Three Roads To Quantum Gravity

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HOW TO WEAVE A STRING 185 What is remarkable ± indeed, what is almost a miracle ± is that the hardest problem faced by each group was precisely the key problem that the other had solved. Loop quantum gravity tells us how to make a background independent quantum theory of space and time. It offers a lot of scope to the M theorist looking for a way to make string theory background independent. On the other hand, if we believe that strings must emerge from the description of space and time provided by loop quantum gravity, we then have a lot of information about how to formulate the theory so that it does describe classical spacetime. The theory must be formulated in such a way that the gravitons appear not on their own, but as modes of excitations of extended objects that behave as strings. It is then possible to entertain the following hypothesis: string theory and loop quantum gravity are each part of a single theory. This new theory will have the same relationship to the existing ones as Newtonian mechanics has to Galileo's theory of falling bodies and Kepler's theory of planetary orbits. Each is correct, in the sense that it describes to a good approximation what is happening in a certain limited domain. Each solves part of the problem. But each also has limits which prevent it from forming the basis for a complete theory of nature. I believe that this the most likely way in which the theory of quantum gravity will be completed, given the present evidence. In this penultimate chapter I shall describe some of this evidence, and the progress that has recently been made towards inventing a theory that uni®es string theory and loop quantum gravity. As a ®rst step we can ask for a rough picture of how the two theories might ®t together. As it happens, there is a very natural way in which strings and loops can emerge from the same theory. The key to this is a subtlety that I have so far only hinted at. Both loop quantum gravity and string theory describe physics on very small scales, roughly the Planck length. But the scale that sets the size of strings is not exactly equal to the Planck length. That scale is called the string length. The ratio of the Planck length to the string length is a number of great signi®cance in string theory. It is a kind of
186 THREE ROADS TO QUANTUM GRAVITY charge, which tells us how strongly strings will interact with one another. When the string scale is much larger than the Planck length this charge is small and strings do not interact very much with one another. We then can ask which scale is larger. There is evidence that, at least in our universe, the string scale is larger than the Planck scale. This is because their ratio determines the fundamental unit of electric charge, and that is itself a small number. We can then envisage scenarios in which loops are more fundamental. The strings will be descriptions of small waves or disturbances travelling through spin networks. Since the string scale is larger, we can explain the fact that string theory relies on a ®xed background, as the needed background can be supplied by a network of loops. The fact that strings seem to experience the background as a continuous space is explained by them being unable to probe down to a distance where they can distinguish a smooth background from a network of loops (see Figure 38 on page 165). One way to talk about this is that space may be `woven' from a network of loops, as shown in Figure 38, just as a piece of cloth is woven from a network of threads. The analogy is fairly precise. The properties of the cloth are explicable in terms of the kind of weave, which is to say in terms of how the threads are knotted and linked with one another. Similarly, the geometry of the space we may weave from a large spin network is determined only by how the loops link and intersect one another. We may then imagine a string as a large loop which makes a kind of embroidery of the weave. From a microscopic point of view, the string can be described by how it knots the loops in the weave. But on a larger scale we would see only the loop making up the string. If we cannot see the ®ne weave that makes up space, the string will appear against a background of some apparently smooth space. This is how the picture of strings against a background space emerges from loop quantum gravity. If this is right, then string theory will turn out to be an approximation to a more fundamental theory described in terms of spin networks. Of course, just because we can argue
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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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CHAPTER 7 .........................
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CHAPTER 9 .........................
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Page 155 and 156: CHAPTER 11 ........................
Page 178 and 179: CHAPTER 12 ........................
Page 180 and 181: THE HOLOGRAPHIC PRINCIPLE 171 gener
Page 182 and 183: THE HOLOGRAPHIC PRINCIPLE 173 FIGUR
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Page 186 and 187: THE HOLOGRAPHIC PRINCIPLE 177 In th
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Page 190 and 191: HOW TO WEAVE A STRING 181 thing!" I
Page 192 and 193: HOW TO WEAVE A STRING 183 other. Th
Page 196 and 197: HOW TO WEAVE A STRING 187 for a pic
Page 198 and 199: HOW TO WEAVE A STRING 189 in Einste
Page 200 and 201: HOW TO WEAVE A STRING 191 p in the
Page 202 and 203: HOW TO WEAVE A STRING 193 may be th
Page 204 and 205: WHAT CHOOSES THE LAWS OF NATURE? 19
Page 216 and 217: EPILOGUE: .........................
Page 218 and 219: EPILOGUE: 209 And quantum gravity i
Page 220 and 221: EPILOGUE: 211 of systems containing
Page 222 and 223: POSTSCRIPT 213 These cosmic rays ar
Page 224 and 225: POSTSCRIPT 215 Three explanations h
Page 226 and 227: POSTSCRIPT 217 light, which is the
Page 228 and 229: POSTSCRIPT 219 This is good news in
Page 230 and 231: POSTSCRIPT 221 But there is a secon
Page 232 and 233: POSTSCRIPT 223 Chopin Soo and Marti
Page 234 and 235: POSTSCRIPT 225 speed of light with
Page 236 and 237: GLOSSARY 227 cannot be greater than
Page 238 and 239: GLOSSARY 229 event In relativity th
Page 240 and 241: GLOSSARY 231 Newton's gravitational
Page 242 and 243: GLOSSARY 233 spin The angular momen
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SUGGESTIONS FOR FURTHER READING ...
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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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