Three Roads to Quantum Gravity Read online

  Table of Contents

  science masters

  Title Page

  Dedication

  Acknowledgements

  PROLOGUE

  I - POINTS OF DEPARTURE

  CHAPTER 1 - THERE IS NOTHING OUTSIDE THE UNIVERSE

  CHAPTER 2 - IN THE FUTURE WE SHALL KNOW MORE

  CHAPTER 3 - MANY OBSERVERS, NOT MANY WORLDS

  CHAPTER 4 - THE UNIVERSE IS MADE OF PROCESSES, NOT THINGS

  II - WHAT WE HAVE LEARNED

  CHAPTER 5 - BLACK HOLES AND HIDDEN REGIONS

  CHAPTER 6 - ACCELERATION AND HEAT

  CHAPTER 7 - BLACK HOLES ARE HOT

  CHAPTER 8 - AREA AND INFORMATION

  CHAPTER 9 - HOW TO COUNT SPACE

  CHAPTER 10 - KNOTS, LINKS AND KINKS

  CHAPTER 11 - THE SOUND OF SPACE IS A STRING

  III - THE PRESENT FRONTIERS

  CHAPTER 12 - THE HOLOGRAPHIC PRINCIPLE

  CHAPTER 13 - HOW TO WEAVE A STRING

  CHAPTER 14 - WHAT CHOOSES THE LAWS OF NATURE?

  EPILOGUE:

  POSTSCRIPT

  GLOSSARY

  SUGGESTIONS FOR FURTHER READING

  INDEX

  ABOUT THE AUTHOR

  Copyright Page

  science masters

  Other books by Lee Smolin include

  The Life of the Cosmos

  To my parents

  Pauline and Michael

  ACKNOWLEDGMENTS

  I must thank first of all the friends and collaborators who formed the community within which I learned most of what I know about quantum gravity. If I had not had the luck to know Julian Barbour, Louis Crane, John Dell, Ted Jacobson and Carlo Rovelli, I doubt that I would have got very far with this subject at all. They will certainly see their ideas and views represented here. Fotini Markopoulou-Kalamara is responsible for changing my views on several important aspects of quantum gravity over the last several years, which got me out of space and back into spacetime. Large parts of Chapters 2, 3 and 4 are suffused by her thinking, as will be clear to anyone who has read her papers. I am also indebted to Chris Isham for the several ideas of his that have seeped into my work, in some cases without my fully realizing it, and for his friendship and for the example of his life and thought. Stuart Kauffman has taught me most of what I know about how to think about self-organized systems, and I thank him for both the gift of his friendship and his willingness to walk with me in the space between our two subjects.

  I am also very indebted for discussions, collaborations and encouragement to Giovanni Amelino-Camelia, Abhay Ashtekar, Per Bak, Herbert Bernstein, Roumen Borissov, Alain Connes, Michael Douglas, Laurant Friedel, Rodolfo Gambini, Murray Gell-Mann, Sameer Gupta, Eli Hawkins, Gary Horowitz, Viqar Husain, Jaron Lanier, Richard Livine, Yi Ling, Renate Loll, Seth Major, Juan Maldecena, Maya Paczuski, Roger Penrose, Jorge Pullin, Martin Rees, Mike Reisenberger, Jurgen Renn, Kelle Stelle, Andrew Strominger, Thomas Thiemann and Edward Witten. I add a special word of appreciation for the founders of the field of quantum gravity, including Peter Bergmann, Bryce DeWitt, David Finkelstein, Charles Misner, Roger Penrose and John Archibald Wheeler. If they see many of their ideas here, it is because these are the ideas that continue to shape how we see our problem. Our work has been supported generously by the National Science Foundation, for which I especially have to thank Richard Issacson. In the last several years generous and unexpected gifts from the Jesse Phillips Foundation have made it possible to concentrate on doing science at a time when nothing was more important than the time and freedom to think and work. I am grateful also to Pennsylvania State University, and especially to my chair, Jayanth Banavar, for the supportive and stimulating home it has given me over the last six years, as well as for showing some understanding of the conflicting demands placed upon me when I found myself with three full-time jobs, as a scientist, teacher and author. The theory group at Imperial College provided a most stimulating and friendly home from home during the year’s sabbatical during which this book was written.

  This book would not exist were it not for the kind encouragement of John Brockman and Katinka Matson, and I am also very grateful to Peter Tallack of Weidenfeld & Nicolson, both for his encouragement and ideas and for being such a good editor, in the old-fashioned sense. Much of the clarity of the text is also due to the artistry and intelligence of John Woodruff’s copy editing. Brian Eno and Michael Smolin read a draft and made invaluable suggestions for the organization of the book, which have greatly improved it. The support of friends has continued to be essential to keeping my own spirit alive, especially Saint Clair Cemin, Jaron Lanier and Donna Moylan. Finally, as always, my greatest debt is to my parents and family, not only for the gift of life but for imparting in me the desire to look beyond what is taught in school, to try to see the world as it may actually be.

  Lee Smolin

  London, July 2000

  PROLOGUE

  THE QUEST FOR QUANTUM GRAVITY

  This book is about the simplest of all questions to ask: ‘What are time and space?’ This is also one of the hardest questions to answer, yet the progress of science can be measured by revolutions that produce new answers to it. We are now in the midst of such a revolution, and not one but several new ideas about space and time are being considered. This book is meant to be a report from the front. My aim is to communicate these new ideas in a language that will enable any interested reader to follow these very exciting developments.

  Space and time are hard to think about because they are the backdrop to all human experience. Everything that exists exists somewhere, and nothing happens that does not happen at some time. So, just as one can live without questioning the assumptions in one’s native culture, it is possible to live without asking about the nature of space and time. But there is at least a moment in every child’s life when they wonder about time. Does it go on for ever? Was there a first moment? Will there be a last moment? If there was a first moment, then how was the universe created? And what happened just a moment before that? If there was no first moment, does that mean that everything has happened before? And the same for space: does it go on and on for ever? If there is an end to space, what is just on the other side of it? If there isn’t an end, can one count the things in the universe?

  I’m sure people have been asking these questions for as long as there have been people to ask them. I would be surprised if the people who painted the walls of their caves tens of thousands of years ago did not ask them of one another as they sat around their fires after their evening meals.

  For the past hundred years or so we have known that matter is made up of atoms, and that these in turn are composed of electrons, protons and neutrons. This teaches us an important lesson - that human perception, amazing as it sometimes is, is too coarse to allow us to see the building blocks of nature directly. We need new tools to see the smallest things. Microscopes let us see the cells that we and other living things are made of, but to see atoms we must look on scales at least a thousand times smaller. We can now do this with electron microscopes. Using other tools, such as particle accelerators, we can see the nucleus of an atom, and we have even seen the quarks that make up the protons and neutrons.

  All this is wonderful, but it raises still more questions. Are the electrons and the quarks the smallest possible things? Or are they themselves made up of still smaller entities? As we continue to probe, will we always find smaller things, or is there a smallest possible entity? We may wonder in the same way not only about matter but also about space: space seems continuous, but is it really? Can a volume of space be divided into as many parts as we like, or is there a smallest unit of space? Is there a smallest distance? Similarly, we want to kno
w whether time is infinitely divisible or whether there might be a smallest possible unit of time. Is there a simplest thing that can happen?

  Until about a hundred years ago there was an accepted set of answers to these questions. They made up the foundations of Newton’s theory of physics. At the beginning of the twentieth century people understood that this edifice, useful as it had been for so many developments in science and engineering, was completely wrong when it came to giving answers to these fundamental questions about space and time. With the overthrow of Newtonian physics came new answers to these questions. They came from new theories: principally from Albert Einstein’s theory of relativity, and from the quantum theory, invented by Neils Bohr, Werner Heisenberg, Erwin Schrödinger, and many others. But this was only the starting point of the revolution, because neither of these two theories is complete enough to serve as a new foundation for physics. While very useful, and able to explain many things, each is incomplete and limited.

  Quantum theory was invented to explain why atoms are stable, and do not instantly fall apart, as was the case for all attempts to describe the structure of atoms using Newton’s physics. Quantum theory also accounts for many of the observed properties of matter and radiation. Its effects differ from those predicted by Newton’s theory primarily, although not exclusively, on the scale of molecules and smaller. In contrast, general relativity is a theory of space, time and cosmology. Its predictions differ strongly from Newton’s mainly on very large scales, so many of the observations that confirm general relativity come from astronomy. However, general relativity seems to break down when it is confronted by the behaviour of atoms and molecules. Equally, quantum theory seems incompatible with the description of space and time that underlies Einstein’s general relativity theory. Thus, one cannot simply bring the two together to construct a single theory that would hold from the atoms up to the solar system and beyond to the whole universe.

  It is not difficult to explain why it is hard to bring relativity and quantum theory together. A physical theory must be more than just a catalogue of what particles and forces exist in the world. Before we even begin to describe what we see when we look around us, we must make some assumptions about what it is that we are doing when we do science. We all dream, yet most of us have no problem distinguishing our dreams from our experiences when awake. We all tell stories, but most of us believe there is a difference between fact and fiction. As a consequence, we talk about dreams, fiction and our ordinary experience in different ways which are based on different assumptions about the relation of each to reality. These assumptions can differ slightly from person to person and from culture to culture, and they are also subject to revision by artists of all kinds. If they are not spelled out the result can be confusion and disorientation, either accidental or intended.

  Similarly, physical theories differ in the basic assumptions they make about observation and reality. If we are not careful to spell them out, confusion can and will occur when we try to compare descriptions of the world that come out of different theories.

  In this book we shall be concerned with two very basic ways in which theories may differ. The first is in the answer they give to the question of what space and time are. Newton’s theory was based on one answer to this question, general relativity on quite another. We shall see shortly what these were, but the important fact is that Einstein altered forever our understanding of space and time.

  Another way in which theories may differ is in how observers are believed to be related to the system they observe. There must be some relationship, otherwise the observers would not even be aware of the existence of the system. But different theories can and do differ strongly in the assumptions they make about the relationship between observer and observed. In particular, quantum theory makes radically different assumptions from those made by Newton about this question.

  The problem is that while quantum theory changed radically the assumptions about the relationship between the observer and the observed, it accepted without alteration Newton’s old answer to the question of what space and time are. Just the opposite happened with Einstein’s general relativity theory, in which the concept of space and time was radically changed, while Newton’s view of the relationship between observer and observed was retained. Each theory seems to be at least partly true, yet each retains assumptions from the old physics that the other contradicts.

  Relativity and quantum theory were therefore just the first steps in a revolution that now, a century later, remains unfinished. To complete the revolution, we must find a single theory that brings together the insights gained from relativity and quantum theory. This new theory must somehow merge the new conception of space and time Einstein introduced with the new conception of the relationship between the observer and the observed which the quantum theory teaches us. If that does not prove possible, it must reject both and find new answers to the questions of what space and time are and what the relationship between observer and observed is.

  The new theory is not yet complete, but it already has a name: it is called the quantum theory of gravity. This is because a key part of it involves extending the quantum theory, which is the basis of our understanding of atoms and the elementary particles, to a theory of gravity. Gravity is presently understood in the context of general relativity, which teaches us that gravity is actually a manifestation of the structure of space and time. This was Einstein’s most surprising and most beautiful insight, and we shall have a great deal to say about it as we go along. The problem we now face is (in the jargon of fundamental physics) to unify Einstein’s theory of general relativity with the quantum theory. The product of this unification will be a quantum theory of gravity.

  When we have it, the quantum theory of gravity will provide new answers to the questions of what space and time are. But that is not all. The quantum theory of gravity will also have to be a theory of matter. It will have to contain all the insights gained over the last century into the elementary particles and the forces that govern them. It must also be a theory of cosmology. It will, when we have it, answer what now seem very mysterious questions about the origin of the universe, such as whether the big bang was the first moment of time or only a transition from a different world that existed previously. It may even help us to answer the question of whether the universe was fated to contain life, or whether our own existence is merely the consequence of a lucky accident.

  As we enter the twenty-first century, there is no more challenging problem in science than the completion of this theory. You may wonder, as many have, whether it is too hard - whether it will remain always unsolved, in the class of impossible problems like certain mathematical problems or the nature of consciousness. It would not be surprising if, once you see the scope of the problem, you were to take this view. Many good physicists have. Twenty-five years ago, when I began to work on the quantum theory of gravity in college, several of my teachers told me that only fools worked on this problem. At that time very few people worked seriously on quantum gravity. I don’t know if they ever all got together for a dinner party, but they might have.

  My advisor in graduate school, Sidney Coleman, tried to talk me into doing something else. When I persisted he told me he would give me a year to get started and that if, as he expected, I made no progress, he would assign me a more doable project in elementary particle physics. Then he did me a great favour: he asked one of the pioneers of the subject, Stanley Deser, to look after me and share my supervision. Deser had recently been one of the inventors of a new theory of gravity called supergravity, which for a few years seemed to solve many of the problems that had resisted all earlier attempts to solve them. I was also lucky during my first year at graduate school to hear lectures by someone else who had made an important contribution to the search for quantum gravity: Gerard ’t Hooft. If I have not always followed either of their directions, I learned a crucial lesson from the example of their work - that it is possible to make progress on a seemingly imp
ossible problem if one just ignores the sceptics and gets on with it. After all, atoms do fall, so the relationship between gravity and the quantum is not a problem for nature. If it is a problem for us it must be because somewhere in our thinking there is at least one, and possibly several, wrong assumptions. At the very least, these assumptions involve our concept of space and time and the connection between the observer and the observed.

  It was obvious to me then that before we could find the quantum theory of gravity we first had to isolate these wrong assumptions. This made it possible to push ahead for there is an obvious strategy for rooting out false assumptions: try to construct the theory, and see where it fails. Since all the avenues that had been followed up to that time had, sooner or later, led to a dead end, there was ample work to do. It may not have inspired many people, but it was necessary work and, for a time, it was enough.

  The situation now is very different. We are still not quite there, but few who work in the field doubt that we have come a long way towards our goal. The reason is that, beginning in the mid-1980s, we began to find ways of combining quantum theory and relativity that did not fail, as all previous attempts had. As a result, it is possible to say that in the last few years large parts of the puzzle have been solved.

  One consequence of our having made progress is that all of a sudden our pursuit has become fashionable. The small number of pioneers who were working on the subject a few decades ago have now grown into a large community of hundreds of people who work full time on some aspect of the problem of quantum gravity. There are, indeed, so many of us that, like the jealous primates we are, we have splintered into different communities pursuing different approaches. These go under different names, such as strings, loops, twistors, non-commutative geometry and topi. This over-specialization has had unfortunate effects. In each community there are people who are sure that their approach is the only key to the problem. Sadly, most of them do not understand in any detail the main results that excite the people working on the other approaches. There are even cases in which someone taking one approach does not seem to realize that a problem they find hard has been completely solved by someone taking another approach. One consequence of this is that many people who work on some aspect of quantum gravity do not have a view of the field that is wide enough to take in all the progress that has recently been made towards its solution.