion. This cancellation is robust against changes in the low energy dynamics on the matter brane, which gets stabilized via the holographic RG without any additional fine-tuning. 1. Introduction The observed smallness of the cosmological constant requires a remarkable cancellation of all vacuum energy contributions [1]. Supersymmetry seems at present the only known symmetry that could naturally explain this cancellation, but thus far no mechanism for supersymmetry breaking is known that would not destroy this property. Nonetheless, in searching for a possible resolution of the cosmological constant problem, it seems natural to include supersymmetry as a central ingredient. What would then be needed, however, is a mechanism – some UV/IR correspondence – by which the short distance cancellations of supersymmetry can somehow be translated into a long distance stability of the cosmological evolution equations.
    [Show full text]
  • A Unitary S-Matrix for 2D Black Hole Formation and Evaporation
    PUPT-1380 IASSNS-HEP-93/8 February 1993 A Unitary S-matrix for 2D Black Hole Formation and Evaporation Erik Verlinde School of Natural Sciences Institute for Advanced Study Princeton, NJ 08540 and Herman Verlinde Joseph Henry Laboratories Princeton University Princeton, NJ 08544 arXiv:hep-th/9302022v1 7 Feb 1993 Abstract We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to N massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum S-matrix for the case that N=24. This S-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity S-matrix and that of the c = 1 matrix model. 1. Introduction The discovery that black holes can evaporate by emitting thermal radiation has led to a longstanding controversy about whether or not quantum coherence can be maintained in this process. Hawking’s original calculation [1] suggests that an initial state, describing matter collapsing into a black hole, will eventually evolve into a mixed state describing the thermal radiation emitted by the black hole. The quantum physics of black holes thus seems inherently unpredictable. However, this is clearly an unsatisfactory conclusion, and several attempts have been made to find a description of black hole evaporation in accordance with the rules of quantum mechanics [2, 3], but so far all these attempts have run into serious difficulties.
    [Show full text]
  • Thesis in Amsterdam
    UvA-DARE (Digital Academic Repository) The physics and mathematics of microstates in string theory: And a monstrous Farey tail de Lange, P. Publication date 2016 Document Version Final published version Link to publication Citation for published version (APA): de Lange, P. (2016). The physics and mathematics of microstates in string theory: And a monstrous Farey tail. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:10 Oct 2021 P a u A dissertation that delves l The Physics & d into physical and e L mathematical aspects of a Microstates Mathematics of n g string theory. In the first e part ot this book, Microstates in T microscopic porperties of h Moonshine e string theoretic black String Theory P h holes are investigated.
    [Show full text]
  • Quantum Gravity Past, Present and Future
    Quantum Gravity past, present and future carlo rovelli vancouver 2017 loop quantum gravity, Many directions of investigation string theory, Hořava–Lifshitz theory, supergravity, Vastly different numbers of researchers involved asymptotic safety, AdS-CFT-like dualities A few offer rather complete twistor theory, tentative theories of quantum gravity causal set theory, entropic gravity, Most are highly incomplete emergent gravity, non-commutative geometry, Several are related, boundaries are fluid group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, Several are only vaguely connected to the actual problem of quantum gravity shape dynamics, ’t Hooft theory non-quantization of geometry Many offer useful insights … loop quantum causal dynamical gravity triangulations string theory asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory shape dynamics causal set supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Several are related Herman Verlinde at LOOP17 in Warsaw No major physical assumptions over GR&QM No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small Supersymmetry string High dimensions theory Strings Lorentz Violation asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory Mostly still shape dynamics causal set classical supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Discriminatory questions: Is Lorentz symmetry violated at the Planck scale or not? Are there supersymmetric particles or not? Is Quantum Mechanics violated in the presence of gravity or not? Are there physical degrees of freedom at any arbitrary small scale or not? Is geometry discrete i the small? Lorentz violations Infinite d.o.f.
    [Show full text]
  • Nov/Dec 2020
    CERNNovember/December 2020 cerncourier.com COURIERReporting on international high-energy physics WLCOMEE CERN Courier – digital edition ADVANCING Welcome to the digital edition of the November/December 2020 issue of CERN Courier. CAVITY Superconducting radio-frequency (SRF) cavities drive accelerators around the world, TECHNOLOGY transferring energy efficiently from high-power radio waves to beams of charged particles. Behind the march to higher SRF-cavity performance is the TESLA Technology Neutrinos for peace Collaboration (p35), which was established in 1990 to advance technology for a linear Feebly interacting particles electron–positron collider. Though the linear collider envisaged by TESLA is yet ALICE’s dark side to be built (p9), its cavity technology is already established at the European X-Ray Free-Electron Laser at DESY (a cavity string for which graces the cover of this edition) and is being applied at similar broad-user-base facilities in the US and China. Accelerator technology developed for fundamental physics also continues to impact the medical arena. Normal-conducting RF technology developed for the proposed Compact Linear Collider at CERN is now being applied to a first-of-a-kind “FLASH-therapy” facility that uses electrons to destroy deep-seated tumours (p7), while proton beams are being used for novel non-invasive treatments of cardiac arrhythmias (p49). Meanwhile, GANIL’s innovative new SPIRAL2 linac will advance a wide range of applications in nuclear physics (p39). Detector technology also continues to offer unpredictable benefits – a powerful example being the potential for detectors developed to search for sterile neutrinos to replace increasingly outmoded traditional approaches to nuclear nonproliferation (p30).
    [Show full text]