Three Roads To Quantum Gravity

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BLACK HOLES AND HIDDEN REGIONS 71 Light cone inside horizon time space Light cones just at the horizon Horizon Horizon Singularity FIGURE 13 Light cones in the vicinity of a black hole. The solid black line is the singularity where the gravitational ®eld is in®nitely strong. The dotted lines are the horizons, consisting of light rays that stay the same distance from the singularity. Light cones just at the horizon are tilted to show that a light ray trying to move away from the black hole just stays at the same distance and travels along the horizon. A light cone inside the horizon is tilted so far that any motion into the future brings one closer to the singularity. their past. The existence of black holes means that this is not just a question of waiting long enough for light from a distant region to reach us. We could be right next to a black hole, yet never be able to see what observers inside it can see, however long we waited. All observers have their own hidden region. The hidden region of each observer consists of all those events that they will not be able to receive information from, no matter how long they wait. Each hidden region will include the interiors
72 THREE ROADS TO QUANTUM GRAVITY of all the black holes in the universe, but there may be other regions hidden as well. For example, if the rate at which the universe expands increases with time, there will be regions of the universe from which we shall never receive light signals, no matter how long we wait. A photon from such a region may be travelling in our direction at the speed of light, but because of the increase in the rate of the expansion of the universe it will always have more distance to travel towards us than it has travelled so far. As long as the expansion continues to accelerate, the photon will never reach us. Unlike black holes, the hidden regions produced by the acceleration of the expansion of the universe depend on the history of each observer. For each observer there is a hidden region, but they are different for different observers. This raises an interesting philosophical point, because objectivity is usually assumed to be connected with observer independence. It is commonly assumed that anything that is observer dependent is subjective, meaning that it is not quite real. But the belief that observer dependence rules out objectivity is a residue of an older philosophy, usually associated with the name of Plato, according to which truth resides not in our world but in an imaginary world consisting of all ideas which are eternally true. According to this philosophy, anybody could have access to any truth about the world, because the process of ®nding truth was held to be akin to a process of remembering, rather than observing. This philosophy is hard to square with Einstein's general theory of relativity because, in a universe de®ned by that theory, something may be both objectively true and at the same time knowable only by some observers and not others. So `objectivity' is not the same as `knowable by all'. A weaker, less stringent interpretation is required: that all those observers who are in a position to ascertain the truth or falsity of some observation should agree with one another. The hidden region of any observer has a boundary that divides the part of the universe they can see from the part they cannot. As with a black hole, this boundary is called the horizon. Like the invisible regions, horizons are observer dependent concepts. For any observer who remains outside
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I POINTS OF DEPARTURE
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CHAPTER 11 ........................
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CHAPTER 12 ........................
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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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THE HOLOGRAPHIC PRINCIPLE 177 In th
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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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HOW TO WEAVE A STRING 193 may be th
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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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