DOCSLIB.ORG

Quantum Field Theory and Mathematics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Field Theory and Mathematics F EATURE Yuji Tachikawa Kavli IPMU Professor Research Area： Theoretical Physics Quantum Field Theory and Mathematics What are we made of? This is a long-standing as difcult subjects, but in fact they are rather well question for human beings. Our body is made of understood as theoretical frameworks, by physicists cells, which are made of molecules. Molecules are and mathematicians. First, there are many textbooks made of atoms, which, in turn, are made of electrons aimed at physics students, which can be read alone and nuclei. The latter are made of neutrons and in principle. Second, it is possible to express these protons, which are nally made of quarks. Electrons frameworks to mathematicians in single sentences: and quarks are known as elementary particles, and we can just say“: general relativity is about studying cannot be further subdivided as far as we know at the Einstein equation on Riemannian manifolds” present. The forces between these particles include and“ quantum mechanics is the study of self-adjoint the electromagnetic force, about which you are operators on Hilbert spaces.” The point here is not probably familiar, and the strong force＊1 which about whether or not you can understand these binds quarks into protons and neutrons. Elementary two sentences, but the fact that there is a way to particles and the forces among them are described tell mathematicians what they are in a concise way. by a framework called quantum eld theory in Now, what is the situation with quantum eld theoretical physics. theory? There are many textbooks for physics As I will explain soon below, the computations students, but they are rather difcult to study alone. based on quantum eld theory reproduce many Furthermore, there is no way to tell mathematicians experimental results extremely well. At the same in a few sentences what quantum eld theory time, our understanding of quantum eld theory is. There might be no need for every physics is quite incomplete. Still, quantum eld theory has theory to be understood by mathematicians, been stimulating the development of various areas but the fact that physicists cannot communicate of mathematics. I would like to say something it in a straightforward way to mathematicians about this mysterious gap in our understanding of should suggest that physicists themselves do not quantum eld theories. understand it well enough. But then, what do I think quantum eld theory is?＊2 For me, the framework called quantum eld Quantum eld theory is incomplete theory is merely a random collection of calculational What do I mean when I say quantum eld theory techniques and results which I learned through is incomplete? Let us compare the situation of textbooks and various original papers. I do not quantum eld theory with that of general relativity have a logical, uniform and straightforward and quantum mechanics, both of which appeared in understanding of it. And it seems it is not just a the early twentieth century. You might know them problem unique to me. For example, when you 4 Kavli IPMU News No. 37 March 2017 open a textbook on quantum eld theory and start This procedure is now carried out using the world’s studying it, you often encounter strange statements fastest supercomputers. In the last ten years, the such as“: the explanation given in the last chapter output of the computation started to show good to the concept X was not quite right. In fact the agreement with experimental results.＊4 correct statement is the following.” You continue One of the Clay Millennium Problems＊5 is reading and then nd“: in the last chapter we said essentially equivalent to proving that this limiting that the correct interpretation of the concept X procedure converges. We now know that the was such and such. But that is not perfectly true numerical value, before actually taking the limit, either. In reality it is...” These things rarely happen already agrees quite well with reality. in the textbooks on general relativity and quantum There are many other cases where the mechanics. computations done using quantum eld theory agree well with experimental results, although there is no satisfactory formulations of quantum eld Quantum eld theory works very well theory. It is expected, therefore, that some well- Still, computations done using quantum eld dened mathematics would be extracted from theory reproduce experimental results quite well. quantum eld theory, just as Euclidean geometry For example, the anomalous magnetic moment of was abstracted from various technical progresses in an electron, which is the strength of an electron ancient Egypt and Babylonia. as a magnet, can be computed in terms of the expansion in the ne structure constant, which is Various exiting formulations of the basic strength of the electromagnetic force. Its quantum eld theory theoretically computed value and the experimentally Of course, there have been many researchers observed value are in extremely good agreement.＊3 who thought exactly in the same way. After all, Feature Let us next discuss the case of the strong force. quantum eld theory itself has been studied for For theoretical physicists, this is dened in terms about one hundred years already. A very early effort of the so-called path integral, which is an innite- in the 1950s is now known as axiomatic quantum dimensional integral. Various physical quantities can eld theory, which successfully axiomatized the be computed by performing this process. However, aspects of quantum eld theory then known. it is impossible to perform the integration an innite Unfortunately, not much of the later developments ＊6 number of times in practice. Instead, the result is on the physics side have been incorporated. Then computed by rst making an approximation by a in the 1980s, a couple of formulations were given nite sum and then taking the limit numerically. to subclasses of quantum eld theory which are 5 Math Hopefully unied soon... 2017 Topological QFT Vertex algebras 1980s Operator algebraic 1960s QFT QFT in condensed Axiomatic QFT matter physics 1950s QFT in high Physics energy physics Figure 1: Existing formulations of quantum eld theory amenable to rigorous mathematical treatment, theory is that we need to justify and make rigorous such as topological quantum eld theory and this integral. This approach is known as constructive vertex algebras. These cannot, however, deal with quantum eld theory. However, in the last ten years, the quantum eld theory which describes our it is recognized on the physics side that there are microscopic world. Also, these formulations, once many examples of quantum eld theories＊7 which mathematical denitions are given, became separate do not seem to be described by the path integral. subdisciplines of mathematics and had their own This means that the completion of the program developments, with not much communications of the constructive quantum eld theory does not between them. Happily, we are starting to see mean a successful mathematical formulation of fruitful interactions among them in the last ten quantum eld theory. years. I summarized the interrelationship of these formulations in Figure 1. Mathematical applications of quantum In addition, the quantum eld theory which eld theory actually describes the real-world elementary So far I emphasized that we do not know how particles is usually described in physics textbooks to formulate quantum eld theory mathematically. in terms of the path integral, which is innite- Still, there have already been many rigorous dimensional. Therefore, a long-standing idea on the mathematical results inspired by the research in proper mathematical formulation of quantum eld quantum eld theory. For example, from the study 6 Kavli IPMU News No. 37 March 2017 spacetime M quantity a(M) quantum eld theory A(M) compute a quantity p should be For physicists: the same compute the same a quantity p quantum eld theory B(W) spacetime W quantity b(W) spacetime M quantity a(M) process a mathematicians are told to do mysteriously For mathematicians: the same process b mathematicians are told to do spacetime W quantity b(W) Figure 2: Mathematicians do not understand the area within the dotted line. of two-dimensional quantum eld theory in the application to mathematics of quantum eld early 1990s, there arose a subarea of mathematics theory. However, these mathematical works known as mirror symmetry. Also, stimulated by the are usually done quite independently from the physics results of Seiberg and Witten concerning mathematical sub-disciplines which deal with four-dimensional quantum eld theory, our formulations of quantum eld theory. Why is there understanding of the topology of four-dimensional such a mismatch? The reason can be understood manifold was greatly improved around 1995. by looking more closely at how these applications This is called the Seiberg-Witten theory in the arose. Let us take mirror symmetry as an example. mathematical literature.＊8 In my own collaboration Feature in theoretical physics with Luis F. Alday and Davide How mathematical applications are Gaiotto around 2010, we nd that there should be extracted a relation between the geometry of the instanton In superstring theory, there are two types of moduli space and the representation theory of strings, called type IIA and type IIB. The motion of innite dimensional algebras. This conjecture was these strings within a spacetime M is described soon mathematically formulated, which got other by a quantum eld theory depending on the type, mathematicians interested and inspired them to A(M) and B(M). Slightly later, it was realized that rigorously prove it. there is a duality where a type IIA string moving In a sense, these can all be considered as an in a spacetime M is equivalent to a type IIB string 7 The interior might It can be quite interesting at the surface! ?? !! Figure 3: Interesting things can happen at the surface even when the interior is not that interesting.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • "Eternal" Questions in the XX-Century Theoretical Physics V
    Philosophical roots of the "eternal" questions in the XX-century theoretical physics V. Ihnatovych Department of Philosophy, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine e-mail: [email protected] Abstract The evolution of theoretical physics in the XX century differs significantly from that in XVII-XIX centuries. While continuous progress is observed for theoretical physics in XVII-XIX centuries, modern physics contains many questions that have not been resolved despite many decades of discussion. Based upon the analysis of works by the founders of the XX-century physics, the conclusion is made that the roots of the "eternal" questions by the XX-century theoretical physics lie in the philosophy used by its founders. The conclusion is made about the need to use the ideas of philosophy that guided C. Huygens, I. Newton, W. Thomson (Lord Kelvin), J. K. Maxwell, and the other great physicists of the XVII-XIX centuries, in all areas of theoretical physics. 1. Classical Physics The history of theoretical physics begins in 1687 with the work “Mathematical Principles of Natural Philosophy” by Isaac Newton. Even today, this work is an example of what a full and consistent outline of the physical theory should be. It contains everything necessary for such an outline – definition of basic concepts, the complete list of underlying laws, presentation of methods of theoretical research, rigorous proofs. In the eighteenth century, such great physicists and mathematicians as Euler, D'Alembert, Lagrange, Laplace and others developed mechanics, hydrodynamics, acoustics and nebular mechanics on the basis of the ideas of Newton's “Principles”.
    [Show full text]
  • The Universe Unveiled Given by Prof Carlo Contaldi
    Friends of Imperial Theoretical Physics We are delighted to announce that the first FITP event of 2015 will be a talk entitled The Universe Unveiled given by Prof Carlo Contaldi. The event is free and open to all but please register by visiting the Eventbrite website via http://tinyurl.com/fitptalk2015. Date: 29th April 2015 Venue: Lecture Theatre 1, Blackett Laboratory, Physics Department, ICL Time: 7-8pm followed by a reception in the level 8 Common room Speaker: Professor Carlo Contaldi The Universe Unveiled The past 25 years have seen our understanding of the Universe we live in being revolutionised by a series of stunning observational campaigns and theoretical advances. We now know the composition, age, geometry and evolutionary history of the Universe to an astonishing degree of precision. A surprising aspect of this journey of discovery is that it has revealed some profound conundrums that challenge the most basic tenets of fundamental physics. We still do not understand the nature of 95% of the matter and energy that seems to fill the Universe, we still do not know why or how the Universe came into being, and we have yet to build a consistent "theory of everything" that can describe the evolution of the Universe during the first few instances after the Big Bang. In this lecture I will review what we know about the Universe today and discuss the exciting experimental and theoretical advances happening in cosmology, including the controversy surrounding last year's BICEP2 "discovery". Biography of the speaker: Professor Contaldi gained his PhD in theoretical physics in 2000 at Imperial College working on theories describing the formation of structures in the universe.
    [Show full text]
  • A Shorter Course of Theoretical Physics Vol. 1. Mechanics and Electrodynamics Vol. 2. Quantum Mechanics Vol. 3. Macroscopic Phys
    A Shorter Course of Theoretical Physics IN THREE VOLUMES Vol. 1. Mechanics and Electrodynamics Vol. 2. Quantum Mechanics Vol. 3. Macroscopic Physics A SHORTER COURSE OF THEORETICAL PHYSICS VOLUME 2 QUANTUM MECHANICS BY L. D. LANDAU AND Ε. M. LIFSHITZ Institute of Physical Problems, U.S.S.R. Academy of Sciences TRANSLATED FROM THE RUSSIAN BY J. B. SYKES AND J. S. BELL PERGAMON PRESS OXFORD · NEW YORK · TORONTO · SYDNEY Pergamon Press Ltd., Headington Hill Hall, Oxford Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523 Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Copyright © 1974 Pergamon Press Ltd. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Pergamon Press Ltd. First edition 1974 Library of Congress Cataloging in Publication Data Landau, Lev Davidovich, 1908-1968. A shorter course of theoretical physics. Translation of Kratkii kurs teoreticheskoi riziki. CONTENTS: v. 1. Mechanics and electrodynamics. —v. 2. Quantum mechanics. 1. Physics. 2. Mechanics. 3. Quantum theory. I. Lifshits, Evgenii Mikhaflovich, joint author. II. Title. QC21.2.L3513 530 74-167927 ISBN 0-08-016739-X (v. 1) ISBN 0-08-017801-4 (v. 2) Translated from Kratkii kurs teoreticheskoi fiziki, Kniga 2: Kvantovaya Mekhanika IzdateFstvo "Nauka", Moscow, 1972 Printed in Hungary PREFACE THIS book continues with the plan originated by Lev Davidovich Landau and described in the Preface to Volume 1: to present the minimum of material in theoretical physics that should be familiar to every present-day physicist, working in no matter what branch of physics.
    [Show full text]
  • Theoretical Physics Introduction
    2 Theoretical Physics Introduction A Single Coupling Constant The gravitational N-body problem can be defined as the challenge to understand the motion of N point masses, acted upon by their mutual gravitational forces (Eq.[1.1]). From the physical point of view a fun- damental feature of these equations is the presence of only one coupling 8 3 1 2 constant: the constant of gravitation, G =6.67 10− cm g− sec− (see Seife 2000 for recent measurements). It is even× possible to remove this altogether by making a choice of units in which G = 1. Matters would be more complicated if there existed some length scale at which the gravitational interaction departed from the inverse square dependence on distance. Despite continuing efforts, no such behaviour has been found (Schwarzschild 2000). The fact that a self-gravitating system of point masses is governed by a law with only one coupling constant (or none, after scaling) has important consequences. In contrast to most macroscopic systems, there is no decoupling of scales. We do not have at our disposal separate dials that can be set in order to study the behaviour of local and global aspects separately. As a consequence, the only real freedom we have, when modeling a self-gravitating system of point masses, is our choice of the value of the dimensionless number N, the number of particles in the system. As we will see, the value of N determines a large number of seemingly independent characteristics of the system: its granularity and thereby its speed of internal heat transport and evolution; the size of the central region of highest density after the system settles down in an asymptotic state; the nature of the oscillations that may occur in this central region; and to a surprisingly weak extent the rate of exponential divergence of nearby trajectories in the system.
    [Show full text]
  • Quantum Gravity, Effective Fields and String Theory
    Quantum gravity, effective fields and string theory Niels Emil Jannik Bjerrum-Bohr The Niels Bohr Institute University of Copenhagen arXiv:hep-th/0410097v1 10 Oct 2004 Thesis submitted for the degree of Doctor of Philosophy in Physics at the Niels Bohr Institute, University of Copenhagen. 28th July 2 Abstract In this thesis we will look into some of the various aspects of treating general relativity as a quantum theory. The thesis falls in three parts. First we briefly study how gen- eral relativity can be consistently quantized as an effective field theory, and we focus on the concrete results of such a treatment. As a key achievement of the investigations we present our calculations of the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. Another part of the thesis deals with the (Kawai-Lewellen-Tye) string theory gauge/gravity relations. Both theories are treated as effective field theories, and we investigate if the KLT oper- ator mapping is extendable to the case of higher derivative operators. The constraints, imposed by the KLT-mapping on the effective coupling constants, are also investigated. The KLT relations are generalized, taking the effective field theory viewpoint, and it is noticed that some remarkable tree-level amplitude relations exist between the field the- ory operators. Finally we look at effective quantum gravity treated from the perspective of taking the limit of infinitely many spatial dimensions.
    [Show full text]
  • Supersymmetry Then And
    UCB-PTH-05/19 LBNL-57959 Supersymmetry Then and Now Bruno Zumino Department of Physics, University of California, and Theoretical Physics Group, 50A-5104, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA ABSTRACT A brief description of some salient aspects of four-dimensional super- symmetry: early history, supermanifolds, the MSSM, cold dark matter, the cosmological constant and the string landscape. arXiv:hep-th/0508127v1 17 Aug 2005 1 A brief history of the beginning of supersymmetry Four dimensional supersymmetry (SUSY) has been discovered independently three times: first in Moscow, by Golfand and Likhtman, then in Kharkov, by Volkov and Akulov, and Volkov and Soroka, and finally by Julius Wess and me, who collaborated at CERN in Geneva and in Karlsruhe. It is re- markable that Volkov and his collaborators didn’t know about the work of Golfand and Likhtman, since all of them were writing papers in Russian in Soviet journals. Julius and I were totally unaware of the earlier work. For information on the life and work of Golfand and Likhtman, I refer to the Yuri Golfand Memorial Volume [1]. For information on Volkov’s life and work, I refer to the Proceedings of the 1997 Volkov Memorial Seminar in Kharkov [2]. Supersymmetry is a symmetry which relates the properties of integral- spin bosons to those of half-integral-spin fermions. The generators of the symmetry form what has come to be called a superalgebra, which is a su- per extension of the Poincar´eLie algebra of quantum field theory (Lorentz transformations and space-time translations) by fermionic generators.
    [Show full text]
  • Uwe Krey · Anthony Owen Basic Theoretical Physics Uwe Krey · Anthony Owen
    Uwe Krey · Anthony Owen Basic Theoretical Physics Uwe Krey · Anthony Owen Basic Theoretical Physics AConciseOverview With 31 Figures 123 Prof. Dr. Uwe Krey University of Regensburg (retired) FB Physik Universitätsstraße 31 93053 Regensburg, Germany E-mail: [email protected] Dr. rer nat habil Anthony Owen University of Regensburg (retired) FB Physik Universitätsstraße 31 93053 Regensburg, Germany E-mail: [email protected] Library of Congress Control Number: 2007930646 ISBN 978-3-540-36804-5 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting and production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: eStudio Calamar S.L., F. Steinen-Broo, Pau/Girona, Spain Printed on acid-free paper SPIN 11492665 57/3180/YL - 5 4 3 2 1 0 Preface This textbook on theoretical physics (I-IV) is based on lectures held by one of the authors at the University of Regensburg in Germany.
    [Show full text]
  • Quantum Gravity: a Primer for Philosophers∗
    Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts.
    [Show full text]
  • The Goal of Theoretical Physics - 2
    The goal of theoretical physics - 2 Werner Heisenberg, discoverer of the famous Uncertainty Principle. Physics becomes even more uncertain when black holes are involved. (Photo Pfeiffer) Last month we published the first part prediction of singularities presuma­ of Stephen Hawking's inaugural lec­ bly indicates that the Classical The­ ture * as Lucasian Professor of Mathe­ ory will break down. However, there matics in the University of Cambridge. seems to be no reason why it should In the second part of the lecture, break down until the gravitational which follows here. Hawking turned field becomes strong enough so that to the subject of gravity. After Ein­ quantum gravitational effects are stein's monumental work on gravita­ important. Thus a quantum theory of tion earlier this century, efforts to gravity is essential if we are to des­ mite this force with the other cribe the early Universe and to give mechanisms found in Nature have some explanation for the initial con­ been consistently unfruitful. But there ditions beyond merely appealing to are indications that this is beginning to the Anthropic Principle, which can change. be paraphrased as 'things are as they are because we are'. Such a theory is also required if we 'So far most of the effort has been are to answer the question 'Does devoted to unifying the first three time really have a beginning and, categories of physical interactions, possibly, an end as is predicted by the strong and weak nuclear forces Classical General Relativity or are and electromagnetism. The fourth the singularities in the Big Bang and and last, gravity, has been neglected.
    [Show full text]