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First published in Great Britain in 2005 by Bantam Press
an imprint of Transworld Publishers
this edition published 2008
Copyright © Stephen W. Hawking and Leonard Mlodinow 2005
Stephen Hawking and Leonard Mlodinow have asserted their right under the Copyright, Designs and Patents Act 1988 to be identified as the authors of this work.
Original art copyright 2005 © The Book Laboratory® Inc.
Image of Professor Stephen Hawking – Pages here, here and here © Steward Cohen
Cover Art – The Book Laboratory® Inc. and Moonrunner Design
Acknowledgements – Book Illustrations – The Book Laboratory® Inc., James Zhang and Kees Veenenbos
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Version 1.0 Epub ISBN 9781407066790
ISBN 9780593056974
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2 4 6 8 10 9 7 5 3 1
Cover Page
Title Page
Acknowledgements
Foreword
1. Thinking About the Universe
2. Our Evolving Picture of the Universe
3. The Nature of a Scientific Theory
4. Newton’s Universe
5. Relativity
6. Curved Space
7. The Expanding Universe
8. The Big Bang, Black Holes, and the Evolution of the Universe
9. Quantum Gravity
10. Wormholes and Time Travel
11. The Forces of Nature and the Unification of Physics
12. Conclusion
Albert Einstein
Galileo Galilei
Isaac Newton
Glossary
Index
Copyright Page
ALSO BY STEPHEN HAWKING
A Brief History of Time
Black Holes and Baby Universes and Other Essays
The Illustrated A Brief History of Time
The Universe in a Nutshell
ALSO BY LEONARD MLODINOW
Euclid’s Window
Feynman’s Rainbow
Thanks to our editor, Ann Harris, at Bantam for lending us her considerable experience and talent in our efforts to hone the manuscript. To Glen Edelstein, Bantam’s art director, for his tireless efforts and his patience. To our art team, Philip Dunn, James Zhang, and Kees Veenenbos, for taking the time to learn some physics, and then, while not sacrificing the scientific content, making the book look fabulous. To our agents, Al Zuckerman and Susan Ginsburg at Writer’s House, for their intelligence, caring, and support. To Monica Guy for proofreading. And to those who kindly read various drafts of the manuscript in our search for passages where clarity could be improved further: Donna Scott, Alexei Mlodinow, Nicolai Mlodinow, Mark Hillery, Joshua Webman, Stephen Youra, Robert Barkovitz, Martha Lowther, Katherine Ball, Amanda Bergen, Jeffrey Boehmer, Kimberly Comer, Peter Cook, Matthew Dickinson, Drew Donovanik, David Fralinger, Eleanor Grewal, Alicia Kingston, Victor Lamond, Michael Melton, Mychael Mulhern, Matthew Richards, Michelle Rose, Sarah Schmitt, Curtis Simmons, Christine Webb, and Christopher Wright.
THE TITLE OF THIS BOOK DIFFERS by only two letters from that of a book first published in 1988. A Brief History of Time was on the London Sunday Times best-seller list for 237 weeks and has sold about one copy for every 750 men, women, and children on earth. It was a remarkable success for a book that addressed some of the most difficult issues in modern physics. Yet those difficult issues are also the most exciting, for they address big, basic questions: What do we really know about the universe? How do we know it? Where did the universe come from, and where is it going? Those questions were the essence of A Brief History of Time, and they are also the focus of this book.
In the years since A Brief History of Time was published, feedback has come in from readers of all ages, of all professions, and from all over the world. One repeated request has been for a new version, one that maintains the essence of A Brief History yet explains the most important concepts in a clearer, more leisurely manner. Although one might expect that such a book would be entitled A Less Brief History of Time, it was also clear from the feedback that few readers are seeking a lengthy dissertation befitting a college-level course in cosmology.
Thus, the present approach. In writing A Briefer History of Time we have maintained and expanded the essential content of the original book, yet taken care to maintain its length and readability. This is a briefer history indeed, for some of the more technical content has been left out, but we feel we have more than compensated for that by the more probing treatment of the material that is really the heart of the book.
We have also taken the opportunity to update the book and include new theoretical and observational results. A Briefer History of Time describes recent progress that has been made in finding a complete unified theory of all the forces of physics. In particular, it describes the progress made in string theory, and the “dualities” or correspondences between apparently different theories of physics that are an indication that there is a unified theory of physics. On the observational side, the book includes important new observations such as those made by the Cosmic Background Explorer satellite (COBE) and by the Hubble Space Telescope.
Some forty years ago Richard Feynman said, “We are lucky to live in an age in which we are still making discoveries. It is like the discovery of America—you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature.” Today, we are closer than ever before to understanding the nature of the universe. Our goal in writing this book is to share some of the excitement of these discoveries, and the new picture of reality that is emerging as a result.
WE LIVE IN A STRANGE AND wonderful universe. Its age, size, violence, and beauty require extraordinary imagination to appreciate. The place we humans hold within this vast cosmos can seem pretty insignificant. And so we try to make sense of it all and to see how we fit in. Some decades ago, a well-known scientist (some say it was Bertrand Russell) gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant turtle.” The scientist gave a superior smile before replying, “What is the turtle standing on?” “You’re very clever, young man, very clever,” said the old lady. “But it’s turtles all the way down!”
Most people nowadays would find the picture of our universe as an infinite tower of turtles rather ridiculous. But why should we think we know better? Forget for a minute what you know—or think you know—about space. Then gaze upwards at the night sky. What would you make of all those points of light? Are they tiny fires? It can be hard to imagine what they really are, for what they really are is far beyond our ordinary experience. If you are a regular stargazer, you have probably seen an elusive light hovering near the horizon at twilight. It is a planet, Mercury, but it is nothing like our own planet. A day on Mercury lasts for two-thirds of the planet’s year. Its surface reaches temperatures of over 400 degrees Celsius when the sun is out, then falls to almost -200 degrees Celsius in the dead of night. Yet as different as Mercury is from our own planet, it is not nearly as hard to imagine as a typical star, which is a huge furnace that burns billions of pounds of matter each second and reaches temperatures of tens of millions of degrees at its core.
Another thing that is hard to imagine is how far away the planets and stars really are. The ancient Chinese built stone towers so they could have a closer look at the stars. It’s natural to think the stars and planets are much closer than they really are—after all, in everyday life we have no experience of the huge distances of space. Those distances are so large that it doesn’t even make sense to measure them in feet or miles, the way we measure most lengths. Instead we use the light-year, which is the distance light travels in a year. In one second, a beam of light will travel 186,000 miles, so a light-year is a very long distance. The nearest star, other than our sun, is called Proxima Centauri (also known as Alpha Centauri C), which is about four light-years away. That is so far that even with the fastest spaceship on the drawing boards today, a trip to it would take about ten thousand years.
Ancient people tried hard to understand the universe, but they hadn’t yet developed our mathematics and science. Today we have powerful tools: mental tools such as mathematics and the scientific method, and technological tools like computers and telescopes. With the help of these tools, scientists have pieced together a lot of knowledge about space. But what do we really know about the universe, and how do we know it? Where did the universe come from? Where is it going? Did the universe have a beginning, and if so, what happened before then? What is the nature of time? Will it ever come to an end? Can we go backwards in time? Recent breakthroughs in physics, made possible in part by new technology, suggest answers to some of these long-standing questions. Someday these answers may seem as obvious to us as the earth orbiting the sun—or perhaps as ridiculous as a tower of turtles. Only time (whatever that may be) will tell.
ALTHOUGH AS LATE AS THE TIME of Christopher Columbus it was common to find people who thought the earth was flat (and you can even find a few such people today), we can trace the roots of modern astronomy back to the ancient Greeks. Around 340 B.C., the
Greek philosopher Aristotle wrote a book called On the Heavens. In that book, Aristotle made good arguments for believing that the earth was a sphere rather than flat like a plate.
One argument was based on eclipses of the moon. Aristotle realized that these eclipses were caused by the earth coming between the sun and the moon. When that happened, the earth would cast its shadow on the moon, causing the eclipse. Aristotle noticed that the earth’s shadow was always round. This is what you would expect if the earth was a sphere, but not if it was a flat disk. If the earth were a flat disk, its shadow would be round only if the eclipse happened at a time when the sun was directly under the centre of the disk. At other times the shadow would be elongated—in the shape of an ellipse (an ellipse is an elongated circle).
The Greeks had another argument for the earth being round. If the earth were flat, you would expect a ship approaching from the horizon to appear first as a tiny, featureless dot. Then, as it sailed closer, you would gradually be able to make out more detail, such as its sails and hull. But that is not what happens. When a ship appears on the horizon, the first things you see are the ship’s sails. Only later do you see its hull. The fact that a ship’s masts, rising high above the hull, are the first part of the ship to poke up over the horizon is evidence that the earth is a ball.
The Greeks also paid a lot of attention to the night sky. By Aristotle’s time, people had for centuries been recording how the lights in the night sky moved. They noticed that although almost all of the thousands of lights they saw seemed to move together across the sky, five of them (not counting the moon) did not. They would sometimes wander off from a regular east–west path and then double back. These lights were named planets—the Greek word for “wanderer”. The Greeks observed only five planets because five are all we can see with the naked eye: Mercury, Venus, Mars, Jupiter, and Saturn. Today we know why the planets take such unusual paths across the sky: though the stars hardly move at all in comparison to our solar system, the planets orbit the sun, so their motion in the night sky is much more complicated than the motion of the distant stars.
Coming over the Horizon
Because the earth is a sphere, the mast and sails of a ship coming over the horizon
show themselves before its hull.
Aristotle thought that the earth was stationary and that the sun, the moon, the planets, and the stars moved in circular orbits about the earth. He believed this because he felt, for mystical reasons, that the earth was the centre of the universe and that circular motion was the most perfect. In the second century A.D. another Greek, Ptolemy, turned this idea into a complete model of the heavens. Ptolemy was passionate about his studies. “When I follow at my pleasure the serried multitude of the stars in their circular course,” he wrote, “my feet no longer touch the earth.”
In Ptolemy’s model, eight rotating spheres surrounded the earth. Each sphere was successively larger than the one before it, something like a Russian nesting doll. The earth was at the centre of the spheres. What lay beyond the last sphere was never made very clear, but it certainly was not part of mankind’s observable universe. Thus the outermost sphere was a kind of boundary, or container, for the universe. The stars occupied fixed positions on that sphere, so when it rotated, the stars stayed in the same positions relative to each other and rotated together, as a group, across the sky, just as we observe. The inner spheres carried the planets. These were not fixed to their respective spheres as the stars were, but moved upon their spheres in small circles called epicycles. As the planetary spheres rotated and the planets themselves moved upon their spheres, the paths they took relative to the earth were complex ones. In this way, Ptolemy was able to account for the fact that the observed paths of the planets were much more complicated than simple circles across the sky.
Ptolemy’s model provided a fairly accurate system for predicting the positions of heavenly bodies in the sky. But in order to predict these positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the earth as at other times. And that meant that the moon ought sometimes to appear twice as big as at other times! Ptolemy recognized this flaw, but nevertheless his model was generally, although not universally, accepted. It was adopted by the Christian church as the picture of the universe that was in accordance with scripture, for it had the great advantage that it left lots of room outside the sphere of fixed stars for heaven and hell.
Ptolemy’s Model
In Ptolemy’s model, the earth stood at the centre of the universe, surrounded by eight
spheres carrying all the known heavenly bodies.
Another model, however, was proposed in 1514 by a Polish priest, Nicolaus Copernicus. (At first, perhaps for fear of being branded a heretic by his church, Copernicus circulated his model anonymously.) Copernicus had the revolutionary idea that not all heavenly bodies must orbit the earth. In fact, his idea was that the sun was stationary at the centre of the solar system and that the earth and planets moved in circular orbits around the sun. Like Ptolemy’s model, Copernicus’s model worked well, but it did not perfectly match observation. Since it was much simpler than Ptolemy’s model, though, one might have expected people to embrace it. Yet nearly a century passed before this idea was taken seriously. Then two astronomers—the German Johannes Kepler and the Italian Galileo Galilei—started publicly to support the Copernican theory.
In 1609, Galileo started observing the night sky with a telescope, which had just been invented. When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites or moons that orbited around it. This implied that everything did not have to orbit directly around the earth, as Aristotle and Ptolemy had thought. At the same time, Kepler improved Copernicus’s theory, suggesting that the planets moved not in circles but in ellipses. With this change the predictions of the theory suddenly matched the observations. These events were the death blows to Ptolemy’s model.
Though elliptical orbits improved Copernicus’s model, as far as Kepler was concerned they were merely a makeshift hypothesis. That is because Kepler had preconceived ideas about nature that were not based on any observation: like Aristotle, he simply believed that ellipses were less perfect than circles. The idea that planets would move along such imperfect paths struck him as too ugly to be the final truth. Another thing that bothered Kepler was that he could not make elliptical orbits consistent with his idea that the planets were made to orbit the sun by magnetic forces. Although he was wrong about magnetic forces being the reason for the planets’ orbits, we have to give him credit for realizing that there must be a force responsible for the motion. The true explanation for why the planets orbit the sun was provided only much later, in 1687, when Sir Isaac Newton published his Philosophiae Naturalis Principia Mathematica, probably the most important single work ever published in the physical sciences.
In Principia, Newton presented a law stating that all objects at rest naturally stay at rest unless a force acts upon them, and described how the effects of force cause an object to move or change an object’s motion. So why do the planets move in ellipses around the sun? Newton said that a particular force was responsible, and claimed that it was the same force that made objects fall to the earth rather than remain at rest when you let go of them. He named that force gravity (before Newton the word gravity meant only either a serious mood or a quality of heaviness). He also invented the mathematics that showed numerically how objects react when a force such as gravity pulls on them, and he solved the resulting equations. In this way he was able to show that due to the gravity of the sun, the earth and other planets should move in an ellipse—just as Kepler had predicted! Newton claimed that his laws applied to everything in the universe, from a falling apple to the stars and planets. It was the first time in history anybody had explained the motion of the planets in terms of laws that also determine motion on earth, and it was the beginning of both modern physics and modern astronomy.
Without the concept of Ptolemy’s spheres, there was no longer any reason to assume the universe had a natural boundary, the outermost sphere. Moreover, since stars did not appear to change their positions apart from a rotation across the sky caused by the earth spinning on its axis, it became natural to suppose that the stars were objects like our sun but very much farther away. We had given up not only the idea that the earth is the centre of the universe but even the idea that our sun, and perhaps our solar system, were unique features of the cosmos. This change in worldview represented a profound transition in human thought: the beginning of our modern scientific understanding of the universe.
IN ORDER TO TALK ABOUT THE nature of the universe and to discuss such questions as whether it has a beginning or an end, you have to be clear about what a scientific theory is. We shall take the simpleminded view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. It exists only in our minds and does not have any other reality (whatever that might mean). A theory is a good theory if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations. For example, Aristotle believed Empedocles’ theory that everything was made out of four elements: earth, air, fire, and water. This was simple enough but did not make any definite predictions. On the other hand, Newton’s theory of gravity was based on an even simpler model, in which bodies attracted each other with a force that was proportional to a quantity called their mass and inversely proportional to the square of the distance between them. Yet it predicts the motions of the sun, the moon, and the planets to a high degree of accuracy.
Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time a result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions, the theory survives and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.
At least that is what is supposed to happen, but you can always question the competence of the person who carried out the observation.
In practice, what often happens is that a new theory is devised that is really an extension of the previous theory. For example, very accurate observations of the planet Mercury revealed a small difference between its motion and the predictions of Newton’s theory of gravity. Einstein’s general theory of relativity predicted a slightly different motion than Newton’s theory did. The fact that Einstein’s predictions matched what was seen, while Newton’s did not, was one of the crucial confirmations of the new theory. However, we still use Newton’s theory for most practical purposes because the difference between its predictions and those of general relativity is very small in the situations that we normally deal with. (Newton’s theory also has the great advantage that it is much simpler to work with than Einstein’s!)
The eventual goal of science is to provide a single theory that describes the whole universe. However, the approach most scientists actually follow is to separate the problem into two parts. First, there are the laws that tell us how the universe changes with time. (If we know what the universe is like at any one time, these physical laws tell us how it will look at any later time.) Second, there is the question of the initial state of the universe. Some people feel that science should be concerned with only the first part; they regard the question of the initial situation as a matter for metaphysics or religion. They would say that God, being omnipotent, could have started the universe off any way He wanted. That may be so, but in that case God also could have made it develop in a completely arbitrary way. Yet it appears that God chose to make it evolve in a very regular way, according to certain laws. It therefore seems equally reasonable to suppose that there are also laws governing the initial state.
It turns out to be very difficult to devise a theory to describe the universe all in one go. Instead, we break the problem up into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities, or representing them by simple sets of numbers. It may be that this approach is completely wrong. If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the problem in isolation. Nevertheless, it is certainly the way that we have made progress in the past. The classic example is again the Newtonian theory of gravity, which tells us that the gravitational force between two bodies depends only on one number associated with each body, its mass, and is otherwise independent of what the bodies are made of. Thus we do not need to have a theory of the structure and constitution of the sun and the planets in order to calculate their orbits.
Today scientists describe the universe in terms of two basic partial theories—the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of the twentieth century. The general theory of relativity describes the force of gravity and the large-scale structure of the universe; that is, the structure on scales from only a few miles to as large as a million million million million (1 with twenty-four zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other—they cannot both be correct. One of the major endeavours in physics today, and the major theme of this book, is the search for a new theory that will incorporate them both—a quantum theory of gravity. We do not yet have such a theory, and we may still be a long way from having one, but we do already know many of the properties that it must have. And we shall see in later chapters that we already know a fair amount about the predictions a quantum theory of gravity must make.
Atoms to Galaxies
In the first half of the twentieth century, physicists extended the reach of their theories
from the everyday world of Isaac Newton to both the smallest and the largest
extremes of our universe.
Now, if you believe that the universe is not arbitrary but is governed by definite laws, you ultimately have to combine the partial theories into a complete unified theory that will describe everything in the universe. But there is a fundamental paradox in the search for such a complete unified theory. The ideas about scientific theories outlined above assume we are rational beings who are free to observe the universe as we want and to draw logical deductions from what we see. In such a scheme it is reasonable to suppose that we might progress ever closer towards the laws that govern our universe. Yet if there really were a complete unified theory, it would also presumably determine our actions—so the theory itself would determine the outcome of our search for it! And why should it determine that we come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong conclusion? Or no conclusion at all?