Why String Theory? Read online

  WHY STRING THEORY?

  WHY STRING THEORY?

  Joseph Conlon

  CRC Press

  Taylor & Francis Group

  6000 Broken Sound Parkway NW, Suite 300

  Boca Raton, FL 33487-2742

  © 2016 by Joseph Conlon

  CRC Press is an imprint of Taylor & Francis Group, an Informa business

  No claim to original U.S. Government works

  Version Date: 20151020

  International Standard Book Number-13: 978-1-4822-4249-2 (eBook - PDF)

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  Contents

  SECTION I Why?

  CHAPTER 1 ■ The Long Wait

  CHAPTER 2 ■ Scales of Science: Little and Large

  CHAPTER 3 ■ Big Lessons of Physics

  3.1 SPACE AND TIME ARE CUT FROM THE SAME CLOTH

  3.2 SPACETIME IS DYNAMICAL

  3.3 THE WORLD IS DESCRIBED BY QUANTUM MECHANICS

  3.4 THE WORLD REALLY, HONESTLY, TRULY IS DESCRIBED BY QUANTUM MECHANICS

  3.5 NATURE LIKES SYMMETRIES

  3.6 THE UNIVERSE WAS YOUNG, SMOOTH AND HOT, BUT IS NOW OLD, COLD AND WRINKLY

  3.7 DIFFERENT CAN BE THE SAME

  3.8 NATURE IS SMARTER THAN WE ARE

  CHAPTER 4 ■ The Truth Is Out There

  SECTION II What?

  CHAPTER 5 ■ What Was String Theory?

  5.1 THE BIRTH

  5.2 THE NAMING CEREMONY

  5.3 THE WILDERNESS YEARS

  5.4 HARBINGERS OF GREAT JOY

  5.5 THE LIMELIGHT

  5.6 THE THEORY FORMERLY KNOWN AS STRINGS

  CHAPTER 6 ■ What Is String Theory?

  6.1 QUANTUM FIELD THEORY BY ANY OTHER NAME

  6.2 THE MISANTHROPIC LANDSCAPE

  6.3 FIFTY YEARS ON

  SECTION III What For?

  CHAPTER 7 ■ Direct Experimental Evidence for String Theory

  CHAPTER 8 ■ Why Strings? Quantum Field Theory

  8.1 THE PROBLEM OF STRONG COUPLING

  8.2 THE ADS/CFT CORRESPONDENCE

  8.3 APPLICATIONS TO COLLISIONS OF HEAVY IONS

  8.4 APPLICATIONS TO CONDENSED MATTER PHYSICS

  CHAPTER 9 ■ Why Strings? Mathematics

  9.1 PEER RESPECT

  9.2 OF MONSTERS AND MOONSHINE

  9.3 MIRROR SYMMETRY

  9.4 CULTS IN PHYSICS

  CHAPTER 10 ■ Why Strings? Cosmology and Particle Physics

  10.1 EXTRA DIMENSIONS AND MODULI

  10.2 WHAT MAKES MODULI AND WHAT MODULI MAKE

  10.3 AXION-LIKE PARTICLES

  10.4 COSMIC MAGNETISM

  10.5 EXPERIMENTAL ENNUI

  CHAPTER 11 ■ Why Strings? Quantum Gravity 1

  11.1 COUNTING BLACK HOLES

  11.2 SINGULARITIES AND TOPOLOGY CHANGE

  11.3 THE ULTIMATE COLLIDER

  SECTION IV Who?

  CHAPTER 12 ■ A Thousand Flowers Blooming: Styles of Science

  12.1 THE REVOLUTIONARIES

  12.2 VORSPRUNG DURCH TECHNIK

  12.3 STOCKHOLM OR BUST

  12.4 THE MOST SUBLIME BRAHMINATE OF PRINCETON

  12.5 IL FAUT CULTIVER NOTRE JARDIN

  CHAPTER 13 ■ #EpicFail? Criticisms of String Theory

  CHAPTER 14 ■ Why String Theory?

  14.1 REASONS FOR SUCCESS

  14.2 RIVALS AND COMPETITORS

  14.3 PREDICTING THE FUTURE

  Notes and Bibliography

  Preface

  This is a book about string theory. I started writing this book in 2010 with two motivations. The first was a desire to give back to those who have given to me – it is an incredible privilege to be paid to think about science and fundamental physics, and those who pay the piper have a right to hear the tune. The second was an intent to heed advice passed on to me since childhood: learn as much by writing as by reading. Writing is fun, and I wanted to go beyond the technical prose of journal articles.

  This book is written in response to the questions of ‘What is string theory?’ and ‘Why do you work on it then?’, and it aims to answer them. String theory is, however, a large subject. Over its history, there have probably been over twenty thousand research papers on it. No one – and certainly not myself! – knows all of this work in detail. Writing a book requires an ordered account. In arranging material I have had to select topics, and in selecting I have aimed for the combination of intrinsic importance and personal familiarity.

  To state the obvious, this is not a textbook. It does not have equations. It will not teach anyone either to do calculations in string theory or to perform research in the subject. There are many good textbooks that do precisely this, and I give references to some of them in the bibliography. What I hope the book does provide is a mental map of the subject, a tourist’s guide to those who want to come and see the sights before returning to their own pursuits. I also hope that it may allow those who aspire to a career in the area a chance to reconnoitre the lay of the land.

  To these ends, I have aimed to describe the physics as accurately as possible consistent with the constraints. Accuracy is not a single standard. The geography of the British Isles can be accurately described either as two triangles or through a bookshelf full of Ordnance Survey maps. Neither is ‘right’ or ‘wrong’; it depends on the desired level of description. I have aimed my account of string theory somewhere between these two extremes.

  The book is written to be read sequentially, but this is not an absolute requirement. A reader already familiar with the big picture of known physics could skip over the first part with little loss. In the third part, on the different applications of string theory, the chapters can be read in any order. The twelfth chapter, on the different styles of scientist, stands alone by itself.

  One of the joys of physics is that it is a connected subject. Ideas repeat themselves, and on occasion in this book the same idea comes up more than once. When this happens I have sometimes allowed myself to re-explain concepts rather than exp
ect the reader to remember an explanation from a hundred pages earlier. It always takes me multiple attempts to understand any concept, and in seminars I find few things more annoying than the speaker who believes that a single mention of an idea allows them to deny the audience any further reminders or clarifications of the topic.

  When quotations occur within the book, I have gathered the details of the original sources into the end-notes and bibliography. Those who require them can find them, and I wish to avoid the academic custom of battering the reader into submission through a fusillade of references to obscure journals.

  Many people have helped bring this book to fruition. I should first thank those, too numerous to mention, who have helped me professionally in learning the subject over the years. I particularly thank my fellow PhD students in Cambridge from 2003 to 2006, my research collaborators, and especially my doctoral supervisor Fernando Quevedo.

  In the early stages of this book a website http://whystringtheory.com was made during summer 2012, constructed by myself and two undergraduate physicists, Edward Hughes and Charlotte Mason, who are now doing PhD degrees at respectively Queen Mary University of London and the University of California at Santa Barbara. I have borrowed the title of the book from the website.

  Two eyes good, many eyes better: I thank those who have read parts of this book in draft form and whose feedback has helped me both sharpen the text and remove errors of physics, grammar and style: Lucy Broomfield, Frank Close, Theresa Conlon, Marcus du Sautoy, Pedro Ferreira, Sven Krippendorf, Fernando Quevedo, Markus Rummel, Andrei Starinets, David Tong, Peter West, and particularly Thomas Conlon, David Marsh and the anonymous copyeditor. The mistakes that remain are my own.

  I also want to thank both my colleagues in the Oxford physics department and the Warden, Fellows, staff and students of New College, Oxford, for providing a stimulating and inspirational environment during the writing of this book.

  I thank my editor at CRC Press, Francesca McGowan, for all her hard work, unfailing enthusiasm, and her many precise and detailed emails.

  And finally, special and last thanks are reserved to Lucy, Alexander and George, for the joy they bring every day.

  JOSEPH CONLON

  New College, Oxford

  September 2015

  I

  Why?

  CHAPTER 1

  The Long Wait

  The 25th of June 1973 did not appear special. The Watergate scandal was rumbling on towards its denouement. In New York, the twin towers of the World Trade Center had opened two months previously. Nearby on Long Island, around the offices of the Physical Review, it was warm but not hot, with neither rain nor wind spoiling a pleasant summer day. The latest issue of Physical Review Letters, the prestige journal of the American Physical Society, had just gone to the printers. Among the articles in the issue that day were two on particle physics, appearing one next to the other. The articles addressed the same topic and had both arrived in the mail six or so weeks earlier. The first was by David Gross, a young 32-year-old associate professor at Princeton University, together with his first graduate student, 22-year-old Frank Wilczek. The second paper was by David Politzer, not much older at 23, who was then a graduate student at Harvard. The respective titles of the two papers were ‘Ultraviolet Behavior of Non-Abelian Gauge Theories’ and ‘Reliable Perturbative Results for Strong Interactions’. Both papers addressed the same question: how the behaviour of certain physical theories varied when examined at large distances compared to when they were examined at small distances. The papers had been received at the journal’s offices less than a week apart, and after favourable review were now appearing consecutively.

  So far, so ordinary. However, from the perspective of forty-two years on, what is special about that summer’s day in 1973 is that, at the time of writing, it represents the last time work in theoretical particle physics was published that would subsequently go on to be awarded the Nobel Prize for Physics.

  There are four known forces in nature: the gravitational force, the electromagnetic force, the weak force and the strong force. The gravitational force is familiar, as are the effects of electromagnetism. The strong force serves to hold atomic nuclei together, but it is entirely absent in the macroscopic world. It remained mysterious for years how the physics of the strong force could be so important in the nucleus and so irrelevant everywhere else. This physics was even more mysterious during the 1950s and 1960s as a vast zoo of particles all interacting under the strong force were discovered, one after another after another. The behaviour of the strong force appeared bizarrely different to any of the others, and at the time it was thought the strong force might defy understanding for fifty or a hundred years.

  It did not. Despite many opinions to the contrary, the equations underlying the strong force were in fact similar to those underlying the electromagnetic and weak forces, and the apparently inexplicable behaviour of the strong force was, surprisingly, understandable in terms of known theories. The work of Gross, Politzer and Wilczek was the key to showing this, and for this discovery they would, in the fullness of time, be awarded the 2004 physics Nobel Prize.

  Since then, there have been more recent Nobel Prizes in particle theory, such as the one won by Peter Higgs and François Englert in 2013, but these have been for work done even earlier than 1973 – in 1964 for the case of Higgs and Englert. This has been neither for want of papers nor for want of effort. It is a stubborn truth that the theory that had just about been written down in the 1970s as an approximate description of nature – the Standard Model – has turned out to be far better than anyone could conceive or imagine at the time. The Standard Model is the modern description of all known elementary particles and their interactions, and it has survived all experimental attempts to prove it wrong. Tests that in the 1970s were either only qualitative in form, or even only an experimental dream, have morphed into successful high-precision probes of the fine structure of the Standard Model.

  Over this period many proposals have been made for new particles and new phenomena beyond those already in the Standard Model. Indeed, there have even been some experimental claims to have found such particles. However, these claims of discoveries have not held up, and the proposals have failed empirical test. No such new particles have yet been observed. This history is full of many experimental triumphs and first discoveries of new particles – most recently the 2012 discovery of the Higgs boson at CERN’s Large Hadron Collider – but these all involve discoveries of previously unobserved particles of the Standard Model. It is not impossible that some of these proposals will eventually turn out in some form to be correct at energies that are beyond current technology. There is however so far no positive evidence for this, and as new experiments replace old ones, the young bloods who with dreams of Stockholm wrote down ideas for new physics are now admiring the first hesitant steps of their grandchildren.

  The big picture of the last forty years, then, is the consolidation of the Standard Model from a house of straw into an enduring edifice of high-energy physics. Over this long period, this fact has led to two broad directions of thought. The first has been towards bettering our understanding of the Standard Model. This has involved answering in ever greater detail the questions: what are the predictions of the Standard Model? What is the most efficient way to work out these predictions? At first, no one could have realised that this was the path they were headed down. The Standard Model originally appeared a temporary ersatz construction that would be good for a few years until something better came along. Understanding the predictions of the Standard Model and discovering the new physics that went beyond it did not appear to be separate enterprises – they were different sides of the same coin. However, with the passage of time the machinery required to compute the predictions of the Standard Model has grown increasingly elaborate, and the tests that are used to look for new physics require ever greater precision. To say something new about the Standard Model, it is no longer sufficient to be an expert – one
must now be an expert even within the community of experts.

  The other direction has been towards deep exploration in the empty quarter of theory space. The direct empirical motivation for many of these peregrinations is somewhere between marginal and non-existent. There is little or no attempt to use these wanderings either to explain current experimental anomalies or to make predictions for experiments on a near-future timescale. It involves theoretical structures that are inspired by those that are observationally relevant, but the inspiration may be loose. The aim is to understand these theoretical, perhaps quasi-mathematical, structures and to grasp their inner mechanics. Such theories may either never be applicable to nature or may only apply at energy scales reaching far beyond those accessible in current particle colliders. The close connection between advances in theory and advances in experiment is put aside in favour of the deep study of theories for their own sake, with mathematics rather than experiment as the closest companion in the attempt to advance the subject.

  One of the best-known finds from these journeys is the subject of this book, string theory. Over a period of almost fifty years from its origins in 1968, string theory has spread from nothing to become a major component of theoretical particle physics. In terms of money, theoretical physics is not a big subject. It is a flea-bite on experimental particle physics, which is itself a flea-bite compared to medical research, which is in turn a flea-bite on the totality of government spending. Yet intellectually, particle theory has always punched far above its financial weight. Its topic is the basic laws governing our universe, and interest in these laws extends far beyond the confines of those who are salaried to think about them. Theoretical physics has provided – certainly not all, but definitely one part – of the answer to the universal questions of who we are and where we come from.

  It is also simply true that within particle theory, string theory is a big subject. There are few large particle theory groups within major universities that do not have at least one person doing string theory. In total, there are probably a couple of thousand people at universities around the world whose mortgage is paid by either doing string theory, using string theory, working with tools made within string theory, solving problems using methods developed in string theory, or simply having their mental map of the world at the smallest possible scales set by string theory.