FROM ETERNITY TO HERE The Quest for the Ultimate Theory of Time SEAN CARROLL Prelims.indd 419 1/12/2011 12:41:15 PM A Oneworld Book First published in Great Britain and the Commonwealth by Oneworld Publications 2011 Copyright © Sean Carroll 2010 Published by arrangement with Dutton, a member of the Penguin Group ( USA) , Inc. Th e moral right of Sean Carroll to be identifi ed as the Author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved Copyright under Berne Convention A CIP record for this title is available from the British Library Photograph on page 37 by Martin Röll, licensed under the Creative Commons Attribution ShareAlike 2.0 License, from Wikimedia Commons. Photograph on page 47 courtesy of the Huntington Library. Image on page 53 by the NASA/WMAP Science Team. Photograph on page 67 courtesy of Corbis Images. Image on page 119 courtesy of Getty Images. Figures on pages 147, 153, 177, 213, 270, 379, and 382 by Sean Carroll. Photograph on page 204 courtesy of the Smithsonian Institution. Photograph on page 259 courtesy of Professor Stephen Hawking. Photograph on page 267 courtesy of Professor Jacob Bekenstein. Photograph on page 295 by Jerry Bauer, from Wikimedia Commons. Photograph on page 315 courtesy of the Massachusetts Institute of Technology. All other images courtesy of Jason Torchinsky. ISBN: 978-1-85168-795-4 (Trade Paperback) ISBN: 978-1-85168-842-5 (Travel Edition) Typeset by Jayvee, Trivandrum, India Cover design by Richard Green Printed and bound by Oneworld Publications 185 Banbury Road Oxford, OX2 7AR England Learn more about Oneworld. Join our mailing list to find out about our latest titles and special offers at: www.oneworld-publications.com OW_310_Prelims.indd iv 1/12/2011 12:38:57 PM Prelims.indd 420 1/12/2011 12:41:15 PM CONTENTS Prologue 1 Th e nature of time, the importance of entropy, and the role of cosmology. PART ONE: TIME, EXPERIENCE, AND THE UNIVERSE 1. The Past Is Present Memory 9 Time has diff erent meanings: a label on diff erent moments, the duration between events, and a medium of change. We can think of the past, present, and future as equally real. 2. The Heavy Hand of Entropy 28 Th e direction of time is governed by the Second Law of Th ermodynamics: In a closed system, entropy only increases or stays the same. Entropy measures the disorder of a system. 3. The Beginning and End of Time 49 Th e evolution of the universe through time, beginning with a hot, dense Big Bang (which may not be the true beginning), expanding and forming stars and galaxies, eventually accelerating into emptiness. PART TWO: TIME IN EINSTEIN’S UNIVERSE 4. Time Is Personal 75 Einstein’s Special Th eory of Relativity. You can’t go faster than the speed of light; you stay within a light cone in spacetime. Time measures the duration elapsed along diff erent trajectories. 5. Time Is Flexible 92 Einstein’s General Th eory of Relativity. Spacetime is curved, which we experience as gravity. Th e curvature of spacetime underlies black holes and the expansion of the universe. Prelims.indd 423 1/12/2011 12:41:15 PM v iii Contents 6. Looping Through Time 105 Closed timelike curves would allow you to visit the past without violating the rules of relativity. A time machine of this sort doesn’t necessarily lead to paradoxes, but might be impossible to create according to the laws of physics. PART THREE: ENTROPY AND TIME’S ARROW 7. Running Time Backwards 135 Th e fundamental laws of physics, as we understand them, conserve information: Th e future and past can be predicted and retrodicted from perfect knowledge of the present state. Microscopic processes are reversible. 8. Entropy and Disorder 162 Ludwig Boltzmann discovered our modern understanding of entropy: the number of ways microscopic constituents can be arranged to form the same macroscopic system. It’s natural for entropy to increase, but only if we assume a “Past Hypothesis” that entropy started very low. 9. Information and Life 202 Th e growth of entropy powers our experience of life: the ability to remember the past, to metabolize free energy, and to process information. Maxwell’s Demon illustrates the connection between entropy and information. 10. Recurrent Nightmares 228 A fi nite system spends most of its time in high- entropy equilibrium, with occasional fl uctuations to lower entropy. A fi nite universe that lasts for all time would behave just that way, and most observers would be disembodied “Boltzmann brains.” 11. Quantum Time 257 Quantum mechanics says that what we can observe is much less than what exists. Th e act of observation seems to be irreversible. One interpretation is that the irreversibility is only apparent, as we exist in “branches of the wave function” that lose touch with other branches. PART FOUR: FROM THE KITCHEN TO THE MULTIVERSE 12. Black Holes: The Ends of Time 293 Stephen Hawking showed that black holes aren’t completely black: Th ey emit radiation. Th at implies that they have entropy, and that they will eventually evaporate away. Black holes provide a crucial clue to the connection between entropy and gravity. Prelims.indd 424 1/12/2011 12:41:15 PM Contents ix 13. The Life of the Universe 325 Near the Big Bang, the entropy of the universe was extremely low. It grew as the universe expanded, as gravity pulled matter together to form stars, galaxies, and black holes. But it remains much smaller than it could be; a state of truly high entropy would look like empty space. 14. Infl ation and the Multiverse 358 Th e smooth state of the early universe can be explained by infl ation— a period of high-energy acceleration at very early times. But infl ation itself requires that the universe began in a state of even lower entropy; by itself, it doesn’t answer our questions. It does open a new possibility in the form of eternal infl ation and the multiverse. 15. The Past Through Tomorrow 386 Th ere are a number of possible explanations of our observed arrow of time, including fundamentally irreversible laws and a boundary condition outside the laws of physics. To explain the arrow using only reversible laws requires that we situate the universe we observe within a time- symmetric multiverse. Th is and other speculative scenarios are topics of ongoing research. 16. Epilogue 417 Th e origin of the universe and the arrow of time are major unsolved problems in our understanding of the natural world. But there is every reason to expect that they will someday be understood using the laws of physics. Th e quest to answer these questions helps make it all meaningful. Appendix: Maths 429 Notes 437 Bibliography 467 Acknowledgements 478 Index 480 Prelims.indd 425 1/12/2011 12:41:15 PM 1 THE PAST IS PRESENT MEMORY What is time? If no one asks me, I know. If I wish to explain it to one that asketh, I know not. —St. Augustine, Confessions Th e next time you fi nd yourself in a bar, or on an airplane, or standing in line at the Department of Motor Vehicles, you can pass the time by ask- ing the strangers around you how they would defi ne the word time. Th at’s what I started doing, anyway, as part of my research for this book. You’ll probably hear interesting answers: “Time is what moves us along through life,” “Time is what separates the past from the future,” “Time is part of the universe,” and more along those lines. My favorite was “Time is how we know when things happen.” All of these concepts capture some part of the truth. We might struggle to put the meaning of “time” into words, but like St. Augustine we never- theless manage to deal with time pretty eff ectively in our everyday lives. Most people know how to read a clock, how to estimate the time it will take to drive to work or make a cup of coff ee, and how to manage to meet their friends for dinner at roughly the appointed hour. Even if we can’t eas- ily articulate what exactly it is we mean by “time,” its basic workings make sense at an intuitive level. Like a Supreme Court justice confronted with obscenity, we know time when we see it, and for most purposes that’s good enough. But certain aspects of time remain deeply mysterious. Do we really know what the word means? ch1.indd 9 1/12/2011 11:38:20 AM 10 FROM ETERNITY TO HERE WHAT WE MEAN BY TIME Th e world does not present us with abstract concepts wrapped up with pretty bows, which we then must work to understand and reconcile with other concepts. Rather, the world presents us with phenomena, things that we observe and make note of, from which we must then work to derive concepts that help us understand how those phenomena relate to the rest of our experience. For subtle concepts such as entropy, this is pretty clear. You don’t walk down the street and bump into some entropy; you have to observe a variety of phenomena in nature and discern a pattern that is best thought of in terms of a new concept you label “entropy.” Armed with this helpful new concept, you observe even more phenomena, and you are inspired to refi ne and improve upon your original notion of what entropy really is.