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Was there a beginning of time? Could time run backwards? Is the universe infinite or does it have boundaries? These are just some of the questions considered in an internationally acclaimed masterpiece by one of the world’s greatest thinkers. It begins by reviewing the great theories of the cosmos from Newton to Einstein, before delving into the secrets which still lie at the heart of space and time, from the Big Bang to black holes, via spiral galaxies and strong theory. To this day A Brief History of Time remains a staple of the scientific canon, and its succinct and clear language continues to introduce millions to the universe and its wonders.

Questions about our origins were once regarded as the territory of philosophers and theologians. But gradually the answers have been provided by science; speculations have been replaced by hard facts. Especially in the last two decades since the 1996 reissue of A Brief History of Time, we have made remarkable progress in understanding the genesis and evolution of the universe. Many of the ideas that I put forward as hypotheses have now been confirmed. And still other developments have been a complete surprise.

For example, in 1998, our picture of the universe’s future was radically revised. Two competing teams using the Hubble Space Telescope independently reached the conclusion that the expansion of our universe is accelerating. The implications for the fate of space are immediate: the eventual re-collapse of the universe (Friedmann’s big crunch, pp.50–2) no longer appears to be an option. Space, it seems, will expand for ever.

Why should space expand at an accelerating rate? The cause has become known as ‘dark energy’. But this is just a name; it doesn’t tell us anything in itself. In fact Friedmann’s original picture seemed compelling: either gravity is strong enough to pull everything back together, and the expansion decelerates over time; or it isn’t strong enough, and the expansion coasts along unimpeded. Neither of those scenarios suggested anything about the expansion actually speeding up.

Einstein’s own work holds part of the answer. At one point, he tried modifying his theory of general relativity to make the universe eternal and unchanging – something he was convinced ought to be true – by introducing a so-called cosmological constant (p.47) into his equations. This constant plays the role of an ‘antigravity’ force built into the very fabric of space-time. That was in 1917, long before the expansion of the universe was established. Later, Einstein retracted the idea once he realized that Friedmann’s models neatly explained Edwin Hubble’s observations (p.10).

The retraction might have been premature. At present, it seems that the acceleration first spotted in 1998 can, in fact, be explained by Einstein’s antigravitation. But that’s not the end of it, because the underlying cosmological constant can be given any value, and therefore can push space apart at any rate. Simple estimates suggest that the acceleration should whip the universe apart long before galaxies can form. So why is the strength of antigravity just as it is?

If the no boundary proposal (p.131) is correct, an infinity of universes exist in parallel. Each of these universes might well have a different strength for antigravity, especially if string theory is on the right track to a complete under - standing of physics. We would then naturally live in one of the universes with a comfortably small dark energy; the anthropic principle (p.140) reminds us that, if galaxies had never formed, we would not be here to discuss the matter.

If the no boundary proposal might be central to understanding these developments, we should re-examine how it holds up in light of our rapidly improving observational handle on the early cosmos. In particular we can now understand the origins of structure in our universe using measurements of cosmic microwave background radiation (p.134).

As the name suggests, this is made up of microwaves – as used by your microwave oven, only much less powerful. They would heat your pizza to only −270.4°C, which isn’t much good for defrosting, let alone cooking. But these ultra-weak microwaves are spectacularly valuable, because there is only one reasonable explanation for their presence: they are radiation left over from an early time when the universe was very hot and dense. As the universe expanded, the radiation cooled until it is just the faint remnant we can detect today.

The existence of the background radiation was established in 1965. Immediately upon its detection, it was seen as powerful direct evidence for predictions based on Einstein’s general relativity. Part of my own PhD thesis work, finished just months before, had been to show that the early hot, dense phase was unavoidable in Einstein’s picture.

But the value of measuring the radiation has become greater still. At first the microwaves seemed to have an identical intensity in every direction. This led to ideas like inflation (p.144), which in its initial formulation was intended to explain how the early universe came to be so uniform. On closer inspection, it actually predicted there would be very slight variations from place to place. The deviations from uniformity come about through quantum mechanical uncertainty, which imposes a minimum level of fluctuations.

As successive generations of space telescopes have measured the microwave background radiation with increasing precision – first COBE in 1992 (p.49), then WMAP in 2001, and most recently Planck in 2013 – this prediction has proved to be correct. There are indeed changes in the intensity of the radiation, at the level of about one part in 100,000. More significantly, we have now determined that the precise pattern of variations agrees with the specific predictions I and others made by combining inflation with the no boundary proposal.

To describe the physical conditions at the big bang, the no boundary proposal combines Einstein’s relativity with quantum theory. It says that when we go back towards the beginning of our universe space and time become fuzzy and ‘cap off ’, somewhat like the North Pole on the surface of the earth. Asking what came before the big bang is meaningless according to the no boundary proposal, because there is no notion of time available to refer to. It would be like asking what lies north of the North Pole.

With my colleagues James Hartle (with whom I first put forward the no boundary proposal more than thirty years ago) and Thomas Hertog I have put all this to the test. We calculated what kind of universe would emerge from the big bang according to the no boundary proposal, and compared this prediction with our observations. This confirms that our universe should have come into existence with a burst of inflation.

So the features now measured in the microwave background radiation appear to confirm inflation and the no boundary proposal. But there is one key prediction of the theory which has yet to be verified. According to inflation, a small part of the fluctuations in the microwave radiation can be traced to gravitational waves generated during the phase of rapid expansion. This primordial gravitational radiation is the analogue of the quantum radiation from black holes and can be regarded as coming from the event horizon of the early inflationary stages of the universe. Its detection would confirm that black holes emit quantum radiation, something almost impossible to confirm directly. I will say more about detection of gravitational waves below, but those generated in the early universe show up most clearly in the polarization of the radiation. We are only in the early stages of measuring this polarization, and there is real hope that it will provide firm and convincing evidence for our theory of the big bang.

Even without a clear view of the polarization, the cosmic microwave background data are so good that we can now start to fill in some of the blanks. Inflation and the no boundary proposal leave a number of details unspecified: the precise energies involved, for example, and the link to the underlying particle physics. These details subtly change the expected patterns; by carefully studying what is seen, we are now beginning to understand physics near the grand unification energy. To put that in context, it is a million million times higher than can be probed by the very best experimental facility on earth, the Large Hadron Collider.

The developments described above mean that in the last two decades, inflation has been transformed from speculation into a cornerstone of modern cosmology. But not everyone likes its conclusions, especially since we now believe inflation likely gives rise to a vast number of universes, known collectively as a multiverse.

As I mentioned above, inflation predicts that the universe will be nearly, but not perfectly, uniform. The deviations from uniformity are imposed by quantum mechanics, and have now been precisely characterized from observations of the cosmic microwave background.

The very same quantum mechanical effect can give rise to the multiverse. Inflation is driven by a strange type of energy that has antigravitational properties; on average, the amount of this energy decreases as inflation proceeds, until there is no longer enough and the accelerated expansion ends. But, in some regions of space-time, quantum fluctuations temporarily reverse the overall trend. Such regions gain more energy and consequently inflate for longer.

In 1986, the Russian–American physicist Andrei Linde calculated that, if inflation starts at a sufficiently high energy, there will always be some place where the fluctuations win: the energy remains high, and inflation continues eternally. But there will be other places where the fluctuations lose, and the expected trend of decreasing energy takes hold. Such patches become entire individual universes such as our own. If we could zoom out far enough, we would see countless other universes, separated by Linde’s regions of the multiverse that are continuing to inflate.

Eternal inflation and the no boundary proposal together predict that our universe is not unique. Instead, from the quantum fuzz at the big bang many different universes emerge, possibly with different local laws of physics and chemistry. We may not live in the most probable of all universes. Rather, we live in one where the conditions are favorable for complexity and the development of life. Even though we cannot go from one universe to another, the successful predictions of the theory for observations in our universe provide support for the world view predicted by the no boundary proposal.

For a long time, many physicists brushed these arguments to one side. The idea of a multiverse makes some people queasy, and they would rather assume inflation to take place at a lower energy, so sidestepping Linde’s argument. However, the latest observations from the Planck satellite make this escapology trick look increasingly implausible.

Using polarization of the cosmic microwave background to show that gravitational waves were produced in the early universe, as mentioned earlier, would be one way to very directly confirm the high energies involved in inflation. I hope that we will not have to wait too long for this development; in the meantime, we have recently seen direct confirmation that gravitational waves (p.101) can be produced in the modern-day universe. Exactly a century after Einstein first predicted their existence, a worldwide consortium of scientists known as the LIGO collaboration announced in 2016 that gravitational waves had been detected for the first time.

The first sixty years were the hardest. During this time there was confusion over the status of the waves: should they exist in practice or are they just a mathematical artefact, unconnected with reality? Even Einstein seemed uncertain, and came close to publishing an erroneous disproof of their physicality in the 1930s. But over time the physics community settled on the view that the waves should be real. One consequence was that energy would be very slowly lost from orbiting bodies. Until recently, such energy loss was our only evidence for the existence of the waves (p.102). This was very convincing, but still indirect.

Actually measuring gravitational waves as they pass through the earth is far more technologically challenging, which is why it took until 2016. But the decades of technological development have proved worthwhile, because we now have a completely new way to study the universe. Even the first events that LIGO detected – waves resulting from the collision and merging of two black holes – allowed us to confirm our understanding of a process that no traditional telescope has ever been, or will ever be, able to probe.

For me, it was really exciting to see observations of colliding black holes. LIGO will observe many such events in the near future. These observations will, I believe, confirm a prediction I made in 1970 – that the surface area of the final black hole was greater than the sum of the initial holes’ areas. This ‘area theorem’, which led to my slightly later realization that black holes will gradually lose their mass over time, was secure on mathematical grounds. But one can never be too sure of an idea until it is tested against nature.

There is a bright future for LIGO and other gravitational wave observatories. We can expect to build up a large catalogue of detections, providing detailed insight into the populations of black holes in our universe. That in turn will allow us to search for even slight deviations from predictions based on Einstein’s theory. As we continue our search for a full quantum theory of gravity, this treasure trove of information about extreme regions of space-time will be immensely valuable.

One reason for my excitement over LIGO’s gravitational wave detections is that the area theorem is directly linked to a major controversy surrounding black holes known as the information paradox. Information is a sacred thing in physics; if we are able to describe the entire state of the universe today with a certain amount of information (the positions and speeds of all the particles, for example), we expect to need the same amount of information to describe the entire state of the universe tomorrow. This assumption underlies our ability to make scientific predictions, and is quietly built into Newton’s and Einstein’s work; it’s even part of quantum mechanics. One might therefore hope it will remain true when we formulate a final theory of quantum gravity.

When a black hole is formed, information about individual objects that have fallen in (their shapes, sizes, and chemical compositions, for example) becomes obscured. The only information about what formed it, is its total mass, its spin and its possible electric charge. This is the so-called ‘no-hair’ theorem.This is not too much of a problem, since the objects can just be regarded as hidden away rather than entirely lost. But if, as I showed in a letter published in Nature in 1974, quantum mechanics allows black holes to lose their mass and disappear (p.119), there is a difficulty. After the black hole is gone, what has then happened to the information?

When I wrote A Brief History of Time, I believed that the information concerning what had fallen into the black hole was truly lost, perhaps residing in a separate universe hived off from our own. In 1997 I even bet Caltech physics professor John Preskill an encyclopedia of his choice that I was right.

It was only later, in 2004, that I realized I had been wrong, after considering what happens to black holes after an infinite amount of time has passed. The amount of information at the start and the end was the same! When I conceded, John asked for an encyclopedia of baseball which I duly gave him. (My attempt to persuade him that cricket is more interesting was unsuccessful.)

My change of opinion started by considering one of the most remarkable discoveries to arise from string theory: there appears to be an exact correspondence between the behavior of gravity and an obscure branch of physics known as conformal field theory. The details of the link don’t matter for our purposes. All one needs to know is that anything described by conformal field theory – now including black holes – demonstrably preserves information. Very recently, it was realized that the ‘no-hair’ theorem was formulated in a way that was too restrictive. There is also supertranslation and superrotation hair. It seems that the information about material that formed the black hole remains preserved on the horizon as supertranslation and superrotation hair. We do not yet know if this is enough information to save the principles of quantum mechanics. Neither do we yet know how the information might emerge from the black hole. Even harder questions can be asked then about the fundamental nature of the singularities of spacetime that general relativity predicts must exist inside black holes.

Of course, this abstract argument doesn’t tell us exactly how the lost information manages to leak back out of a black hole in practice.

One must be clear that, when the information finally makes its way out of the black-hole-like region, it will emerge in a very hard-to-interpret format. It is like burning a book. Information is not technically lost, if one keeps the ashes and the smoke – which makes me think again about the baseball encyclopedia I gave John Preskill.

In the twenty years since the last revision of this book, progress in cosmology has been rapid. Some of the developments, such as the detection of gravitational waves and the steady improvement in our understanding of the early universe, were anticipated; others, like dark energy and the accelerating universe, less so.

Perhaps the most striking trend is one that many find uncomfortable: the no boundary proposal and eternal inflation point increasingly strongly to the idea that our universe is just one of many. Copernicus first suggested in the sixteenth century that we are not placed at the center of even our own universe (p. 4); yet we are still struggling to accept just how vanishingly small a fragment of reality our familiar world represents. It may not be much longer before the evidence for a multiverse becomes overwhelming.

Despite the vastness of the multiverse, there is a sense in which we remain significant: we can still be proud to be part of a species that is working all this out. With that in mind, the coming years should be just as exciting as the last twenty.

A BRIEF

HISTORY

OF TIME

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 synthesiser 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, 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.

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 bestseller 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 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 fingerprints 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.

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 flat 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 (Fig. 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.

FIGURE 1.1

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 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 either that 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 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’s counterargument 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.