A Briefer History of Time.

by Stephen Hawking.

Acknowledgments.

Thanks to our editor, Ann Harris, at Bantam for lending us her considerable experience and talent in our efforts to hone the ma.n.u.script. 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 proof-reading. And to those who kindly read various drafts of the ma.n.u.script in our search for pa.s.sages 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 d.i.c.kinson, Drew Donovanik, David Fralinger, Eleanor Grewal, Alicia Kingston, Victor Lamond, Michael Melton, Mychael Mulhern, Matthew Richards, Mich.e.l.le Rose, Sarah Schmitt, Curtis Simmons, Christine Webb, and Christopher Wright.

Foreword.

THE t.i.tLE OF THIS BOOK DIFFERS by only two letters from that of a book first published in 1988. A Brief History of Time Brief History of Time was on the London was on the London Sunday Times 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 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, Brief History of Time, and they are also the focus of this book. and they are also the focus of this book.

In the years since A Brief History of Time 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 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 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 ent.i.tled yet explains the most important concepts in a clearer, more leisurely manner. Although one might expect that such a book would be ent.i.tled A Less Brief History of A Less Brief History of Time, 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 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 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 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 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 s.p.a.ce Telescope. 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 s.p.a.ce 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-y ou 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.

1.

THINKING ABOUT THE UNIVERSE.

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 center 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 s.p.a.ce. Then gaze upward 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 s.p.a.ce. 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 s.p.a.ceship 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 s.p.a.ce. 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 backward 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.

2.

OUR EVOLVING PICTURE OF THE UNIVERSE.

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 center 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...o...b..t 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 center 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 pa.s.sionate about his studies. "When I follow at my pleasure the serried mult.i.tude 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 center 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 a.s.sumption 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 h.e.l.l.

Ptolemy's Model.

In Ptolemy's model, the earth stood at the center 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 center 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 pa.s.sed 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...o...b..t the sun was provided only much later, in 1687, when Sir Isaac Newton published his Philosophiae Naturalis Principia Mathematica, Philosophiae Naturalis Principia Mathematica, probably the most important single work ever published in the physical sciences. probably the most important single work ever published in the physical sciences.

In Principia, 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 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 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. 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 a.s.sume 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 center 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.

3.

THE NATURE OF A SCIENTIFIC THEORY.

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 quant.i.ties 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 cla.s.s 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's 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 quant.i.ty called their ma.s.s 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 G.o.d, being omnipotent, could have started the universe off any way He wanted. That may be so, but in that case G.o.d also could have made it develop in a completely arbitrary way. Yet it appears that G.o.d 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 cla.s.s of observations, neglecting the effects of other quant.i.ties, 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 cla.s.sic example is again the Newtonian theory of gravity, which tells us that the gravitational force between two bodies depends only on one number a.s.sociated with each body, its ma.s.s, and is otherwise independent of what the bodies are made of. Thus we do not need to have a theory of the structure and const.i.tution 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 endeavors 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 a.s.sume 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 toward 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?

The only answer that we can give to this problem is based on Darwin's principle of natural selection. The idea is that in any population of self-reproducing organisms, there will be variations in the genetic material and upbringing that different individuals have. These differences will mean that some individuals are better able than others to draw the right conclusions about the world around them and to act accordingly. These individuals will be more likely to survive and reproduce, so their pattern of behavior and thought will come to dominate. It has certainly been true in the past that what we call intelligence and scientific discovery have conveyed a survival advantage. It is not so clear that this is still the case: our scientific discoveries may well destroy us all, and even if they don't, a complete unified theory may not make much difference to our chances of survival. However, provided the universe has evolved in a regular way, we might expect that the reasoning abilities that natural selection has given us would also be valid in our search for a complete unified theory and so would not lead us to the wrong conclusions.

Because the partial theories that we already have are sufficient to make accurate predictions in all but the most extreme situations, the search for the ultimate theory of the universe seems difficult to justify on practical grounds. (It is worth noting, though, that similar arguments could have been used against both relativity and quantum mechanics, and these theories have given us both nuclear energy and the microelectronics revolution.) The discovery of a complete unified theory, therefore, may not aid the survival of our species. It may not even affect our lifestyle. But ever since the dawn of civilization, people have not been content to see events as unconnected and inexplicable. We have craved an understanding of the underlying order in the world. Today we still yearn to know why we are here and where we came from. Humanity's deepest desire for knowledge is justification enough for our continuing quest. And our goal is nothing less than a complete description of the universe we live in.

4.

NEWTON'S UNIVERSE OUR PRESENT IDEAS ABOUT THE MOTION of bodies date back to Galileo and Newton. Before them, people believed Aristotle, who said that the natural state of a body was to be at rest, and that it moved only if driven by a force or impulse. It followed that a heavier body should fall faster than a light one because it would have a greater pull toward the earth. The Aristotelian tradition also held that one could work out all the laws that govern the universe by pure thought: it was not necessary to check by observation. So no one until Galileo bothered to see whether bodies of different weights did in fact fall at different speeds. It is said that Galileo demonstrated that Aristotle's belief was false by dropping weights from the Leaning Tower of Pisa in Italy. This story is almost certainly untrue, but Galileo did do something equivalent: he rolled b.a.l.l.s of different weights down a smooth slope. The situation is similar to that of heavy bodies falling vertically, but it is easier to observe because the speeds are smaller. Galileo's measurements indicated that each body increased its speed at the same rate, no matter what its weight. For example, if you let go of a ball on a slope that drops by one meter for every ten meters you go along, the ball will be traveling down the slope at a speed of about one meter per second after one second, two meters per second after two seconds, and so on, however heavy the ball. Of course a lead weight would fall faster than a feather, but that is only because a feather is slowed down by air resistance. If you drop two bodies that don't have much air resistance, such as two different lead weights, they fall at the same rate. (We will see why shortly.) On the moon, where there is no air to slow things down, the astronaut David R. Scott performed the feather-and-lead-weight experiment and found that indeed they did hit the ground at the same time.

Galileo's measurements were used bv Newton as the basis of his laws of motion. In Galileo's experiments, as a body rolled down the slope it was always acted on by the same force (its weight), and the effect was to make it constantly speed up. This showed that the real effect of a force is always to change the speed of a body, rather than just to set it moving, as was previously thought. It also meant that whenever a body is not acted on by any force, it will keep on moving in a straight line at the same speed. This idea was first stated explicitly in 1687, in Newton's Principia Mathematica, Principia Mathematica, and is known as Newton's first law. What happens to a body when a force does act on it is given by Newton's second law. This states that the body will accelerate, or change its speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is twice as great.) The acceleration is also smaller the greater the ma.s.s (or quant.i.ty of matter) of the body. (The same force acting on a body of twice the ma.s.s will produce half the acceleration.) A familiar example is provided by a car: the more powerful the engine, the greater the acceleration, but the heavier the car, the smaller the acceleration for the same engine. and is known as Newton's first law. What happens to a body when a force does act on it is given by Newton's second law. This states that the body will accelerate, or change its speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is twice as great.) The acceleration is also smaller the greater the ma.s.s (or quant.i.ty of matter) of the body. (The same force acting on a body of twice the ma.s.s will produce half the acceleration.) A familiar example is provided by a car: the more powerful the engine, the greater the acceleration, but the heavier the car, the smaller the acceleration for the same engine.

In addition to his laws of motion, which describe how bodies react to forces, Newton's theory of gravity describes how to determine the strength of one particular type of force, gravity. As we have said, that theory states that every body attracts every other body with a force that is proportional to the ma.s.s of each body. Thus, the force between two bodies would be twice as strong if one of the bodies (say, body A) had its ma.s.s doubled. This is what you might expect, because one could think of the new body A as being made of two bodies, each with the original ma.s.s. Each of these would attract body B with the original force. Thus the total force between A and B would be twice the original force. And if, say, one of the bodies had six times the ma.s.s, or one had twice the ma.s.s and the other had three times the ma.s.s, then the force between them would be six times as strong.

You can now see why all bodies fall at the same rate. According to Newton's law of gravity, a body of twice the weight will have twice the force of gravity pulling it down. But it will also have twice the ma.s.s and thus, according to Newton's second law, half the acceleration per unit force. According to Newton's laws, these two effects exactly cancel each other out, so the acceleration will be the same no matter what the weight.

Gravitational Attraction of Composite Bodies.

If the ma.s.s of a body is doubled, so is the gravitational force that it exerts Newton's law of gravity also tells us that the farther apart the bodies, the lesser the force. The law says that the gravitational attraction of a star is exactly one-quarter that of a similar star at half the distance. This law predicts the orbits of the earth, the moon, and the planets with great accuracy. If the law were that the gravitational attraction of a star went down faster or slower with distance, the orbits of the planets would not be elliptical; they would either spiral into the sun or escape from the sun.

The big difference between the ideas of Aristode and those of Galileo and Newton is that Aristotle believed in a preferred state of rest, which any body would take up if it was not driven by some force or impulse. In particular, he thought that the earth was at rest. But it follows from Newton's laws that there is no unique standard of rest. One could equally well say that body A was at rest and body B was moving at constant speed with respect to body A, or that body B was at rest and body A was moving. For example, if you set aside for a moment the rotation of the earth and its...o...b..t around the sun, you could say that the earth was at rest and that a train on it was traveling north at ninety miles per hour or that the train was at rest and the earth was moving south at ninety miles per hour. If you carried out experiments with moving bodies on the train, all Newton's laws would still hold. Is Newton right or is Aristotle, and how do you tell?

One test would be this: imagine you are enclosed in a box, and you do not know whether the box is resting on the floor of a moving train or on solid earth, the latter being the standard of rest according to Aristotle. Is there a way to determine which it is? If so, maybe Aristotle was correct-being at rest on the earth is special. But if you carried out experiments in your box on the train, they would turn out exactly the same as they would within your box on the "stationary" train platform (a.s.suming no b.u.mps, turns, or other imperfections in the train ride). Playing Ping-Pong on the train, you would find that the ball behaved just like a ball on a Ping-Pong table by the track. And if you are in your box and play the game at different speeds relative to the earth, say at zero, fifty, and ninety miles per hour, the ball will behave the same in all these situations. This is how the world behaves, and it is what the mathematics of Newton's laws reflects: there is no way to tell whether it is the train or the earth that is moving. The concept of motion makes sense only as it relates to other objects.

Does it really matter whether Aristotle or Newton is correct? Is this merely a difference in outlook or philosophy, or is it an issue important to science? Actually, the lack of an absolute standard of rest has deep implications for physics: it means that we cannot determine whether two events that took place at different times occurred in the same position in s.p.a.ce.

To picture this, suppose someone on a train bounces a Ping-Pong ball straight up and down, hitting the table twice on the same spot one second apart. To that person, the locations of the first and second bounces will have a spatial separation of zero. To someone standing beside the track, the two bounces would seem to take place about forty meters apart, because the train would have traveled that distance down the track between the bounces. According to Newton, the two observers have an equal right to consider themselves at rest, so both views are equally acceptable. One is not favored over another, as Aristotle had believed. The observed positions of events and the distances between them would be different for a person on the train and one beside the track, and there would be no reason to prefer one person's observations to the other's.

Newton was very worried by this lack of absolute position, or absolute s.p.a.ce, as it was called, because it did not accord with his idea of an absolute G.o.d. In fact, he refused to accept the lack of absolute s.p.a.ce, even though his laws implied it. He was severely criticized for this irrational belief by many people, most notably by Bishop Berkeley, a philosopher who believed that all material objects and s.p.a.ce and time are an illusion. When the famous Dr. Johnson was told of Berkeley's opinion, he cried, "I refute it thus!" and stubbed his toe on a large stone.

Relativity of Distance.

The distance-and the path-that an object travels can look different to different observers.

Both Aristotle and Newton believed in absolute time. That is, they believed that one could unambiguously measure the interval of time between two events and that this time would be the same whoever measured it, provided the person used a good clock. Unlike absolute s.p.a.ce, absolute time was consistent with Newton's laws. And it is what most people would take to be the commonsense view. However, in the twentieth century physicists realized that they had to change their ideas about both time and s.p.a.ce. As we will see, they discovered that the length of time between events, like the distance between the points where the Ping-Pong ball bounced, depends on the observer. They also discovered that time was not completely separate from and independent of s.p.a.ce. The key to these realizations was new insight into the properties of light. They may seem counter to our experience, but although our apparently commonsense notions work well when dealing with things such as apples, or planets that travel comparatively slowly, they don't work at all for things moving at or near the speed of light.

5.

RELATIVITY.

THE FACT THAT LIGHT TRAVELS AT a finite but very high speed was first discovered in 1676 by the Danish astronomer Ole Christensen Roemer. If you observe the moons of Jupiter, you will notice that from time to time they disappear from sight because they pa.s.s behind the giant planet. These eclipses of Jupiter's moons ought to occur at regular intervals, but Roemer observed that the eclipses were not evenly s.p.a.ced. Did the moons somehow speed up and slow down in their orbits? He had another explanation. If light traveled with infinite speed, then we on earth would see the eclipses at regular intervals, at exactly the same time that they occurred, like the ticks of a cosmic clock. Since light would traverse any distance instantaneously, this situation would not change if Jupiter moved closer to the earth or further from it.

Now imagine that light travels with finite speed. If so, we will see each eclipse some time after it happened. This delay depends upon the speed of light and and on the distance of Jupiter from the earth. If Jupiter did not change its distance from the earth, the delay would be the same for every eclipse. However, Jupiter sometimes moves closer to the earth. In such cases, the "signal" from each successive eclipse has less and less distance to travel, so it arrives progressively earlier than if Jupiter had remained at a constant distance. For a.n.a.logous reasons, when Jupiter is receding from the earth, we see the eclipses progressively later. The degree of this early and late arrival depends upon the speed of light, and this allows us to measure it. This is what Roemer did. He noticed that eclipses of one of Jupiter's moons appeared earlier at those times of year when the earth was approaching Jupiter's...o...b..t and later at those times when the earth was moving away, and he used this difference to calculate the speed of light. However, his measurements of the variations in the distance of the earth from Jupiter were not very accurate, so his value for the speed of light was 140,000 miles per second, compared to the modern value of 186,000 miles per second. Nevertheless, Roemer's achievement, not only in proving that light travels at a finite speed but also in measuring that speed, was remarkable, coming as it did eleven years before Newton's publication of on the distance of Jupiter from the earth. If Jupiter did not change its distance from the earth, the delay would be the same for every eclipse. However, Jupiter sometimes moves closer to the earth. In such cases, the "signal" from each successive eclipse has less and less distance to travel, so it arrives progressively earlier than if Jupiter had remained at a constant distance. For a.n.a.logous reasons, when Jupiter is receding from the earth, we see the eclipses progressively later. The degree of this early and late arrival depends upon the speed of light, and this allows us to measure it. This is what Roemer did. He noticed that eclipses of one of Jupiter's moons appeared earlier at those times of year when the earth was approaching Jupiter's...o...b..t and later at those times when the earth was moving away, and he used this difference to calculate the speed of light. However, his measurements of the variations in the distance of the earth from Jupiter were not very accurate, so his value for the speed of light was 140,000 miles per second, compared to the modern value of 186,000 miles per second. Nevertheless, Roemer's achievement, not only in proving that light travels at a finite speed but also in measuring that speed, was remarkable, coming as it did eleven years before Newton's publication of Principia Mathematica. Principia Mathematica.

The Speed of Light and the Timing of Eclipses.

The observed times of the eclipses of Jupiter's moons depend on both the actual time of the eclipses and the time it takes their light to travel from Jupiter to the earth Thus the eclipses seem to appear more frequently when Jupiter is moving toward the earth, and less frequently when it is moving away This effect is exaggerated here for clarity A proper theory of the propagation of light didn't come until 1865, when the British physicist James Clerk Maxwell succeeded in unifying the partial theories that up to then had been used to describe the forces of electricity and magnetism. Though both electricity and magnetism had been known since ancient times, it wasn't until the eighteenth century that British chemist Henry Cavendish and French physicist Charles-Augustin de Coulomb established quant.i.tative laws governing the electric force between two charged bodies. A few decades later, in the early nineteenth century, a number of physicists established a.n.a.logous laws for magnetic forces. Maxwell showed mathematically that these electric and magnetic forces do not arise from particles acting directly on each other; rather, every electric charge and current creates a field in the surrounding s.p.a.ce that exerts a force on every other charge and current located within that s.p.a.ce. He found that a single field carries the electric and magnetic forces; thus, electricity and magnetism are inseparable aspects of the same force. He called that force the electromagnetic force, and the field that carries it the electromagnetic field.

Maxwell's equations predicted that there could be wavelike disturbances in the electromagnetic field and that these waves would travel at a fixed speed, like ripples on a pond. When he calculated this speed, he found it to match exactly the speed of light! Today we know that Maxwell's waves are visible to the human eye as light when they have a wavelength of between forty and eighty millionths of a centimeter. (A wave is a succession of crests and troughs; the wavelength is the distance between wave crests or troughs.) Waves with wavelengths shorter than those of visible light are now known as ultraviolet light, X-rays, and gamma rays. Waves with longer wavelengths are called radio waves (a meter or more), microwaves (around a centimeter), or infrared radiation (less than one ten-thousandth of a centimeter but more than the visible range).

Wavelength.

The wavelength of a wave is the distance between successive peaks or troughs.

Maxwell's theory implied that radio or light waves would travel at a certain fixed speed. This was difficult to reconcile with Newton's theory that there is no absolute standard of rest, because if there is no such standard, there can be no universal agreement on the speed of an object. To understand why, again imagine yourself playing Ping-Pong on the train. If you hit the ball toward the front of the train with a speed your opponent measures to be ten miles per hour, then you'd expect an observer on the platform to perceive the ball moving at one hundred miles per hour-the ten it is moving relative to the train, plus the ninety the train is moving relative to the platform. What is the speed of the ball, ten miles per hour or one hundred? How do you define it- relative to the train or relative to the earth? With no absolute standard of rest, you cannot a.s.sign the ball an absolute speed. The same ball could equally well be said to have any speed, depending upon the frame of reference in which the speed is measured. According to Newton's theory, the same should hold for light. So what does it mean in Maxwell's theory for light waves to travel at a certain fixed speed?

Different Speeds of Ping-Pong b.a.l.l.s.

According to the theory of relativity, although they may disagree, every observer's measurement of an object's speed is equally valid In order to reconcile Maxwell's theory with Newton's laws, it was suggested that there was a substance called the ether that was present everywhere, even in the vacuum of "empty" s.p.a.ce. The idea of the ether had a certain added attraction for scientists who felt in any case that, just as water waves require water or sound waves require air, waves of electromagnetic energy must require some medium to carry them. In this view, light waves travel through the ether as sound waves travel through air, and their "speed" as derived from Maxwell's equations should therefore be measured relative to the ether. Different observers would see light coming toward them at different speeds, but light's speed relative to the ether would remain fixed.

This idea could be tested. Imagine light emitted from some source. According to the ether theory, the light travels through the ether at the speed of light. If you move toward it through the ether, the speed at which you approach the light will be the sum of the speed of light through the ether and your speed through the ether. The light will approach you faster than if, say, you didn't move, or you moved in some other direction. Yet because the speed of light is so great compared to the speeds at which we might move toward a light source, this difference in speed was a very difficult effect to measure.