DOCSLIB.ORG

Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 2-2014 Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes Debajyoti Sarkar Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/107 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes by Debajyoti Sarkar A dissertation submitted to the Graduate Faculty in Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2014 c 2014 Debajyoti Sarkar All rights reserved ii This manuscript has been read and accepted for the Graduate Faculty in Physics in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. Date Prof. Daniel N. Kabat Chair of Examining Committee Date Prof. Steven Greenbaum Executive Officer Prof. Dimitra Karabali Prof. V. Parameswaran Nair Prof. Alexios Polychronakos Prof. Martin Schaden Supervisory Committee THE CITY UNIVERSITY OF NEW YORK iii Abstract Gauge/ Gravity Correspondence, Bulk Locality and Quantum Black Holes by Debajyoti Sarkar Advisor: Daniel N. Kabat, Professor of Physics The aim of this dissertation is threefold. We begin by the study of two parallel ideal cosmic strings in the presence of non-minimal scalar fields and spin-1 gauge fields. We show that the contributions of the non-minimal term on the interaction energy between the strings are similar to that of the gauge field for a particular value of non-minimal coupling parameter. In this context we clarify some of the issues that arise when comparing the renormalization of black hole entropy and entanglement entropy using the replica trick. In the second part of the dissertation we study the process of bound state formation in clusters of Dp- brane collision and Dp shell/ Membrane collapse processes. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and timescale for formation of a bound state agree at the correspondence point, along with other relevant thermodynamic quantities. The timescale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity. Finally we study construction of local operators in AdS using the generalized AdS/ CFT corre- spondence. After briefly sketching previous works on this topic which involve massless and massive iv scalar fields, we present similar construction for spin- 1 and spin- 2 gauge fields. Working in holo- graphic gauge in the bulk, at leading order in 1=N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1=N perturbation theory, and we comment on the issue of general backgrounds. We point out some more recent works on interacting scalar and gauge fields and try to answer the question of what should be the CFT properties to have a dual gravitational descriptions on AdS space. We end with some speculations about finite N and when we have black holes in the bulk. v To My Family vi Acknowledgments On one hand, it is quite impossible for me to properly acknowledge everyone who have contributed to my academic life and stayed beside me leading to my PhD degree and on the other hand it is a pure pleasure. Especially, I think of myself as being exceptionally lucky to be alongside of so many great people and being fortunate enough to have them sometimes as my friend and sometimes as my guide. But being lucky has its own cost: the list is humongous and they come in so many colors and flavors. So without even trying, I will be very precise and will only name those (unsuccessfully) who have been directly involved and have tremendous effect in my academic world leading to my PhD degree. To begin with, of course I should recall my adviser Prof. Daniel Kabat, a fantastic person, who has shared his knowledge and insights to let me and make me mature in physics and paved my way for the future. Once again there are so many things I can say about him, that I will simply stop. Physics-maturity-wise, he shaped me to who I am, with all the defects being entirely my shortcomings. I would also like to thank him for various financial supports which enabled me to participate in various academic frontiers, which was essential towards my graduation. Among the other faculties at City University of New York (CUNY), I should of course mention Prof. Dimitra Karabali, Prof. V. Parameswaran Nair, Prof. Alexios Polychronakos for not only creating a vibrant research atmosphere at City College/ Lehman College, but also for teaching me various courses and finally serving as my thesis committee member. I would also like to thank Prof. Martin Schaden and Prof. Alberto Nicolis for serving respectively at my thesis and pre-thesis defense committee. Special thanks also goes to Prof. Peter Orland for couple of his fabulous QFT classes and his various advice. And finally among the CUNY faculties, I will end with Prof. Justin Vazquez-Poritz. What vii a wonderful friend, philosopher and guide he has been to me! I will not try to enumerate his contributions because I can’t, but will simply acknowledge that I will always regard him as one of the best mentors that I had at CUNY. I would also like to thank all the CUNY academic and administrative staffs, all the CUNY and outside professors, postdocs and graduate students whom I met at CUNY and elsewhere for helping me out, for sharing their knowledge and for easing my way out. Special thanks goes to Shubho Roy, a postdoc in our group for a couple of years with whom I shared many cups of coffee and learned a lot of things. I would also like to thank Diptarka Das, Norihiro Iizuka, Gilad Lifschytz and Xiao Xiao for past and ongoing collaborations. Special thanks also goes to Mr. Daniel Moy, our Physics APO for many interesting conversations and buckets of help. Personally (and also pre-graduate study wise), I would like to start off with my parents and stop right there. No thesis is long enough to fully reflect their contributions to my life. What about my wife and her family? No. I will have to stop again. May be I will simply say that I am grateful to her for her love and life (and also so that she smiles a bit more if she reads this acknowledgement). Then if I am to name friends starting with most recent ones, in my graduate life all names will be after Dario Capasso. Thanks for being such a great friend! Also during my undergraduate and Masters studies, I have had the fortune of having great friends and teachers. Among my friends, Nirupam Dutta for motivating me towards high energy physics and introducing me to Rajsekhar Bhattacharyya, a wonderful teacher that I had in my college days. And there are Arindam, Debmalya, two Partha’s, Soma, Arko . simply so many. Among the teachers Prof. Babul Dutta, Prof. Partha Pratim Basu and again so many; and then again in my school life I had some of my greatest class mates and teachers who offered me a very competitive and intelligent environment to grew up with. The acknowledgment is already nearly two page long now and I am having a feeling of dissatis- faction mixed with satisfaction and nostalgia. But the submission date is near and may be I should simply conclude by saying: “thanks to you all!” viii Contents Abstract iv Acknowledgments vii 1 Introduction 1 2 Cosmic String Interactions Induced by Gauge and Scalar Fields 5 2.1 Non-minimal scalar energy . .8 2.2 Gauge field energy . 11 2.3 Conclusions . 13 3 Black Hole Formation at the Correspondence Point: Part I 16 3.1 Introduction and summary . 16 3.2 Bound state formation in 0-brane collisions . 18 3.2.1 Perturbative string production . 19 3.2.2 Bound state formation in gravity . 20 3.2.3 Correspondence point . 21 3.3 Dp-brane collisions . 22 3.4 Parametric resonance in perturbative SYM . 24 3.5 Comparison of timescales . 28 3.5.1 0-brane parametric resonance . 28 3.5.2 p-brane parametric resonance . 29 3.5.3 Comparison to quasinormal modes . 30 3.6 Comparison to equilibrium properties . 31 ix 3.7 Shell Collapse . 33 3.8 Conclusions . 37 4 Black Hole Formation at the Correspondence Point: Part II 39 4.1 Introduction . 39 4.2 Fuzzy spheres . 40 4.3 Perturbative sphere collapse . 44 4.4 Black hole formation and the correspondence point . 45 4.5 Back-reaction and parametric resonance . 47 4.6 More on the correspondence point .
Load more

Recommended publications
  • States with Regards to Finding If the Cosmological Constant Is, Or Is Not a ‘Vacuum’ Field Andrew Beckwith, [email protected]
    Consequences of squeezing initially coherent (semi classical) states with regards to finding if the cosmological constant is, or is not a ‘vacuum’ field Andrew Beckwith, [email protected], Abstract The following document is to prepare an analysis on if the cosmological constant is a vacuum field. Candidates for how to analyze this issue come up in terms of brane theory, modified treatments of WdM theory (pseudo time component added) and/ or how to look at squeezing of vacuum states, as initially coherent semi classical constructions, or string theory versions of coherent states. The article presents a thought experiment if there is a non zero graviton mass, and at the end, in the conclusion states experimental modeling criteria which may indicate if a non zero graviton mass is measurable, which would indicate the existence, de facto of a possible replacement for DE, based upon non zero mass gravitons, and indications for a replacement for a cosmological constant. Introduction: Dr. Karim1 mailed the author with the following question which will be put in quotes: The challenge of resolving the following question: At the Big Bang the only form of energy released is in the form of geometry – gravity. intense gravity field lifts vacuum fields to positive energies, So an electromagnetic vacuum of density 10122 kg/m3 should collapse under its own gravity. But this does not happen - that is one reason why the cosmological constant cannot be the vacuum field. Why? Answering this question delves into what the initial state of the universe should be, in terms of either vacuum energy, or something else.
    [Show full text]
  • Bohr's Correspondence Principle
    Bohr’s Correspondence Principle Bohr's theory was deliberately incomplete so that he could find principles that would allow a systematic search for a “rational generalization” of classical electrodynamics. A major conceptual tool that characterized Bohr’s atomic work was the correspondence principle, his celebrated asymptotic consistency requirement between quantum theory and classical physics, that took various forms over the years and was often misunderstood by even his closest collaborators [312, p. 114], but guided his research and dominated quantum theory until the emergence of quantum mechanics in 1925-26 [419, p. 81]. It should be emphasized that the correspondence principle is not the elementary recognition that the results of classical and quantum physics converge in the limit ℎ → 0. Bohr said emphatically that this [420] See the print edition of The Quantum Measurement Problem for quotation. Instead, the correspondence principle is deeper and aims at the heart of the differences between quantum and classical physics. Even more than the previous fundamental work of Planck and Einstein on the quantum, Bohr’s atomic work marked a decisive break with classical physics. This was primarily because from the second postulate of Bohr’s theory there can be no relation between the light frequency (or color of the light) and the period of the electron, and thus the theory differed in principle from the classical picture. This disturbed many physicists at the time since experiments had confirmed the classical relation between the period of the waves and the electric currents. However, Bohr was able to show that if one considers increasingly larger orbits characterized by quantum number n, two neighboring orbits will have periods that approach a common value.
    [Show full text]
  • Arxiv:Hep-Th/0209231 V1 26 Sep 2002 Tbs,Daai N Uigi Eurdfrsae Te Hntetemlvcu Olead to Vacuum Thermal the Anisotropy
    SLAC-PUB-9533 BRX TH-505 October 2002 SU-ITP-02/02 Initial conditions for inflation Nemanja Kaloper1;2, Matthew Kleban1, Albion Lawrence1;3;4, Stephen Shenker1 and Leonard Susskind1 1Department of Physics, Stanford University, Stanford, CA 94305 2Department of Physics, University of California, Davis, CA 95616 3Brandeis University Physics Department, MS 057, POB 549110, Waltham, MA 02454y 4SLAC Theory Group, MS 81, 2575 Sand Hill Road, Menlo Park, CA 94025 Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are arXiv:hep-th/0209231 v1 26 Sep 2002 included. We apply these observations to the quantum state of the inflaton, and find that at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy. y Present and permanent address. *Work supported in part by Department of Energy Contract DE-AC03-76SF00515. 1. Introduction In inflationary cosmology, cosmic microwave background (CMB) data place a tanta- lizing upper bound on the vacuum energy density during the inflationary epoch: 4 V M 4 1016 GeV : (1:1) ∼ GUT ∼ Here MGUT is the \unification scale" in supersymmetric grand unified models, as predicted by the running of the observed strong, weak and electromagnetic couplings above 1 T eV in the minimal supersymmetric standard model. If this upper bound is close to the truth, the vacuum energy can be measured directly with detectors sensitive to the polarization of the CMBR.
    [Show full text]
  • Higher Order Schrödinger Equations Rémi Carles, Emmanuel Moulay
    Higher order Schrödinger equations Rémi Carles, Emmanuel Moulay To cite this version: Rémi Carles, Emmanuel Moulay. Higher order Schrödinger equations. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2012, 45 (39), pp.395304. 10.1088/1751- 8113/45/39/395304. hal-00776157 HAL Id: hal-00776157 https://hal.archives-ouvertes.fr/hal-00776157 Submitted on 12 Feb 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. HIGHER ORDER SCHRODINGER¨ EQUATIONS REMI´ CARLES AND EMMANUEL MOULAY Abstract. The purpose of this paper is to provide higher order Schr¨odinger equations from a finite expansion approach. These equations converge toward the semi-relativistic equation for particles whose norm of their velocity vector c is below √2 and are able to take into account some relativistic effects with a certain accuracy in a sense that we define. So, it is possible to take into account some relativistic effects by using Schr¨odinger form equations, even if they cannot be considered as relativistic wave equations. 1. Introduction In quantum mechanics, the Schr¨odinger equation is a fundamental non-relativistic quantum equation that describes how the wave-function of a physical system evolves over time.
    [Show full text]
  • Schrödinger Correspondence Applied to Crystals Arxiv:1812.06577V1
    Schr¨odingerCorrespondence Applied to Crystals Eric J. Heller∗,y,z and Donghwan Kimy yDepartment of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 zDepartment of Physics, Harvard University, Cambridge, MA 02138 E-mail: [email protected] arXiv:1812.06577v1 [cond-mat.other] 17 Dec 2018 1 Abstract In 1926, E. Schr¨odingerpublished a paper solving his new time dependent wave equation for a displaced ground state in a harmonic oscillator (now called a coherent state). He showed that the parameters describing the mean position and mean mo- mentum of the wave packet obey the equations of motion of the classical oscillator while retaining its width. This was a qualitatively new kind of correspondence princi- ple, differing from those leading up to quantum mechanics. Schr¨odingersurely knew that this correspondence would extend to an N-dimensional harmonic oscillator. This Schr¨odingerCorrespondence Principle is an extremely intuitive and powerful way to approach many aspects of harmonic solids including anharmonic corrections. 1 Introduction Figure 1: Photocopy from Schr¨odinger's1926 paper In 1926 Schr¨odingermade the connection between the dynamics of a displaced quantum ground state Gaussian wave packet in a harmonic oscillator and classical motion in the same harmonic oscillator1 (see figure 1). The mean position of the Gaussian (its guiding position center) and the mean momentum (its guiding momentum center) follows classical harmonic oscillator equations of motion, while the width of the Gaussian remains stationary if it initially was a displaced (in position or momentum or both) ground state. This classic \coherent state" dynamics is now very well known.2 Specifically, for a harmonic oscillator 2 2 1 2 2 with Hamiltonian H = p =2m + 2 m! q , a Gaussian wave packet that beginning as A0 2 i i (q; 0) = exp i (q − q0) + p0(q − q0) + s0 (1) ~ ~ ~ becomes, under time evolution, At 2 i i (q; t) = exp i (q − qt) + pt(q − qt) + st : (2) ~ ~ ~ where pt = p0 cos(!t) − m!q0 sin(!t) qt = q0 cos(!t) + (p0=m!) sin(!t) (3) (i.e.
    [Show full text]
  • Dr. Lisa Dyson
    DR. LISA DYSON BIO Dr. Dyson is the CEO of Air Protein, which is focused on feeding the world's population with food made from the most sustainable protein, protein that is made from elements found in the air. Using a proprietary probiotic production process, Air Protein is forging the way into a new era of sustainable food production, and has introduced the world's first food from CO2. Watch Dr. Dyson’s TED Talk about the technology here. Dr. Dyson is also the CEO of Kiverdi, which is remaking supply chains with carbon transformation. Dr. Dyson is a scientist and entrepreneur to her core, taught to solve problems. She was raised by an entrepreneur where she saw ideas come to fruition and she thrives when she is able to use her scientific knowledge to solve problems that are good for business and good for the planet. Lisa has spent the last decade of her career working on climate-positive technologies. As a mission-driven entrepreneur, Dr. Dyson is passionate about challenging business leaders to adopt innovative, sustainable ways of producing. EXPERIENCE AND BACKGROUND ● Management Consultant at The Boston Consulting Group ● PhD in physics from MIT ● Bachelor’s Degree in Mathematics and Physics from Brandeis University ● Master of Science and Fulbright Scholar at the Imperial College London ● Conducted research in bioengineering, energy and physics at Stanford University, UC Berkeley, and Princeton University ACCOLADES ● Inc Magazine - Top 100 Female Founders 2019 ● 2019 Verge Vanguard Award ● Most Creative People in Business 2017 by Fast Company ● San Francisco Business Times’ Forever Influential Honor Roll ● C3E award from MIT and the Department of Energy for her entrepreneurial leadership in energy Dr.
    [Show full text]
  • Negative Mass in Contemporary Physics and Its Application to Propulsion Geoffrey A
    Negative Mass in Contemporary Physics and its Application to Propulsion Geoffrey A. Landis, NASA Glenn Research Center, Cleveland, Ohio, 44135 6th Interstellar Symposium, Wichita KS, Nov. 10-15 2019. 6th Interstellar Symposium, Wichita, Kansas 2019 What do we mean by Mass? Physicists mean several different things when we refer to “mass” • Inertial mass F=mia 2 • Active (source) gravitational mass g=GMg/r *(more complicated in General Relativity) • Passive gravitational mass Fg=mgg 2 2 2 • Schrödinger mass ihdψ/dt=-(h /2ms)d ψ/dx +V *(or the corresponding term in Dirac or relativistic Schrödinger equation) 2 • Conserved mass/energy equivalent of mass: mo=E/c *(relativistic 4-vector) 2 • Quantum number m (e.g., me-= 511 MeV/c ) 6th Interstellar Symposium, Wichita, Kansas 2019 These terms are related by constitutive relations Inertial mass=gravitational mass Equivalence principle Active gravitational mass = Passive gravitational mass: Newton’s third law Schrödinger mass= inertial mass: correspondence principle Energy equivalent mass= inertial mass: special relativity Quantum number quantum indistinguishability 6th Interstellar Symposium, Wichita, Kansas 2019 Can mass ever be negative? • Einstein put “energy condition” into general relativity that energy must be positive. • E=Mc2; so positive energy = positive mass • Condition added to avoid “absurd” solutions to field equations • Many possible formulations: null, weak, strong, dominant energy condition; averaged null, weak, strong, dominant energy condition • Bondi pointed out that negative
    [Show full text]
  • Schrödinger's Wave Equation
    Schrödinger’s wave equation We now have a set of individual operators that can extract dynamical quantities of interest from the wave function, but how do we find the wave function in the first place? The free particle wave function was easy, but what about for a particle under the influence of a potential V(x,t)? Let us use the correspondence principle and classical physics to lead us to a general equation that dictates the form of the wave function, and thus tells us about the dynamics of the system. We know that the total energy for a (non- relativistic) particle is given by E = T +V. We now turn to the operators that we just discovered and replace the quantities in the energy equation by their respective operators: E = T + V ⇒ ∂ 2 ∂ 2 i = − h + V h ∂t 2m ∂x 2 This is an operator equation, and doesn’t really make much sense until we take it and operate on a wave function: 2 2 ∂Ψ()x,t h ∂ Ψ()x,t ih = − 2 + V ()x,t Ψ(x,t) ∂t 2m ∂x Of course, we really only get our expectation values of the quantities when we multiply (from the left) by Ψ* and integrate over all space. But, in order for that to give us reasonable quantities that describe the (quantum mechanical) motion of a particle, the wave function must obey this differential equation. This is Schrödinger’s Equation, and you will spend much of the rest of this semester finding solution to it, assuming different potentials.
    [Show full text]
  • Topics in Cosmology: Island Universes, Cosmological Perturbations and Dark Energy
    TOPICS IN COSMOLOGY: ISLAND UNIVERSES, COSMOLOGICAL PERTURBATIONS AND DARK ENERGY by SOURISH DUTTA Submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy Department of Physics CASE WESTERN RESERVE UNIVERSITY August 2007 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. To the people who have believed in me. Contents Dedication iv List of Tables viii List of Figures ix Abstract xiv 1 The Standard Cosmology 1 1.1 Observational Motivations for the Hot Big Bang Model . 1 1.1.1 Homogeneity and Isotropy . 1 1.1.2 Cosmic Expansion . 2 1.1.3 Cosmic Microwave Background . 3 1.2 The Robertson-Walker Metric and Comoving Co-ordinates . 6 1.3 Distance Measures in an FRW Universe . 11 1.3.1 Proper Distance . 12 1.3.2 Luminosity Distance . 14 1.3.3 Angular Diameter Distance . 16 1.4 The Friedmann Equation . 18 1.5 Model Universes . 21 1.5.1 An Empty Universe . 22 1.5.2 Generalized Flat One-Component Models . 22 1.5.3 A Cosmological Constant Dominated Universe . 24 1.5.4 de Sitter space . 26 1.5.5 Flat Matter Dominated Universe . 27 1.5.6 Curved Matter Dominated Universe . 28 1.5.7 Flat Radiation Dominated Universe . 30 1.5.8 Matter Radiation Equality . 32 1.6 Gravitational Lensing . 34 1.7 The Composition of the Universe .
    [Show full text]
  • Relativistic Quantum Mechanics
    Chapter 10 Relativistic Quantum Mechanics In this Chapter we will address the issue that the laws of physics must be formulated in a form which is Lorentz{invariant, i.e., the description should not allow one to differentiate between frames of reference which are moving relative to each other with a constant uniform velocity ~v. The transformations beween such frames according to the Theory of Special Relativity are described by Lorentz transformations. In case that ~v is oriented along the x1{axis, i.e., ~v = v1x^1, these transformations are v1 x1 v1t t c2 x1 x1 = − ; t0 = − ; x20 = x2 ; x30 = x3 (10.1) 2 2 0 1 v1 1 v1 q − c q − c which connect space time coordinates (x1; x2; x3; t) in one frame with space time coordinates (x10 ; x20 ; x30 ; t0) in another frame. Here c denotes the velocity of light. We will introduce below Lorentz-invariant differential equations which take the place of the Schr¨odingerequation of a par- ticle of mass m and charge q in an electromagnetic field [c.f. (refeq:ham2, 8.45)] described by an electrical potential V (~r; t) and a vector potential A~(~r; t) @ 1 ~ q 2 i~ (~r; t) = A~(~r; t) + qV (~r; t) (~r; t) (10.2) @t 2m i r − c The replacement of (10.2) by Lorentz{invariant equations will have two surprising and extremely important consequences: some of the equations need to be formulated in a representation for which the wave functions (~r; t) are vectors of dimension larger one, the components representing the spin attribute of particles and also representing together with a particle its anti-particle.
    [Show full text]
  • Twenty Years of Debate with Stephen
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server SU-ITP 02-11 hep-th/0204027 Twenty Years of Debate with Stephen L. Susskind Department of Physics Stanford University Stanford, CA 94305-4060 Abstract This is my contribution to Stephen Hawking's 60th birthday party. Happy Birth- day Stephen! 1 Crisis and Paradigm Shift Stephen, as we all know, is by far the most stubborn and infuriating person in the universe. My own scientific relation with him I think can be called adversarial. We have disagreed profoundly about deep issues concerning black holes, information and all that kind of thing. At times he has caused me to pull my hair out in frustration – and you can plainly see the result. I can assure you that when we began to argue more than two decades ago, Ihadafullheadofhair. I can also say that of all the physicists I have known he has had the strongest influence on me and on my thinking. Just about everything I have thought about since 1980 has in one way or another been a response to his profoundly insightful question about the fate of information that falls into a black hole [1]. While I firmly believe his answer was wrong, the question and his insistence on a convincing answer has forced us to rethink the foundations of physics. The result is a wholly new paradigm that is now taking shape. I am deeply honored to be here to celebrate Stephen’s monumental contributions and especially his magnificent stubbornness.
    [Show full text]
  • Ab-Initio Potential Hypersurfaces, 54 Acetylenic CH, 61 Acoustic Phonon
    INDEX Ab-initio potential hypersurfaces, 54 Acetylenic CH, 61 Acoustic phonon, 463 Activation barrier, 172 Active control, 535 Adiabatic approximation, 469 Adiabatic channel potential curves, 243, 256 Adiabatic channel threshold energies, 249 Adiabatic switching, 181, 182 Adiabatic transitions, 257 Aerodynamic Mach number, 436 Alkali halide clusters, 5 Alkyl radicals, 47 Aminotetrazine Ar2 , 87,88 Angular momentum, 181 Anharmonic clusters, 176 Anharmonic interactions, 19 Anharmonic oscillators, 543 Aniline, 429 Anthracene, 416 Argon cluster, 4, 165 Aromatic molecules, 18 Arrhenius formula, 156 Auger process, 374, 553 Auger relaxation, 390 Autocorrelation function, 10 Axilrod-Teller interactions, 5 Axilrod-Teller potential, 2 Aziridine, 269 Bacteriochlorophyll dimer, 559 Bacteriochlorophyll g, 467 Bacteriopheophytin g, 467 Bacteriopheophytons, 559 Benzaldehyde, 364 Benzene, 416 Benzene-biacetyl pair, 416, 417 Bimolecular reaction of water, 217 Birge-Sponer parameters, 29 Boltzmann distribution, 279 Boltzmann function, 279 Bond breaking, 283 Bond fission, 227, 241, 242 573 514 R. D. LEVINE AND J. JOR1NER Bond-selective Coulomb explosion, 553 Bootstrap procedure, 68 Born-Mayer potential, 2, 5 Born-Oppenheimer approximation, 49 Born-Oppenheimer hamiltonian, 336 Born-Oppenheimer potential surface, 122 Cage effect in clusters, 167, 169 Cage effect in photolysis, 206 Carter-Handy surface, 5 Centrifugal couplings, 19 CH-chromophores, 49, 58 Chaotic distribution, 79 charge separation in photosynthesis, 559 Chebychev basis, 71 Chebychev method,
    [Show full text]