Table of Contents
Title Page
Copyright Page
Dedication
PART ONE - TIME, EXPERIENCE, AND THE UNIVERSE
Chapter 1 - THE PAST IS PRESENT MEMORY
Chapter 2 - THE HEAVY HAND OF ENTROPY
Chapter 3 - THE BEGINNING AND END OF TIME
PART TWO - TIME IN EINSTEIN’S UNIVERSE
Chapter 4 - TIME IS PERSONAL
Chapter 5 - TIME IS FLEXIBLE
Chapter 6 - LOOPING THROUGH TIME
PART THREE - ENTROPY AND TIME’S ARROW
Chapter 7 - RUNNING TIME BACKWARD
Chapter 8 - ENTROPY AND DISORDER
Chapter 9 - INFORMATION AND LIFE
Chapter 10 - RECURRENT NIGHTMARES
Chapter 11 - QUANTUM TIME
PART FOUR - FROM THE KITCHEN TO THE MULTIVERSE
Chapter 12 - BLACK HOLES: THE ENDS OF TIME
Chapter 13 - THE LIFE OF THE UNIVERSE
Chapter 14 - INFLATION AND THE MULTIVERSE
Chapter 15 - THE PAST THROUGH TOMORROW
Chapter 16 - EPILOGUE
APPENDIX: MATH
NOTES
BIBLIOGRAPHY
Acknowledgements
INDEX
DUTTON
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Copyright © 2010 by Sean Carroll
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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.
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Carroll, Sean M., 1966-
From eternity to here : the quest for the ultimate theory of time / Sean Carroll.
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1. Space and time. I. Title.
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To Jennifer
For all time
PROLOGUE
Does anybody really know what time it is?
—Chicago, “Does Anybody Really Know What Time It Is?”
This book is about the nature of time, the beginning of the universe, and the underlying structure of physical reality. We’re not thinking small here. The questions we’re tackling are ancient and honorable ones: Where did time and space come from? Is the universe we see all there is, or are there other “universes” beyond what we can observe? How is the future different from the past?
According to researchers at the Oxford English Dictionary, time is the most used noun in the English language. We live through time, keep track of it obsessively, and race against it every day—yet, surprisingly, few people would be able to give a simple explanation of what time actually is.
In the age of the Internet, we might turn to Wikipedia for guidance. As of this writing, the entry on “Time” begins as follows:
Time is a component of a measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects. Time has been a major subject of religion, philosophy, and science, but defining time in a non-controversial manner applicable to all fields of study has consistently eluded the greatest scholars.1
Oh, it’s on. By the end of this book, we will have defined time very precisely, in ways applicable to all fields. Less clear, unfortunately, will be why time has the properties that it does—although we’ll examine some intriguing ideas.
Cosmology, the study of the whole universe, has made extraordinary strides over the past hundred years. Fourteen billion years ago, our universe (or at least the part of it we can observe) was in an unimaginably hot, dense state that we call “the Big Bang.” Ever since, it has been expanding and cooling, and it looks like that’s going to continue for the foreseeable future, and possibly forever.
A century ago, we didn’t know any of that—scientists understood basically nothing about the structure of the universe beyond the Milky Way galaxy. Now we have taken the measure of the observable universe and are able to describe in detail its size and shape, as well as its constituents and the outline of its history. But there are important questions we cannot answer, especially concerning the early moments of the Big Bang. As we will see, those questions play a crucial role in our understanding of time—not just in the far-flung reaches of the cosmos, but in our laboratories on Earth and even in our everyday lives.
TIME SINCE THE BIG BANG
It’s clear that the universe evolves as time passes—the early universe was hot and dense; the current universe is cold and dilute. But I am going to be drawing a much deeper connection. The most mysterious thing about time is that it has a direction: the past is different from the future. That’s the arrow of time—unlike directions in space, al
l of which are created pretty much equal, the universe indisputably has a preferred orientation in time. A major theme of this book is that the arrow of time exists because the universe evolves in a certain way.
The reason why time has a direction is because the universe is full of irreversible processes—things that happen in one direction of time, but never the other. You can turn an egg into an omelet, as the classic example goes, but you can’t turn an omelet into an egg. Milk disperses into coffee; fuels undergo combustion and turn into exhaust; people are born, grow older, and die. Everywhere in Nature we find sequences of events where one kind of event always happens before, and another kind after; together, these define the arrow of time.
Remarkably, a single concept underlies our understanding of irreversible processes: something called entropy, which measures the “disorderliness” of an object or conglomeration of objects. Entropy has a stubborn tendency to increase, or at least stay constant, as time passes—that’s the famous Second Law of Thermodynamics. 2 And the reason why entropy wants to increase is deceptively simple: There are more ways to be disorderly than to be orderly, so (all else being equal) an orderly arrangement will naturally tend toward increasing disorder. It’s not that hard to scramble the egg molecules into the form of an omelet, but delicately putting them back into the arrangement of an egg is beyond our capabilities.
The traditional story that physicists tell themselves usually stops there. But there is one absolutely crucial ingredient that hasn’t received enough attention: If everything in the universe evolves toward increasing disorder, it must have started out in an exquisitely ordered arrangement. This whole chain of logic, purporting to explain why you can’t turn an omelet into an egg, apparently rests on a deep assumption about the very beginning of the universe: It was in a state of very low entropy, very high order.
The arrow of time connects the early universe to something we experience literally every moment of our lives. It’s not just breaking eggs, or other irreversible processes like mixing milk into coffee or how an untended room tends to get messier over time. The arrow of time is the reason why time seems to flow around us, or why (if you prefer) we seem to move through time. It’s why we remember the past, but not the future. It’s why we evolve and metabolize and eventually die. It’s why we believe in cause and effect, and is crucial to our notions of free will.
And it’s all because of the Big Bang.
WHAT WE SEE ISN’T ALL THERE IS
The mystery of the arrow of time comes down to this: Why were conditions in the early universe set up in a very particular way, in a configuration of low entropy that enabled all of the interesting and irreversible processes to come? That’s the question this book sets out to address. Unfortunately, no one yet knows the right answer. But we’ve reached a point in the development of modern science where we have the tools to tackle the question in a serious way.
Scientists and prescientific thinkers have always tried to understand time. In ancient Greece, the pre-Socratic philosophers Heraclitus and Parmenides staked out different positions on the nature of time: Heraclitus stressed the primacy of change, while Parmenides denied the reality of change altogether. The nineteenth century was the heroic era of statistical mechanics—deriving the behavior of macroscopic objects from their microscopic constituents—in which figures like Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs worked out the meaning of entropy and its role in irreversible processes. But they didn’t know about Einstein’s general relativity, or about quantum mechanics, and certainly not about modern cosmology. For the first time in the history of science, we at least have a chance of putting together a sensible theory of time and the evolution of the universe.
I’m going to suggest the following way out: The Big Bang was not the beginning of the universe. Cosmologists sometimes say that the Big Bang represents a true boundary to space and time, before which nothing existed—indeed, time itself did not exist, so the concept of “before” isn’t strictly applicable. But we don’t know enough about the ultimate laws of physics to make a statement like that with confidence. Increasingly, scientists are taking seriously the possibility that the Big Bang is not really a beginning—it’s just a phase through which the universe goes, or at least our part of the universe. If that’s true, the question of our low-entropy beginnings takes on a different cast: not “Why did the universe start out with such a low entropy?” but rather “Why did our part of the universe pass through a period of such low entropy?”
That might not sound like an easier question, but it’s a different one, and it opens up a new set of possible answers. Perhaps the universe we see is only part of a much larger multiverse, which doesn’t start in a low-entropy configuration at all. I’ll argue that the most sensible model for the multiverse is one in which entropy increases because entropy can always increase—there is no state of maximum entropy. As a bonus, the multiverse can be completely symmetric in time: From some moment in the middle where entropy is high, it evolves in the past and future to states where the entropy is even higher. The universe we see is a tiny sliver of an enormously larger ensemble, and our particular journey from a dense Big Bang to an everlasting emptiness is all part of the wider multiverse’s quest to increase its entropy.
That’s one possibility, anyway. I’m putting it out there as an example of the kind of scenarios cosmologists need to be contemplating, if they want to take seriously the problems raised by the arrow of time. But whether or not this particular idea is on the right track, the problems themselves are fascinating and real. Through most of this book, we’ll be examining the problems of time from a variety of angles—time travel, information, quantum mechanics, the nature of eternity. When we aren’t sure of the final answer, it behooves us to ask the question in as many ways as possible.
THERE WILL ALWAYS BE SKEPTICS
Not everyone agrees that cosmology should play a prominent role in our understanding of the arrow of time. I once gave a colloquium on the subject to a large audience at a major physics department. One of the older professors in the department didn’t find my talk very convincing and made sure that everyone in the room knew of his unhappiness. The next day he sent an e-mail around to the department faculty, which he was considerate enough to copy to me:
Finally, the magnitude of the entropy of the universe as a function of time is a very interesting problem for cosmology, but to suggest that a law of physics depends on it is sheer nonsense. Carroll’s statement that the second law owes its existence to cosmology is one of the dum mest [sic] remarks I heard in any of our physics colloquia, apart from [redacted]’s earlier remarks about consciousness in quantum mechanics. I am astounded that physicists in the audience always listen politely to such nonsense. Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.
I hope he reads this book. Many dramatic-sounding statements are contained herein, but I’m going to be as careful as possible to distinguish among three different types: (1) remarkable features of modern physics that sound astonishing but are nevertheless universally accepted as true; (2) sweeping claims that are not necessarily accepted by many working physicists but that should be, as there is no question they are correct; and (3) speculative ideas beyond the comfort zone of contemporary scientific state of the art. We certainly won’t shy away from speculation, but it will always be clearly labeled. When all is said and done, you’ll be equipped to judge for yourself which parts of the story make sense.
The subject of time involves a large number of ideas, from the everyday to the mind-blowing. We’ll be looking at thermodynamics, quantum mechanics, special and general relativity, information theory, cosmology, particle physics, and quantum gravity. Part One of the book can be thought of as a lightning tour of the terrain—entropy and the arrow of time, the evolution of the universe, and different conceptions of the idea of “time” itself. Then we will get a bit more systematic; in Part Two we will think deeply
about spacetime and relativity, including the possibility of travel backward in time. In Part Three we will think deeply about entropy, exploring its role in multiple contexts, from the evolution of life to the mysteries of quantum mechanics.
In Part Four we will put it all together to confront head-on the mysteries that entropy presents to the modern cosmologist: What should the universe look like, and how does that compare to what it actually does look like? I’ll argue that the universe doesn’t look anything like it “should,” after being careful about what that is supposed to mean—at least, not if the universe we see is all there is. If our universe began at the Big Bang, it is burdened with a finely tuned boundary condition for which we have no good explanation. But if the observed universe is part of a bigger ensemble—the multiverse—then we might be able to explain why a tiny part of that ensemble witnesses such a dramatic change in entropy from one end of time to the other.
All of which is unapologetically speculative but worth taking seriously. The stakes are big—time, space, the universe—and the mistakes we are likely to make along the way will doubtless be pretty big as well. It’s sometimes helpful to let our imaginations roam, even if our ultimate goal is to come back down to Earth and explain what’s going on in the kitchen.
PART ONE
TIME, EXPERIENCE, AND THE UNIVERSE
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.
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 1