Not a member of Pastebin yet?
Sign Up,
it unlocks many cool features!
- Chapter 1 - Our Picture of the Universe
- Chapter 2 - Space and Time
- Chapter 3 - The Expanding Universe
- Chapter 4 - The Uncertainty Principle
- Chapter 5 - Elementary Particles and the Forces of Nature
- Chapter 6 - Black Holes
- Chapter 7 - Black Holes Ain't So Black
- Chapter 8 - The Origin and Fate of the Universe
- Chapter 9 - The Arrow of Time
- Chapter 10 - Wormholes and Time Travel
- Chapter 11 - The Unification of Physics
- Chapter 12 - Conclusion
- Glossary
- Acknowledgments & About The Author
- FOREWARD
- I didn’t write a foreword to the original edition of A Brief History of Time. That was done by Carl Sagan. Instead,
- I wrote a short piece titled “Acknowledgments” in which I was advised to thank everyone. Some of the
- foundations that had given me support weren’t too pleased to have been mentioned, however, because it led to
- a great increase in applications.
- I don’t think anyone, my publishers, my agent, or myself, expected the book to do anything like as well as it did.
- It was in the London Sunday Times best-seller list for 237 weeks, longer than any other book (apparently, the
- Bible and Shakespeare aren’t counted). It has been translated into something like forty languages and has sold
- about one copy for every 750 men, women, and children in the world. As Nathan Myhrvold of Microsoft (a
- former post-doc of mine) remarked: I have sold more books on physics than Madonna has on sex.
- The success of A Brief History indicates that there is widespread interest in the big questions like: Where did
- we come from? And why is the universe the way it is?
- I have taken the opportunity to update the book and include new theoretical and observational results obtained
- since the book was first published (on April Fools’ Day, 1988). I have included a new chapter on wormholes
- and time travel. Einstein’s General Theory of Relativity seems to offer the possibility that we could create and
- maintain wormholes, little tubes that connect different regions of space-time. If so, we might be able to use
- them for rapid travel around the galaxy or travel back in time. Of course, we have not seen anyone from the
- A Brief History of Time - Stephen Hawking
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/A Brief History in Time.html (1 of 2) [2/20/2001 3:13:58 AM]
- future (or have we?) but I discuss a possible explanation for this.
- I also describe the progress that has been made recently in finding “dualities” or correspondences between
- apparently different theories of physics. These correspondences are a strong indication that there is a complete
- unified theory of physics, but they also suggest that it may not be possible to express this theory in a single
- fundamental formulation. Instead, we may have to use different reflections of the underlying theory in different
- situations. It might be like our being unable to represent the surface of the earth on a single map and having to
- use different maps in different regions. This would be a revolution in our view of the unification of the laws of
- science but it would not change the most important point: that the universe is governed by a set of rational laws
- that we can discover and understand.
- On the observational side, by far the most important development has been the measurement of fluctuations in
- the cosmic microwave background radiation by COBE (the Cosmic Background Explorer satellite) and other
- collaborations. These fluctuations are the finger-prints of creation, tiny initial irregularities in the otherwise
- smooth and uniform early universe that later grew into galaxies, stars, and all the structures we see around us.
- Their form agrees with the predictions of the proposal that the universe has no boundaries or edges in the
- imaginary time direction; but further observations will be necessary to distinguish this proposal from other
- possible explanations for the fluctuations in the background. However, within a few years we should know
- whether we can believe that we live in a universe that is completely self-contained and without beginning or
- end.
- Stephen Hawking
- A Brief History of Time - Stephen Hawking
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/A Brief History in Time.html (2 of 2) [2/20/2001 3:13:58 AM]
- CHAPTER 1
- OUR PICTURE OF THE UNIVERSE
- A well-known scientist (some say it was Bertrand Russell) once 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
- tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on.” “You’re very
- clever, young man, very clever,” said the old lady. “But it’s turtles all the way down!”
- Most people would find the picture of our universe as an infinite tower of tortoises rather ridiculous, but why do
- we think we know better? What do we know about the universe, and how do we know it? Where did the
- universe come from, and 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 back in time? Recent breakthroughs
- in physics, made possible in part by fantastic new technologies, suggest answers to some of these
- longstanding questions. Someday these answers may seem as obvious to us as the earth orbiting the sun – or
- perhaps as ridiculous as a tower of tortoises. Only time (whatever that may be) will tell.
- As long ago as 340 BC the Greek philosopher Aristotle, in his book On the Heavens, was able to put forward
- two good arguments for believing that the earth was a round sphere rather than a Hat plate. First, he realized
- that eclipses of the moon were caused by the earth coming between the sun and the moon. The earth’s
- shadow on the moon was always round, which would be true only if the earth was spherical. If the earth had
- been a flat disk, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a
- time when the sun was directly under the center of the disk. Second, the Greeks knew from their travels that
- the North Star appeared lower in the sky when viewed in the south than it did in more northerly regions. (Since
- the North Star lies over the North Pole, it appears to be directly above an observer at the North Pole, but to
- someone looking from the equator, it appears to lie just at the horizon. From the difference in the apparent
- position of the North Star in Egypt and Greece, Aristotle even quoted an estimate that the distance around the
- earth was 400,000 stadia. It is not known exactly what length a stadium was, but it may have been about 200
- yards, which would make Aristotle’s estimate about twice the currently accepted figure. The Greeks even had a
- third argument that the earth must be round, for why else does one first see the sails of a ship coming over the
- horizon, and only later see the hull?
- Aristotle thought 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. This idea was elaborated by Ptolemy in
- the second century AD into a complete cosmological model. The earth stood at the center, surrounded by eight
- spheres that carried the moon, the sun, the stars, and the five planets known at the time, Mercury, Venus,
- Mars, Jupiter, and Saturn.
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (1 of 7) [2/20/2001 3:14:06 AM]
- Figure 1:1
- The planets themselves moved on smaller circles attached to their respective spheres in order to account for
- their rather complicated observed paths in the sky. The outermost sphere carried the so-called fixed stars,
- which always stay in the same positions relative to each other but which rotate together across the sky. What
- lay beyond the last sphere was never made very clear, but it certainly was not part of mankind’s observable
- universe.
- Ptolemy’s model provided a reasonably 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.
- A simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus. (At first, perhaps for
- fear of being branded a heretic by his church, Copernicus circulated his model anonymously.) His idea was that
- the sun was stationary at the center and that the earth and the planets moved in circular orbits around the sun.
- Nearly a century passed before this idea was taken seriously. Then two astronomers – the German, Johannes
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (2 of 7) [2/20/2001 3:14:06 AM]
- Kepler, and the Italian, Galileo Galilei – started publicly to support the Copernican theory, despite the fact that
- the orbits it predicted did not quite match the ones observed. The death blow to the Aristotelian/Ptolemaic
- theory came in 1609. In that year, 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. (It was, of course, still possible to believe that the earth was
- stationary at the center of the universe and that the moons of Jupiter moved on extremely complicated paths
- around the earth, giving the appearance that they orbited Jupiter. However, Copernicus’s theory was much
- simpler.) At the same time, Johannes Kepler had modified Copernicus’s theory, suggesting that the planets
- moved not in circles but in ellipses (an ellipse is an elongated circle). The predictions now finally matched the
- observations.
- As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis, and a rather repugnant one
- at that, because ellipses were clearly less perfect than circles. Having discovered almost by accident that
- elliptical orbits fit the observations well, he could not reconcile them with his idea that the planets were made to
- orbit the sun by magnetic forces. An explanation 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 it Newton not only put forward a theory of how bodies move in space and
- time, but he also developed the complicated mathematics needed to analyze those motions. In addition,
- Newton postulated a law of universal gravitation according to which each body in the universe was attracted
- toward every other body by a force that was stronger the more massive the bodies and the closer they were to
- each other. It was this same force that caused objects to fall to the ground. (The story that Newton was inspired
- by an apple hitting his head is almost certainly apocryphal. All Newton himself ever said was that the idea of
- gravity came to him as he sat “in a contemplative mood” and “was occasioned by the fall of an apple.”) Newton
- went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the
- earth and causes the earth and the planets to follow elliptical paths around the sun.
- The Copernican model got rid of Ptolemy’s celestial spheres, and with them, the idea that the universe had a
- natural boundary. Since “fixed 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 fixed stars were objects like
- our sun but very much farther away.
- Newton realized that, according to his theory of gravity, the stars should attract each other, so it seemed they
- could not remain essentially motionless. Would they not all fall together at some point? In a letter in 1691 to
- Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were
- only a finite number of stars distributed over a finite region of space. But he reasoned that if, on the other hand,
- there were an infinite number of stars, distributed more or less uniformly over infinite space, this would not
- happen, because there would not be any central point for them to fall to.
- This argument is an instance of the pitfalls that you can encounter in talking about infinity. In an infinite
- universe, every point can be regarded as the center, because every point has an infinite number of stars on
- each side of it. The correct approach, it was realized only much later, is to consider the finite situation, in which
- the stars all fall in on each other, and then to ask how things change if one adds more stars roughly uniformly
- distributed outside this region. According to Newton’s law, the extra stars would make no difference at all to the
- original ones on average, so the stars would fall in just as fast. We can add as many stars as we like, but they
- will still always collapse in on themselves. We now know it is impossible to have an infinite static model of the
- universe in which gravity is always attractive.
- It is an interesting reflection on the general climate of thought before the twentieth century that no one had
- suggested that the universe was expanding or contracting. It was generally accepted that either the universe
- had existed forever in an unchanging state, or that it had been created at a finite time in the past more or less
- as we observe it today. In part this may have been due to people’s tendency to believe in eternal truths, as well
- as the comfort they found in the thought that even though they may grow old and die, the universe is eternal
- and unchanging.
- Even those who realized that Newton’s theory of gravity showed that the universe could not be static did not
- think to suggest that it might be expanding. Instead, they attempted to modify the theory by making the
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (3 of 7) [2/20/2001 3:14:06 AM]
- gravitational force repulsive at very large distances. This did not significantly affect their predictions of the
- motions of the planets, but it allowed an infinite distribution of stars to remain in equilibrium – with the attractive
- forces between nearby stars balanced by the repulsive forces from those that were farther away. However, we
- now believe such an equilibrium would be unstable: if the stars in some region got only slightly nearer each
- other, the attractive forces between them would become stronger and dominate over the repulsive forces so
- that the stars would continue to fall toward each other. On the other hand, if the stars got a bit farther away
- from each other, the repulsive forces would dominate and drive them farther apart.
- Another objection to an infinite static universe is normally ascribed to the German philosopher Heinrich Olbers,
- who wrote about this theory in 1823. In fact, various contemporaries of Newton had raised the problem, and the
- Olbers article was not even the first to contain plausible arguments against it. It was, however, the first to be
- widely noted. The difficulty is that in an infinite static universe nearly every line of sight would end on the
- surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night.
- Olbers’ counter-argument was that the light from distant stars would be dimmed by absorption by intervening
- matter. However, if that happened the intervening matter would eventually heat up until it glowed as brightly as
- the stars. The only way of avoiding the conclusion that the whole of the night sky should be as bright as the
- surface of the sun would be to assume that the stars had not been shining forever but had turned on at some
- finite time in the past. In that case the absorbing matter might not have heated up yet or the light from distant
- stars might not yet have reached us. And that brings us to the question of what could have caused the stars to
- have turned on in the first place.
- The beginning of the universe had, of course, been discussed long before this. According to a number of early
- cosmologies and the Jewish/Christian/Muslim tradition, the universe started at a finite, and not very distant,
- time in the past. One argument for such a beginning was the feeling that it was necessary to have “First Cause”
- to explain the existence of the universe. (Within the universe, you always explained one event as being caused
- by some earlier event, but the existence of the universe itself could be explained in this way only if it had some
- beginning.) Another argument was put forward by St. Augustine in his book The City of God. He pointed out
- that civilization is progressing and we remember who performed this deed or developed that technique. Thus
- man, and so also perhaps the universe, could not have been around all that long. St. Augustine accepted a
- date of about 5000 BC for the Creation of the universe according to the book of Genesis. (It is interesting that
- this is not so far from the end of the last Ice Age, about 10,000 BC, which is when archaeologists tell us that
- civilization really began.)
- Aristotle, and most of the other Greek philosophers, on the other hand, did not like the idea of a creation
- because it smacked too much of divine intervention. They believed, therefore, that the human race and the
- world around it had existed, and would exist, forever. The ancients had already considered the argument about
- progress described above, and answered it by saying that there had been periodic floods or other disasters that
- repeatedly set the human race right back to the beginning of civilization.
- The questions of whether the universe had a beginning in time and whether it is limited in space were later
- extensively examined by the philosopher Immanuel Kant in his monumental (and very obscure) work Critique of
- Pure Reason, published in 1781. He called these questions antinomies (that is, contradictions) of pure reason
- because he felt that there were equally compelling arguments for believing the thesis, that the universe had a
- beginning, and the antithesis, that it had existed forever. His argument for the thesis was that if the universe did
- not have a beginning, there would be an infinite period of time before any event, which he considered absurd.
- The argument for the antithesis was that if the universe had a beginning, there would be an infinite period of
- time before it, so why should the universe begin at any one particular time? In fact, his cases for both the thesis
- and the antithesis are really the same argument. They are both based on his unspoken assumption that time
- continues back forever, whether or not the universe had existed forever. As we shall see, the concept of time
- has no meaning before the beginning of the universe. This was first pointed out by St. Augustine. When asked:
- “What did God do before he created the universe?” Augustine didn’t reply: “He was preparing Hell for people
- who asked such questions.” Instead, he said that time was a property of the universe that God created, and
- that time did not exist before the beginning of the universe.
- When most people believed in an essentially static and unchanging universe, the question of whether or not it
- had a beginning was really one of metaphysics or theology. One could account for what was observed equally
- well on the theory that the universe had existed forever or on the theory that it was set in motion at some finite
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (4 of 7) [2/20/2001 3:14:06 AM]
- time in such a manner as to look as though it had existed forever. But in 1929, Edwin Hubble made the
- landmark observation that wherever you look, distant galaxies are moving rapidly away from us. In other words,
- the universe is expanding. This means that at earlier times objects would have been closer together. In fact, it
- seemed that there was a time, about ten or twenty thousand million years ago, when they were all at exactly
- the same place and when, therefore, the density of the universe was infinite. This discovery finally brought the
- question of the beginning of the universe into the realm of science.
- Hubble’s observations suggested that there was a time, called the big bang, when the universe was
- infinitesimally small and infinitely dense. Under such conditions all the laws of science, and therefore all ability
- to predict the future, would break down. If there were events earlier than this time, then they could not affect
- what happens at the present time. Their existence can be ignored because it would have no observational
- consequences. One may say that time had a beginning at the big bang, in the sense that earlier times simply
- would not be defined. It should be emphasized that this beginning in time is very different from those that had
- been considered previously. In an unchanging universe a beginning in time is something that has to be
- imposed by some being outside the universe; there is no physical necessity for a beginning. One can imagine
- that God created the universe at literally any time in the past. On the other hand, if the universe is expanding,
- there may be physical reasons why there had to be a beginning. One could still imagine that God created the
- universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there
- had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An
- expanding universe does not preclude a creator, but it does place limits on when he might have carried out his
- job!
- In order to talk about the nature of the universe and to discuss questions such as whether it has a beginning or
- an end, you have to be clear about what a scientific theory is. I 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’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 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 the 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 from Newton’s theory. 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 all 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
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (5 of 7) [2/20/2001 3:14:06 AM]
- 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 he also could have made it
- develop in a completely arbitrary way. Yet it appears that he 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 again is 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, but is otherwise
- independent of what the bodies are made of. Thus one does 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 this 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 predications a quantum theory of gravity must
- make.
- 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 toward the laws that govern
- our universe. Yet if there really is a complete unified theory, it would also presumably determine our actions.
- And 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 I 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 and 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 be valid also in our search for a complete unified theory, and so would not
- lead us to the wrong conclusions.
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (6 of 7) [2/20/2001 3:14:06 AM]
- 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. They 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.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 1
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/n.html (7 of 7) [2/20/2001 3:14:06 AM]
- CHAPTER 2
- SPACE AND TIME
- 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 heavy 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 weight 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. The story is almost certainly untrue, but Galileo
- did do something equivalent: he rolled balls 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 one drops two bodies that don’t
- have much air resistance, such as two different lead weights, they fall at the same rate. 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 by 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 Newton’s
- Principia Mathematica, published in 1687, 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 mass (or quantity of matter) of the body. (The
- same force acting on a body of twice the mass 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, Newton discovered a law to
- describe the force of gravity, which states that every body attracts every other body with a force that is
- proportional to the mass of each body. Thus the force between two bodies would be twice as strong if one of
- the bodies (say, body A) had its mass doubled. This is what you might expect because one could think of the
- new body A as being made of two bodies with the original mass. Each 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
- twice the mass, and the other had three times the mass, then the force would be six times as strong. One can
- now see why all bodies fall at the same rate: a body of twice the weight will have twice the force of gravity
- pulling it down, but it will also have twice the mass. According to Newton’s second law, these two effects will
- exactly cancel each other, so the acceleration will be the same in all cases.
- Newton’s law of gravity also tells us that the farther apart the bodies, the smaller the force. Newton’s law of
- gravity 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 increased more rapidly with distance, the
- orbits of the planets would not be elliptical, they would either spiral in to the sun or escape from the sun.
- The big difference between the ideas of Aristotle and those of Galileo and Newton is that Aristotle believed in a
- preferred state of rest, which any body would take up if it were 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
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (1 of 12) [2/20/2001 3:14:15 AM]
- 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 one sets aside for a
- moment the rotation of the earth and its orbit round the sun, one 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 one carried out experiments with moving bodies on the train, all Newton’s laws
- would still hold. For instance, playing Ping-Pong on the train, one would find that the ball obeyed Newton’s laws
- just like a ball on a table by the track. So there is no way to tell whether it is the train or the earth that is moving.
- The lack of an absolute standard of rest meant that one could not determine whether two events that took place
- at different times occurred in the same position in space. For example, suppose our Ping-Pong ball on the train
- bounces straight up and down, hitting the table twice on the same spot one second apart. To someone on the
- track, the two bounces would seem to take place about forty meters apart, because the train would have
- traveled that far down the track between the bounces. The nonexistence of absolute rest therefore meant that
- one could not give an event an absolute position in space, as Aristotle had believed. The positions of events
- and the distances between them would be different for a person on the train and one on the track, and there
- would be no reason to prefer one person’s position to the other’s.
- Newton was very worried by this lack of absolute position, or absolute space, as it was called, because it did
- not accord with his idea of an absolute God. In fact, he refused to accept lack of absolute space, even though it
- was implied by his laws. 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 space 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.
- 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 they used a good clock. Time was completely separate from and independent of space. This is what
- most people would take to be the commonsense view. However, we have had to change our ideas about space
- and time. Although our apparently commonsense notions work well when dealing with things like apples, or
- planets that travel comparatively slowly, they don’t work at all for things moving at or near the speed of light.
- The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer
- Ole Christensen Roemer. He observed that the times at which the moons of Jupiter appeared to pass behind
- Jupiter were not evenly spaced, as one would expect if the moons went round Jupiter at a constant rate. As the
- earth and Jupiter orbit around the sun, the distance between them varies. Roemer noticed that eclipses of
- Jupiter’s moons appeared later the farther we were from Jupiter. He argued that this was because the light from
- the moons took longer to reach us when we were farther away. His measurements of the variations in the
- distance of the earth from Jupiter were, however, not very accurate, and 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, in not only 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. 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. Maxwell’s equations predicted that there could be wavelike disturbances in the combined
- electromagnetic field, and that these would travel at a fixed speed, like ripples on a pond. If the wavelength of
- these waves (the distance between one wave crest and the next) is a meter or more, they are what we now call
- radio waves. Shorter wavelengths are known as microwaves (a few centimeters) or infrared (more than a
- ten-thousandth of a centimeter). Visible light has a wavelength of between only forty and eighty millionths of a
- centimeter. Even shorter wavelengths are known as ultraviolet, X rays, and gamma rays.
- Maxwell’s theory predicted that radio or light waves should travel at a certain fixed speed. But Newton’s theory
- had got rid of the idea of absolute rest, so if light was supposed to travel at a fixed speed, one would have to
- say what that fixed speed was to be measured relative to.
- It was therefore suggested that there was a substance called the "ether" that was present everywhere, even in
- "empty" space. Light waves should travel through the ether as sound waves travel through air, and their speed
- should therefore be relative to the ether. Different observers, moving relative to the ether, would see light
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (2 of 12) [2/20/2001 3:14:15 AM]
- coming toward them at different speeds, but light's speed relative to the ether would remain fixed. In particular,
- as the earth was moving through the ether on its orbit round the sun, the speed of light measured in the
- direction of the earth's motion through the ether (when we were moving toward the source of the light) should
- be higher than the speed of light at right angles to that motion (when we are not moving toward the source). In
- 1887Albert Michelson (who later became the first American to receive the Nobel Prize for physics) and Edward
- Morley carried out a very careful experiment at the Case School of Applied Science in Cleveland. They
- compared the speed of light in the direction of the earth's motion with that at right angles to the earth's motion.
- To their great surprise, they found they were exactly the same!
- Between 1887 and 1905 there were several attempts, most notably by the Dutch physicist Hendrik Lorentz, to
- explain the result of the Michelson-Morley experiment in terms of objects contracting and clocks slowing down
- when they moved through the ether. However, in a famous paper in 1905, a hitherto unknown clerk in the
- Swiss patent office, Albert Einstein, pointed out that the whole idea of an ether was unnecessary, providing one
- was willing to abandon the idea of absolute time. A similar point was made a few weeks later by a leading
- French mathematician, Henri Poincare. Einstein’s arguments were closer to physics than those of Poincare,
- who regarded this problem as mathematical. Einstein is usually given the credit for the new theory, but
- Poincare is remembered by having his name attached to an important part of it.
- The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be
- the same for all freely moving observers, no matter what their speed. This was true for Newton’s laws of
- motion, but now the idea was extended to include Maxwell’s theory and the speed of light: all observers should
- measure the same speed of light, no matter how fast they are moving. This simple idea has some remarkable
- consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein’s
- famous equation E=mc2 (where E is energy, m is mass, and c is the speed of light), and the law that nothing
- may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an
- object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This
- effect is only really significant for objects moving at speeds close to the speed of light. For example, at 10
- percent of the speed of light an object’s mass is only 0.5 percent more than normal, while at 90 percent of the
- speed of light it would be more than twice its normal mass. As an object approaches the speed of light, its mass
- rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the
- speed of light, because by then its mass would have become infinite, and by the equivalence of mass and
- energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is
- forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that
- have no intrinsic mass, can move at the speed of light.
- An equally remarkable consequence of relativity is the way it has revolutionized our ideas of space and time. In
- Newton’s theory, if a pulse of light is sent from one place to another, different observers would agree on the
- time that the journey took (since time is absolute), but will not always agree on how far the light traveled (since
- space is not absolute). Since the speed of the light is just the distance it has traveled divided by the time it has
- taken, different observers would measure different speeds for the light. In relativity, on the other hand, all
- observers must agree on how fast light travels. They still, however, do not agree on the distance the light has
- traveled, so they must therefore now also disagree over the time it has taken. (The time taken is the distance
- the light has traveled – which the observers do not agree on – divided by the light’s speed – which they do
- agree on.) In other words, the theory of relativity put an end to the idea of absolute time! It appeared that each
- observer must have his own measure of time, as recorded by a clock carried with him, and that identical clocks
- carried by different observers would not necessarily agree.
- Each observer could use radar to say where and when an event took place by sending out a pulse of light or
- radio waves. Part of the pulse is reflected back at the event and the observer measures the time at which he
- receives the echo. The time of the event is then said to be the time halfway between when the pulse was sent
- and the time when the reflection was received back: the distance of the event is half the time taken for this
- round trip, multiplied by the speed of light. (An event, in this sense, is something that takes place at a single
- point in space, at a specified point in time.) This idea is shown here, which is an example of a space-time
- diagram...
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (3 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:1
- Using this procedure, observers who are moving relative to each other will assign different times and positions
- to the same event. No particular observer’s measurements are any more correct than any other observer’s, but
- all the measurements are related. Any observer can work out precisely what time and position any other
- observer will assign to an event, provided he knows the other observer’s relative velocity.
- Nowadays we use just this method to measure distances precisely, because we can measure time more
- accurately than length. In effect, the meter is defined to be the distance traveled by light in
- 0.000000003335640952 second, as measured by a cesium clock. (The reason for that particular number is that
- it corresponds to the historical definition of the meter – in terms of two marks on a particular platinum bar kept
- in Paris.) Equally, we can use a more convenient, new unit of length called a light-second. This is simply
- defined as the distance that light travels in one second. In the theory of relativity, we now define distance in
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (4 of 12) [2/20/2001 3:14:16 AM]
- terms of time and the speed of light, so it follows automatically that every observer will measure light to have
- the same speed (by definition, 1 meter per 0.000000003335640952 second). There is no need to introduce the
- idea of an ether, whose presence anyway cannot be detected, as the Michelson-Morley experiment showed.
- The theory of relativity does, however, force us to change fundamentally our ideas of space and time. We must
- accept that time is not completely separate from and independent of space, but is combined with it to form an
- object called space-time.
- It is a matter of common experience that one can describe the position of a point in space by three numbers, or
- coordinates. For instance, one can say that a point in a room is seven feet from one wall, three feet from
- another, and five feet above the floor. Or one could specify that a point was at a certain latitude and longitude
- and a certain height above sea level. One is free to use any three suitable coordinates, although they have only
- a limited range of validity. One would not specify the position of the moon in terms of miles north and miles
- west of Piccadilly Circus and feet above sea level. Instead, one might describe it in terms of distance from the
- sun, distance from the plane of the orbits of the planets, and the angle between the line joining the moon to the
- sun and the line joining the sun to a nearby star such as Alpha Centauri. Even these coordinates would not be
- of much use in describing the position of the sun in our galaxy or the position of our galaxy in the local group of
- galaxies. In fact, one may describe the whole universe in terms of a collection of overlapping patches. In each
- patch, one can use a different set of three coordinates to specify the position of a point.
- An event is something that happens at a particular point in space and at a particular time. So one can specify it
- by four numbers or coordinates. Again, the choice of coordinates is arbitrary; one can use any three
- well-defined spatial coordinates and any measure of time. In relativity, there is no real distinction between the
- space and time coordinates, just as there is no real difference between any two space coordinates. One could
- choose a new set of coordinates in which, say, the first space coordinate was a combination of the old first and
- second space coordinates. For instance, instead of measuring the position of a point on the earth in miles north
- of Piccadilly and miles west of Piccadilly, one could use miles northeast of Piccadilly, and miles north-west of
- Piccadilly. Similarly, in relativity, one could use a new time coordinate that was the old time (in seconds) plus
- the distance (in light-seconds) north of Piccadilly.
- It is often helpful to think of the four coordinates of an event as specifying its position in a four-dimensional
- space called space-time. It is impossible to imagine a four-dimensional space. I personally find it hard enough
- to visualize three-dimensional space! However, it is easy to draw diagrams of two-dimensional spaces, such as
- the surface of the earth. (The surface of the earth is two-dimensional because the position of a point can be
- specified by two coordinates, latitude and longitude.) I shall generally use diagrams in which time increases
- upward and one of the spatial dimensions is shown horizontally. The other two spatial dimensions are ignored
- or, sometimes, one of them is indicated by perspective. (These are called space-time diagrams, like Figure
- 2:1.)
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (5 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:2
- For example, in Figure 2:2 time is measured upward in years and the distance along the line from the sun to
- Alpha Centauri is measured horizontally in miles. The paths of the sun and of Alpha Centauri through
- space-time are shown as the vertical lines on the left and right of the diagram. A ray of light from the sun
- follows the diagonal line, and takes four years to get from the sun to Alpha Centauri.
- As we have seen, Maxwell’s equations predicted that the speed of light should be the same whatever the
- speed of the source, and this has been confirmed by accurate measurements. It follows from this that if a pulse
- of light is emitted at a particular time at a particular point in space, then as time goes on it will spread out as a
- sphere of light whose size and position are independent of the speed of the source. After one millionth of a
- second the light will have spread out to form a sphere with a radius of 300 meters; after two millionths of a
- second, the radius will be 600 meters; and so on. It will be like the ripples that spread out on the surface of a
- pond when a stone is thrown in. The ripples spread out as a circle that gets bigger as time goes on. If one
- stacks snapshots of the ripples at different times one above the other, the expanding circle of ripples will mark
- out a cone whose tip is at the place and time at which the stone hit the water Figure 2:3.
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (6 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:3
- Similarly, the light spreading out from an event forms a (three-dimensional) cone in (the four-dimensional)
- space-time. This cone is called the future light cone of the event. In the same way we can draw another cone,
- called the past light cone, which is the set of events from which a pulse of light is able to reach the given event
- Figure 2:4.
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (7 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:4
- Given an event P, one can divide the other events in the universe into three classes. Those events that can be
- reached from the event P by a particle or wave traveling at or below the speed of light are said to be in the
- future of P. They will lie within or on the expanding sphere of light emitted from the event P. Thus they will lie
- within or on the future light cone of P in the space-time diagram. Only events in the future of P can be affected
- by what happens at P because nothing can travel faster than light.
- Similarly, the past of P can be defined as the set of all events from which it is possible to reach the event P
- traveling at or below the speed of light. It is thus the set of events that can affect what happens at P. The
- events that do not lie in the future or past of P are said to lie in the elsewhere of P Figure 2:5.
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (8 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:5
- What happens at such events can neither affect nor be affected by what happens at P. For example, if the sun
- were to cease to shine at this very moment, it would not affect things on earth at the present time because they
- would be in the elsewhere of the event when the sun went out Figure 2:6.
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (9 of 12) [2/20/2001 3:14:16 AM]
- Figure 2:6
- We would know about it only after eight minutes, the time it takes light to reach us from the sun. Only then
- would events on earth lie in the future light cone of the event at which the sun went out. Similarly, we do not
- know what is happening at the moment farther away in the universe: the light that we see from distant galaxies
- left them millions of years ago, and in the case of the most distant object that we have seen, the light left some
- eight thousand million years ago. Thus, when we look at the universe, we are seeing it as it was in the past.
- If one neglects gravitational effects, as Einstein and Poincare did in 1905, one has what is called the special
- theory of relativity. For every event in space-time we may construct a light cone (the set of all possible paths of
- light in space-time emitted at that event), and since the speed of light is the same at every event and in every
- direction, all the light cones will be identical and will all point in the same direction. The theory also tells us that
- nothing can travel faster than light. This means that the path of any object through space and time must be
- represented by a line that lies within the light cone at each event on it (Fig. 2.7). The special theory of relativity
- was very successful in explaining that the speed of light appears the same to all observers (as shown by the
- Michelson-Morley experiment) and in describing what happens when things move at speeds close to the speed
- of light. However, it was inconsistent with the Newtonian theory of gravity, which said that objects attracted
- each other with a force that depended on the distance between them. This meant that if one moved one of the
- objects, the force on the other one would change instantaneously. Or in other gravitational effects should travel
- with infinite velocity, instead of at or below the speed of light, as the special theory of relativity required.
- Einstein made a number of unsuccessful attempts between 1908 and 1914 to find a theory of gravity that was
- consistent with special relativity. Finally, in 1915, he proposed what we now call the general theory of relativity.
- Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of
- the fact that space-time is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (10 of 12) [2/20/2001 3:14:16 AM]
- of mass and energy in it. Bodies like the earth are not made to move on curved orbits by a force called gravity;
- instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic. A
- geodesic is the shortest (or longest) path between two nearby points. For example, the surface of the earth is a
- two-dimensional curved space. A geodesic on the earth is called a great circle, and is the shortest route
- between two points (Fig. 2.8). As the geodesic is the shortest path between any two airports, this is the route
- an airline navigator will tell the pilot to fly along. In general relativity, bodies always follow straight lines in
- four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our
- three-dimensional space. (This is rather like watching an airplane flying over hilly ground. Although it follows a
- straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.)
- The mass of the sun curves space-time in such a way that although the earth follows a straight path in
- four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space.
- Fact, the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by
- the Newtonian theory of gravity. However, in the case of Mercury, which, being the nearest planet to the sun,
- feels the strongest gravitational effects, and has a rather elongated orbit, general relativity predicts that the long
- axis of the ellipse should rotate about the sun at a rate of about one degree in ten thousand years. Small
- though this effect is, it had been noticed before 1915 and served as one of the first confirmations of Einstein’s
- theory. In recent years the even smaller deviations of the orbits of the other planets from the Newtonian
- predictions have been measured by radar and found to agree with the predictions of general relativity.
- Light rays too must follow geodesics in space-time. Again, the fact that space is curved means that light no
- longer appears to travel in straight lines in space. So general relativity predicts that light should be bent by
- gravitational fields. For example, the theory predicts that the light cones of points near the sun would be slightly
- bent inward, on account of the mass of the sun. This means that light from a distant star that happened to pass
- near the sun would be deflected through a small angle, causing the star to appear in a different position to an
- observer on the earth (Fig. 2.9). Of course, if the light from the star always passed close to the sun, we would
- not be able to tell whether the light was being deflected or if instead the star was really where we see it.
- However, as the earth orbits around the sun, different stars appear to pass behind the sun and have their light
- deflected. They therefore change their apparent position relative to other stars. It is normally very difficult to see
- this effect, because the light from the sun makes it impossible to observe stars that appear near to the sun the
- sky. However, it is possible to do so during an eclipse of the sun, when the sun’s light is blocked out by the
- moon. Einstein’s prediction of light deflection could not be tested immediately in 1915, because the First World
- War was in progress, and it was not until 1919 that a British expedition, observing an eclipse from West Africa,
- showed that light was indeed deflected by the sun, just as predicted by the theory. This proof of a German
- theory by British scientists was hailed as a great act of reconciliation between the two countries after the war. It
- is ionic, therefore, that later examination of the photographs taken on that expedition showed the errors were as
- great as the effect they were trying to measure. Their measurement had been sheer luck, or a case of knowing
- the result they wanted to get, not an uncommon occurrence in science. The light deflection has, however, been
- accurately confirmed by a number of later observations.
- Another prediction of general relativity is that time should appear to slower near a massive body like the earth.
- This is because there is a relation between the energy of light and its frequency (that is, the number of waves of
- light per second): the greater the energy, the higher frequency. As light travels upward in the earth’s
- gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between
- one wave crest and the next goes up.) To someone high up, it would appear that everything down below was
- making longer to happen. This prediction was tested in 1962, using a pair of very accurate clocks mounted at
- the top and bottom of a water tower. The clock at the bottom, which was nearer the earth, was found to run
- slower, in exact agreement with general relativity. The difference in the speed of clocks at different heights
- above the earth is now of considerable practical importance, with the advent of very accurate navigation
- systems based on signals from satellites. If one ignored the predictions of general relativity, the position that
- one calculated would be wrong by several miles!
- Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of
- absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the
- other stays at sea level. The first twin would age faster than the second. Thus, if they met again, one would be
- older than the other. In this case, the difference in ages would be very small, but it would be much larger if one
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (11 of 12) [2/20/2001 3:14:16 AM]
- of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be
- much younger than the one who stayed on earth. This is known as the twins paradox, but it is a paradox only if
- one has the idea of absolute time at the back of one’s mind. In the theory of relativity there is no unique
- absolute time, but instead each individual has his own personal measure of time that depends on where he is
- and how he is moving.
- Before 1915, space and time were thought of as a fixed arena in which events took place, but which was not
- affected by what happened in it. This was true even of the special theory of relativity. Bodies moved, forces
- attracted and repelled, but time and space simply continued, unaffected. It was natural to think that space and
- time went on forever.
- The situation, however, is quite different in the general theory of relativity. Space and time are now dynamic
- quantities: when a body moves, or a force acts, it affects the curvature of space and time – and in turn the
- structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but
- also are affected by everything that happens in the universe. Just as one cannot talk about events in the
- universe without the notions of space and time, so in general relativity it became meaningless to talk about
- space and time outside the limits of the universe.
- In the following decades this new understanding of space and time was to revolutionize our view of the
- universe. The old idea of an essentially unchanging universe that could have existed, and could continue to
- exist, forever was replaced by the notion of a dynamic, expanding universe that seemed to have begun a finite
- time ago, and that might end at a finite time in the future. That revolution forms the subject of the next chapter.
- And years later, it was also to be the starting point for my work in theoretical physics. Roger Penrose and I
- showed that Einstein’s general theory of relativity implied that the universe must have a beginning and,
- possibly, an end.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 2
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/a.html (12 of 12) [2/20/2001 3:14:16 AM]
- CHAPTER 3
- THE EXPANDING UNIVERSE
- If one looks at the sky on a clear, moonless night, the brightest objects one sees are likely to be the planets
- Venus, Mars, Jupiter, and Saturn. There will also be a very large number of stars, which are just like our own
- sun but much farther from us. Some of these fixed stars do, in fact, appear to change very slightly their
- positions relative to each other as earth orbits around the sun: they are not really fixed at all! This is because
- they are comparatively near to us. As the earth goes round the sun, we see them from different positions
- against the background of more distant stars. This is fortunate, because it enables us to measure directly the
- distance of these stars from us: the nearer they are, the more they appear to move. The nearest star, called
- Proxima Centauri, is found to be about four light-years away (the light from it takes about four years to reach
- earth), or about twenty-three million million miles. Most of the other stars that are visible to the naked eye lie
- within a few hundred light-years of us. Our sun, for comparison, is a mere light-minutes away! The visible stars
- appear spread all over the night sky, but are particularly concentrated in one band, which we call the Milky
- Way. As long ago as 1750, some astronomers were suggesting that the appearance of the Milky Way could be
- explained if most of the visible stars lie in a single disklike configuration, one example of what we now call a
- spiral galaxy. Only a few decades later, the astronomer Sir William Herschel confirmed this idea by
- painstakingly cataloging the positions and distances of vast numbers of stars. Even so, the idea gained
- complete acceptance only early this century.
- Our modern picture of the universe dates back to only 1924, when the American astronomer Edwin Hubble
- demonstrated that ours was not the only galaxy. There were in fact many others, with vast tracts of empty
- space between them. In order to prove this, he needed to determine the distances to these other galaxies,
- which are so far away that, unlike nearby stars, they really do appear fixed. Hubble was forced, therefore, to
- use indirect methods to measure the distances. Now, the apparent brightness of a star depends on two factors:
- how much light it radiates (its luminosity), and how far it is from us. For nearby stars, we can measure their
- apparent brightness and their distance, and so we can work out their luminosity. Conversely, if we knew the
- luminosity of stars in other galaxies, we could work out their distance by measuring their apparent brightness.
- Hubble noted that certain types of stars always have the same luminosity when they are near enough for us to
- measure; therefore, he argued, if we found such stars in another galaxy, we could assume that they had the
- same luminosity – and so calculate the distance to that galaxy. If we could do this for a number of stars in the
- same galaxy, and our calculations always gave the same distance, we could be fairly confident of our estimate.
- In this way, Edwin Hubble worked out the distances to nine different galaxies. We now know that our galaxy is
- only one of some hundred thousand million that can be seen using modern telescopes, each galaxy itself
- containing some hundred thousand million stars. Figure 3:1 shows a picture of one spiral galaxy that is similar
- to what we think ours must look like to someone living in another galaxy.
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (1 of 9) [2/20/2001 3:14:24 AM]
- Figure 3:1
- We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating; the stars in its
- spiral arms orbit around its center about once every several hundred million years. Our sun is just an ordinary,
- average-sized, yellow star, near the inner edge of one of the spiral arms. We have certainly come a long way
- since Aristotle and Ptolemy, when thought that the earth was the center of the universe!
- Stars are so far away that they appear to us to be just pinpoints of light. We cannot see their size or shape. So
- how can we tell different types of stars apart? For the vast majority of stars, there is only one characteristic
- feature that we can observe – the color of their light. Newton discovered that if light from the sun passes
- through a triangular-shaped piece of glass, called a prism, it breaks up into its component colors (its spectrum)
- as in a rainbow. By focusing a telescope on an individual star or galaxy, one can similarly observe the spectrum
- of the light from that star or galaxy. Different stars have different spectra, but the relative brightness of the
- different colors is always exactly what one would expect to find in the light emitted by an object that is glowing
- red hot. (In fact, the light emitted by any opaque object that is glowing red hot has a characteristic spectrum
- that depends only on its temperature – a thermal spectrum. This means that we can tell a star’s temperature
- from the spectrum of its light.) Moreover, we find that certain very specific colors are missing from stars’
- spectra, and these missing colors may vary from star to star. Since we know that each chemical element
- absorbs a characteristic set of very specific colors, by matching these to those that are missing from a star’s
- spectrum, we can determine exactly which elements are present in the star’s atmosphere.
- In the 1920s, when astronomers began to look at the spectra of stars in other galaxies, they found something
- most peculiar: there were the same characteristic sets of missing colors as for stars in our own galaxy, but they
- were all shifted by the same relative amount toward the red end of the spectrum. To understand the
- implications of this, we must first understand the Doppler effect. As we have seen, visible light consists of
- fluctuations, or waves, in the electromagnetic field. The wavelength (or distance from one wave crest to the
- next) of light is extremely small, ranging from four to seven ten-millionths of a meter. The different wavelengths
- of light are what the human eye sees as different colors, with the longest wavelengths appearing at the red end
- of the spectrum and the shortest wavelengths at the blue end. Now imagine a source of light at a constant
- distance from us, such as a star, emitting waves of light at a constant wavelength. Obviously the wavelength of
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (2 of 9) [2/20/2001 3:14:24 AM]
- the waves we receive will be the same as the wavelength at which they are emitted (the gravitational field of the
- galaxy will not be large enough to have a significant effect). Suppose now that the source starts moving toward
- us. When the source emits the next wave crest it will be nearer to us, so the distance between wave crests will
- be smaller than when the star was stationary. This means that the wavelength of the waves we receive is
- shorter than when the star was stationary. Correspondingly, if the source is moving away from us, the
- wavelength of the waves we receive will be longer. In the case of light, therefore, means that stars moving
- away from us will have their spectra shifted toward the red end of the spectrum (red-shifted) and those moving
- toward us will have their spectra blue-shifted. This relationship between wavelength and speed, which is called
- the Doppler effect, is an everyday experience. Listen to a car passing on the road: as the car is approaching, its
- engine sounds at a higher pitch (corresponding to a shorter wavelength and higher frequency of sound waves),
- and when it passes and goes away, it sounds at a lower pitch. The behavior of light or radio waves is similar.
- Indeed, the police make use of the Doppler effect to measure the speed of cars by measuring the wavelength
- of pulses of radio waves reflected off them.
- ln the years following his proof of the existence of other galaxies, Rubble spent his time cataloging their
- distances and observing their spectra. At that time most people expected the galaxies to be moving around
- quite randomly, and so expected to find as many blue-shifted spectra as red-shifted ones. It was quite a
- surprise, therefore, to find that most galaxies appeared red-shifted: nearly all were moving away from us! More
- surprising still was the finding that Hubble published in 1929: even the size of a galaxy’s red shift is not random,
- but is directly proportional to the galaxy’s distance from us. Or, in other words, the farther a galaxy is, the faster
- it is moving away! And that meant that the universe could not be static, as everyone previously had thought, is
- in fact expanding; the distance between the different galaxies is changing all the time.
- The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth
- century. With hindsight, it is easy wonder why no one had thought of it before. Newton, and others should have
- realized that a static universe would soon start to contract under the influence of gravity. But suppose instead
- that the universe is expanding. If it was expanding fairly slowly, the force of gravity would cause it eventually to
- stop expanding and then to start contracting. However, if it was expanding at more than a certain critical rate,
- gravity would never be strong enough to stop it, and the universe would continue to expand forever. This is a bit
- like what happens when one fires a rocket upward from the surface of the earth. If it has a fairly low speed,
- gravity will eventually stop the rocket and it will start falling back. On the other hand, if the rocket has more than
- a certain critical speed (about seven miles per second), gravity will not be strong enough to pull it back, so it will
- keep going away from the earth forever. This behavior of the universe could have been predicted from
- Newton’s theory of gravity at any time in the nineteenth, the eighteenth, or even the late seventeenth century.
- Yet so strong was the belief in a static universe that it persisted into the early twentieth century. Even Einstein,
- when he formulated the general theory of relativity in 1915, was so sure that the universe had to be static that
- he modified his theory to make this possible, introducing a so-called cosmological constant into his equations.
- Einstein introduced a new “antigravity” force, which, unlike other forces, did not come from any particular
- source but was built into the very fabric of space-time. He claimed that space-time had an inbuilt tendency to
- expand, and this could be made to balance exactly the attraction of all the matter in the universe, so that a
- static universe would result. Only one man, it seems, was willing to take general relativity at face value, and
- while Einstein and other physicists were looking for ways of avoiding general relativity’s prediction of a
- nonstatic universe, the Russian physicist and mathematician Alexander Friedmann instead set about explaining
- it.
- Friedmann made two very simple assumptions about the universe: that the universe looks identical in
- whichever direction we look, and that this would also be true if we were observing the universe from anywhere
- else. From these two ideas alone, Friedmann showed that we should not expect the universe to be static. In
- fact, in 1922, several years before Edwin Hubble’s discovery, Friedmann predicted exactly what Hubble found!
- The assumption that the universe looks the same in every direction is clearly not true in reality. For example, as
- we have seen, the other stars in our galaxy form a distinct band of light across the night sky, called the Milky
- Way. But if we look at distant galaxies, there seems to be more or less the same number of them. So the
- universe does seem to be roughly the same in every direction, provided one views it on a large scale compared
- to the distance between galaxies, and ignores the differences on small scales. For a long time, this was
- sufficient justification for Friedmann’s assumption – as a rough approximation to the real universe. But more
- recently a lucky accident uncovered the fact that Friedmann’s assumption is in fact a remarkably accurate
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (3 of 9) [2/20/2001 3:14:24 AM]
- description of our universe.
- In 1965 two American physicists at the Bell Telephone Laboratories in New Jersey, Arno Penzias and Robert
- Wilson, were testing a very sensitive microwave detector. (Microwaves are just like light waves, but with a
- wavelength of around a centimeter.) Penzias and Wilson were worried when they found that their detector was
- picking up more noise than it ought to. The noise did not appear to be coming from any particular direction.
- First they discovered bird droppings in their detector and checked for other possible malfunctions, but soon
- ruled these out. They knew that any noise from within the atmosphere would be stronger when the detector
- was not pointing straight up than when it was, because light rays travel through much more atmosphere when
- received from near the horizon than when received from directly overhead. The extra noise was the same
- whichever direction the detector was pointed, so it must come from outside the atmosphere. It was also the
- same day and night and throughout the year, even though the earth was rotating on its axis and orbiting around
- the sun. This showed that the radiation must come from beyond the Solar System, and even from beyond the
- galaxy, as otherwise it would vary as the movement of earth pointed the detector in different directions.
- In fact, we know that the radiation must have traveled to us across most of the observable universe, and since
- it appears to be the same in different directions, the universe must also be the same in every direction, if only
- on a large scale. We now know that whichever direction we look, this noise never varies by more than a tiny
- fraction: so Penzias and Wilson had unwittingly stumbled across a remarkably accurate confirmation of
- Friedmann’s first assumption. However, because the universe is not exactly the same in every direction, but
- only on average on a large scale, the microwaves cannot be exactly the same in every direction either. There
- have to be slight variations between different directions. These were first detected in 1992 by the Cosmic
- Background Explorer satellite, or COBE, at a level of about one part in a hundred thousand. Small though these
- variations are, they are very important, as will be explained in Chapter 8.
- At roughly the same time as Penzias and Wilson were investigating noise in their detector, two American
- physicists at nearby Princeton University, Bob Dicke and Jim Peebles, were also taking an interest in
- microwaves. They were working on a suggestion, made by George Gamow (once a student of Alexander
- Friedmann), that the early universe should have been very hot and dense, glowing white hot. Dicke and
- Peebles argued that we should still be able to see the glow of the early universe, because light from very
- distant parts of it would only just be reaching us now. However, the expansion of the universe meant that this
- light should be so greatly red-shifted that it would appear to us now as microwave radiation. Dicke and Peebles
- were preparing to look for this radiation when Penzias and Wilson heard about their work and realized that they
- had already found it. For this, Penzias and Wilson were awarded the Nobel Prize in 1978 (which seems a bit
- hard on Dicke and Peebles, not to mention Gamow!).
- Now at first sight, all this evidence that the universe looks the same whichever direction we look in might seem
- to suggest there is something special about our place in the universe. In particular, it might seem that if we
- observe all other galaxies to be moving away from us, then we must be at the center of the universe. There is,
- however, an alternate explanation: the universe might look the same in every direction as seen from any other
- galaxy too. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for, or
- against, this assumption. We believe it only on grounds of modesty: it would be most remarkable if the universe
- looked the same in every direction around us, but not around other points in the universe! In Friedmann’s
- model, all the galaxies are moving directly away from each other. The situation is rather like a balloon with a
- number of spots painted on it being steadily blown up. As the balloon expands, the distance between any two
- spots increases, but there is no spot that can be said to be the center of the expansion. Moreover, the farther
- apart the spots are, the faster they will be moving apart. Similarly, in Friedmann’s model the speed at which any
- two galaxies are moving apart is proportional to the distance between them. So it predicted that the red shift of
- a galaxy should be directly proportional to its distance from us, exactly as Hubble found. Despite the success of
- his model and his prediction of Hubble’s observations, Friedmann’s work remained largely unknown in the West
- until similar models were discovered in 1935 by the American physicist Howard Robertson and the British
- mathematician Arthur Walker, in response to Hubble’s discovery of the uniform expansion of the universe.
- Although Friedmann found only one, there are in fact three different kinds of models that obey Friedmann’s two
- fundamental assumptions. In the first kind (which Friedmann found) the universe is expanding sufficiently
- slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and
- eventually to stop. The galaxies then start to move toward each other and the universe contracts.
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (4 of 9) [2/20/2001 3:14:24 AM]
- Figure 3:2
- Figure 3:2 shows how the distance between two neighboring galaxies changes as time increases. It starts at
- zero, increases to a maximum, and then decreases to zero again. In the second kind of solution, the universe is
- expanding so rapidly that the gravitational attraction can never stop it, though it does slow it down a bit.
- Figure 3:3
- Figure 3:3 Shows the Separation between neighboring galaxies in this model. It starts at zero and eventually
- the galaxies are moving apart at a steady speed. Finally, there is a third kind of solution, in which the universe
- is expanding only just fast enough to avoid recollapse.
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (5 of 9) [2/20/2001 3:14:24 AM]
- Figure 3:4
- In this case the separation, shown in Figure 3:4, also starts at zero and increases forever. However, the speed
- at which the galaxies are moving apart gets smaller and smaller, although it never quite reaches zero.
- A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but
- neither does space have any boundary. Gravity is so strong that space is bent round onto itself, making it rather
- like the surface of the earth. If one keeps traveling in a certain direction on the surface of the earth, one never
- comes up against an impassable barrier or falls over the edge, but eventually comes back to where one
- started.
- In the first kind of Friedmann model, space is just like this, but with three dimensions instead of two for the
- earth’s surface. The fourth dimension, time, is also finite in extent, but it is like a line with two ends or
- boundaries, a beginning and an end. We shall see later that when one combines general relativity with the
- uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without any edges
- or boundaries.
- The idea that one could go right round the universe and end up where one started makes good science fiction,
- but it doesn’t have much practical significance, because it can be shown that the universe would recollapse to
- zero size before one could get round. You would need to travel faster than light in order to end up where you
- started before the universe came to an end – and that is not allowed!
- In the first kind of Friedmann model, which expands and recollapses, space is bent in on itself, like the surface
- of the earth. It is therefore finite in extent. In the second kind of model, which expands forever, space is bent
- the other way, like the surface of a saddle. So in this case space is infinite. Finally, in the third kind of
- Friedmann model, with just the critical rate of expansion, space is flat (and therefore is also infinite).
- But which Friedmann model describes our universe? Will the universe eventually stop expanding and start
- contracting, or will it expand forever? To answer this question we need to know the present rate of expansion of
- the universe and its present average density. If the density is less than a certain critical value, determined by
- the rate of expansion, the gravitational attraction will be too weak to halt the expansion. If the density is greater
- than the critical value, gravity will stop the expansion at some time in the future and cause the universe to
- recollapse.
- We can determine the present rate of expansion by measuring the velocities at which other galaxies are
- moving away from us, using the Doppler effect. This can be done very accurately. However, the distances to
- the galaxies are not very well known because we can only measure them indirectly. So all we know is that the
- universe is expanding by between 5 percent and 10 percent every thousand million years. However, our
- uncertainty about the present average density of the universe is even greater. If we add up the masses of all
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (6 of 9) [2/20/2001 3:14:24 AM]
- the stars that we can see in our galaxy and other galaxies, the total is less than one hundredth of the amount
- required to halt the expansion of the universe, even for the lowest estimate of the rate of expansion. Our galaxy
- and other galaxies, however, must contain a large amount of “dark matter” that we cannot see directly, but
- which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the
- galaxies. Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more
- dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies. When we add
- up all this dark matter, we still get only about one tenth of the amount required to halt the expansion. However,
- we cannot exclude the possibility that there might be some other form of matter, distributed almost uniformly
- throughout the universe, that we have not yet detected and that might still raise the average density of the
- universe up to the critical value needed to halt the expansion. The present evidence therefore suggests that the
- universe will probably expand forever, but all we can really be sure of is that even if the universe is going to
- recollapse, it won’t do so for at least another ten thousand million years, since it has already been expanding
- for at least that long. This should not unduly worry us: by that time, unless we have colonized beyond the Solar
- System, mankind will long since have died out, extinguished along with our sun!
- All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand
- million years ago) the distance between neighboring galaxies must have been zero. At that time, which we call
- the big bang, the density of the universe and the curvature of space-time would have been infinite. Because
- mathematics cannot really handle infinite numbers, this means that the general theory of relativity (on which
- Friedmann’s solutions are based) predicts that there is a point in the universe where the theory itself breaks
- down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science
- are formulated on the assumption that space-time is smooth and nearly fiat, so they break down at the big bang
- singularity, where the curvature of space-time is infinite. This means that even if there were events before the
- big bang, one could not use them to determine what would happen afterward, because predictability would
- break down at the big bang.
- Correspondingly, if, as is the case, we know only what has happened since the big bang, we could not
- determine what happened beforehand. As far as we are concerned, events before the big bang can have no
- consequences, so they should not form part of a scientific model of the universe. We should therefore cut them
- out of the model and say that time had a beginning at the big bang.
- Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention.
- (The Catholic Church, on the other hand, seized on the big bang model and in 1951officially pronounced it to
- be in accordance with the Bible.) There were therefore a number of attempts to avoid the conclusion that there
- had been a big bang. The proposal that gained widest support was called the steady state theory. It was
- suggested in 1948 by two refugees from Nazi-occupied Austria, Hermann Bondi and Thomas Gold, together
- with a Briton, Fred Hoyle, who had worked with them on the development of radar during the war. The idea was
- that as the galaxies moved away from each other, new galaxies were continually forming in the gaps in
- between, from new matter that was being continually created. The universe would therefore look roughly the
- same at all times as well as at all points of space. The steady state theory required a modification of general
- relativity to allow for the continual creation of matter, but the rate that was involved was so low (about one
- particle per cubic kilometer per year) that it was not in conflict with experiment. The theory was a good scientific
- theory, in the sense described in Chapter 1: it was simple and it made definite predictions that could be tested
- by observation. One of these predictions was that the number of galaxies or similar objects in any given volume
- of space should be the same wherever and whenever we look in the universe. In the late 1950s and early
- 1960s a survey of sources of radio waves from outer space was carried out at Cambridge by a group of
- astronomers led by Martin Ryle (who had also worked with Bondi, Gold, and Hoyle on radar during the war).
- The Cambridge group showed that most of these radio sources must lie outside our galaxy (indeed many of
- them could be identified with other galaxies) and also that there were many more weak sources than strong
- ones. They interpreted the weak sources as being the more distant ones, and the stronger ones as being
- nearer. Then there appeared to be less common sources per unit volume of space for the nearby sources than
- for the distant ones. This could mean that we are at the center of a great region in the universe in which the
- sources are fewer than elsewhere. Alternatively, it could mean that the sources were more numerous in the
- past, at the time that the radio waves left on their journey to us, than they are now. Either explanation
- contradicted the predictions of the steady state theory. Moreover, the discovery of the microwave radiation by
- Penzias and Wilson in 1965 also indicated that the universe must have been much denser in the past. The
- steady state theory therefore had to be abandoned.
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (7 of 9) [2/20/2001 3:14:24 AM]
- Another attempt to avoid the conclusion that there must have been a big bang, and therefore a beginning of
- time, was made by two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, in 1963. They suggested that
- the big bang might be a peculiarity of Friedmann’s models alone, which after all were only approximations to
- the real universe. Perhaps, of all the models that were roughly like the real universe, only Friedmann’s would
- contain a big bang singularity. In Friedmann’s models, the galaxies are all moving directly away from each
- other – so it is not surprising that at some time in the past they were all at the same place. In the real universe,
- however, the galaxies are not just moving directly away from each other – they also have small sideways
- velocities. So in reality they need never have been all at exactly the same place, only very close together.
- Perhaps then the current expanding universe resulted not from a big bang singularity, but from an earlier
- contracting phase; as the universe had collapsed the particles in it might not have all collided, but had flown
- past and then away from each other, producing the present expansion of the the universe that were roughly like
- Friedmann’s models but took account of the irregularities and random velocities of galaxies in the real universe.
- They showed that such models could start with a big bang, even though the galaxies were no longer always
- moving directly away from each other, but they claimed that this was still only possible in certain exceptional
- models in which the galaxies were all moving in just the right way. They argued that since there seemed to be
- infinitely more Friedmann-like models without a big bang singularity than there were with one, we should
- conclude that there had not in reality been a big bang. They later realized, however, that there was a much
- more general class of Friedmann-like models that did have singularities, and in which the galaxies did not have
- to be moving any special way. They therefore withdrew their claim in 1970.
- The work of Lifshitz and Khalatnikov was valuable because it showed that the universe could have had a
- singularity, a big bang, if the general theory of relativity was correct. However, it did not resolve the crucial
- question: Does general relativity predict that our universe should have had a big bang, a beginning of time?
- The answer to this carne out of a completely different approach introduced by a British mathematician and
- physicist, Roger Penrose, in 1965. Using the way light cones behave in general relativity, together with the fact
- that gravity is always attractive, he showed that a star collapsing under its own gravity is trapped in a region
- whose surface eventually shrinks to zero size. And, since the surface of the region shrinks to zero, so too must
- its volume. All the matter in the star will be compressed into a region of zero volume, so the density of matter
- and the curvature of space-time become infinite. In other words, one has a singularity contained within a region
- of space-time known as a black hole.
- At first sight, Penrose’s result applied only to stars; it didn’t have anything to say about the question of whether
- the entire universe had a big bang singularity in its past. However, at the time that Penrose produced his
- theorem, I was a research student desperately looking for a problem with which to complete my Ph.D. thesis.
- Two years before, I had been diagnosed as suffering from ALS, commonly known as Lou Gehrig’s disease, or
- motor neuron disease, and given to understand that I had only one or two more years to live. In these
- circumstances there had not seemed much point in working on my Ph.D.– I did not expect to survive that long.
- Yet two years had gone by and I was not that much worse. In fact, things were going rather well for me and I
- had gotten engaged to a very nice girl, Jane Wilde. But in order to get married, I needed a job, and in order to
- get a job, I needed a Ph.D.
- In 1965 I read about Penrose’s theorem that any body undergoing gravitational collapse must eventually form a
- singularity. I soon realized that if one reversed the direction of time in Penrose’s theorem, so that the collapse
- became an expansion, the conditions of his theorem would still hold, provided the universe were roughly like a
- Friedmann model on large scales at the present time. Penrose’s theorem had shown that any collapsing star
- must end in a singularity; the time-reversed argument showed that any Friedmann-like expanding universe
- must have begun with a singularity. For technical reasons, Penrose’s theorem required that the universe be
- infinite in space. So I could in fact, use it to prove that there should be a singularity only if the universe was
- expanding fast enough to avoid collapsing again (since only those Friedmann models were infinite in space).
- During the next few years I developed new mathematical techniques to remove this and other technical
- conditions from the theorems that proved that singularities must occur. The final result was a joint paper by
- Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided
- only that general relativity is correct and the universe contains as much matter as we observe. There was a lot
- of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and
- partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of
- Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (8 of 9) [2/20/2001 3:14:24 AM]
- became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang
- singularity. It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that
- there was in fact no singularity at the beginning of the universe – as we shall see later, it can disappear once
- quantum effects are taken into account.
- We have seen in this chapter how, in less than half a century, man’s view of the universe formed over millennia
- has been transformed. Hubble’s discovery that the universe was expanding, and the realization of the
- insignificance of our own planet in the vastness of the universe, were just the starting point. As experimental
- and theoretical evidence mounted, it became more and more clear that the universe must have had a
- beginning in time, until in 1970 this was finally proved by Penrose and myself, on the basis of Einstein’s general
- theory of relativity. That proof showed that general relativity is only an incomplete theory: it cannot tell us how
- the universe started off, because it predicts that all physical theories, including itself, break down at the
- beginning of the universe. However, general relativity claims to be only a partial theory, so what the singularity
- theorems really show is that there must have been a time in the very early universe when the universe was so
- small that one could no longer ignore the small-scale effects of the other great partial theory of the twentieth
- century, quantum mechanics. At the start of the 1970s, then, we were forced to turn our search for an
- understanding of the universe from our theory of the extraordinarily vast to our theory of the extraordinarily tiny.
- That theory, quantum mechanics, will be described next, before we turn to the efforts to combine the two partial
- theories into a single quantum theory of gravity.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 3
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/b.html (9 of 9) [2/20/2001 3:14:24 AM]
- CHAPTER 4
- THE UNCERTAINTY PRINCIPLE
- The success of scientific theories, particularly Newton’s theory of gravity, led the French scientist the Marquis de Laplace
- at the beginning of the nineteenth century to argue that the universe was completely deterministic. Laplace suggested
- that there should be a set of scientific laws that would allow us to predict everything that would happen in the universe, if
- only we knew the complete state of the universe at one time. For example, if we knew the positions and speeds of the
- sun and the planets at one time, then we could use Newton’s laws to calculate the state of the Solar System at any other
- time. Determinism seems fairly obvious in this case, but Laplace went further to assume that there were similar laws
- governing everything else, including human behavior.
- The doctrine of scientific determinism was strongly resisted by many people, who felt that it infringed God’s freedom to
- intervene in the world, but it remained the standard assumption of science until the early years of this century. One of the
- first indications that this belief would have to be abandoned came when calculations by the British scientists Lord
- Rayleigh and Sir James Jeans suggested that a hot object, or body, such as a star, must radiate energy at an infinite
- rate. According to the laws we believed at the time, a hot body ought to give off electromagnetic waves (such as radio
- waves, visible light, or X rays) equally at all frequencies. For example, a hot body should radiate the same amount of
- energy in waves with frequencies between one and two million million waves a second as in waves with frequencies
- between two and three million million waves a second. Now since the number of waves a second is unlimited, this would
- mean that the total energy radiated would be infinite.
- In order to avoid this obviously ridiculous result, the German scientist Max Planck suggested in 1900 that light, X rays,
- and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quanta. Moreover,
- each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at a high
- enough frequency the emission of a single quantum would require more energy than was available. Thus the radiation at
- high frequencies would be reduced, and so the rate at which the body lost energy would be finite.
- The quantum hypothesis explained the observed rate of emission of radiation from hot bodies very well, but its
- implications for determinism were not realized until 1926, when another German scientist, Werner Heisenberg,
- formulated his famous uncertainty principle. In order to predict the future position and velocity of a particle, one has to be
- able to measure its present position and velocity accurately. The obvious way to do this is to shine light on the particle.
- Some of the waves of light will be scattered by the particle and this will indicate its position. However, one will not be able
- to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs
- to use light of a short wavelength in order to measure the position of the particle precisely. Now, by Planck’s quantum
- hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will
- disturb the particle and change its velocity in a way that cannot be predicted. moreover, the more accurately one
- measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single
- quantum. So the velocity of the particle will be disturbed by a larger amount. In other words, the more accurately you try
- to measure the position of the particle, the less accurately you can measure its speed, and vice versa. Heisenberg
- showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the
- particle can never be smaller than a certain quantity, which is known as Planck’s constant. Moreover, this limit does not
- depend on the way in which one tries to measure the position or velocity of the particle, or on the type of particle:
- Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.
- The uncertainty principle had profound implications for the way in which we view the world. Even after more than seventy
- years they have not been fully appreciated by many philosophers, and are still the subject of much controversy. The
- uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be
- completely deterministic: one certainly cannot predict future events exactly if one cannot even measure the present state
- of the universe precisely! We could still imagine that there is a set of laws that determine events completely for some
- supernatural being, who could observe the present state of the universe without disturbing it. However, such models of
- the universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as
- Occam’s razor and cut out all the features of the theory that cannot be observed. This approach led Heisenberg, Erwin
- Schrodinger, and Paul Dirac in the 1920s to reformulate mechanics into a new theory called quantum mechanics, based
- on the uncertainty principle. In this theory particles no longer had separate, well-defined positions and velocities that
- could not be observed, Instead, they had a quantum state, which was a combination of position and velocity.
- In general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number
- of different possible outcomes and tells us how likely each of these is. That is to say, if one made the same measurement
- on a large number of similar systems, each of which started off in the same way, one would find that the result of the
- A Brief History of Time - Stephen Hawking... Chapter 4
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (1 of 5) [2/20/2001 3:14:40 AM]
- measurement would be A in a certain number of cases, B in a different number, and so on. One could predict the
- approximate number of times that the result would be A or B, but one could not predict the specific result of an individual
- measurement. Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into
- science. Einstein objected to this very strongly, despite the important role he had played in the development of these
- ideas. Einstein was awarded the Nobel Prize for his contribution to quantum theory. Nevertheless, Einstein never
- accepted that the universe was governed by chance; his feelings were summed up in his famous statement “God does
- not play dice.” Most other scientists, however, were willing to accept quantum mechanics because it agreed perfectly with
- experiment. Indeed, it has been an outstandingly successful theory and underlies nearly all of modern science and
- technology. It governs the behavior of transistors and integrated circuits, which are the essential components of
- electronic devices such as televisions and computers, and is also the basis of modern chemistry and biology. The only
- areas of physical science into which quantum mechanics has not yet been properly incorporated are gravity and the
- large-scale structure of the universe.
- Although light is made up of waves, Planck’s quantum hypothesis tells us that in some ways it behaves as if it were
- composed of particles: it can be emitted or absorbed only in packets, or quanta. Equally, Heisenberg’s uncertainty
- principle implies that particles behave in some respects like waves: they do not have a definite position but are “smeared
- out” with a certain probability distribution. The theory of quantum mechanics is based on an entirely new type of
- mathematics that no longer describes the real world in terms of particles and waves; it is only the observations of the
- world that may be described in those terms. There is thus a duality between waves and particles in quantum mechanics:
- for some purposes it is helpful to think of particles as waves and for other purposes it is better to think of waves as
- particles. An important consequence of this is that one can observe what is called interference between two sets of
- waves or particles. That is to say, the crests of one set of waves may coincide with the troughs of the other set. The two
- sets of waves then cancel each other out rather than adding up to a stronger wave as one might expect Figure 4:1.
- Figure 4:1
- A familiar example of interference in the case of light is the colors that are often seen in soap bubbles. These are caused
- by reflection of light from the two sides of the thin film of water forming the bubble. White light consists of light waves of
- all different wavelengths, or colors, For certain wavelengths the crests of the waves reflected from one side of the soap
- film coincide with the troughs reflected from the other side. The colors corresponding to these wavelengths are absent
- from the reflected light, which therefore appears to be colored. Interference can also occur for particles, because of the
- duality introduced by quantum mechanics. A famous example is the so-called two-slit experiment Figure 4:2.
- A Brief History of Time - Stephen Hawking... Chapter 4
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (2 of 5) [2/20/2001 3:14:40 AM]
- Figure 4:2
- Consider a partition with two narrow parallel slits in it. On one side of the partition one places a source of fight of a
- particular color (that is, of a particular wavelength). Most of the light will hit the partition, but a small amount will go
- through the slits. Now suppose one places a screen on the far side of the partition from the light. Any point on the screen
- will receive waves from the two slits. However, in general, the distance the light has to travel from the source to the
- screen via the two slits will be different. This will mean that the waves from the slits will not be in phase with each other
- when they arrive at the screen: in some places the waves will cancel each other out, and in others they will reinforce
- each other. The result is a characteristic pattern of light and dark fringes.
- The remarkable thing is that one gets exactly the same kind of fringes if one replaces the source of light by a source of
- particles such as electrons with a definite speed (this means that the corresponding waves have a definite length). It
- seems the more peculiar because if one only has one slit, one does not get any fringes, just a uniform distribution of
- electrons across the screen. One might therefore think that opening another slit would just increase the number of
- electrons hitting each point of the screen, but, because of interference, it actually decreases it in some places. If
- electrons are sent through the slits one at a time, one would expect each to pass through one slit or the other, and so
- behave just as if the slit it passed through were the only one there – giving a uniform distribution on the screen. In reality,
- however, even when the electrons are sent one at a time, the fringes still appear. Each electron, therefore, must be
- A Brief History of Time - Stephen Hawking... Chapter 4
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (3 of 5) [2/20/2001 3:14:40 AM]
- passing through both slits at the same time!
- The phenomenon of interference between particles has been crucial to our understanding of the structure of atoms, the
- basic units of chemistry and biology and the building blocks out of which we, and everything around us, are made. At the
- beginning of this century it was thought that atoms were rather like the planets orbiting the sun, with electrons (particles
- of negative electricity) orbiting around a central nucleus, which carried positive electricity. The attraction between the
- positive and negative electricity was supposed to keep the electrons in their orbits in the same way that the gravitational
- attraction between the sun and the planets keeps the planets in their orbits. The trouble with this was that the laws of
- mechanics and electricity, before quantum mechanics, predicted that the electrons would lose energy and so spiral
- inward until they collided with the nucleus. This would mean that the atom, and indeed all matter, should rapidly collapse
- to a state of very high density. A partial solution to this problem was found by the Danish scientist Niels Bohr in 1913. He
- suggested that maybe the electrons were not able to orbit at just any distance from the central nucleus but only at certain
- specified distances. If one also supposed that only one or two electrons could orbit at any one of these distances, this
- would solve the problem of the collapse of the atom, because the electrons could not spiral in any farther than to fill up
- the orbits with e least distances and energies.
- This model explained quite well the structure of the simplest atom, hydrogen, which has only one electron orbiting around
- the nucleus. But it was not clear how one ought to extend it to more complicated atoms. Moreover, the idea of a limited
- set of allowed orbits seemed very arbitrary. The new theory of quantum mechanics resolved this difficulty. It revealed that
- an electron orbiting around the nucleus could be thought of as a wave, with a wavelength that depended on its velocity.
- For certain orbits, the length of the orbit would correspond to a whole number (as opposed to a fractional number) of
- wavelengths of the electron. For these orbits the wave crest would be in the same position each time round, so the
- waves would add up: these orbits would correspond to Bohr’s allowed orbits. However, for orbits whose lengths were not
- a whole number of wavelengths, each wave crest would eventually be canceled out by a trough as the electrons went
- round; these orbits would not be allowed.
- A nice way of visualizing the wave/particle duality is the so-called sum over histories introduced by the American scientist
- Richard Feynman. In this approach the particle is not supposed to have a single history or path in space-time, as it would
- in a classical, nonquantum theory. Instead it is supposed to go from A to B by every possible path. With each path there
- are associated a couple of numbers: one represents the size of a wave and the other represents the position in the cycle
- (i.e., whether it is at a crest or a trough). The probability of going from A to B is found by adding up the waves for all the
- paths. In general, if one compares a set of neighboring paths, the phases or positions in the cycle will differ greatly. This
- means that the waves associated with these paths will almost exactly cancel each other out. However, for some sets of
- neighboring paths the phase will not vary much between paths. The waves for these paths will not cancel out Such paths
- correspond to Bohr’s allowed orbits.
- With these ideas, in concrete mathematical form, it was relatively straightforward to calculate the allowed orbits in more
- complicated atoms and even in molecules, which are made up of a number of atoms held together by electrons in orbits
- that go round more than one nucleus. Since the structure of molecules and their reactions with each other underlie all of
- chemistry and biology, quantum mechanics allows us in principle to predict nearly everything we see around us, within
- the limits set by the uncertainty principle. (In practice, however, the calculations required for systems containing more
- than a few electrons are so complicated that we cannot do them.)
- Einstein’s general theory of relativity seems to govern the large-scale structure of the universe. It is what is called a
- classical theory; that is, it does not take account of the uncertainty principle of quantum mechanics, as it should for
- consistency with other theories. The reason that this does not lead to any discrepancy with observation is that all the
- gravitational fields that we normally experience are very weak. How-ever, the singularity theorems discussed earlier
- indicate that the gravitational field should get very strong in at least two situations, black holes and the big bang. In such
- strong fields the effects of quantum mechanics should be important. Thus, in a sense, classical general relativity, by
- predicting points of infinite density, predicts its own downfall, just as classical (that is, nonquantum) mechanics predicted
- its downfall by suggesting that atoms should collapse to infinite density. We do not yet have a complete consistent theory
- that unifies general relativity and quantum mechanics, but we do know a number of the features it should have. The
- consequences that these would have for black holes and the big bang will be described in later chapters. For the
- moment, however, we shall turn to the recent attempts to bring together our understanding of the other forces of nature
- into a single, unified quantum theory.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 4
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (4 of 5) [2/20/2001 3:14:40 AM]
- A Brief History of Time - Stephen Hawking... Chapter 4
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/c.html (5 of 5) [2/20/2001 3:14:40 AM]
- CHAPTER 5
- ELEMENTARY PARTICLES AND THE FORCES OF NATURE
- Aristotle believed that all the matter in the universe was made up of four basic elements – earth, air, fire, and water.
- These elements were acted on by two forces: gravity, the tendency for earth and water to sink, and levity, the tendency
- for air and fire to rise. This division of the contents of the universe into matter and forces is still used today. Aristotle
- believed that matter was continuous, that is, one could divide a piece of matter into smaller and smaller bits without any
- limit: one never came up against a grain of matter that could not be divided further. A few Greeks, however, such as
- Democritus, held that matter was inherently grainy and that everything was made up of large numbers of various different
- kinds of atoms. (The word atom means “indivisible” in Greek.) For centuries the argument continued without any real
- evidence on either side, but in 1803 the British chemist and physicist John Dalton pointed out that the fact that chemical
- compounds always combined in certain proportions could be explained by the grouping together of atoms to form units
- called molecules. However, the argument between the two schools of thought was not finally settled in favor of the
- atomists until the early years of this century. One of the important pieces of physical evidence was provided by Einstein.
- In a paper written in 1905, a few weeks before the famous paper on special relativity, Einstein pointed out that what was
- called Brownian motion – the irregular, random motion of small particles of dust suspended in a liquid – could be
- explained as the effect of atoms of the liquid colliding with the dust particles.
- By this time there were already suspicions that these atoms were not, after all, indivisible. Several years previously a
- fellow of Trinity College, Cambridge, J. J. Thomson, had demonstrated the existence of a particle of matter, called the
- electron, that had a mass less than one thousandth of that of the lightest atom. He used a setup rather like a modern TV
- picture tube: a red-hot metal filament gave off the electrons, and because these have a negative electric charge, an
- electric field could be used to accelerate them toward a phosphor-coated screen. When they hit the screen, flashes of
- light were generated. Soon it was realized that these electrons must be coming from within the atoms themselves, and in
- 1911 the New Zealand physicist Ernest Rutherford finally showed that the atoms of matter do have internal structure:
- they are made up of an extremely tiny, positively charged nucleus, around which a number of electrons orbit. He deduced
- this by analyzing the way in which alpha-particles, which are positively charged particles given off by radioactive atoms,
- are deflected when they collide with atoms.
- At first it was thought that the nucleus of the atom was made up of electrons and different numbers of a positively
- charged particle called the proton, from the Greek word meaning “first,” because it was believed to be the fundamental
- unit from which matter was made. However, in 1932 a colleague of Rutherford’s at Cambridge, James Chadwick,
- discovered that the nucleus contained another particle, called the neutron, which had almost the same mass as a proton
- but no electrical charge. Chadwick received the Nobel Prize for his discovery, and was elected Master of Gonville and
- Caius College, Cambridge (the college of which I am now a fellow). He later resigned as Master because of
- disagreements with the Fellows. There had been a bitter dispute in the college ever since a group of young Fellows
- returning after the war had voted many of the old Fellows out of the college offices they had held for a long time. This
- was before my time; I joined the college in 1965 at the tail end of the bitterness, when similar disagreements forced
- another Nobel Prize – winning Master, Sir Nevill Mott, to resign.
- Up to about thirty years ago, it was thought that protons and neutrons were “elementary” particles, but experiments in
- which protons were collided with other protons or electrons at high speeds indicated that they were in fact made up of
- smaller particles. These particles were named quarks by the Caltech physicist Murray Gell-Mann, who won the Nobel
- Prize in 1969 for his work on them. The origin of the name is an enigmatic quotation from James Joyce: “Three quarks for
- Muster Mark!” The word quark is supposed to be pronounced like quart, but with a k at the end instead of a t, but is
- usually pronounced to rhyme with lark.
- There are a number of different varieties of quarks: there are six “flavors,” which we call up, down, strange, charmed,
- bottom, and top. The first three flavors had been known since the 1960s but the charmed quark was discovered only in
- 1974, the bottom in 1977, and the top in 1995. Each flavor comes in three “colors,” red, green, and blue. (It should be
- emphasized that these terms are just labels: quarks are much smaller than the wavelength of visible light and so do not
- have any color in the normal sense. It is just that modern physicists seem to have more imaginative ways of naming new
- particles and phenomena – they no longer restrict themselves to Greek!) A proton or neutron is made up of three quarks,
- one of each color. A proton contains two up quarks and one down quark; a neutron contains two down and one up. We
- can create particles made up of the other quarks (strange, charmed, bottom, and top), but these all have a much greater
- mass and decay very rapidly into protons and neutrons.
- We now know that neither the atoms nor the protons and neutrons within them are indivisible. So the question is: what
- are the truly elementary particles, the basic building blocks from which everything is made? Since the wavelength of light
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (1 of 8) [2/20/2001 3:14:54 AM]
- is much larger than the size of an atom, we cannot hope to “look” at the parts of an atom in the ordinary way. We need to
- use something with a much smaller wave-length. As we saw in the last chapter, quantum mechanics tells us that all
- particles are in fact waves, and that the higher the energy of a particle, the smaller the wavelength of the corresponding
- wave. So the best answer we can give to our question depends on how high a particle energy we have at our disposal,
- because this determines on how small a length scale we can look. These particle energies are usually measured in units
- called electron volts. (In Thomson’s experiments with electrons, we saw that he used an electric field to accelerate the
- electrons. The energy that an electron gains from an electric field of one volt is what is known as an electron volt.) In the
- nineteenth century, when the only particle energies that people knew how to use were the low energies of a few electron
- volts generated by chemical reactions such as burning, it was thought that atoms were the smallest unit. In Rutherford’s
- experiment, the alpha-particles had energies of millions of electron volts. More recently, we have learned how to use
- electromagnetic fields to give particles energies of at first millions and then thousands of millions of electron volts. And so
- we know that particles that were thought to be “elementary” thirty years ago are, in fact, made up of smaller particles.
- May these, as we go to still higher energies, in turn be found to be made from still smaller particles? This is certainly
- possible, but we do have some theoretical reasons for believing that we have, or are very near to, a knowledge of the
- ultimate building blocks of nature.
- Using the wave/particle duality discussed in the last chapter, every-thing in the universe, including light and gravity, can
- be described in terms of particles. These particles have a property called spin. One way of thinking of spin is to imagine
- the particles as little tops spinning about an axis. However, this can be misleading, because quantum mechanics tells us
- that the particles do not have any well-defined axis. What the spin of a particle really tells us is what the particle looks like
- from different directions. A particle of spin 0 is like a dot: it looks the same from every direction Figure 5:1-i. On the other
- hand, a particle of spin 1 is like an arrow: it looks different from different directions Figure 5:1-ii. Only if one turns it round
- a complete revolution (360 degrees) does the particle look the same. A particle of spin 2 is like a double-headed arrow
- Figure 5:1-iii: it looks the same if one turns it round half a revolution (180 degrees). Similarly, higher spin particles look
- the same if one turns them through smaller fractions of a complete revolution. All this seems fairly straightforward, but the
- remark-able fact is that there are particles that do not look the same if one turns them through just one revolution: you
- have to turn them through two complete revolutions! Such particles are said to have spin ½.
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (2 of 8) [2/20/2001 3:14:54 AM]
- Figure 5:1
- All the known particles in the universe can be divided into two groups: particles of spin ½, which make up the matter in
- the universe, and particles of spin 0, 1, and 2, which, as we shall see, give rise to forces between the matter particles.
- The matter particles obey what is called Pauli’s exclusion principle. This was discovered in 1925 by an Austrian physicist,
- Wolfgang Pauli – for which he received the Nobel Prize in 1945. He was the archetypal theoretical physicist: it was said
- of him that even his presence in the same town would make experiments go wrong! Pauli’s exclusion principle says that
- two similar particles can-not exist in the same state; that is, they cannot have both the same position and the same
- velocity, within the limits given by the uncertainty principle. The exclusion principle is crucial because it explains why
- matter particles do not collapse to a state of very high density under the influence of the forces produced by the particles
- of spin 0, 1, and 2: if the matter particles have very nearly the same positions, they must have different velocities, which
- means that they will not stay in the same position for long. If the world had been created without the exclusion principle,
- quarks would not form separate, well-defined protons and neutrons. Nor would these, together with electrons, form
- separate, well-defined atoms. They would all collapse to form a roughly uniform, dense “soup.”
- A proper understanding of the electron and other spin-½ particles did not come until 1928, when a theory was proposed
- by Paul Dirac, who later was elected to the Lucasian Professorship of Mathematics at Cambridge (the same
- professorship that Newton had once held and that I now hold). Dirac’s theory was the first of its kind that was consistent
- with both quantum mechanics and the special theory of relativity. It explained mathematically why the electron had
- spin-½; that is, why it didn’t look the same if you turned it through only one complete revolution, but did if you turned it
- through two revolutions. It also predicted that the electron should have a partner: an anti-electron, or positron. The
- discovery of the positron in 1932 confirmed Dirac’s theory and led to his being awarded the Nobel Prize for physics in
- 1933. We now know that every particle has an antiparticle, with which it can annihilate. (In the case of the force-carrying
- particles, the antiparticles are the same as the particles themselves.) There could be whole antiworlds and antipeople
- made out of antiparticles. However, if you meet your antiself, don’t shake hands! You would both vanish in a great flash
- of light. The question of why there seem to be so many more particles than antiparticles around us is extremely
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (3 of 8) [2/20/2001 3:14:54 AM]
- important, and I shall return to it later in the chapter.
- In quantum mechanics, the forces or interactions between matter particles are all supposed to be carried by particles of
- integer spin – 0, 1, or 2. What happens is that a matter particle, such as an electron or a quark, emits a force-carrying
- particle. The recoil from this emission changes the velocity of the matter particle. The force-carrying particle then collides
- with another matter particle and is absorbed. This collision changes the velocity of the second particle, just as if there had
- been a force between the two matter particles. It is an important property of ' the force-carrying particles that they do not
- obey the exclusion principle. This means that there is no limit to the number that can be exchanged, and so they can give
- rise to a strong force. However, if the force-carrying particles have a high mass, it will be difficult to produce and
- exchange them over a large distance. So the forces that they carry will have only a short range. On the other hand, if the
- force-carrying particles have no mass of their own, the forces will be long range. The force-carrying particles exchanged
- between matter particles are said to be virtual particles because, unlike “real” particles, they cannot be directly detected
- by a particle detector. We know they exist, however, because they do have a measurable effect: they give rise to forces
- between matter particles. Particles of spin 0, 1, or 2 do also exist in some circumstances as real particles, when they can
- be directly detected. They then appear to us as what a classical physicist would call waves, such as waves of light or
- gravitational waves. They may sometimes be emitted when matter particles interact with each other by exchanging virtual
- force-carrying particles. (For example, the electric repulsive force between two electrons is due to the exchange of virtual
- photons, which can never be directly detected; but if one electron moves past another, real photons may be given off,
- which we detect as light waves.)
- Force-carrying particles can be grouped into four categories according to the strength of the force that they carry and the
- particles with which they interact. It should be emphasized that this division into four classes is man-made; it is
- convenient for the construction of partial theories, but it may not correspond to anything deeper. Ultimately, most
- physicists hope to find a unified theory that will explain all four forces as different aspects of a single force. Indeed, many
- would say this is the prime goal of physics today. Recently, successful attempts have been made to unify three of the
- four categories of force – and I shall describe these in this chapter. The question of the unification of the remaining
- category, gravity, we shall leave till later.
- The first category is the gravitational force. This force is universal, that is, every particle feels the force of gravity,
- according to its mass or energy. Gravity is the weakest of the four forces by a long way; it is so weak that we would not
- notice it at all were it not for two special properties that it has: it can act over large distances, and it is always attractive.
- This means that the very weak gravitational forces between the individual particles in two large bodies, such as the earth
- and the sun, can all add up to produce a significant force. The other three forces are either short range, or are sometimes
- attractive and some-times repulsive, so they tend to cancel out. In the quantum mechanical way of looking at the
- gravitational field, the force between two matter particles is pictured as being carried by a particle of spin 2 called the
- graviton. This has no mass of its own, so the force that it carries is long range. The gravitational force between the sun
- and the earth is ascribed to the exchange of gravitons between the particles that make up these two bodies. Although the
- exchanged particles are virtual, they certainly do produce a measurable effect – they make the earth orbit the sun! Real
- gravitons make up what classical physicists would call gravitational waves, which are very weak – and so difficult to
- detect that they have not yet been observed.
- The next category is the electromagnetic force, which interacts with electrically charged particles like electrons and
- quarks, but not with uncharged particles such as gravitons. It is much stronger than the gravitational force: the
- electromagnetic force between two electrons is about a million million million million million million million (1 with forty-two
- zeros after it) times bigger than the gravitational force. However, there are two kinds of electric charge, positive and
- negative. The force between two positive charges is repulsive, as is the force between two negative charges, but the
- force is attractive between a positive and a negative charge. A large body, such as the earth or the sun, contains nearly
- equal numbers of positive and negative charges. Thus the attractive and repulsive forces between the individual particles
- nearly cancel each other out, and there is very little net electromagnetic force. However, on the small scales of atoms
- and molecules, electromagnetic forces dominate. The electromagnetic attraction between negatively charged electrons
- and positively charged protons in the nucleus causes the electrons to orbit the nucleus of the atom, just as gravitational
- attraction causes the earth to orbit the sun. The electromagnetic attraction is pictured as being caused by the exchange
- of large numbers of virtual massless particles of spin 1, called photons. Again, the photons that are exchanged are virtual
- particles. However, when an electron changes from one allowed orbit to another one nearer to the nucleus, energy is
- released and a real photon is emitted – which can be observed as visible light by the human eye, if it has the right
- wave-length, or by a photon detector such as photographic film. Equally, if a real photon collides with an atom, it may
- move an electron from an orbit nearer the nucleus to one farther away. This uses up the energy of the photon, so it is
- absorbed.
- The third category is called the weak nuclear force, which is responsible for radioactivity and which acts on all matter
- particles of spin-½, but not on particles of spin 0, 1, or 2, such as photons and gravitons. The weak nuclear force was not
- well understood until 1967, when Abdus Salam at Imperial College, London, and Steven Weinberg at Harvard both
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (4 of 8) [2/20/2001 3:14:54 AM]
- proposed theories that unified this interaction with the electromagnetic force, just as Maxwell had unified electricity and
- magnetism about a hundred years earlier. They suggested that in addition to the photon, there were three other spin-1
- particles, known collectively as massive vector bosons, that carried the weak force. These were called W+ (pronounced
- W plus), W- (pronounced W minus), and Zº (pronounced Z naught), and each had a mass of around 100 GeV (GeV
- stands for gigaelectron-volt, or one thousand million electron volts). The Weinberg-Salam theory exhibits a property
- known as spontaneous symmetry breaking. This means that what appear to be a number of completely different particles
- at low energies are in fact found to be all the same type of particle, only in different states. At high energies all these
- particles behave similarly. The effect is rather like the behavior of a roulette ball on a roulette wheel. At high energies
- (when the wheel is spun quickly) the ball behaves in essentially only one way – it rolls round and round. But as the wheel
- slows, the energy of the ball decreases, and eventually the ball drops into one of the thirty-seven slots in the wheel. In
- other words, at low energies there are thirty-seven different states in which the ball can exist. If, for some reason, we
- could only observe the ball at low energies, we would then think that there were thirty-seven different types of ball!
- In the Weinberg-Salam theory, at energies much greater than 100 GeV, the three new particles and the photon would all
- behave in a similar manner. But at the lower particle energies that occur in most normal situations, this symmetry
- between the particles would be broken. WE, W, and Zº would acquire large masses, making the forces they carry have a
- very short range. At the time that Salam and Weinberg proposed their theory, few people believed them, and particle
- accelerators were not powerful enough to reach the energies of 100 GeV required to produce real W+, W-, or Zº particles.
- However, over the next ten years or so, the other predictions of the theory at lower energies agreed so well with
- experiment that, in 1979, Salam and Weinberg were awarded the Nobel Prize for physics, together with Sheldon
- Glashow, also at Harvard, who had suggested similar unified theories of the electromagnetic and weak nuclear forces.
- The Nobel committee was spared the embarrassment of having made a mistake by the discovery in 1983 at CERN
- (European Centre for Nuclear Research) of the three massive partners of the photon, with the correct predicted masses
- and other properties. Carlo Rubbia, who led the team of several hundred physicists that made the discovery, received the
- Nobel Prize in 1984, along with Simon van der Meer, the CERNengineer who developed the antimatter storage system
- employed. (It is very difficult to make a mark in experimental physics these days unless you are already at the top! )
- The fourth category is the strong nuclear force, which holds the quarks together in the proton and neutron, and holds the
- protons and neutrons together in the nucleus of an atom. It is believed that this force is carried by another spin-1 particle,
- called the gluon, which interacts only with itself and with the quarks. The strong nuclear force has a curious property
- called confinement: it always binds particles together into combinations that have no color. One cannot have a single
- quark on its own because it would have a color (red, green, or blue). Instead, a red quark has to be joined to a green and
- a blue quark by a “string” of gluons (red + green + blue = white). Such a triplet constitutes a proton or a neutron. Another
- possibility is a pair consisting of a quark and an antiquark (red + antired, or green + antigreen, or blue + antiblue = white).
- Such combinations make up the particles known as mesons, which are unstable because the quark and antiquark can
- annihilate each other, producing electrons and other particles. Similarly, confinement prevents one having a single gluon
- on its own, because gluons also have color. Instead, one has to have a collection of gluons whose colors add up to white.
- Such a collection forms an unstable particle called a glueball.
- The fact that confinement prevents one from observing an isolated quark or gluon might seem to make the whole notion
- of quarks and gluons as particles somewhat metaphysical. However, there is another property of the strong nuclear
- force, called asymptotic freedom, that makes the concept of quarks and gluons well defined. At normal energies, the
- strong nuclear force is indeed strong, and it binds the quarks tightly together. However, experiments with large particle
- accelerators indicate that at high energies the strong force becomes much weaker, and the quarks and gluons behave
- almost like free particles.
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (5 of 8) [2/20/2001 3:14:54 AM]
- Figure 5:2
- Figure 5:2 shows a photograph of a collision between a high-energy proton and antiproton. The success of the unification
- of the electromagnetic and weak nuclear forces led to a number of attempts to combine these two forces with the strong
- nuclear force into what is called a grand unified theory (or GUT). This title is rather an exaggeration: the resultant theories
- are not all that grand, nor are they fully unified, as they do not include gravity. Nor are they really complete theories,
- because they contain a number of parameters whose values cannot be predicted from the theory but have to be chosen
- to fit in with experiment. Nevertheless, they may be a step toward a complete, fully unified theory. The basic idea of
- GUTs is as follows: as was mentioned above, the strong nuclear force gets weaker at high energies. On the other hand,
- the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies. At some very high
- energy, called the grand unification energy, these three forces would all have the same strength and so could just be
- different aspects of a single force. The GUTs also predict that at this energy the different spin-½ matter particles, like
- quarks and electrons, would also all be essentially the same, thus achieving another unification.
- The value of the grand unification energy is not very well known, but it would probably have to be at least a thousand
- million million GeV. The present generation of particle accelerators can collide particles at energies of about one hundred
- GeV, and machines are planned that would raise this to a few thousand GeV. But a machine that was powerful enough to
- accelerate particles to the grand unification energy would have to be as big as the Solar System – and would be unlikely
- to be funded in the present economic climate. Thus it is impossible to test grand unified theories directly in the laboratory.
- However, just as in the case of the electromagnetic and weak unified theory, there are low-energy consequences of the
- theory that can be tested.
- The most interesting of these is the prediction that protons, which make up much of the mass of ordinary matter, can
- spontaneously decay into lighter particles such as antielectrons. The reason this is possible is that at the grand
- unification energy there is no essential difference between a quark and an antielectron. The three quarks inside a proton
- normally do not have enough energy to change into antielectrons, but very occasionally one of them may acquire
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (6 of 8) [2/20/2001 3:14:54 AM]
- sufficient energy to make the transition because the uncertainty principle means that the energy of the quarks inside the
- proton cannot be fixed exactly. The proton would then decay. The probability of a quark gaining sufficient energy is so
- low that one is likely to have to wait at least a million million million million million years (1 followed by thirty zeros). This is
- much longer than the time since the big bang, which is a mere ten thousand million years or so (1 followed by ten zeros).
- Thus one might think that the possibility of spontaneous proton decay could not be tested experimentally. However, one
- can increase one’s chances of detecting a decay by observing a large amount of matter containing a very large number
- of protons. (If, for example, one observed a number of protons equal to 1 followed by thirty-one zeros for a period of one
- year, one would expect, according to the simplest GUT, to observe more than one proton decay.)
- A number of such experiments have been carried out, but none have yielded definite evidence of proton or neutron
- decay. One experiment used eight thousand tons of water and was performed in the Morton Salt Mine in Ohio (to avoid
- other events taking place, caused by cosmic rays, that might be confused with proton decay). Since no spontaneous
- proton decay had been observed during the experiment, one can calculate that the probable life of the proton must be
- greater than ten million million million million million years (1 with thirty-one zeros). This is longer than the lifetime
- predicted by the simplest grand unified theory, but there are more elaborate theories in which the predicted lifetimes are
- longer. Still more sensitive experiments involving even larger quantities of matter will be needed to test them.
- Even though it is very difficult to observe spontaneous proton decay, it may be that our very existence is a consequence
- of the reverse process, the production of protons, or more simply, of quarks, from an initial situation in which there were
- no more quarks than antiquarks, which is the most natural way to imagine the universe starting out. Matter on the earth is
- made up mainly of protons and neutrons, which in turn are made up of quarks. There are no antiprotons or antineutrons,
- made up from antiquarks, except for a few that physicists produce in large particle accelerators. We have evidence from
- cosmic rays that the same is true for all the matter in our galaxy: there are no antiprotons or antineutrons apart from a
- small number that are produced as particle/ antiparticle pairs in high-energy collisions. If there were large regions of
- antimatter in our galaxy, we would expect to observe large quantities of radiation from the borders between the regions of
- matter and antimatter, where many particles would be colliding with their anti-particles, annihilating each other and giving
- off high-energy radiation.
- We have no direct evidence as to whether the matter in other galaxies is made up of protons and neutrons or antiprotons
- and anti-neutrons, but it must be one or the other: there cannot be a mixture in a single galaxy because in that case we
- would again observe a lot of radiation from annihilations. We therefore believe that all galaxies are composed of quarks
- rather than antiquarks; it seems implausible that some galaxies should be matter and some antimatter.
- Why should there be so many more quarks than antiquarks? Why are there not equal numbers of each? It is certainly
- fortunate for us that the numbers are unequal because, if they had been the same, nearly all the quarks and antiquarks
- would have annihilated each other in the early universe and left a universe filled with radiation but hardly any matter.
- There would then have been no galaxies, stars, or planets on which human life could have developed. Luckily, grand
- unified theories may provide an explanation of why the universe should now contain more quarks than antiquarks, even if
- it started out with equal numbers of each. As we have seen, GUTs allow quarks to change into antielectrons at high
- energy. They also allow the reverse processes, antiquarks turning into electrons, and electrons and antielectrons turning
- into antiquarks and quarks. There was a time in the very early universe when it was so hot that the particle energies
- would have been high enough for these transformations to take place. But why should that lead to more quarks than
- antiquarks? The reason is that the laws of physics are not quite the same for particles and antiparticles.
- Up to 1956 it was believed that the laws of physics obeyed each of three separate symmetries called C, P, and T. The
- symmetry C means that the laws are the same for particles and antiparticles. The symmetry P means that the laws are
- the same for any situation and its mirror image (the mirror image of a particle spinning in a right-handed direction is one
- spinning in a left-handed direction). The symmetry T means that if you reverse the direction of motion of all particles and
- antiparticles, the system should go back to what it was at earlier times; in other words, the laws are the same in the
- forward and backward directions of time. In 1956 two American physicists, Tsung-Dao Lee and Chen Ning Yang,
- suggested that the weak force does not in fact obey the symmetry P. In other words, the weak force would make the
- universe develop in a different way from the way in which the mirror image of the universe would develop. The same
- year, a colleague, Chien-Shiung Wu, proved their prediction correct. She did this by lining up the nuclei of radioactive
- atoms in a magnetic field, so that they were all spinning in the same direction, and showed that the electrons were given
- off more in one direction than another. The following year, Lee and Yang received the Nobel Prize for their idea. It was
- also found that the weak force did not obey the symmetry C. That is, it would cause a universe composed of antiparticles
- to behave differently from our universe. Nevertheless, it seemed that the weak force did obey the combined symmetry
- CP. That is, the universe would develop in the same way as its mirror image if, in addition, every particle was swapped
- with its antiparticle! However, in 1964 two more Americans, J. W. Cronin and Val Fitch, discovered that even the CP
- symmetry was not obeyed in the decay of certain particles called K-mesons. Cronin and Fitch eventually received the
- Nobel Prize for their work in 1980. (A lot of prizes have been awarded for showing that the universe is not as simple as
- we might have thought!)
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (7 of 8) [2/20/2001 3:14:54 AM]
- There is a mathematical theorem that says that any theory that obeys quantum mechanics and relativity must always
- obey the combined symmetry CPT. In other words, the universe would have to behave the same if one replaced particles
- by antiparticles, took the mirror image, and also reversed the direction of time. But Cronin and Fitch showed that if one
- replaces particles by antiparticles and takes the mirror image, but does not reverse the direction of time, then the
- universe does not behave the same. The laws of physics, therefore, must change if one reverses the direction of time –
- they do not obey the symmetry T.
- Certainly the early universe does not obey the symmetry T: as time runs forward the universe expands – if it ran
- backward, the universe would be contracting. And since there are forces that do not obey the symmetry T, it follows that
- as the universe expands, these forces could cause more antielectrons to turn into quarks than electrons into antiquarks.
- Then, as the universe expanded and cooled, the antiquarks would annihilate with the quarks, but since there would be
- more quarks than antiquarks, a small excess of quarks would remain. It is these that make up the matter we see today
- and out of which we ourselves are made. Thus our very existence could be regarded as a confirmation of grand unified
- theories, though a qualitative one only; the uncertainties are such that one cannot predict the numbers of quarks that will
- be left after the annihilation, or even whether it would be quarks or antiquarks that would remain. (Had it been an excess
- of antiquarks, however, we would simply have named antiquarks quarks, and quarks antiquarks.)
- Grand unified theories do not include the force of gravity. This does not matter too much, because gravity is such a weak
- force that its effects can usually be neglected when we are dealing with elementary particles or atoms. However, the fact
- that it is both long range and always attractive means that its effects all add up. So for a sufficiently large number of
- matter particles, gravitational forces can dominate over all other forces. This is why it is gravity that determines the
- evolution of the universe. Even for objects the size of stars, the attractive force of gravity can win over all the other forces
- and cause the star to collapse. My work in the 1970s focused on the black holes that can result from such stellar collapse
- and the intense gravitational fields around them. It was this that led to the first hints of how the theories of quantum
- mechanics and general relativity might affect each other – a glimpse of the shape of a quantum theory of gravity yet to
- come.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 5
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/d.html (8 of 8) [2/20/2001 3:14:54 AM]
- CHAPTER 6
- BLACK HOLES
- The term black hole is of very recent origin. It was coined in 1969 by the American scientist John Wheeler as a graphic
- description of an idea that goes back at least two hundred years, to a time when there were two theories about light:
- one, which Newton favored, was that it was composed of particles; the other was that it was made of waves. We now
- know that really both theories are correct. By the wave/particle duality of quantum mechanics, light can be regarded as
- both a wave and a particle. Under the theory that light is made up of waves, it was not clear how it would respond to
- gravity. But if light is composed of particles, one might expect them to be affected by gravity in the same way that
- cannonballs, rockets, and planets are. At first people thought that particles of light traveled infinitely fast, so gravity
- would not have been able to slow them down, but the discovery by Roemer that light travels at a finite speed meant that
- gravity might have an important effect.
- On this assumption, a Cambridge don, John Michell, wrote a paper in 1783 in the Philosophical Transactions of the
- Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such
- a strong gravitational field that light could not escape: any light emitted from the surface of the star would be dragged
- back by the star’s gravitational attraction before it could get very far. Michell suggested that there might be a large
- number of stars like this. Although we would not be able to see them because the light from them would not reach us,
- we would still feel their gravitational attraction. Such objects are what we now call black holes, because that is what
- they are: black voids in space. A similar suggestion was made a few years later by the French scientist the Marquis de
- Laplace, apparently independently of Michell. Interestingly enough, Laplace included it in only the first and second
- editions of his book The System of the World, and left it out of later editions; perhaps he decided that it was a crazy
- idea. (Also, the particle theory of light went out of favor during the nineteenth century; it seemed that everything could
- be explained by the wave theory, and according to the wave theory, it was not clear that light would be affected by
- gravity at all.)
- In fact, it is not really consistent to treat light like cannonballs in Newton’s theory of gravity because the speed of light is
- fixed. (A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a
- photon, however, must continue upward at a constant speed. How then can Newtonian grav-ity affect light?) A
- consistent theory of how gravity affects light did not come along until Einstein proposed general relativity in 1915. And
- even then it was a long time before the implications of the theory for massive stars were understood.
- To understand how a black hole might be formed, we first need an understanding of the life cycle of a star. A star is
- formed when a large amount of gas (mostly hydrogen) starts to collapse in on itself due to its gravitational attraction. As
- it contracts, the atoms of the gas collide with each other more and more frequently and at greater and greater speeds –
- the gas heats up. Eventually, the gas will be so hot that when the hydrogen atoms collide they no longer bounce off
- each other, but instead coalesce to form helium. The heat released in this reaction, which is like a controlled hydrogen
- bomb explosion, is what makes the star shine. This additional heat also increases the pressure of the gas until it is
- sufficient to balance the gravitational attraction, and the gas stops contracting. It is a bit like a balloon – there is a
- balance between the pressure of the air inside, which is trying to make the balloon expand, and the tension in the
- rubber, which is trying to make the balloon smaller. Stars will remain stable like this for a long time, with heat from the
- nuclear reactions balancing the gravitational attraction. Eventually, however, the star will run out of its hydrogen and
- other nuclear fuels. Paradoxically, the more fuel a star starts off with, the sooner it runs out. This is because the more
- massive the star is, the hotter it needs to be to balance its gravitational attraction. And the hotter it is, the faster it will
- use up its fuel. Our sun has probably got enough fuel for another five thousand million years or so, but more massive
- stars can use up their fuel in as little as one hundred million years, much less than the age of the universe. When a star
- runs out of fuel, it starts to cool off and so to contract. What might happen to it then was first understood only at the end
- of the 1920s.
- In 1928 an Indian graduate student, Subrahmanyan Chandrasekhar, set sail for England to study at Cambridge with the
- British astronomer Sir Arthur Eddington, an expert on general relativity. (According to some accounts, a journalist told
- Eddington in the early 1920s that he had heard there were only three people in the world who understood general
- relativity. Eddington paused, then replied, “I am trying to think who the third person is.”) During his voyage from India,
- Chandrasekhar worked out how big a star could be and still support itself against its own gravity after it had used up all
- its fuel. The idea was this: when the star becomes small, the matter particles get very near each other, and so
- according to the Pauli exclusion principle, they must have very different velocities. This makes them move away from
- each other and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance
- between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (1 of 9) [2/20/2001 3:15:08 AM]
- gravity was balanced by the heat.
- Chandrasekhar realized, however, that there is a limit to the repulsion that the exclusion principle can provide. The
- theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light.
- This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than
- the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of
- the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar
- limit.) A similar discovery was made about the same time by the Russian scientist Lev Davidovich Landau.
- This had serious implications for the ultimate fate of massive stars. If a star’s mass is less than the Chandrasekhar limit,
- it can eventually stop contracting and settle down to a possible final state as a “white dwarf” with a radius of a few
- thousand miles and a density of hundreds of tons per cubic inch. A white dwarf is supported by the exclusion principle
- repulsion between the electrons in its matter. We observe a large number of these white dwarf stars. One of the first to
- be discovered is a star that is orbiting around Sirius, the brightest star in the night sky.
- Landau pointed out that there was another possible final state for a star, also with a limiting mass of about one or two
- times the mass of the sun but much smaller even than a white dwarf. These stars would be supported by the exclusion
- principle repulsion between neutrons and protons, rather than between electrons. They were therefore called neutron
- stars. They would have a radius of only ten miles or so and a density of hundreds of millions of tons per cubic inch. At
- the time they were first predicted, there was no way that neutron stars could be observed. They were not actually
- detected until much later.
- Stars with masses above the Chandrasekhar limit, on the other hand, have a big problem when they come to the end of
- their fuel. In some cases they may explode or manage to throw off enough matter to reduce their mass below the limit
- and so avoid catastrophic gravitational collapse, but it was difficult to believe that this always happened, no matter how
- big the star. How would it know that it had to lose weight? And even if every star managed to lose enough mass to
- avoid collapse, what would happen if you added more mass to a white dwarf 'or neutron star to take it over the limit?
- Would it collapse to infinite density? Eddington was shocked by that implication, and he refused to believe
- Chandrasekhar’s result. Eddington thought it was simply not possible that a star could collapse to a point. This was the
- view of most scientists: Einstein himself wrote a paper in which he claimed that stars would not shrink to zero size. The
- hostility of other scientists, particularly Eddington, his former teacher and the leading authority on the structure of stars,
- persuaded Chandrasekhar to abandon this line of work and turn instead to other problems in astronomy, such as the
- motion of star clusters. However, when he was awarded the Nobel Prize in 1983, it was, at least in part, for his early
- work on the limiting mass of cold stars.
- Chandrasekhar had shown that the exclusion principle could not halt the collapse of a star more massive than the
- Chandrasekhar limit, but the problem of understanding what would happen to such a star, according to general
- relativity, was first solved by a young American, Robert Oppenheimer, in 1939. His result, however, suggested that
- there would be no observational consequences that could be detected by the telescopes of the day. Then World War II
- intervened and Oppenheimer himself became closely involved in the atom bomb project. After the war the problem of
- gravitational collapse was largely forgotten as most scientists became caught up in what happens on the scale of the
- atom and its nucleus. In the 1960s, however, interest in the large-scale problems of astronomy and cosmology was
- revived by a great increase in the number and range of astronomical observations brought about by the application of
- modern technology. Oppenheimer’s work was then rediscovered and extended by a number of people.
- The picture that we now have from Oppenheimer’s work is as follows. The gravitational field of the star changes the
- paths of light rays in space-time from what they would have been had the star not been present. The light cones, which
- indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the
- surface of the star. This can be seen in the bending of light from distant stars observed during an eclipse of the sun. As
- the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This
- makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a
- distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes
- so strong that the light cones are bent inward so much that light can no longer escape Figure 6:1.
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (2 of 9) [2/20/2001 3:15:08 AM]
- Figure 6:1
- According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything
- else; everything is dragged back by the gravitational field. So one has a set of events, a region of space-time, from
- which it is not possible to escape to reach a distant observer. This region is what we now call a black hole. Its boundary
- is called the event horizon and it coincides with the paths of light rays that just fail to escape from the black hole.
- In order to understand what you would see if you were watching a star collapse to form a black hole, one has to
- remember that in the theory of relativity there is no absolute time. Each observer has his own measure of time. The time
- for someone on a star will be different from that for someone at a distance, because of the gravitational field of the star.
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (3 of 9) [2/20/2001 3:15:08 AM]
- Suppose an intrepid astronaut on the surface of the collapsing star, collapsing inward with it, sent a signal every
- second, according to his watch, to his spaceship orbiting about the star. At some time on his watch, say 11:00, the star
- would shrink below the critical radius at which the gravitational field becomes so strong nothing can escape, and his
- signals would no longer reach the spaceship. As 11:00 approached his companions watching from the spaceship would
- find the intervals between successive signals from the astronaut getting longer and longer, but this effect would be very
- small before 10:59:59. They would have to wait only very slightly more than a second between the astronaut’s 10:59:58
- signal and the one that he sent when his watch read 10:59:59, but they would have to wait forever for the 11:00 signal.
- The light waves emitted from the surface of the star between 10:59:59 and 11:00, by the astronaut’s watch, would be
- spread out over an infinite period of time, as seen from the spaceship. The time interval between the arrival of
- successive waves at the spaceship would get longer and longer, so the light from the star would appear redder and
- redder and fainter and fainter. Eventually, the star would be so dim that it could no longer be seen from the spaceship:
- all that would be left would be a black hole in space. The star would, however, continue to exert the same gravitational
- force on the spaceship, which would continue to orbit the black hole. This scenario is not entirely realistic, however,
- because of the following problem. Gravity gets weaker the farther you are from the star, so the gravitational force on our
- intrepid astronaut’s feet would always be greater than the force on his head. This difference in the forces would stretch
- our astronaut out like spaghetti or tear him apart before the star had contracted to the critical radius at which the event
- horizon formed! However, we believe that there are much larger objects in the universe, like the central regions of
- galaxies, that can also undergo gravitational collapse to produce black holes; an astronaut on one of these would not be
- torn apart before the black hole formed. He would not, in fact, feel anything special as he reached the critical radius,
- and could pass the point of no return without noticing it However, within just a few hours, as the region continued to
- collapse, the difference in the gravitational forces on his head and his feet would become so strong that again it would
- tear him apart.
- The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must
- be a singularity of infinite density and space-time curvature within a black hole. This is rather like the big bang at the
- beginning of time, only it would be an end of time for the collapsing body and the astronaut. At this singularity the laws
- of science and our ability to predict the future would break down. However, any observer who remained outside the
- black hole would not be affected by this failure of predictability, because neither light nor any other signal could reach
- him from the singularity. This remarkable fact led Roger Penrose to propose the cosmic censorship hypothesis, which
- might be paraphrased as “God abhors a naked singularity.” In other words, the singularities produced by gravitational
- collapse occur only in places, like black holes, where they are decently hidden from outside view by an event horizon.
- Strictly, this is what is known as the weak cosmic censorship hypothesis: it protects observers who remain outside the
- black hole from the consequences of the breakdown of predictability that occurs at the singularity, but it does nothing at
- all for the poor unfortunate astronaut who falls into the hole.
- There are some solutions of the equations of general relativity in which it is possible for our astronaut to see a naked
- singularity: he may be able to avoid hitting the singularity and instead fall through a "wormhole” and come out in another
- region of the universe. This would offer great possibilities for travel in space and time, but unfortunately it seems that
- these solutions may all be highly unstable; the least disturbance, such as the presence of an astronaut, may change
- them so that the astronaut could not see the singularity until he hit it and his time came to an end. In other words, the
- singularity would always lie in his future and never in his past. The strong version of the cosmic censorship hypothesis
- states that in a realistic solution, the singularities would always lie either entirely in the future (like the singularities of
- gravitational collapse) or entirely in the past (like the , big bang). I strongly believe in cosmic censorship so I bet Kip
- Thorne and John Preskill of Cal Tech that it would always hold. I lost the bet on a technicality because examples were
- produced of solutions with a singularity that was visible from a long way away. So I had to pay up, which according to
- the terms of the bet meant I had to clothe their nakedness. But I can claim a moral victory. The naked singularities were
- unstable: the least disturbance would cause them either to disappear or to be hidden behind an event horizon. So they
- would not occur in realistic situations.
- The event horizon, the boundary of the region of space-time from which it is not possible to escape, acts rather like a
- one-way membrane around the black hole: objects, such as unwary astronauts, can fall through the event horizon into
- the black hole, but nothing can ever get out of the black hole through the event horizon. (Remember that the event
- horizon is the path in space-time of light that is trying to escape from the black hole, and nothing can travel faster than
- light.) One could well say of the event horizon what the poet Dante said of the entrance to Hell: “All hope abandon, ye
- who enter here.” Anything or anyone who falls through the event horizon will soon reach the region of infinite density
- and the end of time.
- General relativity predicts that heavy objects that are moving will cause the emission of gravitational waves, ripples in
- the curvature of space that travel at the speed of light. These are similar to light waves, which are ripples of the
- electromagnetic field, but they are much harder to detect. They can be observed by the very slight change in separation
- they produce between neighboring freely moving objects. A number of detectors are being built in the United States,
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (4 of 9) [2/20/2001 3:15:08 AM]
- Europe, and Japan that will measure displacements of one part in a thousand million million million (1 with twenty-one
- zeros after it), or less than the nucleus of an atom over a distance of ten miles.
- Like light, gravitational waves carry energy away from the objects that emit them. One would therefore expect a system
- of massive objects to settle down eventually to a stationary state, because the energy in any movement would be
- carried away by the emission of gravitational waves. (It is rather like dropping a cork into water: at first it bobs up and
- down a great deal, but as the ripples carry away its energy, it eventually settles down to a stationary state.) For
- example, the movement of the earth in its orbit round the sun produces gravitational waves. The effect of the energy
- loss will be to change the orbit of the earth so that gradually it gets nearer and nearer to the sun, eventually collides with
- it, and settles down to a stationary state. The rate of energy loss in the case of the earth and the sun is very low – about
- enough to run a small electric heater. This means it will take about a thousand million million million million years for the
- earth to run into the sun, so there’s no immediate cause for worry! The change in the orbit of the earth is too slow to be
- observed, but this same effect has been observed over the past few years occurring in the system called PSR 1913 +
- 16 (PSR stands for “pulsar,” a special type of neutron star that emits regular pulses of radio waves). This system
- contains two neutron stars orbiting each other, and the energy they are losing by the emission of gravitational waves is
- causing them to spiral in toward each other. This confirmation of general relativity won J. H. Taylor and R. A. Hulse the
- Nobel Prize in 1993. It will take about three hundred million . years for them to collide. Just before they do, they will be
- orbiting so fast that they will emit enough gravitational waves for detectors like LIGO to pick up.
- During the gravitational collapse of a star to form a black hole, the movements would be much more rapid, so the rate at
- which energy is carried away would be much higher. It would therefore not be too long ' before it settled down to a
- stationary state. What would this final stage look like? One might suppose that it would depend on all the complex
- features of the star from which it had formed – not only its mass and rate of rotation, but also the different densities of
- various parts of the star, and the complicated movements of the gases within the star. And if black holes were as varied
- as the objects that collapsed to form them, it might be very difficult to make any predictions about black holes in
- general.
- In 1967, however, the study of black holes was revolutionized by Werner Israel, a Canadian scientist (who was born in
- Berlin, brought up in South Africa, and took his doctoral degree in Ireland). Israel showed that, according to general
- relativity, non-rotating black holes must be very simple; they were perfectly spherical, their size depended only on their
- mass, and any two such black holes with the same mass were identical. They could, in fact, be described by a
- particular solution of Einstein’s equations that had been known since 1917, found by Karl Schwarzschild shortly after
- the discovery of general relativity. At first many people, including Israel himself, argued that since black holes had to be
- perfectly spherical, a black hole could only form from the collapse of a perfectly spherical object. Any real star – which
- would never be perfectly spherical – could therefore only collapse to form a naked singularity.
- There was, however, a different interpretation of Israel’s result, which was advocated by Roger Penrose and John
- Wheeler in particular. They argued that the rapid movements involved in a star’s collapse would mean that the
- gravitational waves it gave off would make it ever more spherical, and by the time it had settled down to a stationary
- state, it would be precisely spherical. According to this view, any non-rotating star, however complicated its shape and
- internal structure, would end up after gravitational collapse as a perfectly spherical black hole, whose size would
- depend only on its mass. Further calculations supported this view, and it soon came to be adopted generally.
- Israel’s result dealt with the case of black holes formed from non-rotating bodies only. In 1963, Roy Kerr, a New
- Zealander, found a set of solutions of the equations of general relativity that described rotating black holes. These
- “Kerr” black holes rotate at a constant rate, their size and shape depending only on their mass and rate of rotation. If the
- rotation is zero, the black hole is perfectly round and the solution is identical to the Schwarzschild solution. If the
- rotation is non-zero, the black hole bulges outward near its equator (just as the earth or the sun bulge due to their
- rotation), and the faster it rotates, the more it bulges. So, to extend Israel’s result to include rotating bodies, it was
- conjectured that any rotating body that collapsed to form a black hole would eventually settle down to a stationary state
- described by the Kerr solution. In 1970 a colleague and fellow research student of mine at Cambridge, Brandon Carter,
- took the first step toward proving this conjecture. He showed that, provided a stationary rotating black hole had an axis
- of symmetry, like a spinning top, its size and shape would depend only on its mass and rate of rotation. Then, in 1971, I
- proved that any stationary rotating black hole would indeed have such an axis of symmetry. Finally, in 1973, David
- Robinson at Kings College, London, used Carter’s and my results to show that the conjecture had been correct: such a
- black hole had indeed to be the Kerr solution. So after gravitational collapse a black hole must settle down into a state
- in which it could be rotating, but not pulsating. Moreover, its size and shape would depend only on its mass and rate of
- rotation, and not on the nature of the body that had collapsed to form it. This result became known by the maxim: “A
- black hole has no hair.” The “no hair” theorem is of great practical importance, because it so greatly restricts the
- possible types of black holes. One can therefore make detailed models of objects that might contain black holes and
- compare the predictions of the models with observations. It also means that a very large amount of information about
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (5 of 9) [2/20/2001 3:15:08 AM]
- the body that has collapsed must be lost when a black hole is formed, because afterward all we can possibly measure
- about the body is its mass and rate of rotation. The significance of this will be seen in the next chapter.
- Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in
- great detail as a mathematical model before there was any evidence from observations that it was correct. Indeed, this
- used to be the main argument of opponents of black holes: how could one believe in objects for which the only
- evidence was calculations based on the dubious theory of general relativity? In 1963, however, Maarten Schmidt, an
- astronomer at the Palomar Observatory in California, measured the red shift of a faint starlike object in the direction of
- the source of radio waves called 3C273 (that is, source number 273 in the third Cambridge catalogue of radio sources).
- He found it was too large to be caused by a gravitational field: if it had been a gravitational red shift, the object would
- have to be so massive and so near to us that it would disturb the orbits of planets in the Solar System. This suggested
- that the red shift was instead caused by the expansion of the universe, which, in turn, meant that the object was a very
- long distance away. And to be visible at such a great distance, the object must be very bright, must, in other words, be
- emitting a huge amount of energy. The only mechanism that people could think of that would produce such large
- quantities of energy seemed to be the gravitational collapse not just of a star but of a whole central region of a galaxy. A
- number of other similar “quasi-stellar objects,” or quasars, have been discovered, all with large red shifts. But they are
- all too far away and therefore too difficult to observe to provide conclusive evidence of black holes.
- Further encouragement for the existence of black holes came in 1967 with the discovery by a research student at
- Cambridge, Jocelyn Bell-Burnell, of objects in the sky that were emitting regular pulses of radio waves. At first Bell and
- her supervisor, Antony Hewish, thought they might have made contact with an alien civilization in the galaxy! Indeed, at
- the seminar at which they announced their discovery, I remember that they called the first four sources to be found
- LGM 1 – 4, LGM standing for “Little Green Men.” In the end, however, they and everyone else came to the less
- romantic conclusion that these objects, which were given the name pulsars, were in fact rotating neutron stars that were
- emitting pulses of radio waves because of a complicated interaction between their magnetic fields and surrounding
- matter. This was bad news for writers of space westerns, but very hopeful for the small number of us who believed in
- black holes at that time: it was the first positive evidence that neutron stars existed. A neutron star has a radius of about
- ten miles, only a few times the critical radius at which a star becomes a black hole. If a star could collapse to such a
- small size, it is not unreasonable to expect that other stars could collapse to even smaller size and become black holes.
- How could we hope to detect a black hole, as by its very definition it does not emit any light? It might seem a bit like
- looking for a black cat in a coal cellar. Fortunately, there is a way. As John Michell pointed out in his pioneering paper in
- 1783, a black hole still exerts a gravitational fierce on nearby objects. Astronomers have observed many systems in
- which two stars orbit around each other, attracted toward each other by gravity. They also observe systems in which
- there is only one visible star that is orbiting around some unseen companion. One cannot, of course, immediately
- conclude that the companion is a black hole: it might merely be a star that is too faint to be seen. However, some of
- these systems, like the one called Cygnus X-1 Figure 6:2, are also strong sources of X-rays.
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (6 of 9) [2/20/2001 3:15:08 AM]
- Figure 6:2
- The best explanation for this phenomenon is that matter has been blown off the surface of the visible star. As it falls
- toward the unseen companion, it develops a spiral motion (rather like water running out of a bath), and it gets very hot,
- emitting X-rays Figure 6:3.
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (7 of 9) [2/20/2001 3:15:08 AM]
- Figure 6:3
- For this mechanism to work, the unseen object has to be very small, like a white dwarf, neutron star, or black hole.
- From the observed orbit of the visible star, one can determine the lowest possible mass of the unseen object. In the
- case of Cygnus X-l, this is about six times the mass of the sun, which, according to Chandrasekhar’r result, is too great
- for the unseen object to be a white dwarf. It is also too large a mass to be a neutron star. It seems, therefore, that it
- must be a black hole.
- There are other models to explain Cygnus X-1 that do not include a black hole, but they are all rather far-fetched. A
- black hole seems to be the only really natural explanation of the observations. Despite this, I had a bet with Kip Thorne
- of the California Institute of Technology that in fact Cygnus X-1 does not contain a black hole! This was a form f
- insurance policy for me. I have done a lot of work on black holes, and it would all be wasted if it turned out that black
- holes do not exist. But in that case, I would have the consolation of winning my bet, which would bring me four years of
- the magazine Private Eye. In fact, although the situation with Cygnus X-1 has not changed much since we made the bet
- in 1975, there is now so much other observational evidence in favor of black holes that I have conceded the bet. I paid
- the specified penalty, which was a one-year subscription to Penthouse, to the outrage of Kip’s liberated wife.
- We also now have evidence for several other black holes in systems like Cygnus X-1 in our galaxy and in two
- neighboring galaxies called the Magellanic Clouds. The number of black holes, however, is almost certainly very much
- higher; in the long history of the universe, many stars must have burned all their nuclear fuel and have had to collapse.
- The number of black holes may well be greater even than the number of visible stars, which totals about a hundred
- thousand million in our galaxy alone. The extra gravitational attraction of such a large number of black holes could
- explain why our galaxy rotates at the rate it does: the mass of the visible stars is insufficient to account for this. We also
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (8 of 9) [2/20/2001 3:15:08 AM]
- have some evidence that there is a much larger black hole, with a mass of about a hundred thousand times that of the
- sun, at the center of our galaxy. Stars in the galaxy that come too near this black hole will be torn apart by the
- difference in the gravitational forces on their near and far sides. Their remains and gas that is thrown off other stars, will
- fall toward the black hole. As in the case of Cygnus X-l, the gas will spiral inward and will heat up, though not as much
- as in that case. It will not get hot enough to emit X rays, but it could account for the very compact source of radio waves
- and infrared rays that is observed at the galactic center.
- It is thought that similar but even larger black holes, with masses of about a hundred million times the mass of the sun,
- occur at the centers of quasars. For example, observations with the Hubble telescope of the galaxy known as M87
- reveal that it contains a disk of gas 130 light-years across rotating about a central object two thousand million times the
- mass of the sun. This can only be a black hole. Matter falling into such a supermassive black hole would provide the
- only source of power great enough to explain the enormous amounts of energy that these objects are emitting. As the
- matter spirals into the black hole, it would make the black hole rotate in the same direction, causing it to develop a
- magnetic field rather like that of the earth. Very high-energy particles would be generated near the black hole by the
- in-falling matter. The magnetic field would be so strong that it could focus these particles into jets ejected outward along
- the axis of rotation of the black hole, that is, in the directions of its north and south poles. Such jets are indeed observed
- in a number of galaxies and quasars. One can also consider the possibility that there might be black holes with masses
- much less than that of the sun. Such black holes could not be formed by gravitational collapse, because their masses
- are below the Chandrasekhar mass limit: stars of this low mass can support themselves against the force of gravity
- even when they have exhausted their nuclear fuel. Low-mass black holes could form only if matter was compressed to
- enormous densities by very large external pressures. Such conditions could occur in a very big hydrogen bomb: the
- physicist John Wheeler once calculated that if one took all the heavy water in all the oceans of the world, one could
- build a hydrogen bomb that would compress matter at the center so much that a black hole would be created. (Of
- course, there would be no one left to observe it!) A more practical possibility is that such low-mass black holes might
- have been formed in the high temperatures and pressures of the very early universe. Black holes would have been
- formed only if the early universe had not been perfectly smooth and uniform, because only a small region that was
- denser than average could be compressed in this way to form a black hole. But we know that there must have been
- some irregularities, because otherwise the matter in the universe would still be perfectly uniformly distributed at the
- present epoch, instead of being clumped together in stars and galaxies.
- Whether the irregularities required to account for stars and galaxies would have led to the formation of a significant
- number of “primordial” black holes clearly depends on the details of the conditions in the early universe. So if we could
- determine how many primordial black holes there are now, we would learn a lot about the very early stages of the
- universe. Primordial black holes with masses more than a thousand million tons (the mass of a large mountain) could
- be detected only by their gravitational influence on other, visible matter or on the expansion of the universe. However,
- as we shall learn in the next chapter, black holes are not really black after all: they glow like a hot body, and the smaller
- they are, the more they glow. So, paradoxically, smaller black holes might actually turn out to be easier to detect than
- large ones!
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 6
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (9 of 9) [2/20/2001 3:15:08 AM]
- CHAPTER 7
- BLACK HOLES AIN’T SO BLACK
- Before 1970, my research on general relativity had concentrated mainly on the question of whether or not there had
- been a big bang singularity. However, one evening in November that year, shortly after the birth of my daughter, Lucy,
- I started to think about black holes as I was getting into bed. My disability makes this rather a slow process, so I had
- plenty of time. At that date there was no precise definition of which points in space-time lay inside a black hole and
- which lay outside. I had already discussed with Roger Penrose the idea of defining a black hole as the set of events
- from which it was not possible to escape to a large distance, which is now the generally accepted definition. It means
- that the boundary of the black hole, the event horizon, is formed by the light rays that just fail to escape from the black
- hole, hovering forever just on the edge Figure 7:1. It is a bit like running away from the police and just managing to
- keep one step ahead but not being able to get clear away!
- Figure 7:1
- Suddenly I realized that the paths of these light rays could never approach one another. If they did they must
- eventually run into one another. It would be like meeting someone else running away from the police in the opposite
- direction – you would both be caught! (Or, in this case, fall into a black hole.) But if these light rays were swallowed up
- by the black hole, then they could not have been on the boundary of the black hole. So the paths of light rays in the
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (1 of 8) [2/20/2001 3:15:18 AM]
- event horizon had always to be moving parallel to, or away from, each other. Another way of seeing this is that the
- event horizon, the boundary of the black hole, is like the edge of a shadow – the shadow of impending doom. If you
- look at the shadow cast by a source at a great distance, such as the sun, you will see that the rays of light in the edge
- are not approaching each other.
- If the rays of light that form the event horizon, the boundary of the black hole, can never approach each other, the area
- of the event horizon might stay the same or increase with time, but it could never decrease because that would mean
- that at least some of the rays of light in the boundary would have to be approaching each other. In fact, the area would
- increase whenever matter or radiation fell into the black hole Figure 7:2.
- Figures 7:2 & 7:3
- Or if two black holes collided and merged together to form a single black hole, the area of the event horizon of the final
- black hole would be greater than or equal to the sum of the areas of the event horizons of the original black holes
- Figure 7:3. This nondecreasing property of the event horizon’s area placed an important restriction on the possible
- behavior of black holes. I was so excited with my discovery that I did not get much sleep that night. The next day I rang
- up Roger Penrose. He agreed with me. I think, in fact, that he had been aware of this property of the area. However,
- he had been using a slightly different definition of a black hole. He had not realized that the boundaries of the black
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (2 of 8) [2/20/2001 3:15:18 AM]
- hole according to the two definitions would be the same, and hence so would their areas, provided the black hole had
- settled down to a state in which it was not changing with time.
- The nondecreasing behavior of a black hole’s area was very reminiscent of the behavior of a physical quantity called
- entropy, which measures the degree of disorder of a system. It is a matter of common experience that disorder will
- tend to increase if things are left to themselves. (One has only to stop making repairs around the house to see that!)
- One can create order out of disorder (for example, one can paint the house), but that requires expenditure of effort or
- energy and so decreases the amount of ordered energy available.
- A precise statement of this idea is known as the second law of thermodynamics. It states that the entropy of an isolated
- system always increases, and that when two systems are joined together, the entropy of the combined system is
- greater than the sum of the entropies of the individual systems. For example, consider a system of gas molecules in a
- box. The molecules can be thought of as little billiard balls continually colliding with each other and bouncing off the
- walls of the box. The higher the temperature of the gas, the faster the molecules move, and so the more frequently and
- harder they collide with the walls of the box and the greater the outward pressure they exert on the walls. Suppose that
- initially the molecules are all confined to the left-hand side of the box by a partition. If the partition is then removed, the
- molecules will tend to spread out and occupy both halves of the box. At some later time they could, by chance, all be in
- the right half or back in the left half, but it is overwhelmingly more probable that there will be roughly equal numbers in
- the two halves. Such a state is less ordered, or more disordered, than the original state in which all the molecules were
- in one half. One therefore says that the entropy of the gas has gone up. Similarly, suppose one starts with two boxes,
- one containing oxygen molecules and the other containing nitrogen molecules. If one joins the boxes together and
- removes the intervening wall, the oxygen and the nitrogen molecules will start to mix. At a later time the most probable
- state would be a fairly uniform mixture of oxygen and nitrogen molecules throughout the two boxes. This state would
- be less ordered, and hence have more entropy, than the initial state of two separate boxes.
- The second law of thermodynamics has a rather different status than that of other laws of science, such as Newton's
- law of gravity, for example, because it does not hold always, just in the vast majority of cases. The probability of all the
- gas molecules in our first box
- found in one half of the box at a later time is many millions of millions to one, but it can happen. However, if one has a
- black hole around there seems to be a rather easier way of violating the second law: just throw some matter with a lot
- of entropy such as a box of gas, down the black hole. The total entropy of matter outside the black hole would go
- down. One could, of course, still say that the total entropy, including the entropy inside the black hole, has not gone
- down - but since there is no way to look inside the black hole, we cannot see how much entropy the matter inside it
- has. It would be nice, then, if there was some feature of the black hole by which observers outside the black hole could
- tell its entropy, and which would increase whenever matter carrying entropy fell into the black hole. Following the
- discovery, described above, that the area of the event horizon increased whenever matter fell into a black hole, a
- research student at Princeton named Jacob Bekenstein suggested that the area of the event horizon was a measure of
- the entropy of the black hole. As matter carrying entropy fell into a black hole, the area of its event horizon would go
- up, so that the sum of the entropy of matter outside black holes and the area of the horizons would never go down.
- This suggestion seemed to prevent the second law of thermodynamics from being violated in most situations.
- However, there was one fatal flaw. If a black hole has entropy, then it ought to also have a temperature. But a body
- with a particular temperature must emit radiation at a certain rate. It is a matter of common experience that if one heats
- up a poker in a fire it glows red hot and emits radiation, but bodies at lower temperatures emit radiation too; one just
- does not normally notice it because the amount is fairly small. This radiation is required in order to prevent violation of
- the second law. So black holes ought to emit radiation. But by their very definition, black holes are objects that are not
- supposed to emit anything. It therefore seemed that the area of the event horizon of a black hole could not be regarded
- as its entropy. In 1972 I wrote a paper with Brandon Carter and an American colleague, Jim Bardeen, in which we
- pointed out that although there were many similarities between entropy and the area of the event horizon, there was
- this apparently fatal difficulty. I must admit that in writing this paper I was motivated partly by irritation with Bekenstein,
- who, I felt, had misused my discovery of the increase of the area of the event horizon. However, it turned out in the end
- that he was basically correct, though in a manner he had certainly not expected.
- In September 1973, while I was visiting Moscow, I discussed black holes with two leading Soviet experts, Yakov
- Zeldovich and Alexander Starobinsky. They convinced me that, according to the quantum mechanical uncertainty
- principle, rotating black holes should create and emit particles. I believed their arguments on physical grounds, but I did
- not like the mathematical way in which they calculated the emission. I therefore set about devising a better
- mathematical treatment, which I described at an informal seminar in Oxford at the end of November 1973. At that time I
- had not done the calculations to find out how much would actually be emitted. I was expecting to discover just the
- radiation that Zeldovich and Starobinsky had predicted from rotating black holes. However, when I did the calculation, I
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (3 of 8) [2/20/2001 3:15:18 AM]
- found, to my surprise and annoyance, that even non-rotating black holes should apparently create and emit particles at
- a steady rate. At first I thought that this emission indicated that one of the approximations I had used was not valid. I
- was afraid that if Bekenstein found out about it, he would use it as a further argument to support his ideas about the
- entropy of black holes, which I still did not like. However, the more I thought about it, the more it seemed that the
- approximations really ought to hold. But what finally convinced me that the emission was real was that the spectrum of
- the emitted particles was exactly that which would be emitted by a hot body, and that the black hole was emitting
- particles at exactly the correct rate to prevent violations of the second law. Since then the calculations have been
- repeated in a number of different forms by other people. They all confirm that a black hole ought to emit particles and
- radiation as if it were a hot body with a temperature that depends only on the black hole’s mass: the higher the mass,
- the lower the temperature.
- How is it possible that a black hole appears to emit particles when we know that nothing can escape from within its
- event horizon? The answer, quantum theory tells us, is that the particles do not come from within the black hole, but
- from the “empty” space just outside the black hole’s event horizon! We can understand this in the following way: what
- we think of as “empty” space cannot be completely empty because that would mean that all the fields, such as the
- gravitational and electromagnetic fields, would have to be exactly zero. However, the value of a field and its rate of
- change with time are like the position and velocity of a particle: the uncertainty principle implies that the more
- accurately one knows one of these quantities, the less accurately one can know the other. So in empty space the field
- cannot be fixed at exactly zero, because then it would have both a precise value (zero) and a precise rate of change
- (also zero). There must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field.
- One can think of these fluctuations as pairs of particles of light or gravity that appear together at some time, move
- apart, and then come together again and annihilate each other. These particles are virtual particles like the particles
- that carry the gravitational force of the sun: unlike real particles, they cannot be observed directly with a particle
- detector. However, their indirect effects, such as small changes in the energy of electron orbits in atoms, can be
- measured and agree with the theoretical predictions to a remarkable degree of accuracy. The uncertainty principle also
- predicts that there will be similar virtual pairs of matter particles, such as electrons or quarks. In this case, however,
- one member of the pair will be a particle and the other an antiparticle (the antiparticles of light and gravity are the same
- as the particles).
- Because energy cannot be created out of nothing, one of the partners in a particle/antiparticle pair will have positive
- energy, and the other partner negative energy. The one with negative energy is condemned to be a short-lived virtual
- particle because real particles always have positive energy in normal situations. It must therefore seek out its partner
- and annihilate with it. However, a real particle close to a massive body has less energy than if it were far away,
- because it would take energy to lift it far away against the gravitational attraction of the body. Normally, the energy of
- the particle is still positive, but the gravitational field inside a black hole is so strong that even a real particle can have
- negative energy there. It is therefore possible, if a black hole is present, for the virtual particle with negative energy to
- fall into the black hole and become a real particle or antiparticle. In this case it no longer has to annihilate with its
- partner. Its forsaken partner may fall into the black hole as well. Or, having positive energy, it might also escape from
- the vicinity of the black hole as a real particle or antiparticle Figure 7:4.
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (4 of 8) [2/20/2001 3:15:18 AM]
- Figure 7:4
- To an observer at a distance, it will appear to have been emitted from the black hole. The smaller the black hole, the
- shorter the distance the particle with negative energy will have to go before it becomes a real particle, and thus the
- greater the rate of emission, and the apparent temperature, of the black hole.
- The positive energy of the outgoing radiation would be balanced by a flow of negative energy particles into the black
- hole. By Einstein’s equation E = mc2 (where E is energy, m is mass, and c is the speed of light), energy is proportional
- to mass. A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the
- area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for
- by the entropy of the emitted radiation, so the second law is never violated.
- Moreover, the lower the mass of the black hole, the higher its temperature. So as the black hole loses mass, its
- temperature and rate of emission increase, so it loses mass more quickly. What happens when the mass of the black
- hole eventually becomes extremely small is not quite clear, but the most reasonable guess is that it would disappear
- completely in a tremendous final burst of emission, equivalent to the explosion of millions of H-bombs.
- A black hole with a mass a few times that of the sun would have a temperature of only one ten millionth of a degree
- above absolute zero. This is much less than the temperature of the microwave radiation that fills the universe (about
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (5 of 8) [2/20/2001 3:15:18 AM]
- 2.7º above absolute zero), so such black holes would emit even less than they absorb. If the universe is destined to go
- on expanding forever, the temperature of the microwave radiation will eventually decrease to less than that of such a
- black hole, which will then begin to lose mass. But, even then, its temperature would be so low that it would take about
- a million million million million million million million million million million million years (1 with sixty-six zeros after it) to
- evaporate completely. This is much longer than the age of the universe, which is only about ten or twenty thousand
- million years (1 or 2 with ten zeros after it). On the other hand, as mentioned in Chapter 6, there might be primordial
- black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of
- the universe. Such black holes would have a much higher temperature and would be emitting radiation at a much
- greater rate. A primordial black hole with an initial mass of a thousand million tons would have a lifetime roughly equal
- to the age of the universe. Primordial black holes with initial masses less than this figure would already have
- completely evaporated, but those with slightly greater masses would still be emitting radiation in the form of X rays and
- gamma rays. These X rays and gamma rays are like waves of light, but with a much shorter wavelength. Such holes
- hardly deserve the epithet black: they really are white hot and are emitting energy at a rate of about ten thousand
- megawatts.
- One such black hole could run ten large power stations, if only we could harness its power. This would be rather
- difficult, however: the black hole would have the mass of a mountain compressed into less than a million millionth of an
- inch, the size of the nucleus of an atom! If you had one of these black holes on the surface of the earth, there would be
- no way to stop it from falling through the floor to the center of the earth. It would oscillate through the earth and back,
- until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the
- energy that it emitted, would be in orbit around the earth – and the only way that one could get it to orbit the earth
- would be to attract it there by towing a large mass in front of it, rather like a carrot in front of a donkey. This does not
- sound like a very practical proposition, at least not in the immediate future.
- But even if we cannot harness the emission from these primordial black holes, what are our chances of observing
- them? We could look for the gamma rays that the primordial black holes emit during most of their lifetime. Although the
- radiation from most would be very weak because they are far away, the total from all of them might be detectable. We
- do observe such a background of gamma rays: Figure 7:5 shows how the observed intensity differs at different
- frequencies (the number of waves per second). However, this background could have been, and probably was,
- generated by processes other than primordial black holes. The dotted line in Figure 7:5 shows how the intensity should
- vary with frequency for gamma rays given off by primordial black holes, if there were on average 300 per cubic
- light-year. One can therefore say that the observations of the gamma ray background do not provide any positive
- evidence for primordial black holes, but they do tell us that on average there cannot be more than 300 in every cubic
- light-year in the universe. This limit means that primordial black holes could make up at most one millionth of the
- matter in the universe.
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (6 of 8) [2/20/2001 3:15:18 AM]
- Figure 7:5
- With primordial black holes being so scarce, it might seem unlikely that there would be one near enough for us to
- observe as an individual source of gamma rays. But since gravity would draw primordial black holes toward any matter,
- they should be much more common in and around galaxies. So although the gamma ray background tells us that there
- can be no more than 300 primordial black holes per cubic light-year on average, it tells us nothing about how common
- they might be in our own galaxy. If they were, say, a million times more common than this, then the nearest black hole
- to us would probably be at a distance of about a thousand million kilometers, or about as far away as Pluto, the farthest
- known planet. At this distance it would still be very difficult to detect the steady emission of a black hole, even if it was
- ten thousand megawatts. In order to observe a primordial black hole one would have to detect several gamma ray
- quanta coming from the same direction within a reasonable space of time, such as a week. Otherwise, they might
- simply be part of the background. But Planck’s quantum principle tells us that each gamma ray quantum has a very
- high energy, because gamma rays have a very high frequency, so it would not take many quanta to radiate even ten
- thousand megawatts. And to observe these few coming from the distance of Pluto would require a larger gamma ray
- detector than any that have been constructed so far. Moreover, the detector would have to be in space, because
- gamma rays cannot penetrate the atmosphere.
- Of course, if a black hole as close as Pluto were to reach the end of its life and blow up, it would be easy to detect the
- final burst of emission. But if the black hole has been emitting for the last ten or twenty thousand million years, the
- chance of it reaching the end of its life within the next few years, rather than several million years in the past or future,
- is really rather small! So in order to have a reasonable chance of seeing an explosion before your research grant ran
- out, you would have to find a way to detect any explosions within a distance of about one light-year. In fact bursts of
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (7 of 8) [2/20/2001 3:15:18 AM]
- gamma rays from space have been detected by satellites originally constructed to look for violations of the Test Ban
- Treaty. These seem to occur about sixteen times a month and to be roughly uniformly distributed in direction across
- the sky. This indicates that they come from outside the Solar System since otherwise we would expect them to be
- concentrated toward the plane of the orbits of the planets. The uniform distribution also indicates that the sources are
- either fairly near to us in our galaxy or right outside it at cosmological distances because otherwise, again, they would
- be concentrated toward the plane of the galaxy. In the latter case, the energy required to account for the bursts would
- be far too high to have been produced by tiny black holes, but if the sources were close in galactic terms, it might be
- possible that they were exploding black holes. I would very much like this to be the case but I have to recognize that
- there are other possible explanations for the gamma ray bursts, such as colliding neutron stars. New observations in
- the next few years, particularly by gravitational wave detectors like LIGO, should enable us to discover the origin of the
- gamma ray bursts.
- Even if the search for primordial black holes proves negative, as it seems it may, it will still give us important
- information about the very early stages of the universe. If the early universe had been chaotic or irregular, or if the
- pressure of matter had been low, one would have expected it to produce many more primordial black holes than the
- limit already set by our observations of the gamma ray background. Only if the early universe was very smooth and
- uniform, with a high pressure, can one explain the absence of observable numbers of primordial black holes.
- The idea of radiation from black holes was the first example of a prediction that depended in an essential way on both
- the great theories of this century, general relativity and quantum mechanics. It aroused a lot of opposition initially
- because it upset the existing viewpoint: “How can a black hole emit anything?” When I first announced the results of
- my calculations at a conference at the Rutherford-Appleton Laboratory near Oxford, I was greeted with general
- incredulity. At the end of my talk the chairman of the session, John G. Taylor from Kings College, London, claimed it
- was all nonsense. He even wrote a paper to that effect. However, in the end most people, including John Taylor, have
- come to the conclusion that black holes must radiate like hot bodies if our other ideas about general relativity and
- quantum mechanics are correct. Thus, even though we have not yet managed to find a primordial black hole, there is
- fairly general agreement that if we did, it would have to be emitting a lot of gamma rays and X rays.
- The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as
- we once thought. If an astronaut falls into a black hole, its mass will increase, but eventually the energy equivalent of
- that extra mass will be returned to the universe in the form of radiation. Thus, in a sense, the astronaut will be
- “recycled.” It would be a poor sort of immortality, however, because any personal concept of time for the astronaut
- would almost certainly come to an end as he was torn apart inside the black hole! Even the types of particles that were
- eventually emitted by the black hole would in general be different from those that made up the astronaut: the only
- feature of the astronaut that would survive would be his mass or energy.
- The approximations I used to derive the emission from black holes should work well when the black hole has a mass
- greater than a fraction of a gram. However, they will break down at the end of the black hole’s life when its mass gets
- very small. The most likely outcome seems to be that the black hole will just disappear, at least from our region of the
- universe, taking with it the astronaut and any singularity there might be inside it, if indeed there is one. This was the
- first indication that quantum mechanics might remove the singularities that were predicted by general relativity.
- However, the methods that I and other people were using in 1974 were not able to answer questions such as whether
- singularities would occur in quantum gravity. From 1975 onward I therefore started to develop a more powerful
- approach to quantum gravity based on Richard Feynrnan’s idea of a sum over histories. The answers that this
- approach suggests for the origin and fate of the universe and its contents, such as astronauts, will be de-scribed in the
- next two chapters. We shall see that although the uncertainty principle places limitations on the accuracy of all our
- predictions, it may at the same time remove the fundamental unpredictability that occurs at a space-time singularity.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 7
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/f.html (8 of 8) [2/20/2001 3:15:18 AM]
- CHAPTER 8
- THE ORIGIN AND FATE OF THE UNIVERSE
- Einstein’s general theory of relativity, on its own, predicted that space-time began at the big bang singularity and
- would come to an end either at the big crunch singularity (if the whole universe recollapsed), or at a singularity inside
- a black hole (if a local region, such as a star, were to collapse). Any matter that fell into the hole would be destroyed
- at the singularity, and only the gravitational effect of its mass would continue to be felt outside. On the other hand,
- when quantum effects were taken into account, it seemed that the mass or energy of the matter would eventually be
- returned to the rest of the universe, and that the black hole, along with any singularity inside it, would evaporate
- away and finally disappear. Could quantum mechanics have an equally dramatic effect on the big bang and big
- crunch singularities? What really happens during the very early or late stages of the universe, when gravitational
- fields are so strong that quantum effects cannot be ignored? Does the universe in fact have a beginning or an end?
- And if so, what are they like?
- Throughout the 1970s I had been mainly studying black holes, but in 1981 my interest in questions about the origin
- and fate of the universe was reawakened when I attended a conference on cosmology organized by the Jesuits in
- the Vatican. The Catholic Church had made a bad mistake with Galileo when it tried to lay down the law on a
- question of science, declaring that the sun went round the earth. Now, centuries later, it had decided to invite a
- number of experts to advise it on cosmology. At the end of the conference the participants were granted an audience
- with the Pope. He told us that it was all right to study the evolution of the universe after the big bang, but we should
- not inquire into the big bang itself because that was the moment of Creation and therefore the work of God. I was
- glad then that he did not know the subject of the talk I had just given at the conference – the possibility that
- space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation. I had no
- desire to share the fate of Galileo, with whom I feel a strong sense of identity, partly because of the coincidence of
- having been born exactly 300 years after his death!
- In order to explain the ideas that I and other people have had about how quantum mechanics may affect the origin
- and fate of the universe, it is necessary first to understand the generally accepted history of the universe, according
- to what is known as the “hot big bang model.” This assumes that the universe is described by a Friedmann model,
- right back to the big bang. In such models one finds that as the universe expands, any matter or radiation in it gets
- cooler. (When the universe doubles in size, its temperature falls by half.) Since temperature is simply a measure of
- the average energy – or speed – of the particles, this cooling of the universe would have a major effect on the matter
- in it. At very high temperatures, particles would be moving around so fast that they could escape any attraction
- toward each other due to nuclear or electromagnetic forces, but as they cooled off one would expect particles that
- attract each other to start to clump together. Moreover, even the types of particles that exist in the universe would
- depend on the temperature. At high enough temperatures, particles have so much energy that whenever they collide
- many different particle/antiparticle pairs would be produced – and although some of these particles would annihilate
- on hitting antiparticles, they would be produced more rap-idly than they could annihilate. At lower temperatures,
- however, when colliding particles have less energy, particle/antiparticle pairs would be produced less quickly – and
- annihilation would become faster than production.
- At the big bang itself the universe is thought to have had zero size, and so to have been infinitely hot. But as the
- universe expanded, the temperature of the radiation decreased. One second after the big bang, it would have fallen
- to about ten thousand million degrees. This is about a thousand times the temperature at the center of the sun, but
- temperatures as high as this are reached in H-bomb explosions. At this time the universe would have contained
- mostly photons, electrons, and neutrinos (extremely light particles that are affected only by the weak force and
- gravity) and their antiparticles, together with some protons and neutrons. As the universe continued to expand and
- the temperature to drop, the rate at which electron/antielectron pairs were being produced in collisions would have
- fallen below the rate at which they were being destroyed by annihilation. So most of the electrons and antielectrons
- would have annihilated with each other to produce more photons, leaving only a few electrons left over. The
- neutrinos and antineutrinos, however, would not have annihilated with each other, because these particles interact
- with themselves and with other particles only very weakly. So they should still be around today. If we could observe
- them, it would provide a good test of this picture of a very hot early stage of the universe. Unfortunately, their
- energies nowadays would be too low for us to observe them directly. However, if neutrinos are not massless, but
- have a small mass of their own, as suggested by some recent experiments, we might be able to detect them
- indirectly: they could be a form of “dark matter,” like that mentioned earlier, with sufficient gravitational attraction to
- stop the expansion of the universe and cause it to collapse again.
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (1 of 11) [2/20/2001 3:15:29 AM]
- About one hundred seconds after the big bang, the temperature would have fallen to one thousand million degrees,
- the temperature inside the hottest stars. At this temperature protons and neutrons would no longer have sufficient
- energy to escape the attraction of the strong nuclear force, and would have started to combine together to produce
- the nuclei of atoms of deuterium (heavy hydrogen), which contain one proton and one neutron. The deuterium nuclei
- would then have combined with more protons and neutrons to make helium nuclei, which contain two protons and
- two neutrons, and also small amounts of a couple of heavier elements, lithium and beryllium. One can calculate that
- in the hot big bang model about a quarter of the protons and neutrons would have been converted into helium nuclei,
- along with a small amount of heavy hydrogen and other elements. The remaining neutrons would have decayed into
- protons, which are the nuclei of ordinary hydrogen atoms.
- This picture of a hot early stage of the universe was first put forward by the scientist George Gamow in a famous
- paper written in 1948 with a student of his, Ralph Alpher. Gamow had quite a sense of humor – he persuaded the
- nuclear scientist Hans Bethe to add his name to the paper to make the list of authors “Alpher, Bethe, Gamow,” like
- the first three letters of the Greek alphabet, alpha, beta, gamma: particularly appropriate for a paper on the beginning
- of the universe! In this paper they made the remarkable prediction that radiation (in the form of photons) from the
- very hot early stages of the universe should still be around today, but with its temperature reduced to only a few
- degrees above absolute zero (–273ºC). It was this radiation that Penzias and Wilson found in 1965. At the time that
- Alpher, Bethe, and Gamow wrote their paper, not much was known about the nuclear reactions of protons and
- neutrons. Predictions made for the proportions of various elements in the early universe were therefore rather
- inaccurate, but these calculations have been repeated in the light of better knowledge and now agree very well with
- what we observe. It is, moreover, very difficult to explain in any other way why there should be so much helium in the
- universe. We are therefore fairly confident that we have the right picture, at least back to about one second after the
- big bang.
- Within only a few hours of the big bang, the production of helium and other elements would have stopped. And after
- that, for the next million years or so, the universe would have just continued expanding, without anything much
- happening. Eventually, once the temperature had dropped to a few thousand degrees, and electrons and nuclei no
- longer had enough energy to overcome the electromagnetic attraction between them, they would have started
- combining to form atoms. The universe as a whole would have continued expanding and cooling, but in regions that
- were slightly denser than average, the expansion would have been slowed down by the extra gravitational attraction.
- This would eventually stop expansion in some regions and cause them to start to recollapse. As they were
- collapsing, the gravitational pull of matter outside these regions might start them rotating slightly. As the collapsing
- region got smaller, it would spin faster – just as skaters spinning on ice spin faster as they draw in their arms.
- Eventually, when the region got small enough, it would be spinning fast enough to balance the attraction of gravity,
- and in this way disklike rotating galaxies were born. Other regions, which did not happen to pick up a rotation, would
- become oval-shaped objects called elliptical galaxies. In these, the region would stop collapsing because individual
- parts of the galaxy would be orbiting stably round its center, but the galaxy would have no overall rotation.
- As time went on, the hydrogen and helium gas in the galaxies would break up into smaller clouds that would collapse
- under their own gravity. As these contracted, and the atoms within them collided with one another, the temperature
- of the gas would increase, until eventually it became hot enough to start nuclear fusion reactions. These would
- convert the hydrogen into more helium, and the heat given off would raise the pressure, and so stop the clouds from
- contracting any further. They would remain stable in this state for a long time as stars like our sun, burning hydrogen
- into helium and radiating the resulting energy as heat and light. More massive stars would need to be hotter to
- balance their stronger gravitational attraction, making the nuclear fusion reactions proceed so much more rapidly that
- they would use up their hydrogen in as little as a hundred million years. They would then contract slightly, and as
- they heated up further, would start to convert helium into heavier elements like carbon or oxygen. This, however,
- would not release much more energy, so a crisis would occur, as was described in the chapter on black holes. What
- happens next is not completely clear, but it seems likely that the central regions of the star would collapse to a very
- dense state, such as a neutron star or black hole. The outer regions of the star may sometimes get blown off in a
- tremendous explosion called a supernova, which would outshine all the other stars in its galaxy. Some of the heavier
- elements produced near the end of the star’s life would be flung back into the gas in the galaxy, and would provide
- some of the raw material for the next generation of stars. Our own sun contains about 2 percent of these heavier
- elements, because it is a second- or third-generation star, formed some five thousand million years ago out of a
- cloud of rotating gas containing the debris of earlier supernovas. Most of the gas in that cloud went to form the sun or
- got blown away, but a small amount of the heavier elements collected together to form the bodies that now orbit the
- sun as planets like the earth.
- The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (2 of 11) [2/20/2001 3:15:29 AM]
- atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have
- survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide (the gas
- that gives rotten eggs their smell). There are, however, other primitive forms of life that can flourish under such
- conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into
- large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar
- structures. They would thus have reproduced themselves and multiplied. In some cases there would be errors in the
- reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and
- eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that
- were even better at reproducing themselves. They would have therefore had an advantage and would have tended
- to replace the original macromolecules. In this way a process of evolution was started that led to the development of
- more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials,
- including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it
- has today, and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the
- human race.
- This picture of a universe that started off very hot and cooled as it expanded is in agreement with all the
- observational evidence that we have today. Nevertheless, it leaves a number of important questions unanswered:
- 1. Why was the early universe so hot?
- 2. Why is the universe so uniform on a large scale? Why does it look the same at all points of space and in all
- directions? In particular, why is the temperature of the microwave back-ground radiation so nearly the same when we
- look in different directions? It is a bit like asking a number of students an exam question. If they all give exactly the
- same answer, you can be pretty sure they have communicated with each other. Yet, in the model described above,
- there would not have been time since the big bang for light to get from one distant region to another, even though the
- regions were close together in the early universe. According to the theory of relativity, if light cannot get from one
- region to another, no other information can. So there would be no way in which different regions in the early universe
- could have come to have the same temperature as each other, unless for some unexplained reason they happened
- to start out with the same temperature.
- 3. Why did the universe start out with so nearly the critical rate of expansion that separates models that recollapse
- from those that go on expanding forever, that even now, ten thousand million years later, it is still expanding at nearly
- the critical rate? If the rate of expansion one second after the big bang had been smaller by even one part in a
- hundred thousand million million, the universe would have recollapsed before it ever reached its present size.
- 4. Despite the fact that the universe is so uniform and homogeneous on a large scale, it contains local irregularities,
- such as stars and galaxies. These are thought to have developed from small differences in the density of the early
- universe from one region to another. What was the origin of these density fluctuations?
- The general theory of relativity, on its own, cannot explain these features or answer these questions because of its
- prediction that the universe started off with infinite density at the big bang singularity. At the singularity, general
- relativity and all other physical laws would break down: one couldn’t predict what would come out of the singularity.
- As explained before, this means that one might as well cut the big bang, and any events before it, out of the theory,
- because they can have no effect on what we observe. Space-time would have a boundary – a beginning at the big
- bang.
- Science seems to have uncovered a set of laws that, within the limits set by the uncertainty principle, tell us how the
- universe will develop with time, if we know its state at any one time. These laws may have originally been decreed by
- God, but it appears that he has since left the universe to evolve according to them and does not now intervene in it.
- But how did he choose the initial state or configuration of the universe? What were the “boundary conditions” at the
- beginning of time?
- One possible answer is to say that God chose the initial configuration of the universe for reasons that we cannot
- hope to understand. This would certainly have been within the power of an omnipotent being, but if he had started it
- off in such an incomprehensible way, why did he choose to let it evolve according to laws that we could understand?
- The whole history of science has been the gradual realization that events do not happen in an arbitrary manner, but
- that they reflect a certain underlying order, which may or may not be divinely inspired. It would be only natural to
- suppose that this order should apply not only to the laws, but also to the conditions at the boundary of space-time
- that specify the initial state of the universe. There may be a large number of models of the universe with different
- initial conditions that all obey the laws. There ought to be some principle that picks out one initial state, and hence
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (3 of 11) [2/20/2001 3:15:29 AM]
- one model, to represent our universe.
- One such possibility is what are called chaotic boundary conditions. These implicitly assume either that the universe
- is spatially infinite or that there are infinitely many universes. Under chaotic boundary conditions, the probability of
- finding any particular region of space in any given configuration just after the big bang is the same, in some sense,
- as the probability of finding it in any other configuration: the initial state of the universe is chosen purely randomly.
- This would mean that the early universe would have probably been very chaotic and irregular because there are
- many more chaotic and disordered configurations for the universe than there are smooth and ordered ones. (If each
- configuration is equally probable, it is likely that the universe started out in a chaotic and disordered state, simply
- because there are so many more of them.) It is difficult to see how such chaotic initial conditions could have given
- rise to a universe that is so smooth and regular on a large scale as ours is today. One would also have expected the
- density fluctuations in such a model to have led to the formation of many more primordial black holes than the upper
- limit that has been set by observations of the gamma ray background.
- If the universe is indeed spatially infinite, or if there are infinitely many universes, there would probably be some large
- regions somewhere that started out in a smooth and uniform manner. It is a bit like the well-known horde of monkeys
- hammering away on typewriters – most of what they write will be garbage, but very occasionally by pure chance they
- will type out one of Shakespeare’s sonnets. Similarly, in the case of the universe, could it be that we are living in a
- region that just happens by chance to be smooth and uniform? At first sight this might seem very improbable,
- because such smooth regions would be heavily outnumbered by chaotic and irregular regions. However, suppose
- that only in the smooth regions were galaxies and stars formed and were conditions right for the development of
- complicated self-replicating organisms like ourselves who were capable of asking the question: why is the universe
- so smooth.? This is an example of the application of what is known as the anthropic principle, which can be
- paraphrased as “We see the universe the way it is because we exist.”
- There are two versions of the anthropic principle, the weak and the strong. The weak anthropic principle states that
- in a universe that is large or infinite in space and/or time, the conditions necessary for the development of intelligent
- life will be met only in certain regions that are limited in space and time. The intelligent beings in these regions
- should therefore not be surprised if they observe that their locality in the universe satisfies the conditions that are
- necessary for their existence. It is a bit like a rich person living in a wealthy neighborhood not seeing any poverty.
- One example of the use of the weak anthropic principle is to “explain” why the big bang occurred about ten thousand
- million years ago – it takes about that long for intelligent beings to evolve. As explained above, an early generation of
- stars first had to form. These stars converted some of the original hydrogen and helium into elements like carbon and
- oxygen, out of which we are made. The stars then exploded as supernovas, and their debris went to form other stars
- and planets, among them those of our Solar System, which is about five thousand million years old. The first one or
- two thousand million years of the earth’s existence were too hot for the development of anything complicated. The
- remaining three thousand million years or so have been taken up by the slow process of biological evolution, which
- has led from the simplest organisms to beings who are capable of measuring time back to the big bang.
- Few people would quarrel with the validity or utility of the weak anthropic principle. Some, however, go much further
- and propose a strong version of the principle. According to this theory, there are either many different universes or
- many different regions of a single universe, each with its own initial configuration and, perhaps, with its own set of
- laws of science. In most of these universes the conditions would not be right for the development of complicated
- organisms; only in the few universes that are like ours would intelligent beings develop and ask the question, “Why is
- the universe the way we see it?” The answer is then simple: if it had been different, we would not be here!
- The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric
- charge of the electron and the ratio of the masses of the proton and the electron. We cannot, at the moment at least,
- predict the values of these numbers from theory – we have to find them by observation. It may be that one day we
- shall discover a complete unified theory that predicts them all, but it is also possible that some or all of them vary
- from universe to universe or within a single universe. The remarkable fact is that the values of these numbers seem
- to have been very finely adjusted to make possible the development of life. For example, if the electric charge of the
- electron had been only slightly different, stars either would have been unable to burn hydrogen and helium, or else
- they would not have exploded. Of course, there might be other forms of intelligent life, not dreamed of even by
- writers of science fiction, that did not require the light of a star like the sun or the heavier chemical elements that are
- made in stars and are flung back into space when the stars explode. Nevertheless, it seems clear that there are
- relatively few ranges of values for the numbers that would allow the development of any form of intelligent life. Most
- sets of values would give rise to universes that, although they might be very beautiful, would contain no one able to
- wonder at that beauty. One can take this either as evidence of a divine purpose in Creation and the choice of the
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (4 of 11) [2/20/2001 3:15:29 AM]
- laws of science or as support for the strong anthropic principle.
- There are a number of objections that one can raise to the strong anthropic principle as an explanation of the
- observed state of the universe. First, in what sense can all these different universes be said to exist? If they are
- really separate from each other, what happens in another universe can have no observable consequences in our
- own universe. We should therefore use the principle of economy and cut them out of the theory. If, on the other
- hand, they are just different regions of a single universe, the laws of science would have to be the same in each
- region, because otherwise one could not move continuously from one region to another. In this case the only
- difference between the regions would be their initial configurations and so the strong anthropic principle would
- reduce to the weak one.
- A second objection to the strong anthropic principle is that it runs against the tide of the whole history of science. We
- have developed from the geocentric cosmologies of Ptolemy and his forebears, through the heliocentric cosmology
- of Copernicus and Galileo, to the modern picture in which the earth is a medium-sized planet orbiting around an
- average star in the outer suburbs of an ordinary spiral galaxy, which is itself only one of about a million million
- galaxies in the observable universe. Yet the strong anthropic principle would claim that this whole vast construction
- exists simply for our sake. This is very hard to believe. Our Solar System is certainly a prerequisite for our existence,
- hand one might extend this to the whole of our galaxy to allow for an earlier generation of stars that created the
- heavier elements. But there does not seem to be any need for all those other galaxies, nor for the universe to be so
- uniform and similar in every direction on the large scale.
- One would feel happier about the anthropic principle, at least in its weak version, if one could show that quite a
- number of different initial configurations for the universe would have evolved to produce a universe like the one we
- observe. If this is the case, a universe that developed from some sort of random initial conditions should contain a
- number of regions that are smooth and uniform and are suitable for the evolution of intelligent life. On the other hand,
- if the initial state of the universe had to be chosen extremely carefully to lead to something like what we see around
- us, the universe would be unlikely to contain any region in which life would appear. In the hot big bang model
- described above, there was not enough time in the early universe for heat to have flowed from one region to another.
- This means that the initial state of the universe would have to have had exactly the same temperature everywhere in
- order to account for the fact that the microwave back-ground has the same temperature in every direction we look.
- The initial rate of expansion also would have had to be chosen very precisely for the rate of expansion still to be so
- close to the critical rate needed to avoid recollapse. This means that the initial state of the universe must have been
- very carefully chosen indeed if the hot big bang model was correct right back to the beginning of time. It would be
- very difficult to explain why the universe should have begun in just this way, except as the act of a God who intended
- to create beings like us.
- In an attempt to find a model of the universe in which many different initial configurations could have evolved to
- something like the present universe, a scientist at the Massachusetts Institute of Technology, Alan Guth, suggested
- that the early universe might have gone through a period of very rapid expansion. This expansion is said to be
- “inflationary,” meaning that the universe at one time expanded at an increasing rate rather than the decreasing rate
- that it does today. According to Guth, the radius of the universe increased by a million million million million million (1
- with thirty zeros after it) times in only a tiny fraction of a second.
- Guth suggested that the universe started out from the big bang in a very hot, but rather chaotic, state. These high
- temperatures would have meant that the particles in the universe would be moving very fast and would have high
- energies. As we discussed earlier, one would expect that at such high temperatures the strong and weak nuclear
- forces and the electromagnetic force would all be unified into a single force. As the universe expanded, it would cool,
- and particle energies would go down. Eventually there would be what is called a phase transition and the symmetry
- between the forces would be broken: the strong force would become different from the weak and electromagnetic
- forces. One common example of a phase transition is the freezing of water when you cool it down. Liquid water is
- symmetrical, the same at every point and in every direction. However, when ice crystals form, they will have definite
- positions and will be lined up in some direction. This breaks water’s symmetry.
- In the case of water, if one is careful, one can “supercool” it: that is, one can reduce the temperature below the
- freezing point (OºC) without ice forming. Guth suggested that the universe might behave in a similar way: the
- temperature might drop below the critical value without the symmetry between the forces being broken. If this
- happened, the universe would be in an unstable state, with more energy than if the symmetry had been broken. This
- special extra energy can be shown to have an antigravitational effect: it would have acted just like the cosmological
- constant that Einstein introduced into general relativity when he was trying to construct a static model of the
- universe. Since the universe would already be expanding just as in the hot big bang model, the repulsive effect of
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (5 of 11) [2/20/2001 3:15:29 AM]
- this cosmological constant would therefore have made the universe expand at an ever-increasing rate. Even in
- regions where there were more matter particles than average, the gravitational attraction of the matter would have
- been outweighed by the repulsion of the effective cosmological constant. Thus these regions would also expand in
- an accelerating inflationary manner. As they expanded and the matter particles got farther apart, one would be left
- with an expanding universe that contained hardly any particles and was still in the supercooled state. Any
- irregularities in the universe would simply have been smoothed out by the expansion, as the wrinkles in a balloon are
- smoothed away when you blow it up. Thus the present smooth and uniform state of the universe could have evolved
- from many different non-uniform initial states.
- In such a universe, in which the expansion was accelerated by a cosmological constant rather than slowed down by
- the gravitational attraction of matter, there would be enough time for light to travel from one region to another in the
- early universe. This could provide a solution to the problem, raised earlier, of why different regions in the early
- universe have the same properties. Moreover, the rate of expansion of the universe would automatically become
- very close to the critical rate determined by the energy density of the universe. This could then explain why the rate
- of expansion is still so close to the critical rate, without having to assume that the initial rate of expansion of the
- universe was very carefully chosen.
- The idea of inflation could also explain why there is so much matter in the universe. There are something like ten
- million million million million million million million million million million million million million million (1 with eighty
- zeros after it) particles in the region of the universe that we can observe. Where did they all come from? The answer
- is that, in quantum theory, particles can be created out of energy in the form of particle/antiparticle pairs. But that just
- raises the question of where the energy came from. The answer is that the total energy of the universe is exactly
- zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity.
- Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart,
- because you have to expend energy to separate them against the gravitational force that is pulling them together.
- Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform
- in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the
- matter. So the total energy of the universe is zero.
- Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the
- negative gravitational energy without violation of the conservation of energy. This does not happen in the normal
- expansion of the universe in which the matter energy density goes down as the universe gets bigger. It does happen,
- however, in the inflationary expansion because the energy density of the supercooled state remains constant while
- the universe expands: when the universe doubles in size, the positive matter energy and the negative gravitational
- energy both double, so the total energy remains zero. During the inflationary phase, the universe increases its size
- by a very large amount. Thus the total amount of energy available to make particles becomes very large. As Guth
- has remarked, “It is said that there’s no such thing as a free lunch. But the universe is the ultimate free lunch.”
- The universe is not expanding in an inflationary way today. Thus there has to be some mechanism that would
- eliminate the very large effective cosmological constant and so change the rate of expansion from an accelerated
- one to one that is slowed down by gravity, as we have today. In the inflationary expansion one might expect that
- eventually the symmetry between the forces would be broken, just as super-cooled water always freezes in the end.
- The extra energy of the unbroken symmetry state would then be released and would reheat the universe to a
- temperature just below the critical temperature for symmetry between the forces. The universe would then go on to
- expand and cool just like the hot big bang model, but there would now be an explanation of why the universe was
- expanding at exactly the critical rate and why different regions had the same temperature.
- In Guth’s original proposal the phase transition was supposed to occur suddenly, rather like the appearance of ice
- crystals in very cold water. The idea was that “bubbles” of the new phase of broken symmetry would have formed in
- the old phase, like bubbles of steam surrounded by boiling water. The bubbles were supposed to expand and meet
- up with each other until the whole universe was in the new phase. The trouble was, as I and several other people
- pointed out, that the universe was expanding so fast that even if the bubbles grew at the speed of light, they would
- be moving away from each other and so could not join up. The universe would be left in a very non-uniform state,
- with some regions still having symmetry between the different forces. Such a model of the universe would not
- correspond to what we see.
- In October 1981, I went to Moscow for a conference on quantum gravity. After the conference I gave a seminar on
- the inflationary model and its problems at the Sternberg Astronomical Institute. Before this, I had got someone else
- to give my lectures for me, because most people could not understand my voice. But there was not time to prepare
- this seminar, so I gave it myself, with one of my graduate students repeating my words. It worked well, and gave me
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (6 of 11) [2/20/2001 3:15:29 AM]
- much more contact with my audience. In the audience was a young Russian, Andrei Linde, from the Lebedev
- Institute in Moscow. He said that the difficulty with the bubbles not joining up could be avoided if the bubbles were so
- big that our region of the universe is all contained inside a single bubble. In order for this to work, the change from
- symmetry to broken symmetry must have taken place very slowly inside the bubble, but this is quite possible
- according to grand unified theories. Linde’s idea of a slow breaking of symmetry was very good, but I later realized
- that his bubbles would have to have been bigger than the size of the universe at the time! I showed that instead the
- symmetry would have broken everywhere at the same time, rather than just inside bubbles. This would lead to a
- uniform universe, as we observe. I was very excited by this idea and discussed it with one of my students, Ian Moss.
- As a friend of Linde’s, I was rather embarrassed, however, when I was later sent his paper by a scientific journal and
- asked whether it was suitable for publication. I replied that there was this flaw about the bubbles being bigger than
- the universe, but that the basic idea of a slow breaking of symmetry was very good. I recommended that the paper ¿
- published as it was because it would take Linde several months to correct it, since anything he sent to the West
- would have to be passed by Soviet censorship, which was neither very skillful nor very quick with scientific papers.
- Instead, I wrote a short paper with Ian Moss in the same journal in which we pointed out this problem with the bubble
- and showed how it could be resolved.
- The day after I got back from Moscow I set out for Philadelphia, where I was due to receive a medal from the
- Franklin Institute. My secretary, Judy Fella, had used her not inconsiderable charm to persuade British Airways to
- give herself and me free seats on a Concorde as a publicity venture. However, I .was held up on my way to the
- airport by heavy rain and I missed the plane. Nevertheless, I got to Philadelphia in the end and received my medal. I
- was then asked to give a seminar on the inflationary universe at Drexel University in Philadelphia. I gave the same
- seminar about the problems of the inflationary universe, just as in Moscow.
- A very similar idea to Linde’s was put forth independently a few months later by Paul Steinhardt and Andreas
- Albrecht of the University of Pennsylvania. They are now given joint credit with Linde for what is called “the new
- inflationary model,” based on the idea of a slow breaking of symmetry. (The old inflationary model was Guth’s
- original suggestion of fast symmetry breaking with the formation of bubbles.)
- The new inflationary model was a good attempt to explain why the universe is the way it is. However, I and several
- other people showed that, at least in its original form, it predicted much greater variations in the temperature of the
- microwave background radiation than are observed. Later work has also cast doubt on whether there could be a
- phase transition in the very early universe of the kind required. In my personal opinion, the new inflationary model is
- now dead as a scientific theory, although a lot of people do not seem to have heard of its demise and are still writing
- papers as if it were viable. A better model, called the chaotic inflationary model, was put forward by Linde in 1983. In
- this there is no phase transition or supercooling. Instead, there is a spin 0 field, which, because of quantum
- fluctuations, would have large values in some regions of the early universe. The energy of the field in those regions
- would behave like a cosmological constant. It would have a repulsive gravitational effect, and thus make those
- regions expand in an inflationary manner. As they expanded, the energy of the field in them would slowly decrease
- until the inflationary expansion changed to an expansion like that in the hot big bang model. One of these regions
- would become what we now see as the observable universe. This model has all the advantages of the earlier
- inflationary models, but it does not depend on a dubious phase transition, and it can moreover give a reasonable size
- for the fluctuations in the temperature of the microwave background that agrees with observation.
- This work on inflationary models showed that the present state of the universe could have arisen from quite a large
- number of different initial configurations. This is important, because it shows that the initial state of the part of the
- universe that we inhabit did not have to be chosen with great care. So we may, if we wish, use the weak anthropic
- principle to explain why the universe looks the way it does now. It cannot be the case, however, that every initial
- configuration would have led to a universe like the one we observe. One can show this by considering a very
- different state for the universe at the present time, say, a very lumpy and irregular one. One could use the laws of
- science to evolve the universe back in time to determine its configuration at earlier times. According to the singularity
- theorems of classical general relativity, there would still have been a big bang singularity. If you evolve such a
- universe forward in time according to the laws of science, you will end up with the lumpy and irregular state you
- started with. Thus there must have been initial configurations that would not have given rise to a universe like the
- one we see today. So even the inflationary model does not tell us why the initial configuration was not such as to
- produce something very different from what we observe. Must we turn to the anthropic principle for an explanation?
- Was it all just a lucky chance? That would seem a counsel of despair, a negation of all our hopes of understanding
- the underlying order of the universe.
- In order to predict how the universe should have started off, one needs laws that hold at the beginning of time. If the
- classical theory of general relativity was correct, the singularity theorems that Roger Penrose and I proved show that
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (7 of 11) [2/20/2001 3:15:29 AM]
- the beginning of time would have been a point of infinite density and infinite curvature of space-time. All the known
- laws of science would break down at such a point. One might suppose that there were new laws that held at
- singularities, but it would be very difficult even to formulate such laws at such badly behaved points, and we would
- have no guide from observations as to what those laws might be. However, what the singularity theorems really
- indicate is that the gravitational field becomes so strong that quantum gravitational effects become important:
- classical theory is no longer a good description of the universe. So one has to use a quantum theory of gravity to
- discuss the very early stages of the universe. As we shall see, it is possible in the quantum theory for the ordinary
- laws of science to hold everywhere, including at the beginning of time: it is not necessary to postulate new laws for
- singularities, because there need not be any singularities in the quantum theory.
- We don’t yet have a complete and consistent theory that combines quantum mechanics and gravity. However, we
- are fairly certain of some features that such a unified theory should have. One is that it should incorporate
- Feynman’s proposal to formulate quantum theory in terms of a sum over histories. In this approach, a particle does
- not have just a single history, as it would in a classical theory. Instead, it is supposed to follow every possible path in
- space-time, and with each of these histories there are associated a couple of numbers, one represent-ing the size of
- a wave and the other representing its position in the cycle (its phase). The probability that the particle, say, passes
- through some particular point is found by adding up the waves associated with every possible history that passes
- through that point. When one actually tries to perform these sums, however, one runs into severe technical
- problems. The only way around these is the following peculiar prescription: one must add up the waves for particle
- histories that are not in the “real” time that you and I experience but take place in what is called imaginary time.
- Imaginary time may sound like science fiction but it is in fact a well-defined mathematical concept. If we take any
- ordinary (or “real”) number and multiply it by itself, the result is a positive number. (For example, 2 times 2 is 4, but
- so is – 2 times – 2.) There are, however, special numbers (called imaginary numbers) that give negative numbers
- when multiplied by themselves. (The one called i, when multiplied by itself, gives – 1, 2i multiplied by itself gives – 4,
- and so on.)
- One can picture real and imaginary numbers in the following way: The real numbers can be represented by a line
- going from left to right, with zero in the middle, negative numbers like – 1, – 2, etc. on the left, and positive numbers,
- 1, 2, etc. on the right. Then imaginary numbers are represented by a line going up and down the page, with i, 2i, etc.
- above the middle, and – i, – 2i, etc. below. Thus imaginary numbers are in a sense numbers at right angles to
- ordinary real numbers.
- To avoid the technical difficulties with Feynman’s sum over histories, one must use imaginary time. That is to say, for
- the purposes of the calculation one must measure time using imaginary numbers, rather than real ones. This has an
- interesting effect on space-time: the distinction between time and space disappears completely. A space-time in
- which events have imaginary values of the time coordinate is said to be Euclidean, after the ancient Greek Euclid,
- who founded the study of the geometry of two-dimensional surfaces. What we now call Euclidean space-time is very
- similar except that it has four dimensions instead of two. In Euclidean space-time there is no difference between the
- time direction and directions in space. On the other hand, in real space-time, in which events are labeled by ordinary,
- real values of the time coordinate, it is easy to tell the difference – the time direction at all points lies within the light
- cone, and space directions lie outside. In any case, as far as everyday quantum mechanics is concerned, we may
- regard our use of imaginary time and Euclidean space-time as merely a mathematical device (or trick) to calculate
- answers about real space-time.
- A second feature that we believe must be part of any ultimate theory is Einstein’s idea that the gravitational field is
- represented by curved space-time: particles try to follow the nearest thing to a straight path in a curved space, but
- because space-time is not flat their paths appear to be bent, as if by a gravitational field. When we apply Feynman’s
- sum over histories to Einstein’s view of gravity, the analogue of the history of a particle is now a complete curved
- space-time that represents the history of the whole universe. To avoid the technical difficulties in actually performing
- the sum over histories, these curved space-times must be taken to be Euclidean. That is, time is imaginary and is
- indistinguishable from directions in space. To calculate the probability of finding a real space-time with some certain
- property, such as looking the same at every point and in every direction, one adds up the waves associated with all
- the histories that have that property.
- In the classical theory of general relativity, there are many different possible curved space-times, each corresponding
- to a different initial state of the universe. If we knew the initial state of our universe, we would know its entire history.
- Similarly, in the quantum theory of gravity, there are many different possible quantum states for the universe. Again,
- if we knew how the Euclidean curved space-times in the sum over histories behaved at early times, we would know
- the quantum state of the universe.
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (8 of 11) [2/20/2001 3:15:29 AM]
- In the classical theory of gravity, which is based on real space-time, there are only two possible ways the universe
- can behave: either it has existed for an infinite time, or else it had a beginning at a singularity at some finite time in
- the past. In the quantum theory of gravity, on the other hand, a third possibility arises. Because one is using
- Euclidean space-times, in which the time direction is on the same footing as directions in space, it is possible for
- space-time to be finite in extent and yet to have no singularities that formed a boundary or edge. Space-time would
- be like the surface of the earth, only with two more dimensions. The surface of the earth is finite in extent but it
- doesn’t have a boundary or edge: if you sail off into the sunset, you don’t fall off the edge or run into a singularity. (I
- know, because I have been round the world!)
- If Euclidean space-time stretches back to infinite imaginary time, or else starts at a singularity in imaginary time, we
- have the same problem as in the classical theory of specifying the initial state of the universe: God may know how
- the universe began, but we cannot give any particular reason for thinking it began one way rather than another. On
- the other hand, the quantum theory of gravity has opened up a new possibility, in which there would be no boundary
- to space-time and so there would be no need to specify the behavior at the boundary. There would be no
- singularities at which the laws of science broke down, and no edge of space-time at which one would have to appeal
- to God or some new law to set the boundary conditions for space-time. One could say: “The boundary condition of
- the universe is that it has no boundary.” The universe would be completely self-contained and not affected by
- anything outside itself. It would neither be created nor destroyed, It would just BE.
- It was at the conference in the Vatican mentioned earlier that I first put forward the suggestion that maybe time and
- space together formed a surface that was finite in size but did not have any boundary or edge. My paper was rather
- mathematical, however, so its implications for the role of God in the creation of the universe were not generally
- recognized at the time (just as well for me). At the time of the Vatican conference, I did not know how to use the “no
- boundary” idea to make predictions about the universe. However, I spent the following sum-mer at the University of
- California, Santa Barbara. There a friend and colleague of mine, Jim Hartle, worked out with me what conditions the
- universe must satisfy if space-time had no boundary. When I returned to Cambridge, I continued this work with two of
- my research students, Julian Luttrel and Jonathan Halliwell.
- I’d like to emphasize that this idea that time and space should be finite “without boundary” is just a proposal: it cannot
- be deduced from some other principle. Like any other scientific theory, it may initially be put forward for aesthetic or
- metaphysical reasons, but the real test is whether it makes predictions that agree with observation. This, how-ever, is
- difficult to determine in the case of quantum gravity, for two reasons. First, as will be explained in Chapter 11, we are
- not yet sure exactly which theory successfully combines general relativity and quantum mechanics, though we know
- quite a lot about the form such a theory must have. Second, any model that described the whole universe in detail
- would be much too complicated mathematically for us to be able to calculate exact predictions. One therefore has to
- make simplifying assumptions and approximations – and even then, the problem of extracting predictions remains a
- formidable one.
- Each history in the sum over histories will describe not only the space-time but everything in it as well, including any
- complicated organisms like human beings who can observe the history of the universe. This may provide another
- justification for the anthropic principle, for if all the histories are possible, then so long as we exist in one of the
- histories, we may use the anthropic principle to explain why the universe is found to be the way it is. Exactly what
- meaning can be attached to the other histories, in which we do not exist, is not clear. This view of a quantum theory
- of gravity would be much more satisfactory, however, if one could show that, using the sum over histories, our
- universe is not just one of the possible histories but one of the most probable ones. To do this, we must perform the
- sum over histories for all possible Euclidean space-times that have no boundary.
- Under the “no boundary” proposal one learns that the chance of the universe being found to be following most of the
- possible histories is negligible, but there is a particular family of histories that are much more probable than the
- others. These histories may be pictured as being like the surface of the earth, with the distance from the North Pole
- representing imaginary time and the size of a circle of constant distance from the North Pole representing the spatial
- size of the universe. The universe starts at the North Pole as a single point. As one moves south, the circles of
- latitude at constant distance from the North Pole get bigger, corresponding to the universe expanding with imaginary
- time Figure 8:1. The universe would reach a maximum size at the equator and would contract with increasing
- imaginary time to a single point at the South Pole. Ever though the universe would have zero size at the North and
- South Poles, these points would not be singularities, any more than the North aid South Poles on the earth are
- singular. The laws of science will hold at them, just as they do at the North and South Poles on the earth.
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (9 of 11) [2/20/2001 3:15:29 AM]
- Figure 8:1
- The history of the universe in real time, however, would look very different. At about ten or twenty thousand million
- years ago, it would have a minimum size, which was equal to the maximum radius of the history in imaginary time. At
- later real times, the universe would expand like the chaotic inflationary model proposed by Linde (but one would not
- now have to assume that the universe was created somehow in the right sort of state). The universe would expand to
- a very large size Figure 8:1 and eventually it would collapse again into what looks like a singularity in real time. Thus,
- in a sense, we are still all doomed, even if we keep away from black holes. Only if we could picture the universe in
- terms of imaginary time would there be no singularities.
- If the universe really is in such a quantum state, there would be no singularities in the history of the universe in
- imaginary time. It might seem therefore that my more recent work had completely undone the results of my earlier
- work on singularities. But, as indicated above, the real importance of the singularity theorems was that they showed
- that the gravitational field must become so strong that quantum gravitational effects could not be ignored. This in turn
- led to the idea that the universe could be finite in imaginary time but without boundaries or singularities. When one
- goes back to the real time in which we live, however, there will still appear to be singularities. The poor astronaut
- who falls into a black hole will still come to a sticky end; only if he lived in imaginary time would he encounter no
- singularities.
- This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a
- figment of our imaginations. In real time, the universe has a beginning and an end at singularities that form a
- boundary to space-time and at which the laws of science break down. But in imaginary time, there are no
- singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just
- an idea that we invent to help us describe what we think the universe is like. But according to the approach I
- described in Chapter 1, a scientific theory is just a mathematical model we make to describe our observations: it
- exists only in our minds. So it is meaningless to ask: which is real, “real” or “imaginary” time? It is simply a matter of
- which is the more useful description.
- One can also use the sum over histories, along with the no boundary proposal, to find which properties of the
- universe are likely to occur together. For example, one can calculate the probability that the universe is expanding at
- nearly the same rate in all different directions at a time when the density of the universe has its present value. In the
- simplified models that have been examined so far, this probability turns out to be high; that is, the proposed no
- boundary condition leads to the prediction that it is extremely probable that the present rate of expansion of the
- universe is almost the same in each direction. This is consistent with the observations of the microwave background
- radiation, which show that it has almost exactly the same intensity in any direction. If the universe were expanding
- faster in some directions than in others, the intensity of the radiation in those directions would be reduced by an
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (10 of 11) [2/20/2001 3:15:29 AM]
- additional red shift.
- Further predictions of the no boundary condition are currently being worked out. A particularly interesting problem is
- the size of the small departures from uniform density in the early universe that caused the formation first of the
- galaxies, then of stars, and finally of us. The uncertainty principle implies that the early universe cannot have been
- completely uniform because there must have been some uncertainties or fluctuations in the positions and velocities
- of the particles. Using the no boundary condition, we find that the universe must in fact have started off with just the
- minimum possible non-uniformity allowed by the uncertainty principle. The universe would have then undergone a
- period of rapid expansion, as in the inflationary models. During this period, the initial non-uniformities would have
- been amplified until they were big enough to explain the origin of the structures we observe around us. In 1992 the
- Cosmic Background Explorer satellite (COBE) first detected very slight variations in the intensity of the microwave
- background with direction. The way these non-uniformities depend on direction seems to agree with the predictions
- of the inflationary model and the no boundary proposal. Thus the no boundary proposal is a good scientific theory in
- the sense of Karl Popper: it could have been falsified by observations but instead its predictions have been
- confirmed. In an expanding universe in which the density of matter varied slightly from place to place, gravity would
- have caused the denser regions to slow down their expansion and start contracting. This would lead to the formation
- of galaxies, stars, and eventually even insignificant creatures like ourselves. Thus all the complicated structures that
- we see in the universe might be explained by the no boundary condition for the universe together with the uncertainty
- principle of quantum mechanics.
- The idea that space and time may form a closed surface without boundary also has profound implications for the role
- of God in the affairs of the universe. With the success of scientific theories in describing events, most people have
- come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the
- universe to break these laws. However, the laws do not tell us what the universe should have looked like when it
- started – it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe
- had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no
- boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 8
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/g.html (11 of 11) [2/20/2001 3:15:29 AM]
- CHAPTER 9
- THE ARROW OF TIME
- In previous chapters we have seen how our views of the nature of time have changed over the years. Up to the
- beginning of this century people believed in an absolute time. That is, each event could be labeled by a number
- called “time” in a unique way, and all good clocks would agree on the time interval between two events.
- However, the discovery that the speed of light appeared the same to every observer, no matter how he was
- moving, led to the theory of relativity – and in that one had to abandon the idea that there was a unique
- absolute time. Instead, each observer would have his own measure of time as recorded by a clock that he
- carried: clocks carried by different observers would not necessarily agree. Thus time became a more personal
- concept, relative to the observer who measured it.
- When one tried to unify gravity with quantum mechanics, one had to introduce the idea of “imaginary” time.
- Imaginary time is indistinguishable from directions in space. If one can go north, one can turn around and head
- south; equally, if one can go forward in imaginary time, one ought to be able to turn round and go backward.
- This means that there can be no important difference between the forward and backward directions of
- imaginary time. On the other hand, when one looks at “real” time, there’s a very big difference between the
- forward and backward directions, as we all know. Where does this difference between the past and the future
- come from? Why do we remember the past but not the future?
- The laws of science do not distinguish between the past and the future. More precisely, as explained earlier,
- the laws of science are unchanged under the combination of operations (or symmetries) known as C, P, and T.
- (C means changing particles for antiparticles. P means taking the mirror image, so left and right are
- interchanged. And T means reversing the direction of motion of all particles: in effect, running the motion
- backward.) The laws of science that govern the behavior of matter under all normal situations are unchanged
- under the combination of the two operations C and P on their own. In other words, life would be just the same
- for the inhabitants of another planet who were both mirror images of us and who were made of antimatter,
- rather than matter.
- If the laws of science are unchanged by the combination of operations C and P, and also by the combination C,
- P, and T, they must also be unchanged under the operation T alone. Yet there is a big difference between the
- forward and backward directions of real time in ordinary life. Imagine a cup of water falling off a table and
- breaking into pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or
- backward. If you run it backward you will see the pieces suddenly gather themselves together off the floor and
- jump back to form a whole cup on the table. You can tell that the film is being run backward because this kind
- of behavior is never observed in ordinary life. If it were, crockery manufacturers would go out of business.
- The explanation that is usually given as to why we don’t see broken cups gathering themselves together off the
- floor and jumping back onto the table is that it is forbidden by the second law of thermodynamics. This says that
- in any closed system disorder, or entropy, always increases with time. In other words, it is a form of Murphy’s
- law: things always tend to go wrong! An intact cup on the table is a state of high order, but a broken cup on the
- floor is a disordered state. One can go readily from the cup on the table in the past to the broken cup on the
- floor in the future, but not the other way round.
- The increase of disorder or entropy with time is one example of what is called an arrow of time, something that
- distinguishes the past from the future, giving a direction to time. There are at least three different arrows of
- time. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy
- increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the
- direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This
- is the direction of time in which the universe is expanding rather than contracting.
- In this chapter I shall argue that the no boundary condition for the universe, together with the weak anthropic
- principle, can explain why all three arrows point in the same direction – and moreover, why a well-defined arrow
- of time should exist at all. I shall argue that the psychological arrow is determined by the thermodynamic arrow,
- A Brief History of Time - Stephen Hawking... Chapter 9
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/h.html (1 of 5) [2/20/2001 3:15:38 AM]
- and that these two arrows necessarily always point in the same direction. If one assumes the no boundary
- condition for the universe, we shall see that there must be well-defined thermodynamic and cosmological
- arrows of time, but they will not point in the same direction for the whole history of the universe. However, I
- shall argue that it is only when they do point in the same direction that conditions are suitable for the
- development of intelligent beings who can ask the question: why does disorder increase in the same direction
- of time as that in which the universe expands?
- I shall discuss first the thermodynamic arrow of time. The second law of thermodynamics results from the fact
- that there are always many more disordered states than there are ordered ones. For example, consider the
- pieces of a jigsaw in a box. There is one, and. only one, arrangement in which the pieces make a complete
- picture. On the other hand, there are a very large number of arrangements in which the pieces are disordered
- and don’t make a picture.
- Suppose a system starts out in one of the small number of ordered states. As time goes by, the system will
- evolve according to the laws of science and its state will change. At a later time, it is more probable that the
- system will be in a disordered state than in an ordered one because there are more disordered states. Thus
- disorder will tend to increase with time if the system obeys an initial condition of high order.
- Suppose the pieces of the jigsaw start off in a box in the ordered arrangement in which they form a picture. If
- you shake the box, the pieces will take up another arrangement. This will probably be a disordered
- arrangement in which the pieces don’t form a proper picture, simply because there are so many more
- disordered arrangements. Some groups of pieces may still form parts of the picture, but the more you shake
- the box, the more likely it is that these groups will get broken up and the pieces will be in a completely jumbled
- state in which they don’t form any sort of picture. So the disorder of the pieces will probably increase with time if
- the pieces obey the initial condition that they start off in a condition of high order.
- Suppose, however, that God decided that the universe should finish up in a state of high order but that it didn’t
- matter what state it started in. At early times the universe would probably be in a disordered state. This would
- mean that disorder would decrease with time. You would see broken cups gathering themselves together and
- jumping back onto the table. However, any human beings who were observing the cups would be living in a
- universe in which disorder decreased with time. I shall argue that such beings would have a psychological
- arrow of time that was backward. That is, they would remember events in the future, and not remember events
- in their past. When the cup was broken, they would remember it being on the table, but when it was on the
- table, they would not remember it being on the floor.
- It is rather difficult to talk about human memory because we don’t know how the brain works in detail. We do,
- however, know all about how computer memories work. I shall therefore discuss the psychological arrow of
- time for computers. I think it is reasonable to assume that the arrow for computers is the same as that for
- humans. If it were not, one could make a killing on the stock exchange by having a computer that would
- remember tomorrow’s prices! A computer memory is basically a device containing elements that can exist in
- either of two states. A simple example is an abacus. In its simplest form, this consists of a number of wires; on
- each wire there are a number of beads that can be put in one of two positions. Before an item is recorded in a
- computer’s memory, the memory is in a disordered state, with equal probabilities for the two possible states.
- (The abacus beads are scattered randomly on the wires of the abacus.) After the memory interacts with the
- system to be remembered, it will definitely be in one state or the other, according to the state of the system.
- (Each abacus bead will be at either the left or the right of the abacus wire.) So the memory has passed from a
- disordered state to an ordered one. However, in order to make sure that the memory is in the right state, it is
- necessary to use a certain amount of energy (to move the bead or to power the computer, for example). This
- energy is dissipated as heat, and increases the amount of disorder in the universe. One can show that this
- increase in disorder is always greater than the increase in the order of the memory itself. Thus the heat
- expelled by the computer’s cooling fan means that when a computer records an item in memory, the total
- amount of disorder in the universe still goes up. The direction of time in which a computer remembers the past
- is the same as that in which disorder increases.
- Our subjective sense of the direction of time, the psychological arrow of time, is therefore determined within our
- brain by the thermodynamic arrow of time. Just like a computer, we must remember things in the order in which
- entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time
- A Brief History of Time - Stephen Hawking... Chapter 9
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/h.html (2 of 5) [2/20/2001 3:15:38 AM]
- because we measure time in the direction in which disorder increases You can’t have a safer bet than that!
- But why should the thermodynamic arrow of time exist at all? Or, in other words, why should the universe be in
- a state of high order at one end of time, the end that we call the past? Why is it not in a state of complete
- disorder at all times? After all, this might seem more probable. And why is the direction of time in which
- disorder increases the same as that in which the universe expands?
- In the classical theory of general relativity one cannot predict how the universe would have begun because all
- the known laws of science would have broken down at the big bang singularity. The universe could have
- started out in a very smooth and ordered state. This would have led to well-defined thermodynamic and
- cosmological arrows of time, as we observe. But it could equally well have started out in a very lumpy and
- disordered state. In that case, the universe would already be in a state of complete disorder, so disorder could
- not increase with time. It would either stay constant, in which case there would be no well-defined
- thermodynamic arrow of time, or it would decrease, in which case the thermodynamic arrow of time would point
- in the opposite direction to the cosmological arrow. Neither of these possibilities agrees with what we observe.
- However, as we have seen, classical general relativity predicts its own downfall. When the curvature of
- space-time becomes large, quantum gravitational effects will become important and the classical theory will
- cease to be a good description of the universe. One has to use a quantum theory of gravity to understand how
- the universe began.
- In a quantum theory of gravity, as we saw in the last chapter, in order to specify the state of the universe one
- would still have to say how the possible histories of the universe would behave at the boundary of space-time in
- the past. One could avoid this difficulty of having to describe what we do not and cannot know only if the
- histories satisfy the no boundary condition: they are finite in extent but have no boundaries, edges, or
- singularities. In that case, the beginning of time would be a regular, smooth point of space-time and the
- universe would have begun its expansion in a very smooth and ordered state. It could not have been
- completely uniform, because that would violate the uncertainty principle of quantum theory. There had to be
- small fluctuations in the density and velocities of particles. The no boundary condition, however, implied that
- these fluctuations were as small as they could be, consistent with the uncertainty principle.
- The universe would have started off with a period of exponential or “inflationary” expansion in which it would
- have increased its size by a very large factor. During this expansion, the density fluctuations would have
- remained small at first, but later would have started to grow. Regions in which the density was slightly higher
- than average would have had their expansion slowed down by the gravitational attraction of the extra mass.
- Eventually, such regions would stop expanding and collapse to form galaxies, stars, and beings like us. The
- universe would have started in a smooth and ordered state, and would become lumpy and disordered as time
- went on. This would explain the existence of the thermodynamic arrow of time.
- But what would happen if and when the universe stopped expanding and began to contract? Would the
- thermodynamic arrow reverse and disorder begin to decrease with time? This would lead to all sorts of
- science-fiction-like possibilities for people who survived from the expanding to the contracting phase. Would
- they see broken cups gathering themselves together off the floor and jumping back onto the table? Would they
- be able to remember tomorrow’s prices and make a fortune on the stock market? It might seem a bit academic
- to worry about what will happen when the universe collapses again, as it will not start to contract for at least
- another ten thousand million years. But there is a quicker way to find out what will happen: jump into a black
- hole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole
- universe. So if disorder were to decrease in the contracting phase of the universe, one might also expect it to
- decrease inside a black hole. So perhaps an astronaut who fell into a black hole would be able to make money
- at roulette by remembering where the ball went before he placed his bet. (Unfortunately, however, he would not
- have long to play before he was turned to spaghetti. Nor would he be able to let us know about the reversal of
- the thermodynamic arrow, or even bank his winnings, because he would be trapped behind the event horizon
- of the black hole.)
- At first, I believed that disorder would decrease when the universe recollapsed. This was because I thought that
- the universe had to return to a smooth and ordered state when it became small again. This would mean that
- the contracting phase would be like the time reverse of the expanding phase. People in the contracting phase
- would live their lives backward: they would die before they were born and get younger as the universe
- A Brief History of Time - Stephen Hawking... Chapter 9
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/h.html (3 of 5) [2/20/2001 3:15:38 AM]
- contracted.
- This idea is attractive because it would mean a nice symmetry between the expanding and contracting phases.
- However, one cannot adopt it on its own, independent of other ideas about the universe. The question is: is it
- implied by the no boundary condition, or is it inconsistent with that condition? As I said, I thought at first that the
- no boundary condition did indeed imply that disorder would decrease in the contracting phase. I was misled
- partly by the analogy with the surface of the earth. If one took the beginning of the universe to correspond to
- the North Pole, then the end of the universe should be similar to the beginning, just as the South Pole is similar
- to the North. However, the North and South Poles correspond to the beginning and end of the universe in
- imaginary time. The beginning and end in real time can be very different from each other. I was also misled by
- work I had done on a simple model of the universe in which the collapsing phase looked like the time reverse of
- the expanding phase. However, a colleague of mine, Don Page, of Penn State University, pointed out that the
- no boundary condition did not require the contracting phase necessarily to be the time reverse of the expanding
- phase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, the
- collapse of the universe was very different from the expansion. I realized that I had made a mistake: the no
- boundary condition implied that disorder would in fact continue to increase during the contraction. The
- thermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, or
- inside black holes.
- What should you do when you find you have made a mistake like that? Some people never admit that they are
- wrong and continue to find new, and often mutually inconsistent, arguments to support their case – as
- Eddington did in opposing black hole theory. Others claim to have never really supported the incorrect view in
- the first place or, if they did, it was only to show that it was inconsistent. It seems to me much better and less
- confusing if you admit in print that you were wrong. A good example of this was Einstein, who called the
- cosmological constant, which he introduced when he was trying to make a static model of the universe, the
- biggest mistake of his life.
- To return to the arrow of time, there remains the question: why do we observe that the thermodynamic and
- cosmological arrows point in the same direction? Or in other words, why does disorder increase in the same
- direction of time as that in which the universe expands? If one believes that the universe will expand and then
- contract again, as the no boundary proposal seems to imply, this becomes a question of why we should be in
- the expanding phase rather than the contracting phase.
- One can answer this on the basis of the weak anthropic principle. Conditions in the contracting phase would not
- be suitable for the existence of intelligent beings who could ask the question: why is disorder increasing in the
- same direction of time as that in which the universe is expanding? The inflation in the early stages of the
- universe, which the no boundary proposal predicts, means that the universe must be expanding at very close to
- the critical rate at which it would just avoid recollapse, and so will not recollapse for a very long time. By then all
- the stars will have burned out and the protons and neutrons in them will probably have decayed into light
- particles and radiation. The universe would be in a state of almost complete disorder. There would be no strong
- thermodynamic arrow of time. Disorder couldn’t increase much because the universe would be in a state of
- almost complete disorder already. However, a strong thermodynamic arrow is necessary for intelligent life to
- operate. In order to survive, human beings have to consume food, which is an ordered form of energy, and
- convert it into heat, which is a disordered form of energy. Thus intelligent life could not exist in the contracting
- phase of the universe. This is the explanation of why we observe that the thermodynamic and cosmological
- arrows of time point in the same direction. It is not that the expansion of the universe causes disorder to
- increase. Rather, it is that the no boundary condition causes disorder to increase and the conditions to be
- suitable for intelligent life only in the expanding phase.
- To summarize, the laws of science do not distinguish between the forward and backward directions of time.
- However, there are at least three arrows of time that do distinguish the past from the future. They are the
- thermodynamic arrow, the direction of time in which disorder increases; the psychological arrow, the direction
- of time in which we remember the past and not the future; and the cosmological arrow, the direction of time in
- which the universe expands rather than contracts. I have shown that the psychological arrow is essentially the
- same as the thermodynamic arrow, so that the two would always point in the same direction. The no boundary
- proposal for the universe predicts the existence of a well-defined thermodynamic arrow of time because the
- universe must start off in a smooth and ordered state. And the reason we observe this thermodynamic arrow to
- A Brief History of Time - Stephen Hawking... Chapter 9
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/h.html (4 of 5) [2/20/2001 3:15:38 AM]
- agree with the cosmological arrow is that intelligent beings can exist only in the expanding phase. The
- contracting phase will be unsuitable because it has no strong thermodynamic arrow of time.
- The progress of the human race in understanding the universe has established a small corner of order in an
- increasingly disordered universe. If you remember every word in this book, your memory will have recorded
- about two million pieces of information: the order in your brain will have increased by about two million units.
- However, while you have been reading the book, you will have converted at least a thousand calories of
- ordered energy, in the form of food, into disordered energy, in the form of heat that you lose to the air around
- you by convection and sweat. This will increase the disorder of the universe by about twenty million million
- million million units – or about ten million million million times the increase in order in your brain – and that’s if
- you remember everything in this book. In the next chapter but one I will try to increase the order in our neck of
- the woods a little further by explaining how people are trying to fit together the partial theories I have described
- to form a complete unified theory that would cover everything in the universe.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 9
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/h.html (5 of 5) [2/20/2001 3:15:38 AM]
- CHAPTER 10
- WORMHOLES AND TIME TRAVEL
- The last chapter discussed why we see time go forward: why disorder increases and why we remember the
- past but not the future. Time was treated as if it were a straight railway line on which one could only go one way
- or the other.
- But what if the railway line had loops and branches so that a train could keep going forward but come back to a
- station it had already passed? In other words, might it be possible for someone to travel into the future or the
- past?
- H. G. Wells in The Time Machine explored these possibilities as have countless other writers of science fiction.
- Yet many of the ideas of science fiction, like submarines and travel to the moon, have become matters of
- science fact. So what are the prospects for time travel?
- The first indication that the laws of physics might really allow people to travel in time came in 1949 when Kurt
- Godel discovered a new space-time allowed by general relativity. Godel was a mathematician who was famous
- for proving that it is impossible to prove all true statements, even if you limit yourself to trying to prove all the
- true statements in a subject as apparently cut and dried as arithmetic. Like the uncertainty principle, Godel’s
- incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe,
- but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.
- Godel got to know about general relativity when he and Einstein spent their later years at the Institute for
- Advanced Study in Princeton. His space-time had the curious property that the whole universe was rotating.
- One might ask: “Rotating with respect to what?” The answer is that distant matter would be rotating with
- respect to directions that little tops or gyroscopes point in.
- This had the side effect that it would be possible for someone to go off in a rocket ship and return to earth
- before he set out. This property really upset Einstein, who had thought that general relativity wouldn’t allow time
- travel. However, given Einstein’s record of ill-founded opposition to gravitational collapse and the uncertainty
- principle, maybe this was an encouraging sign. The solution Godel found doesn’t correspond to the universe
- we live in because we can show that the universe is not rotating. It also had a non-zero value of the
- cosmological constant that Einstein introduced when he thought the universe was unchanging. After Hubble
- discovered the expansion of the universe, there was no need for a cosmological constant and it is now
- generally believed to be zero. However, other more reasonable space-times that are allowed by general
- relativity and which permit travel into the past have since been found. One is in the interior of a rotating black
- hole. Another is a space-time that contains two cosmic strings moving past each other at high speed. As their
- name suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section.
- Actually, they are more like rubber bands because they are under enormous tension, something like a million
- million million million tons. A cosmic string attached to the earth could accelerate it from 0 to 60 mph in 1/30th
- of a second. Cosmic strings may sound like pure science fiction but there are reasons to believe they could
- have formed in the early universe as a result of symmetry-breaking of the kind discussed in Chapter 5.
- Because they would be under enormous tension and could start in any configuration, they might accelerate to
- very high speeds when they straighten out.
- The Godel solution and the cosmic string space-time start out so distorted that travel into the past was always
- possible. God might have created such a warped universe but we have no reason to believe he did.
- Observations of the microwave background and of the abundances of the light elements indicate that the early
- universe did not have the kind of curvature required to allow time travel. The same conclusion follows on
- theoretical grounds if the no boundary proposal is correct. So the question is: if the universe starts out without
- the kind of curvature required for time travel, can we subsequently warp local regions of space-time sufficiently
- to allow it?
- A closely related problem that is also of concern to writers of science fiction is rapid interstellar or intergalactic
- A Brief History of Time - Stephen Hawking... Chapter 10
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/i.html (1 of 5) [2/20/2001 3:15:45 AM]
- travel. According to relativity, nothing can travel faster than light. If we therefore sent a spaceship to our nearest
- neighboring star, Alpha Centauri, which is about four light-years away, it would take at least eight years before
- we could expect the travelers to return and tell us what they had found. If the expedition were to the center of
- our galaxy, it would be at least a hundred thousand years before it came back. The theory of relativity does
- allow one consolation. This is the so-called twins paradox mentioned in Chapter 2.
- Because there is no unique standard of time, but rather observers each have their own time as measured by
- clocks that they carry with them, it is possible for the journey to seem to be much shorter for the space travelers
- than for those who remain on earth. But there would not be much joy in returning from a space voyage a few
- years older to find that everyone you had left behind was dead and gone thousands of years ago. So in order to
- have any human interest in their stories, science fiction writers had to suppose that we would one day discover
- how to travel faster than light. What most of thee authors don’t seem to have realized is that if you can travel
- faster than light, the theory of relativity implies you can also travel back in the, as the following limerick says:
- There was a young lady of Wight
- Who traveled much faster than light.
- She departed one day,
- In a relative way,
- And arrived on the previous night
- The point is that the theory of relativity says hat there is no unique measure of time that all observers will agree
- on Rather, each observer has his or her own measure of time. If it is possible for a rocket traveling below the
- speed of light to get from event A (say, the final of the 100-meter race of the Olympic Games in 202) to event B
- (say, the opening of the 100,004th meeting of the Congress of Alpha Centauri), then all observers will agree
- that event A happened before event B according to their times. Suppose, however, that the spaceship would
- have to travel faster than light to carry the news of the race to the Congress. Then observers moving at
- different speeds can disagree about whether event A occurred before B or vice versa. According to the time of
- an observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thus
- this observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-light
- speed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light,
- it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race.
- The theory of relativity says that the laws of physics appear the same to observers moving at different speeds.
- This has been well tested by experiment and is likely to remain a feature even if we find a more advanced
- theory to replace relativity Thus the moving observer would say that if faster-than-light travel is possible, it
- should be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If one
- went slightly faster, one could even get back before the race and place a bet on it in the sure knowledge that
- one would win.
- There is a problem with breaking the speed-of-light barrier. The theory of relativity says that the rocket power
- needed to accelerate a spaceship gets greater and greater the nearer it gets to the speed of light. We have
- experimental evidence for this, not with spaceships but with elementary particles in particle accelerators like
- those at Fermilab or CERN (European Centre for Nuclear Research). We can accelerate particles to 99.99
- percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-light
- barrier. Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyond
- the speed of light.
- That might seem to rule out both rapid space travel and travel back in time. However, there is a possible way
- out. It might be that one could warp space-time so that there was a shortcut between A and B One way of doing
- this would be to create a wormhole between A and B. As its name suggests, a wormhole is a thin tube of
- space-time which can connect two nearly flat regions far apart.
- There need be no relation between the distance through the wormhole and the separation of its ends in the
- nearly Hat background. Thus one could imagine that one could create or find a wormhole that world lead from
- the vicinity of the Solar System to Alpha Centauri. The distance through the wormhole might be only a few
- million miles even though earth and Alpha Centauri are twenty million million miles apart in ordinary space. This
- would allow news of the 100-meter race to reach the opening of the Congress. But then an observer moving
- toward 6e earth should also be able to find another wormhole that would enable him to get from the opening of
- A Brief History of Time - Stephen Hawking... Chapter 10
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/i.html (2 of 5) [2/20/2001 3:15:45 AM]
- the Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any other
- possible form of travel faster than light, would allow one to travel into the past.
- The idea of wormholes between different regions of space-time was not an invention of science fiction writers
- but came from a very respectable source.
- In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what
- they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long
- enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off.
- However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open.
- To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a
- region of space-time with negative curvature, like the surface of a saddle. Ordi-nary matter, which has a
- positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs,
- in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.
- Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to
- the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So
- these classical laws would have ruled out any possibility of time travel. However, as has been described in
- earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle. The
- quantum laws are more liberal and allow you to be overdrawn on one or two accounts provided the total
- balance is positive. In other words, quantum theory allows the energy density to be negative in some places,
- provided that this is made up for by positive energy densities in other places, so that the total energy re-mains
- positive. An example of how quantum theory can allow negative energy densities is provided by what is called
- the Casimir effect. As we saw in Chapter 7, even what we think of as “empty” space is filled with pairs of virtual
- particles and antiparticles that appear together, move apart, and come back together and annihilate each other.
- Now, suppose one has two parallel metal plates a short distance apart. The plates will act like mirrors for the
- virtual photons or particles of light. In fact they will form a cavity between them, a bit like an organ pipe that will
- resonate only at certain notes. This means that virtual photons can occur in the space between the plates only
- if their wavelengths (the distance between the crest of one wave and the next) fit a whole number of times into
- the gap between the plates. If the width of a cavity is a whole number of wavelengths plus a fraction of a
- wave-length, then after some reflections backward and forward between the plates, the crests of one wave will
- coincide with the troughs of another and the waves will cancel out.
- Because the virtual photons between the plates can have only the resonant wavelengths, there will be slightly
- fewer of them than in the region outside the plates where virtual photons can have any wavelength. Thus there
- will be slightly fewer virtual photons hitting the inside surfaces of the plates than the outside surfaces. One
- would therefore expect a force on the plates, pushing them toward each other. This force has actually been
- detected and has the predicted value. Thus we have experimental evidence that virtual particles exist and have
- real effects.
- The fact that there are fewer virtual photons between the plates means that their energy density will be less
- than elsewhere. But the total energy density in “empty” space far away from the plates must be zero, because
- otherwise the energy density would warp the space and it would not be almost flat. So, if the energy density
- between the plates is less than the energy density far away, it must be negative.
- We thus have experimental evidence both that space-time can be warped (from the bending of light during
- eclipses) and that it can be curved in the way necessary to allow time travel (from the Casimir effect). One
- might hope therefore that as we advance in science and technology, we would eventually manage to build a
- time machine. But if so, why hasn’t anyone come back from the future and told us how to do it? There might be
- good reasons why it would be unwise to give us the secret of time travel at our present primitive state of
- development, but unless human nature changes radically, it is difficult to believe that some visitor from the
- future wouldn’t spill the beans. Of course, some people would claim that sightings of UFOs are evidence that
- we are being visited either by aliens or by people from the future. (If the aliens were to get here in reasonable
- time, they would need faster-than-light travel, so the two possibilities may be equivalent.)
- However, I think that any visit by aliens or people from the future would be much more obvious and, probably,
- much more unpleasant. If they are going to reveal themselves at all, why do so only to those who are not
- A Brief History of Time - Stephen Hawking... Chapter 10
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/i.html (3 of 5) [2/20/2001 3:15:45 AM]
- regarded as reliable witnesses? If they are trying to warn us of some great danger, they are not being very
- effective.
- A possible way to explain the absence of visitors from the future would be to say that the past is fixed because
- we have observed it and seen that it does not have the kind of warping needed to allow travel back from the
- future. On the other hand, the future is unknown and open, so it might well have the curvature required. This
- would mean that any time travel would be confined to the future. There would be no chance of Captain Kirk and
- the Starship Enterprise turning up at the present time.
- This might explain why we have not yet been overrun by tourists from the future, but it would not avoid the
- problems that would arise if one were able to go back and change history. Suppose, for example, you went
- back and killed your great-great-grandfather while he was still a child. There are many versions of this paradox
- but they are essentially equivalent: one would get contradictions if one were free to change the past.
- There seem to be two possible resolutions to the paradoxes posed by time travel. One I shall call the consistent
- histories approach. It says that even if space-time is warped so that it would be possible to travel into the past,
- what happens in space-time must be a consistent solution of the laws of physics. According to this viewpoint,
- you could not go back in time unless history showed that you had already arrived in the past and, while there,
- had not killed your great-great-grandfather or committed any other acts that would conflict with your current
- situation in the present. Moreover, when you did go back, you wouldn’t be able to change recorded history.
- That means you wouldn’t have free will to do what you wanted. Of course, one could say that free will is an
- illusion anyway. If there really is a complete unified theory that governs everything, it presumably also
- determines your actions. But it does so in a way that is impossible to calculate for an organism that is as
- complicated as a human being. The reason we say that humans have free will is because we can’t predict what
- they will do. However, if the human then goes off in a rocket ship and comes back before he or she set off, we
- will be able to predict what he or she will do because it will be part of recorded history. Thus, in that situation,
- the time traveler would have no free will.
- The other possible way to resolve the paradoxes of time travel might be called the alternative histories
- hypothesis. The idea here is that when time travelers go back to the past, they enter alternative histories which
- differ from recorded history. Thus they can act freely, without the constraint of consistency with their previous
- history. Steven Spiel-berg had fun with this notion in the Back to the Future films: Marty McFly was able to go
- back and change his parents’ courtship to a more satisfactory history.
- The alternative histories hypothesis sounds rather like Richard Feynman’s way of expressing quantum theory
- as a sum over histories, which was described in Chapters 4 and 8. This said that the universe didn’t just have a
- single history: rather it had every possible history, each with its own probability. However, there seems to be an
- important difference between Feynman’s proposal and alternative histories. In Feynman’s sum, each history
- comprises a complete space-time and everything in it. The space-time may be so warped that it is possible to
- travel in a rocket into the past. But the rocket would remain in the same space-time and therefore the same
- history, which would have to be consistent. Thus Feynman’s sum over histories proposal seems to support the
- consistent histories hypothesis rather than the alternative histories.
- The Feynman sum over histories does allow travel into the past on a microscopic scale. In Chapter 9 we saw
- that the laws of science are unchanged by combinations of the operations C, P, and T. This means that an
- antiparticle spinning in the anticlockwise direction and moving from A to B can also be viewed as an ordinary
- particle spinning clockwise and moving backward in time from B to A. Similarly, an ordinary particle moving
- forward in time is equivalent to an antiparticle moving backward in time. As has been discussed in this chapter
- and Chapter 7, “empty” space is filled with pairs of virtual particles and antiparticles that appear together, move
- apart, and then come back together and annihilate each other.
- So, one can regard the pair of particles as a single particle moving on a closed loop in space-time. When the
- pair is moving forward in time (from the event at which it appears to that at which it annihilates), it is called a
- particle. But when the particle is traveling back in time (from the event at which the pair annihilates to that at
- which it appears), it is said to be an antiparticle traveling forward in time.
- The explanation of how black holes can emit particles and radiation (given in Chapter 7) was that one member
- A Brief History of Time - Stephen Hawking... Chapter 10
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/i.html (4 of 5) [2/20/2001 3:15:45 AM]
- of a virtual particle/ antiparticle pair (say, the antiparticle) might fall into the black hole, leaving the other
- member without a partner with which to annihilate. The forsaken particle might fall into the hole as well, but it
- might also escape from the vicinity of the black hole. If so, to an observer at a distance it would appear to be a
- particle emitted by the black hole.
- One can, however, have a different but equivalent intuitive picture of the mechanism for emission from black
- holes. One can regard the member of the virtual pair that fell into the black hole (say, the antiparticle) as a
- particle traveling backward in time out of the hole. When it gets to the point at which the virtual
- particle/antiparticle pair appeared together, it is scattered by the gravitational field into a particle traveling
- forward in time and escaping from the black hole. If, instead, it were the particle member of the virtual pair that
- fell into the hole, one could regard it as an antiparticle traveling back in time and coming out of the black hole.
- Thus the radiation by black holes shows that quantum theory allows travel back in time on a microscopic scale
- and that such time travel can produce observable effects.
- One can therefore ask: does quantum theory allow time travel on a macroscopic scale, which people could
- use? At first sight, it seems it should. The Feynman sum over histories proposal is supposed to be over all
- histories. Thus it should include histories in which space-time is so warped that it is possible to travel into the
- past. Why then aren’t we in trouble with history? Suppose, for example, someone had gone back and given the
- Nazis the secret of the atom bomb?
- One would avoid these problems if what I call the chronology protection conjecture holds. This says that the
- laws of physics conspire to prevent macroscopic bodies from carrying information into the past. Like the cosmic
- censorship conjecture, it has not been proved but there are reasons to believe it is true.
- The reason to believe that chronology protection operates is that when space-time is warped enough to make
- travel into the past possible, virtual particles moving on closed loops in space-time can become real particles
- traveling forward in time at or below the speed of light. As these particles can go round the loop any number of
- times, they pass each point on their route many times. Thus their energy is counted over and over again and
- the energy density will become very large. This could give space-time a positive curvature that would not allow
- travel into the past. It is not yet clear whether these particles would cause positive or negative curvature or
- whether the curvature produced by some kinds of virtual particles might cancel that produced by other kinds.
- Thus the possibility of time travel remains open. But I’m not going to bet on it. My opponent might have the
- unfair advantage of knowing the future.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 10
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/i.html (5 of 5) [2/20/2001 3:15:45 AM]
- CHAPTER 11
- THE UNIFICATION OF PHYSICS
- As was explained in the first chapter, it would be very difficult to construct a complete unified theory of
- everything in the universe all at one go. So instead we have made progress by finding partial theories that
- describe a limited range of happenings and by neglecting other effects or approximating them by certain
- numbers. (Chemistry, for example, allows us to calculate the interactions of atoms, without knowing the internal
- structure of an atom’s nucleus.) Ultimately, however, one would hope to find a complete, consistent, unified
- theory that would include all these partial theories as approximations, and that did not need to be adjusted to fit
- the facts by picking the values of certain arbitrary numbers in the theory. The quest for such a theory is known
- as “the unification of physics.” Einstein spent most of his later years unsuccessfully searching for a unified
- theory, but the time was not ripe: there were partial theories for gravity and the electromagnetic force, but very
- little was known about the nuclear forces. Moreover, Einstein refused to believe in the reality of quantum
- mechanics, despite the important role he had played in its development. Yet it seems that the uncertainty
- principle is a fundamental feature of the universe we live in. A successful unified theory must, therefore,
- necessarily incorporate this principle.
- As I shall describe, the prospects for finding such a theory seem to be much better now because we know so
- much more about the universe. But we must beware of overconfidence – we have had false dawns before! At
- the beginning of this century, for example, it was thought that everything could be explained in terms of the
- properties of continuous matter, such as elasticity and heat conduction. The discovery of atomic structure and
- the uncertainty principle put an emphatic end to that. Then again, in 1928, physicist and Nobel Prize winner
- Max Born told a group of visitors to Gottingen University, “Physics, as we know it, will be over in six months.”
- His confidence was based on the recent discovery by Dirac of the equation that governed the electron. It was
- thought that a similar equation would govern the proton, which was the only other particle known at the time,
- and that would be the end of theoretical physics. However, the discovery of the neutron and of nuclear forces
- knocked that one on the head too. Having said this, I still believe there are grounds for cautious optimism that
- we may now be near the end of the search for the ultimate laws of nature.
- In previous chapters I have described general relativity, the partial theory of gravity, and the partial theories that
- govern the weak, the strong, and the electromagnetic forces. The last three may be combined in so-called
- grand unified theories, or GUTs, which are not very satisfactory because they do not include gravity and
- because they contain a number of quantities, like the relative masses of different particles, that cannot be
- predicted from the theory but have to be chosen to fit observations. The main difficulty in finding a theory that
- unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate
- the uncertainty principle of quantum mechanics. On the other hand, the other partial theories depend on
- quantum mechanics in an essential way. A necessary first step, therefore, is to combine general relativity with
- the uncertainty principle. As we have seen, this can produce some remarkable consequences, such as black
- holes not being black, and the universe not having any singularities but being completely self-contained and
- without a boundary. The trouble is, as explained in Chapter 7, that the uncertainty principle means that even
- “empty” space is filled with pairs of virtual particles and antiparticles. These pairs would have an infinite amount
- of energy and, therefore, by Einstein’s famous equation E = mc2, they would have an infinite amount of mass.
- Their gravitational attraction would thus curve up the universe to infinitely small size.
- Rather similar, seemingly absurd infinities occur in the other partial theories, but in all these cases the infinities
- can be canceled out by a process called renormalization. This involves canceling the infinities by introducing
- other infinities. Although this technique is rather dubious mathematically, it does seem to work in practice, and
- has been used with these theories to make predictions that agree with observations to an extraordinary degree
- of accuracy. Renormalization, however, does have a serious drawback from the point of view of trying to find a
- complete theory, because it means that the actual values of the masses and the strengths of the forces cannot
- be predicted from the theory, but have to be chosen to fit the observations.
- In attempting to incorporate the uncertainty principle into general relativity, one has only two quantities that can
- be adjusted: the strength of gravity and the value of the cosmological constant. But adjusting these is not
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (1 of 11) [2/20/2001 3:15:56 AM]
- sufficient to remove all the infinities. One therefore has a theory that seems to predict that certain quantities,
- such as the curvature of space-time, are really infinite, yet these quantities can be observed and measured to
- be perfectly finite! This problem in combining general relativity and the uncertainty principle had been
- suspected for some time, but was finally confirmed by detailed calculations in 1972. Four years later, a possible
- solution, called “supergravity,” was suggested. The idea was to combine the spin-2 particle called the graviton,
- which carries the gravitational force, with certain other particles of spin 3/2, 1, ½, and 0. In a sense, all these
- particles could then be regarded as different aspects of the same “superparticle,” thus unifying the matter
- particles with spin ½ and 3/2 with the force-carrying particles of spin 0, 1, and 2. The virtual particle/antiparticle
- pairs of spin ½ and 3/2 would have negative energy, and so would tend to cancel out the positive energy of the
- spin 2, 1, and 0 virtual pairs. This would cause many of the possible infinities to cancel out, but it was
- suspected that some infinities might still remain. However, the calculations required to find out whether or not
- there were any infinities left uncancelled were so long and difficult that no one was prepared to undertake them.
- Even with a computer it was reckoned it would take at least four years, and the chances were very high that
- one would make at least one mistake, probably more. So one would know one had the right answer only if
- someone else repeated the calculation and got the same answer, and that did not seem very likely!
- Despite these problems, and the fact that the particles in the super-gravity theories did not seem to match the
- observed particles, most scientists believed that supergravity was probably the right answer to the problem of
- the unification of physics. It seemed the best way of unifying gravity with the other forces. However, in 1984
- there was a remarkable change of opinion in favor of what are called string theories. In these theories the basic
- objects are not particles, which occupy a single point of space, but things that have a length but no other
- dimension, like an infinitely thin piece of string. These strings may have ends (the so-called open strings) or
- they may be joined up with themselves in closed loops (closed strings) Figure 11:1 and Figure 11:2.
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (2 of 11) [2/20/2001 3:15:56 AM]
- Figures 11:1 & 11:2
- A particle occupies one point of space at each instant of time. Thus its history can be represented by a line in
- space-time (the “world-line”). A string, on the other hand, occupies a line in space at each moment of time. So
- its history in space-time is a two-dimensional surface called the world-sheet. (Any point on such a world-sheet
- can be described by two numbers, one specifying the time and the other the position of the point on the string.)
- The world-sheet of an open string is a strip: its edges represent the paths through space-time of the ends of the
- string Figure 11:1. The world-sheet of a closed string is a cylinder or tube Figure 11:2: a slice through the tube
- is a circle, which represents the position of the string at one particular time.
- Two pieces of string can join together to form a single string; in the case of open strings they simply join at the
- ends Figure 11:3, while in the case of closed strings it is like the two legs joining on a pair of trousers Figure
- 11:4.
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (3 of 11) [2/20/2001 3:15:56 AM]
- Figure 11:3
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (4 of 11) [2/20/2001 3:15:56 AM]
- Figure 11:4
- Similarly, a single piece of string can divide into two strings. In string theories, what were previously thought of
- as particles are now pictured as waves traveling down the string, like waves on a vibrating kite string. The
- emission or absorption of one particle by another corresponds to the dividing or joining together of strings. For
- example, the gravitational force of the sun on the earth was pictured in particle theories as being caused by the
- emission of a graviton by a particle in the sun and its absorption by a particle in the earth Figure 11:5.
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (5 of 11) [2/20/2001 3:15:56 AM]
- Figures 11:5 & 11:6
- In string theory, this process corresponds to an H-shaped tube or pipe Figure 11:6 (string theory is rather like
- plumbing, in a way). The two vertical sides of the H correspond to the particles in the sun and the earth, and the
- horizontal crossbar corresponds to the graviton that travels between them.
- String theory has a curious history. It was originally invented in the late 1960s in an attempt to find a theory to
- describe the strong force. The idea was that particles like the proton and the neutron could be regarded as
- waves on a string. The strong forces between the particles would correspond to pieces of string that went
- between other bits of string, as in a spider’s web. For this theory to give the observed value of the strong force
- between particles, the strings had to be like rubber bands with a pull of about ten tons.
- In 1974 Joel Scherk from Paris and John Schwarz from the California Institute of Technology published a paper
- in which they showed that string theory could describe the gravitational force, but only if the tension in the string
- were very much higher, about a thousand million million million million million million tons (1 with thirty-nine
- zeros after it). The predictions of the string theory would be just the same as those of general relativity on
- normal length scales, but they would differ at very small distances, less than a thousand million million million
- million millionth of a centimeter (a centimeter divided by 1 with thirty-three zeros after it). Their work did not
- receive much attention, however, because at just about that time most people abandoned the original string
- theory of the strong force in favor of the theory based on quarks and gluons, which seemed to fit much better
- with observations. Scherk died in tragic circumstances (he suffered from diabetes and went into a coma when
- no one was around to give him an injection of insulin). So Schwarz was left alone as almost the only supporter
- of string theory, but now with the much higher proposed value of the string tension.
- In 1984 interest in strings suddenly revived, apparently for two reasons. One was that people were not really
- making much progress toward showing that supergravity was finite or that it could explain the kinds of particles
- that we observe. The other was the publication of a paper by John Schwarz and Mike Green of Queen Mary
- College, London, that showed that string theory might be able to explain the existence of particles that have a
- built-in left-handedness, like some of the particles that we observe. Whatever the reasons, a large number of
- people soon began to work on string theory and a new version was developed, the so-called heterotic string,
- which seemed as if it might be able to explain the types of particles that we observe.
- String theories also lead to infinities, but it is thought they will all cancel out in versions like the heterotic string
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (6 of 11) [2/20/2001 3:15:56 AM]
- (though this is not yet known for certain). String theories, however, have a bigger problem: they seem to be
- consistent only if space-time has either ten or twenty-six dimensions, instead of the usual four! Of course, extra
- space-time dimensions are a commonplace of science fiction indeed, they provide an ideal way of overcoming
- the normal restriction of general relativity that one cannot travel faster than light or back in time (see Chapter
- 10). The idea is to take a shortcut through the extra dimensions. One can picture this in the following way.
- Imagine that the space we live in has only two dimensions and is curved like the surface of an anchor ring or
- torus Figure 11:7.
- Figure 11:7
- If you were on one side of the inside edge of the ring and you wanted to get to a point on the other side, you
- would have to go round the inner edge of the ring. However, if you were able to travel in the third dimension,
- you could cut straight across.
- Why don’t we notice all these extra dimensions, if they are really there? Why do we see only three space
- dimensions and one time dimension? The suggestion is that the other dimensions are curved up into a space of
- very small size, something like a million million million million millionth of an inch. This is so small that we just
- don’t notice it: we see only one time dimension and three space dimensions, in which space-time is fairly flat. It
- is like the surface of a straw. If you look at it closely, you see it is two-dimensional (the position of a point on the
- straw is described by two numbers, the length along the straw and the distance round the circular direction).
- But if you look at it from a distance, you don’t see the thickness of the straw and it looks one-dimensional (the
- position of a point is specified only by the length along the straw). So it is with space-time: on a very small scale
- it is ten-dimensional and highly curved, but on bigger scales you don’t see the curvature or the extra
- dimensions. If this picture is correct, it spells bad news for would-be space travelers: the extra dimensions
- would be far too small to allow a spaceship through. However, it raises another major problem. Why should
- some, but not all, of the dimensions be curled up into a small ball? Presumably, in the very early universe all
- the dimensions would have been very curved. Why did one time dimension and three space dimensions flatten
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (7 of 11) [2/20/2001 3:15:56 AM]
- out, while the other dimensions remain tightly curled up?
- One possible answer is the anthropic principle. Two space dimensions do not seem to be enough to allow for
- the development of complicated beings like us. For example, two-dimensional animals living on a
- one-dimensional earth would have to climb over each other in order to get past each other. If a two-dimensional
- creature ate something it could not digest completely, it would have to bring up the remains the same way it
- swallowed them, because if there were a passage right through its body, it would divide the creature into two
- separate halves: our two-dimensional being would fall apart Figure 11:8. Similarly, it is difficult to see how there
- could be any circulation of the blood in a two-dimensional creature.
- Figure 11:8
- There would also be problems with more than three space dimensions. The gravitational force between two
- bodies would decrease more rapidly with distance than it does in three dimensions. (In three dimensions, the
- gravitational force drops to 1/4 if one doubles the distance. In four dimensions it would drop to 1/5, in five
- dimensions to 1/6, and so on.) The significance of this is that the orbits of planets, like the earth, around the sun
- would be unstable: the least disturbance from a circular orbit (such as would be caused by the gravitational
- attraction of other planets) would result in the earth spiraling away from or into the sun. We would either freeze
- or be burned up. In fact, the same behavior of gravity with distance in more than three space dimensions
- means that the sun would not be able to exist in a stable state with pressure balancing gravity. It would either
- fall apart or it would collapse to form a black hole. In either case, it would not be of much use as a source of
- heat and light for life on earth. On a smaller scale, the electrical forces that cause the electrons to orbit round
- the nucleus in an atom would behave in the same way as gravitational forces. Thus the electrons would either
- escape from the atom altogether or would spiral into the nucleus. In either case, one could not have atoms as
- we know them.
- It seems clear then that life, at least as we know it, can exist only in regions of space-time in which one time
- dimension and three space dimensions are not curled up small. This would mean that one could appeal to the
- weak anthropic principle, provided one could show that string theory does at least allow there to be such
- regions of the universe – and it seems that indeed string theory does. There may well be other regions of the
- universe, or other universes (whatever that may mean), in which all the dimensions are curled up small or in
- which more than four dimensions are nearly flat, but there would be no intelligent beings in such regions to
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (8 of 11) [2/20/2001 3:15:56 AM]
- observe the different number of effective dimensions.
- Another problem is that there are at least four different string theories (open strings and three different closed
- string theories) and millions of ways in which the extra dimensions predicted by string theory could be curled
- up. Why should just one string theory and one kind of curling up be picked out? For a time there seemed no
- answer, and progress got bogged down. Then, from about 1994, people started discovering what are called
- dualities: different string theories and different ways of curling up the extra dimensions could lead to the same
- results in four dimensions. Moreover, as well as particles, which occupy a single point of space, and strings,
- which are lines, there were found to be other objects called p-branes, which occupied two-dimensional or
- higher-dimensional volumes in space. (A particle can be regarded as a 0-brane and a string as a 1-brane but
- there were also p-branes for p=2 to p=9.) What this seems to indicate is that there is a sort of democracy
- among supergravity, string, and p-brane theories: they seem to fit together but none can be said to be more
- fundamental than the others. They appear to be different approximations to some fundamental theory that are
- valid in different situations.
- People have searched for this underlying theory, but without any success so far. However, I believe there may
- not be any single formulation of the fundamental theory any more than, as Godel showed, one could formulate
- arithmetic in terms of a single set of axioms. Instead it may be like maps – you can’t use a single map to
- describe the surface of the earth or an anchor ring: you need at least two maps in the case of the earth and four
- for the anchor ring to cover every point. Each map is valid only in a limited region, but different maps will have a
- region of overlap. The collection of maps provides a complete description of the surface. Similarly, in physics it
- may be necessary to use different formulations in different situations, but two different formulations would agree
- in situations where they can both be applied. The whole collection of different formulations could be regarded
- as a complete unified theory, though one that could not be expressed in terms of a single set of postulates.
- But can there really be such a unified theory? Or are we perhaps just chasing a mirage? There seem to be
- three possibilities:
- 1. There really is a complete unified theory (or a collection of overlapping formulations), which we will someday
- discover if we are smart enough.
- 2. There is no ultimate theory of the universe, just an infinite sequence of theories that describe the universe
- more and more accurately.
- 3. There is no theory of the universe: events cannot be predicted beyond a certain extent but occur in a random
- and arbitrary manner.
- Some would argue for the third possibility on the grounds that if there were a complete set of laws, that would
- infringe God’s freedom to change his mind and intervene in the world. It’s a bit like the old paradox: can God
- make a stone so heavy that he can’t lift it? But the idea that God might want to change his mind is an example
- of the fallacy, pointed out by St. Augustine, of imagining God as a being existing in time: time is a property only
- of the universe that God created. Presumably, he knew what he intended when he set it up!
- With the advent of quantum mechanics, we have come to recognize that events cannot be predicted with
- complete accuracy but that there is always a degree of uncertainty. If one likes, one could ascribe this
- randomness to the intervention of God, but it would be a very strange kind of intervention: there is no evidence
- that it is directed toward any purpose. Indeed, if it were, it would by definition not be random. In modern times,
- we have effectively removed the third possibility above by redefining the goal of science: our aim is to formulate
- a set of laws that enables us to predict events only up to the limit set by the uncertainty principle.
- The second possibility, that there is an infinite sequence of more and more refined theories, is in agreement
- with all our experience so far. On many occasions we have increased the sensitivity of our measurements or
- made a new class of observations, only to discover new phenomena that were not predicted by the existing
- theory, and to account for these we have had to develop a more advanced theory. It would therefore not be
- very surprising if the present generation of grand unified theories was wrong in claiming that nothing essentially
- new will happen between the electroweak unification energy of about 100 GeV and the grand unification energy
- of about a thousand million million GeV. We might indeed expect to find several new layers of structure more
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (9 of 11) [2/20/2001 3:15:56 AM]
- basic than the quarks and electrons that we now regard as “elementary” particles.
- However, it seems that gravity may provide a limit to this sequence of “boxes within boxes.” If one had a
- particle with an energy above what is called the Planck energy, ten million million million GeV (1 followed by
- nineteen zeros), its mass would be so concentrated that it would cut itself off from the rest of the universe and
- form a little black hole. Thus it does seem that the sequence of more and more refined theories should have
- some limit as we go to higher and higher energies, so that there should be some ultimate theory of the
- universe. Of course, the Planck energy is a very long way from the energies of around a hundred GeV, which
- are the most that we can produce in the laboratory at the present time. We shall not bridge that gap with
- particle accelerators in the foreseeable future! The very early stages of the universe, however, are an arena
- where such energies must have occurred. I think that there is a good chance that the study of the early
- universe and the requirements of mathematical consistency will lead us to a complete unified theory within the
- lifetime of some of us who are around today, always presuming we don’t blow ourselves up first.
- What would it mean if we actually did discover the ultimate theory of the universe? As was explained in Chapter
- 1, we could never be quite sure that we had indeed found the correct theory, since theories can’t be proved.
- But if the theory was mathematically consistent and always gave predictions that agreed with observations, we
- could be reasonably confident that it was the right one. It would bring to an end a long and glorious chapter in
- the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionize the
- ordinary person’s understanding of the laws that govern the universe. In Newton’s time it was possible for an
- educated person to have a grasp of the whole of human knowledge, at least in outline. But since then, the pace
- of the development of science has made this impossible. Because theories are always being changed to
- account for new observations, they are never properly digested or simplified so that ordinary people can
- understand them. You have to be a specialist, and even then you can only hope to have a proper grasp of a
- small proportion of the scientific theories. Further, the rate of progress is so rapid that what one learns at school
- or university is always a bit out of date. Only a few people can keep up with the rapidly advancing frontier of
- knowledge, and they have to devote their whole time to it and specialize in a small area. The rest of the
- population has little idea of the advances that are being made or the excitement they are generating. Seventy
- years ago, if Eddington is to be believed, only two people understood the general theory of relativity. Nowadays
- tens of thousands of university graduates do, and many millions of people are at least familiar with the idea. If a
- complete unified theory was discovered, it would only be a matter of time before it was digested and simplified
- in the same way and taught in schools, at least in outline. We would then all be able to have some
- understanding of the laws that govern the universe and are responsible for our existence.
- Even if we do discover a complete unified theory, it would not mean that we would be able to predict events in
- general, for two reasons. The first is the limitation that the uncertainty principle of quantum mechanics sets on
- our powers of prediction. There is nothing we can do to get around that. In practice, however, this first limitation
- is less restrictive than the second one. It arises from the fact that we could not solve the equations of the theory
- exactly, except in very simple situations. (We cannot even solve exactly for the motion of three bodies in
- Newton’s theory of gravity, and the difficulty increases with the number of bodies and the complexity of the
- theory.) We already know the laws that govern the behavior of matter under all but the most extreme
- conditions. In particular, we know the basic laws that underlie all of chemistry and biology. Yet we have
- certainly not reduced these subjects to the status of solved problems: we have, as yet, had little success in
- predicting human behavior from mathematical equations! So even if we do find a complete set of basic laws,
- there will still be in the years ahead the intellectually challenging task of developing better approximation
- methods, so that we can make useful predictions of the probable outcomes in complicated and realistic
- situations. A complete, consistent, unified theory is only the first step: our goal is a complete understanding of
- the events around us, and of our own existence.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (10 of 11) [2/20/2001 3:15:56 AM]
- A Brief History of Time - Stephen Hawking... Chapter 11
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (11 of 11) [2/20/2001 3:15:56 AM]
- CHAPTER 12
- CONCLUSION
- We find ourselves in a bewildering world. We want to make sense of what we see around us and to ask: What
- is the nature of the universe? What is our place in it and where did it and we come from? Why is it the way it is?
- To try to answer these questions we adopt some “world picture.” Just as an infinite tower of tortoises supporting
- the fiat earth is such a picture, so is the theory of superstrings. Both are theories of the universe, though the
- latter is much more mathematical and precise than the former. Both theories lack observational evidence: no
- one has ever seen a giant tortoise with the earth on its back, but then, no one has seen a superstring either.
- However, the tortoise theory fails to be a good scientific theory because it predicts that people should be able to
- fall off the edge of the world. This has not been found to agree with experience, unless that turns out to be the
- explanation for the people who are supposed to have disappeared in the Bermuda Triangle!
- The earliest theoretical attempts to describe and explain the universe involved the idea that events and natural
- phenomena were controlled by spirits with human emotions who acted in a very humanlike and unpredictable
- manner. These spirits inhabited natural objects, like rivers and mountains, including celestial bodies, like the
- sun and moon. They had to be placated and their favor sought in order to ensure the fertility of the soil and the
- rotation of the seasons. Gradually, however, it must have been noticed that there were certain regularities: the
- sun always rose in the east and set in the west, whether or not a sacrifice had been made to the sun god.
- Further, the sun, the moon, and the planets followed precise paths across the sky that could be predicted in
- advance with considerable accuracy. The sun and the moon might still be gods, but they were gods who
- obeyed strict laws, apparently without any exceptions, if one discounts stories like that of the sun stopping for
- Joshua.
- At first, these regularities and laws were obvious only in astronomy and a few other situations. However, as
- civilization developed, and particularly in the last 300 years, more and more regularities and laws were
- discovered. The success of these laws led Laplace at the beginning of the nineteenth century to postulate
- scientific determinism; that is, he suggested that there would be a set of laws that would determine the
- evolution of the universe precisely, given its configuration at one time.
- Laplace’s determinism was incomplete in two ways. It did not say how the laws should be chosen and it did not
- specify the initial configuration of the universe. These were left to God. God would choose how the universe
- began and what laws it obeyed, but he would not intervene in the universe once it had started. In effect, God
- was confined to the areas that nineteenth-century science did not understand.
- We now know that Laplace’s hopes of determinism cannot be realized, at least in the terms he had in mind.
- The uncertainty principle of quantum mechanics implies that certain pairs of quantities, such as the position and
- velocity of a particle, cannot both be predicted with complete accuracy. Quantum mechanics deals with this
- situation via a class of quantum theories in which particles don’t have well-defined positions and velocities but
- are represented by a wave. These quantum theories are deterministic in the sense that they give laws for the
- evolution of the wave with time. Thus if one knows the wave at one time, one can calculate it at any other time.
- The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions
- and velocities of particles. But maybe that is our mistake: maybe there are no particle positions and velocities,
- but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The
- resulting mismatch is the cause of the apparent unpredictability.
- In effect, we have redefined the task of science to be the discovery of laws that will enable us to predict events
- up to the limits set by the uncertainty principle. The question remains, however: how or why were the laws and
- the initial state of the universe chosen?
- In this book I have given special prominence to the laws that govern gravity, because it is gravity that shapes
- the large-scale structure of the universe, even though it is the weakest of the four categories of forces. The
- laws of gravity were incompatible with the view held until quite recently that the universe is unchanging in time:
- A Brief History of Time - Stephen Hawking... Chapter 12
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/k.html (1 of 4) [2/20/2001 3:16:08 AM]
- the fact that gravity is always attractive implies that the universe must be either expanding or contracting.
- According to the general theory of relativity, there must have been a state of infinite density in the past, the big
- bang, which would have been an effective beginning of time. Similarly, if the whole universe recollapsed, there
- must be another state of infinite density in the future, the big crunch, which would be an end of time. Even if the
- whole universe did not recollapse, there would be singularities in any localized regions that collapsed to form
- black holes. These singularities would be an end of time for anyone who fell into the black hole. At the big bang
- and other singularities, all the laws would have broken down, so God would still have had complete freedom to
- choose what happened and how the universe began.
- When we combine quantum mechanics with general relativity, there seems to be a new possibility that did not
- arise before: that space and time together might form a finite, four-dimensional space without singularities or
- boundaries, like the surface of the earth but with more dimensions. It seems that this idea could explain many
- of the observed features of the universe, such as its large-scale uniformity and also the smaller-scale
- departures from homogeneity, like galaxies, stars, and even human beings. It could even account for the arrow
- of time that we observe. But if the universe is completely self-contained, with no singularities or boundaries,
- and completely described by a unified theory, that has profound implications for the role of God as Creator.
- Einstein once asked the question: “How much choice did God have in constructing the universe?” If the no
- boundary proposal is correct, he had no freedom at all to choose initial conditions. He would, of course, still
- have had the freedom to choose the laws that the universe obeyed. This, however, may not really have been all
- that much of a choice; there may well be only one, or a small number, of complete unified theories, such as the
- heterotic string theory, that are self-consistent and allow the existence of structures as complicated as human
- beings who can investigate the laws of the universe and ask about the nature of God.
- Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes
- fire into the equations and makes a universe for them to describe? The usual approach of science of
- constructing a mathematical model cannot answer the questions of why there should be a universe for the
- model to describe. Why does the universe go to all the bother of existing? Is the unified theory so compelling
- that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on
- the universe? And who created him?
- Up to now, most scientists have been too occupied with the development of new theories that describe what
- the universe is to ask the question why. On the other hand, the people whose business it is to ask why, the
- philosophers, have not been able to keep up with the advance of scientific theories. In the eighteenth century,
- philosophers considered the whole of human knowledge, including science, to be their field and discussed
- questions such as: did the universe have a beginning? However, in the nineteenth and twentieth centuries,
- science became too technical and mathematical for the philosophers, or anyone else except a few specialists.
- Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of
- this century, said, “The sole remaining task for philosophy is the analysis of language.” What a comedown from
- the great tradition of philosophy from Aristotle to Kant!
- However, if we do discover a complete theory, it should in time be understandable in broad principle by
- everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able
- to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to
- that, it would be the ultimate triumph of human reason – for then we would know the mind of God.
- ALBERT EINSTEIN
- Einstein’s connection with the politics of the nuclear bomb is well known: he signed the famous letter to
- President Franklin Roosevelt that persuaded the United States to take the idea seriously, and he engaged in
- postwar efforts to prevent nuclear war. But these were not just the isolated actions of a scientist dragged into
- the world of politics. Einstein’s life was, in fact, to use his own words, “divided between politics and equations.”
- Einstein’s earliest political activity came during the First World War, when he was a professor in Berlin.
- Sickened by what he saw as the waste of human lives, he became involved in antiwar demonstrations. His
- A Brief History of Time - Stephen Hawking... Chapter 12
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/k.html (2 of 4) [2/20/2001 3:16:08 AM]
- advocacy of civil disobedience and public encouragement of people to refuse conscription did little to endear
- him to his colleagues. Then, following the war, he directed his efforts toward reconciliation and improving
- international relations. This too did not make him popular, and soon his politics were making it difficult for him to
- visit the United States, even to give lectures.
- Einstein’s second great cause was Zionism. Although he was Jewish by descent, Einstein rejected the biblical
- idea of God. However, a growing awareness of anti-Semitism, both before and during the First World War, led
- him gradually to identify with the Jewish community, and later to become an outspoken supporter of Zionism.
- Once more unpopularity did not stop him from speaking his mind. His theories came under attack; an
- anti-Einstein organization was even set up. One man was convicted of inciting others to murder Einstein (and
- fined a mere six dollars). But Einstein was phlegmatic. When a book was published entitled 100 Authors
- Against Einstein, he retorted, “If I were wrong, then one would have been enough!”
- In 1933, Hitler came to power. Einstein was in America, and declared he would not return to Germany. Then,
- while Nazi militia raided his house and confiscated his bank account, a Berlin newspaper displayed the
- headline “Good News from Einstein – He’s Not Coming Back.” In the face of the Nazi threat, Einstein
- renounced pacifism, and eventually, fearing that German scientists would build a nuclear bomb, proposed that
- the United States should develop its own. But even before the first atomic bomb had been detonated, he was
- publicly warning of the dangers of nuclear war and proposing international control of nuclear weaponry.
- Throughout his life, Einstein’s efforts toward peace probably achieved little that would last – and certainly won
- him few friends. His vocal support of the Zionist cause, however, was duly recognized in 1952, when he was
- offered the presidency of Israel. He declined, saying he thought he was too naive in politics. But perhaps his
- real reason was different: to quote him again, “Equations are more important to me, because politics is for the
- present, but an equation is something for eternity.”
- GALILEO GALILEI
- Galileo, perhaps more than any other single person, was responsible for the birth of modern science. His
- renowned conflict with the Catholic Church was central to his philosophy, for Galileo was one of the first to
- argue that man could hope to understand how the world works, and, moreover, that we could do this by
- observing the real world.
- Galileo had believed Copernican theory (that the planets orbited the sun) since early on, but it was only when
- he found the evidence needed to support the idea that he started to publicly support it. He wrote about
- Copernicus’s theory in Italian (not the usual academic Latin), and soon his views became widely supported
- outside the universities. This annoyed the Aristotelian professors, who united against him seeking to persuade
- the Catholic Church to ban Copernicanism.
- Galileo, worried by this, traveled to Rome to speak to the ecclesiastical authorities. He argued that the Bible
- was not intended to tell us anything about scientific theories, and that it was usual to assume that, where the
- Bible conflicted with common sense, it was being allegorical. But the Church was afraid of a scandal that might
- undermine its fight against Protestantism, and so took repressive measures. It declared Copernicanism “false
- and erroneous” in 1616, and commanded Galileo never again to “defend or hold” the doctrine. Galileo
- acquiesced.
- In 1623, a longtime friend of Galileo’s became the Pope. Immediately Galileo tried to get the 1616 decree
- revoked. He failed, but he did manage to get permission to write a book discussing both Aristotelian and
- Copernican theories, on two conditions: he would not take sides and would come to the conclusion that man
- could in any case not determine how the world worked because God could bring about the same effects in
- ways unimagined by man, who could not place restrictions on God’s omnipotence.
- The book, Dialogue Concerning the Two Chief World Systems, was completed and published in 1632, with the
- full backing of the censors – and was immediately greeted throughout Europe as a literary and philosophical
- masterpiece. Soon the Pope, realizing that people were seeing the book as a convincing argument in favor of
- A Brief History of Time - Stephen Hawking... Chapter 12
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/k.html (3 of 4) [2/20/2001 3:16:08 AM]
- Copernicanism, regretted having allowed its publication. The Pope argued that although the book had the
- official blessing of the censors, Galileo had nevertheless contravened the 1616 decree. He brought Galileo
- before the Inquisition, who sentenced him to house arrest for life and commanded him to publicly renounce
- Copernicanism. For a second time, Galileo acquiesced.
- Galileo remained a faithful Catholic, but his belief in the independence of science had not been crushed. Four
- years before his death in 1642, while he was still under house arrest, the manuscript of his second major book
- was smuggled to a publisher in Holland. It was this work, referred to as Two New Sciences, even more than his
- support for Copernicus, that was to be the genesis of modern physics.
- ISAAC NEWTON
- Isaac Newton was not a pleasant man. His relations with other academics were notorious, with most of his later
- life spent embroiled in heated disputes. Following publication of Principia Mathematica – surely the most
- influential book ever written in physics – Newton had risen rapidly into public prominence. He was appointed
- president of the Royal Society and became the first scientist ever to be knighted.
- Newton soon clashed with the Astronomer Royal, John Flamsteed, who had earlier provided Newton with
- much-needed data for Principia, but was now withholding information that Newton wanted. Newton would not
- take no for an answer: he had himself appointed to the governing body of the Royal Observatory and then tried
- to force immediate publication of the data. Eventually he arranged for Flamsteed’s work to be seized and
- prepared for publication by Flamsteed’s mortal enemy, Edmond Halley. But Flamsteed took the case to court
- and, in the nick of time, won a court order preventing distribution of the stolen work. Newton was incensed and
- sought his revenge by systematically deleting all references to Flamsteed in later editions of Principia.
- A more serious dispute arose with the German philosopher Gottfried Leibniz. Both Leibniz and Newton had
- independently developed a branch of mathematics called calculus, which underlies most of modern physics.
- Although we now know that Newton discovered calculus years before Leibniz, he published his work much
- later. A major row ensued over who had been first, with scientists vigorously defending both contenders. It is
- remarkable, however, that most of the articles appearing in defense of Newton were originally written by his
- own hand – and only published in the name of friends! As the row grew, Leibniz made the mistake of appealing
- to the Royal Society to resolve the dispute. Newton, as president, appointed an “impartial” committee to
- investigate, coincidentally consisting entirely of Newton’s friends! But that was not all: Newton then wrote the
- committee’s report himself and had the Royal Society publish it, officially accusing Leibniz of plagiarism. Still
- unsatisfied, he then wrote an anonymous review of the report in the Royal Society’s own periodical. Following
- the death of Leibniz, Newton is reported to have declared that he had taken great satisfaction in “breaking
- Leibniz’s heart.”
- During the period of these two disputes, Newton had already left Cambridge and academe. He had been active
- in anti-Catholic politics at Cambridge, and later in Parliament, and was rewarded eventually with the lucrative
- post of Warden of the Royal Mint. Here he used his talents for deviousness and vitriol in a more socially
- acceptable way, successfully conducting a major campaign against counterfeiting, even sending several men to
- their death on the gallows.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Chapter 12
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/k.html (4 of 4) [2/20/2001 3:16:08 AM]
- GLOSSARY
- Absolute zero: The lowest possible temperature, at which substances contain no heat energy.
- Acceleration: The rate at which the speed of an object is changing.
- Anthropic principle: We see the universe the way it is because if it were different we would not be here to
- observe it.
- Antiparticle: Each type of matter particle has a corresponding antiparticle. When a particle collides with its
- antiparticle, they annihilate, leaving only energy.
- Atom: The basic unit of ordinary matter, made up of a tiny nucleus (consisting of protons and neutrons)
- surrounded by orbiting electrons.
- Big bang: The singularity at the beginning of the universe.
- Big crunch: The singularity at the end of the universe.
- Black hole: A region of space-time from which nothing, not even light, can escape, because gravity is so
- strong.
- Casimir effect: The attractive pressure between two flat, parallel metal plates placed very near to each other in
- a vacuum. The pressure is due to a reduction in the usual number of virtual particles in the space between the
- plates.
- Chandrasekhar limit: The maximum possible mass of a stable cold star, above which it must collapse into a
- black hole.
- Conservation of energy: The law of science that states that energy (or its equivalent in mass) can neither be
- created nor destroyed.
- Coordinates: Numbers that specify the position of a point in space and time.
- Cosmological constant: A mathematical device used by Einstein to give space-time an inbuilt tendency to
- expand.
- Cosmology: The study of the universe as a whole.
- Dark matter: Matter in galaxies, clusters, and possibly between clusters, that can not be observed directly but
- can be detected by its gravitational effect. As much as 90 percent of the mass of the universe may be in the
- form of dark matter.
- Duality: A correspondence between apparently different theories that lead to the same physical results.
- Einstein-Rosen bridge: A thin tube of space-time linking two black holes. Also see Wormhole.
- Electric charge: A property of a particle by which it may repel (or attract) other particles that have a charge of
- similar (or opposite) sign.
- Electromagnetic force: The force that arises between particles with electric charge; the second strongest of
- the four fundamental forces.
- Electron: A particle with negative electric charge that orbits the nucleus of an atom.
- Electroweak unification energy: The energy (around 100 GeV) above which the distinction between the
- electromagnetic force and the weak force disappears.
- A Brief History of Time - Stephen Hawking... Glossary
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/l.html (1 of 4) [2/20/2001 3:16:19 AM]
- Elementary particle: A particle that, it is believed, cannot be subdivided.
- Event: A point in space-time, specified by its time and place.
- Event horizon: The boundary of a black hole.
- Exclusion principle: The idea that two identical spin-1/2 particles cannot have (within the limits set by the
- uncertainty principle) both the same position and the same velocity.
- Field: Something that exists throughout space and time, as opposed to a particle that exists at only one point at
- a time.
- Frequency: For a wave, the number of complete cycles per second.
- Gamma rays: Electromagnetic rays of very short wavelength, produced in radio-active decay or by collisions of
- elementary particles.
- General relativity: Einstein’s theory based on the idea that the laws of science should be the same for all
- observers, no matter how they are moving. It explains the force of gravity in terms of the curvature of a
- four-dimensional space-time.
- Geodesic: The shortest (or longest) path between two points.
- Grand unification energy: The energy above which, it is believed, the electro-magnetic force, weak force, and
- strong force become indistinguishable from each other.
- Grand unified theory (GUT): A theory which unifies the electromagnetic, strong, and weak forces.
- Imaginary time: Time measured using imaginary numbers.
- Light cone: A surface in space-time that marks out the possible directions for light rays passing through a
- given event.
- Light-second (light-year): The distance traveled by light in one second (year).
- Magnetic field: The field responsible for magnetic forces, now incorporated along with the electric field, into the
- electromagnetic field.
- Mass: The quantity of matter in a body; its inertia, or resistance to acceleration.
- Microwave background radiation: The radiation from the glowing of the hot early universe, now so greatly
- red-shifted that it appears not as light but as microwaves (radio waves with a wavelength of a few centimeters).
- Also see COBE, on page 145.
- Naked singularity: A space-time singularity not surrounded by a black hole.
- Neutrino: An extremely light (possibly massless) particle that is affected only by the weak force and gravity.
- Neutron: An uncharged particle, very similar to the proton, which accounts for roughly half the particles in an
- atomic nucleus.
- Neutron star: A cold star, supported by the exclusion principle repulsion between neutrons.
- No boundary condition: The idea that the universe is finite but has no boundary (in imaginary time).
- Nuclear fusion: The process by which two nuclei collide and coalesce to form a single, heavier nucleus.
- Nucleus: The central part of an atom, consisting only of protons and neutrons, held together by the strong
- A Brief History of Time - Stephen Hawking... Glossary
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/l.html (2 of 4) [2/20/2001 3:16:19 AM]
- force.
- Particle accelerator: A machine that, using electromagnets, can accelerate moving charged particles, giving
- them more energy.
- Phase: For a wave, the position in its cycle at a specified time: a measure of whether it is at a crest, a trough,
- or somewhere in between.
- Photon: A quantum of light.
- Planck’s quantum principle: The idea that light (or any other classical waves) can be emitted or absorbed
- only in discrete quanta, whose energy is proportional to their wavelength.
- Positron: The (positively charged) antiparticle of the electron.
- Primordial black hole: A black hole created in the very early universe.
- Proportional: ‘X is proportional to Y’ means that when Y is multiplied by any number, so is X. ‘X is inversely
- proportional to Y’ means that when Y is multiplied by any number, X is divided by that number.
- Proton: A positively charged particle, very similar to the neutron, that accounts for roughly half the particles in
- the nucleus of most atoms.
- Pulsar: A rotating neutron star that emits regular pulses of radio waves.
- Quantum: The indivisible unit in which waves may be emitted or absorbed.
- Quantum chromodynamics (QCD): The theory that describes the interactions of quarks and gluons.
- Quantum mechanics: The theory developed from Planck’s quantum principle and Heisenberg’s uncertainty
- principle.
- Quark: A (charged) elementary particle that feels the strong force. Protons and neutrons are each composed of
- three quarks.
- Radar: A system using pulsed radio waves to detect the position of objects by measuring the time it takes a
- single pulse to reach the object and be reflected back.
- Radioactivity: The spontaneous breakdown of one type of atomic nucleus into another.
- Red shift: The reddening of light from a star that is moving away from us, due to the Doppler effect.
- Singularity: A point in space-time at which the space-time curvature becomes infinite.
- Singularity theorem: A theorem that shows that a singularity must exist under certain circumstances – in
- particular, that the universe must have started with a singularity.
- Space-time: The four-dimensional space whose points are events.
- Spatial dimension: Any of the three dimensions that are spacelike – that is, any except the time dimension.
- Special relativity: Einstein’s theory based on the idea that the laws of science should be the same for all
- observers, no matter how they are moving, in the absence of gravitational phenomena.
- Spectrum: The component frequencies that make up a wave. The visible part of the sun’s spectrum can be
- seen in a rainbow.
- Spin: An internal property of elementary particles, related to, but not identical to, the everyday concept of spin.
- A Brief History of Time - Stephen Hawking... Glossary
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/l.html (3 of 4) [2/20/2001 3:16:19 AM]
- Stationary state: One that is not changing with time: a sphere spinning at a constant rate is stationary because
- it looks identical at any given instant.
- String theory: A theory of physics in which particles are described as waves on strings. Strings have length but
- no other dimension.
- Strong force: The strongest of the four fundamental forces, with the shortest range of all. It holds the quarks
- together within protons and neutrons, and holds the protons and neutrons together to form atoms.
- Uncertainty principle: The principle, formulated by Heisenberg, that one can never be exactly sure of both the
- position and the velocity of a particle; the more accurately one knows the one, the less accurately one can
- know the other.
- Virtual particle: In quantum mechanics, a particle that can never be directly detected, but whose existence
- does have measurable effects.
- Wave/particle duality: The concept in quantum mechanics that there is no distinction between waves and
- particles; particles may sometimes behave like waves, and waves like particles.
- Wavelength: For a wave, the distance between two adjacent troughs or two adjacent crests.
- Weak force: The second weakest of the four fundamental forces, with a very short range. It affects all matter
- particles, but not force-carrying particles.
- Weight: The force exerted on a body by a gravitational field. It is proportional to, but not the same as, its mass.
- White dwarf: A stable cold star, supported by the exclusion principle repulsion between electrons.
- Wormhole: A thin tube of space-time connecting distant regions of the universe. Wormholes might also link to
- parallel or baby universes and could provide the possibility of time travel.
- PREVIOUS NEXT
- A Brief History of Time - Stephen Hawking... Glossary
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/l.html (4 of 4) [2/20/2001 3:16:19 AM]
- ACKNOWLEDGMENTS
- Many people have helped me in writing this book. My scientific colleagues have without exception been
- inspiring. Over the years my principal associates and collaborators were Roger Penrose, Robert Geroch,
- Brandon Carter, George Ellis, Gary Gibbons, Don Page, and Jim Hartle. I owe a lot to them, and to my
- research students, who have always given me help when needed.
- One of my students, Brian Whitt, gave me a lot of help writing the first edition of this book. My editor at Bantam
- Books, Peter Guzzardi, made innumerable comments which improved the book considerably. In addition, for
- this edition, I would like to thank Andrew Dunn, who helped me revise the text.
- I could not have written this book without my communication system. The software, called Equalizer, was
- donated by Walt Waltosz of Words Plus Inc., in Lancaster, California. My speech synthesizer was donated by
- Speech Plus, of Sunnyvale, California. The synthesizer and laptop computer were mounted on my wheelchair
- by David Mason, of Cambridge Adaptive Communication Ltd. With this system I can communicate better now
- than before I lost my voice.
- I have had a number of secretaries and assistants over the years in which I wrote and revised this book. On the
- secretarial side, I’m very grateful to Judy Fella, Ann Ralph, Laura Gentry, Cheryl Billington, and Sue Masey. My
- assistants have been Colin Williams, David Thomas, and Raymond Laflamme, Nick Phillips, Andrew Dunn,
- Stuart Jamieson, Jonathan Brenchley, Tim Hunt, Simon Gill, Jon Rogers, and Tom Kendall. They, my nurses,
- colleagues, friends, and family have enabled me to live a very full life and to pursue my research despite my
- disability.
- Stephen Hawking
- ABOUT THE AUTHOR
- Stephen Hawking, who was born in 1942 on the anniversary of Galileo’s death, holds Isaac Newton’s chair as
- Lucasian Professor of Mathematics at the University of Cambridge. Widely regarded as the most brilliant
- theoretical physicist since Einstein, he is also the author of Black Holes and Baby Universes, published in 1993,
- as well as numerous scientific papers and books.
- PREVIOUS
- A Brief History of Time - Stephen Hawking... Acknowledgments
- file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/m.html [2/20/2001 3:16:30 AM]
Add Comment
Please, Sign In to add comment