Three Roads To Quantum Gravity

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THE SOUND OF SPACE IS A STRING 155 time space The electron and the photon are now part of a string FIGURE 35 In string theory there is only one kind of thing that moves, and that is a string ± a loop drawn in space. Different modes of vibration of the string behave like the different kinds of elementary particle. space time FIGURE 36 All the different kinds of interaction between particles are interpreted in string theory in terms of the splitting and joining of strings. to in®nite expressions. This is because there are loops in the diagrams where particles are created, interact, and are then destroyed. These are called virtual particles because they exist only for a very short time. According to the uncertainty principle, because virtual particles live for a very short time
156 THREE ROADS TO QUANTUM GRAVITY they can have any energy, as the conservation of energy is suspended during their brief lives. This creates big problems. One has to add up all the diagrams to get the overall probability for the process to occur, but if some particles can have any energy between zero and in®nity, then the list of possible processes one has to add up will be in®nite. This leads to mathematical expressions that are no more than complicated ways of writing the number in®nity. As a result, Feynman's method seems at ®rst to give nonsensical answers to questions about the interactions of electrons and photons. Quite ingeniously, Feynman and others discovered that the theory was giving silly answers to only a few questions, such as `What is the mass of the electron?' and `What is its charge?' The theory predicts that these are in®nite! Feynman ®gured out that if one simply crosses out these in®nite answers wherever they appear, and substitutes the right, ®nite answer, the answers to all other questions become sensible. All the in®nite expressions can be removed if one forces the theory to give the right answer for the mass and the charge of the electron. This procedure is called renormalization. When it works for a theory, that theory is called renormalizable. The procedure works very well for quantum electrodynamics. It also works for quantum chromodynamics, and for the Weinberg±Salam theory, which is our theory of radioactive decay. When this procedure does not work, we say that a theory is not renormalizable ± the method fails to give a sensible theory. This is actually the case for most theories; only certain special ones can be made sense of by these methods. The most important theory that cannot be made sense of in this way is Einstein's theory of gravity. The reason has to do with the fact that arbitrarily large energies can appear in the particles moving inside the diagrams. But the strength of the gravitational force is proportional to the energy, because energy is mass, from Einstein, and gravity pulls on mass, from Newton. So the diagrams with larger energies give correspondingly larger effects. But according to the theory, the energies inside the diagrams can be arbitrarily large. The result is a kind of runaway feedback process in which we lose all control over what is happening inside the diagrams. No
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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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Page 115 and 116: CHAPTER 9 .........................
Page 155 and 156: CHAPTER 11 ........................
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Page 180 and 181: THE HOLOGRAPHIC PRINCIPLE 171 gener
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Page 184 and 185: THE HOLOGRAPHIC PRINCIPLE 175 the g
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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 194 and 195: HOW TO WEAVE A STRING 185 What is r
Page 196 and 197: HOW TO WEAVE A STRING 187 for a pic
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WHAT CHOOSES THE LAWS OF NATURE? 20
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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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