Three Roads To Quantum Gravity

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HOW TO COUNT SPACE 123 string theory might be an important step towards a quantum theory of gravity, it could not be the complete theory. But nevertheless, as it did for many other physicists, string theory changed the direction of my research. I began to look for a way to make a background independent theory which would reduce to string theory as an approximation useful in situations in which spacetime could be regarded as a ®xed background. <strong>To</strong> get inspiration for this project I recalled the seminar given by Polyakov that had so excited me as a beginning graduate student. I wondered whether I could use the method he had used, which was to try to express QCD in terms in which the fundamental objects were loops of colour-electric ¯ux. I needed a theory in which there was no lattice to get in the way, and he had worked without a lattice. I worked for about a year on this idea, with Louis Crane. I was then a postdoc at the University of Chicago, and Louis Crane was a graduate student. He was older than me, but he had actually been a child prodigy, perhaps the last of a distinguished series of scientists and scholars that the University of Chicago admitted to college in their early teens. He had suffered the misfortune of being expelled from graduate school for leading a strike against the invasion of Cambodia, and it had taken him ten years to ®nd his way back to graduate school. Louis has since become one of a handful of mathematicians who has made signi®cant creative contributions to the development of our ideas about quantum gravity. Some of his contributions have been absolutely seminal for developments in the ®eld. I was very fortunate to become his friend at that time, and count myself lucky to be his friend still. Louis and I worked on two projects. In the ®rst we tried to formulate a gravitational theory based on the dynamics of interacting loops of quantized electric ¯ux. We failed to formulate a string theory, and as a result we published none of this work, but it was to have very important consequences. In the second project we showed that a theory in which spacetime was discrete on small scales could solve many of the problems of quantum gravity. We did this by studying the implications of the hypothesis that the structure of spacetime
124 THREE ROADS TO QUANTUM GRAVITY was like a fractal at Planck scales. This overcame many of the dif®culties of quantum gravity, by eliminating the in®nities and making the theory ®nite. We realized during that work that one way of making such a fractal spacetime is to build it up from a network of interacting loops. Both collaborations with Louis Crane persuaded me that we should try to construct a theory of spacetime based on relationships among an evolving network of loops. The problem was, how should we go about this? This was how things stood when a discovery was made that completely changed how we understand Einstein's theory of general relativity.
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I POINTS OF DEPARTURE
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CHAPTER 2 .........................
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II WHAT WE HAVE LEARNED
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Page 180 and 181: THE HOLOGRAPHIC PRINCIPLE 171 gener
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THE HOLOGRAPHIC PRINCIPLE 173 FIGUR
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THE HOLOGRAPHIC PRINCIPLE 175 the g
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CHAPTER 13 ........................
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HOW TO WEAVE A STRING 181 thing!" I
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HOW TO WEAVE A STRING 183 other. Th
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HOW TO WEAVE A STRING 185 What is r
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HOW TO WEAVE A STRING 187 for a pic
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HOW TO WEAVE A STRING 189 in Einste
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HOW TO WEAVE A STRING 191 p in the
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WHAT CHOOSES THE LAWS OF NATURE? 19
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EPILOGUE: .........................
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EPILOGUE: 209 And quantum gravity i
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EPILOGUE: 211 of systems containing
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POSTSCRIPT 213 These cosmic rays ar
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POSTSCRIPT 215 Three explanations h
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POSTSCRIPT 217 light, which is the
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POSTSCRIPT 219 This is good news in
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POSTSCRIPT 221 But there is a secon
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POSTSCRIPT 223 Chopin Soo and Marti
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POSTSCRIPT 225 speed of light with
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GLOSSARY 227 cannot be greater than
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GLOSSARY 229 event In relativity th
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GLOSSARY 231 Newton's gravitational
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GLOSSARY 233 spin The angular momen
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SUGGESTIONS FOR FURTHER READING ...
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SUGGESTIONS FOR FURTHER READING 237
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SUGGESTIONS FOR FURTHER READING 239
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INDEX .............................
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INDEX 243 black hole, 70, 73±4, 17
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INDEX 245 black hole formation, 189
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Three Roads To Quantum Gravity

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