The Universe in a Nutshell

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Overview

Stephen Hawking’s phenomenal, multimillion-copy bestseller, A Brief History of Time, introduced the ideas of this brilliant theoretical physicist to readers all over the world.

Now, in a major publishing event, Hawking returns with a ...

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Overview

Stephen Hawking’s phenomenal, multimillion-copy bestseller, A Brief History of Time, introduced the ideas of this brilliant theoretical physicist to readers all over the world.

Now, in a major publishing event, Hawking returns with a lavishly illustrated sequel that unravels the mysteries of the major breakthroughs that have occurred in the years since the release of his acclaimed first book.

The Universe in a Nutshell

• Quantum mechanics
• M-theory
• General relativity
• 11-dimensional supergravity
• 10-dimensional membranes
• Superstrings
• P-branes
• Black holes

One of the most influential thinkers of our time, Stephen Hawking is an intellectual icon, known not only for the adventurousness of his ideas but for the clarity and wit with which he expresses them. In this new book Hawking takes us to the cutting edge of theoretical physics, where truth is often stranger than fiction, to explain in laymen’s terms the principles that control our universe.

Like many in the community of theoretical physicists, Professor Hawking is seeking to uncover the grail of science — the elusive Theory of Everything that lies at the heart of the cosmos. In his accessible and often playful style, he guides us on his search to uncover the secrets of the universe — from supergravity to supersymmetry, from quantum theory to M-theory, from holography to duality.

He takes us to the wild frontiers of science, where superstring theory and p-branes may hold the final clue to the puzzle. And he lets us behind the scenes of one of his most exciting intellectual adventures as he seeks “to combine Einstein’s General Theory of Relativity and Richard Feynman’s idea of multiple histories into one complete unified theory that will describe everything that happens in the universe.”

With characteristic exuberance, Professor Hawking invites us to be fellow travelers on this extraordinary voyage through space-time. Copious four-color illustrations help clarify this journey into a surreal wonderland where particles, sheets, and strings move in eleven dimensions; where black holes evaporate and disappear, taking their secret with them; and where the original cosmic seed from which our own universe sprang was a tiny nut.

The Universe in a Nutshell is essential reading for all of us who want to understand the universe in which we live. Like its companion volume, A Brief History of Time, it conveys the excitement felt within the scientific community as the secrets of the cosmos reveal themselves.

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Editorial Reviews

From Barnes & Noble
The adage "Truth is stranger than fiction" is particularly apt when applied to physics and cosmology. And there is no one better qualified as a guide than Stephen Hawking. This gorgeous coffee table book, filled throughout with four-color visuals, is Hawking's sequel to his groundbreaking A Brief History of Time and includes all the weird and wonderful new theories that have arisen in the last decade, illustrated in stunning fashion.
Library Journal
Explaining cosmology to a popular audience is a difficult task, but Hawking has the gift of making extraordinarily complex concepts understandable. An eminent theoretical physicist at Cambridge University and author of the best-selling A Brief History of Time, Hawking here describes scientists' latest theories about the origin, structure, and evolution of the universe. The book's title refers both to its purpose as a summary of current cosmological thinking and to the particular theory of imaginary time as a "tiny, slightly flattened sphere." The helpful color illustrations, which comprise about half of the book, clarify the surreal aspects of the universe, such as the shape of time and the ten or 11 dimensions in which we exist. Hawking's occasional wit and his ability not to take himself too seriously help place our strange universe in a more human context. Highly recommended for all libraries. [Previewed in Prepub Alert, LJ 6/15/01.] Jeffrey Beall, Univ. of Colorado Lib., Denver Copyright 2001 Cahners Business Information.
School Library Journal
Adult/High School-Writing in a lighthearted, personal, often humorous style and with colorful and entertaining graphics on every page, Hawking succeeds in communicating his love and enthusiasm for science. Without seeming to condescend, he makes a valiant attempt to clarify many fascinating and elusive topics such as relativity and time; multiple universes and dimensions; black holes and dark matter; prediction of the future; and the possibility of time travel. Those usually daunted by scientific texts might enjoy puzzling over the graphics; many of them, together with excellent captions, fully restate the content of the text in an alternative (and, for some, more understandable) manner. Also, Hawking enriches readers' vocabularies with many of the sometimes-playful words, phrases, and acronyms essential to an acquaintance with modern physics-supergravity and supersymmetry, "p-branes" and proto-galaxies, MACHOS and WIMPS. Among teens, Universe might well prove to have appeal beyond its obvious audience of science students and readers of popular science and science fiction.-Christine C. Menefee, Fairfax County Public Library, VA Copyright 2002 Cahners Business Information.
From the Publisher
“Clear, concise and accessible. And he leavens it further with occasional wry humor.”—St Louis Post-Dispatch

“Provocative and informed ... plenty of comprehensible analogies and no small amount of humor, often self-deprecating.... Best of all, the book is liberally sprinkled with well-conceived, gorgeously rendered and frequently whimsical illustrations.”—Time

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Product Details

  • ISBN-13: 9780553802023
  • Publisher: Random House Publishing Group
  • Publication date: 11/28/2001
  • Edition description: Reissue
  • Pages: 224
  • Sales rank: 179,038
  • Product dimensions: 7.80 (w) x 10.16 (h) x 0.81 (d)

Meet the Author

Stephen Hawking
Stephen Hawking is Lucasian Professor of Mathematics at the University of Cambridge and is regarded as one of the most brilliant theoretical physicists since Einstein.

Biography

In the universe as a whole, the nature of black holes may be one of the most puzzling mysteries. No less puzzling, in the slightly smaller universe of book publishing, is the astounding popular success of Stephen Hawking's 1988 book on the matter, or anti-matter, as it were: A Brief History of Time: From the Big Bang to Black Holes.

Clocking in at just over 200 pages, it was, indeed, brief, but it was hardly the easy read its marketers promised. Nor did it stray much beyond the tone of a scholarly lecture, though at times it did take quick autobiographical peeks into Hawking's personal life. Still, it is just the author's persona that may have been the selling point prompting more than 10 million people worldwide to pick up a copy -- and to have it translated into more than 40 languages in the 10 years since its release.

For Stephen Hawking is an instantly recognizable public figure -- even for those who haven't delved into his so far unprovable theories about black holes. Stricken by amyotrophic lateral sclerosis (ALS) -- or Lou Gehrig's disease, as it is called in the States -- while he was working toward his doctorate at Cambridge University, this Englishman is known for the keen wit and intellect that reside within his severely disabled body. He uses a motorized wheelchair to get around and a voice synthesizer to communicate -- a development, he complains, that has given him an American accent. He has guest-starred, in cartoon form, on an episode of The Simpsons and has appeared in the flesh on Star Trek: The Next Generation, using the benefits of time travel to play poker with Albert Einstein and Isaac Newton. (He has said he doesn't believe in the theory himself, noting that the most powerful evidence of its impossibility is the present-day dearth of time-traveling tourists from the future.)

The son of a research biologist, Hawking resisted familial urging that he major in biology and instead studied physics and chemistry -- as a nod to his father -- when he went to Oxford University as a 17-year-old. In academic writing, Hawking had an extensive career pre-History, starting with The Large Scale Structure of Space-Time, coauthored with G.F.R. Ellis in 1973. But in the late 1980s, faced with the expenses incurred by his illness, he took up Bantam Books' offer to explain the mysteries of the universe to the lay public.

"This is one of the best books for laymen on this subject that has appeared in recent years," The Christian Science Monitor wrote in 1988. "Hawking is one of the greatest theoretical cosmologists of our time. He is greater, by consensus among his colleagues, than other expert authors who have written good popular books on the subject recently. And he is greater, by far, than the ‘experts' who have ‘explained' quantum physics and cosmology in terms that support a religious agenda." And The New York Times in April 1988 said, "Through his cerebral journeys, Mr. Hawking is bravely taking some of the first, though tentative, steps toward quantizing the early universe, and he offers us a provocative glimpse of the work in progress."

Since then, A Brief History of Time has been republished in an illustrated edition (1996) and as an updated and expanded 10th anniversary edition (1998). In Black Holes and Baby Universes and Other Essays, a collection of 13 essays and the transcript of an extended interview with the BBC, Hawking turned more autobiographical, mixing stories about his studies in college and the beginning of his awareness that he had ALS with thoughts on how black holes can spawn baby universes and on the scientific community's efforts to create a unified theory that will explain everything in the universe. And in The Universe in a Nutshell, his sequel to A Brief History of Time, Hawking takes the same approach as he did in his first bestseller, explaining to the lay reader such ideas as the superstring theory, supergravity, time travel, and quantum theory.

A common current in Hawking's writing -- aside from his grasp of the complexities of the universe -- is a sharp wit. In one of the rare personal reflections in A Brief History of Time, he said he began thinking about black holes in the early 1970s in the evenings as he was getting ready for bed: "My disability makes this rather a slow process, so I had plenty of time." In life, he has a reputation for quickly turning his wheelchair away of a conversation that displeases him, even running his wheels over the toes of the offending conversant.

Even questions about his muse are likely to draw an answer tinged with pointed humor. When Time asked Hawking why he decided to add explaining the universe to a schedule already taxed by his scholarly writing and lecture tours, he answered, "I have to pay for my nurses."

Good To Know

Hawking worked 1,000 hours in his three years at Oxford, roughly an hour a day. "I'm not proud of this lack of work," he said in Stephen Hawking's a Brief History of Time: A Reader's Companion. "I'm just describing my attitude at the time, which I shared with most of my fellow students: an attitude of complete boredom and feeling that nothing was worth making an effort for."

Despite his science degrees, Hawking has no formal training in math and has said he had to pick up what he knows as he went along.

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    1. Hometown:
      Cambridge, England
    1. Date of Birth:
      January 8, 1942
    2. Place of Birth:
      Oxford, England

Read an Excerpt

CHAPTER 2

THE SHAPE OF TIME

EINSTEIN’S GENERAL RELATIVITY GIVES TIME A SHAPE.

HOW THIS CAN BE RECONCILED WITH QUANTUM THEORY.

What is time? Is it an ever-rolling stream that bears all our dreams away, as the old hymn says? Or is it a railroad track? Maybe it has loops and branches, so you can keep going forward and yet return to an earlier station on the line.

The nineteenth-century author Charles Lamb wrote: “Nothing puzzles me like time and space. And yet nothing troubles me less than time and space, because I never think of them.” Most of us don’t worry about time and space most of the time, whatever that may be; but we all do wonder sometimes what time is, how it began, and where it is leading us.

Any sound scientific theory, whether of time or of any other concept, should in my opinion be based on the most workable philosophy of science: the positivist approach put forward by Karl Popper and others. According to this way of thinking, a scientific theory is a mathematical model that describes and codifies the observations we make. A good theory will describe a large range of phenomena on the basis of a few simple postulates and will make definite predictions that can be tested. If the predictions agree with the observations, the theory survives that test, though it can never be proved to be correct.

On the other hand, if the observations disagree with the predictions, one has to discard or modify the theory. (At least, that is what is supposed to happen. In practice, people often question the accuracy of the observations and the reliability and moral character of those making the observations.) If one takesthe positivist position, as I do, one cannot say what time actually is. All one can do is describe what has been found to be a very good mathematical model for time and say what predictions it makes.

Isaac Newton gave us the first mathematical model for time and space in his PRINCIPIA MATHEMATICA, published in 1687. Newton occupied the Lucasian chair at Cambridge that I now hold, though it wasn’t electrically operated in his time. In Newton’s model, time and space were a background in which events took place but which weren’t affected by them. Time was separate from space and was considered to be a single line, or railroad track, that was infinite in both directions. Time itself was considered eternal, in the sense that it had existed, and would exist, forever.

By contrast, most people thought the physical universe had been created more or less in its present state only a few thousand years ago. This worried philosophers such as the German thinker Immanuel Kant. If the universe had indeed been created, why had there been an infinite wait before the creation? On the other hand, if the universe had existed forever, why hadn’t everything that was going to happen already happened, meaning that history was over? In particular, why hadn’t the universe reached thermal equilibrium, with everything at the same temperature?

Kant called this problem an “antimony of pure reason,” because it seemed to be a logical contradiction; it didn’t have a resolution. But it was a contradiction only within the context of the Newtonian mathematical model, in which time was an infinite line, independent of what was happening in the universe. However, as we saw in Chapter 1, in 1915 a completely new mathematical model was put forward by Einstein: the general theory of relativity. In the years since Einstein’s paper, we have added a few ribbons and bows, but our model of time and space is still based on what Einstein proposed. This and the following chapters will describe how our ideas have developed in the years since Einstein’s revolutionary paper. It has been a success story of the work of a large number of people, and I’m proud to have made a small contribution.

General relativity combines the time dimension with the three dimensions of space to form what is called spacetime. The theory incorporates the effect of gravity by saying that the distribution of matter and energy in the universe warps and distorts spacetime, so that it is not flat. Objects in this spacetime try to move in straight lines, but because spacetime is curved, their paths appear bent. They move as if affected by a gravitational field.

As a rough analogy, not to be taken too literally, imagine a sheet of rubber. One can place a large ball on the sheet to represent the Sun. The weight of the ball will depress the sheet and cause it to be curved near the Sun. If one now rolls little ball bearings on the sheet, they won’t roll straight across to the other side but instead will go around the heavy weight, like planets orbiting the Sun.

The analogy is incomplete because in it only a two-dimensional section of space (the surface of the rubber sheet) is curved, and time is left undisturbed, as it is in Newtonian theory. However, in the theory of relativity, which agrees with a large number of experiments, time and space are inextricably tangled up. One cannot curve space without involving time as well. Thus time has a shape. By curving space and time, general relativity changes them from being a passive background against which events take place to being active, dynamic participants in what happens. In Newtonian theory, where time existed independently of anything else, one could ask: What did God do before He created the universe? As Saint Augustine said, one should not joke about this, as did a man who said, “He was preparing Hell for those who pry too deep.” It is a serious question that people have pondered down the ages. According to Saint Augustine, before God made heaven and earth, He did not make anything at all. In fact, this is very close to modern ideas.

In general relativity, on the other hand, time and space do not exist independently of the universe or of each other. They are defined by measurements within the universe, such as the number of vibrations of a quartz crystal in a clock or the length of a ruler. It is quite conceivable that time defined in this way, within the universe, should have a minimum or maximum value—in other words, a beginning or an end. It would make no sense to ask what happened before the beginning or after the end, because such times would not be defined.

It was clearly important to decide whether the mathematical model of general relativity predicted that the universe, and time itself, should have a beginning or end. The general prejudice among theoretical physicists, including Einstein, held that time should be infinite in both directions. Otherwise, there were awkward questions about the creation of the universe, which seemed to be outside the realm of science. Solutions of the Einstein equations were known in which time had a beginning or end, but these were all very special, with a large amount of symmetry. It was thought that in a real body, collapsing under its own gravity, pressure or sideways velocities would prevent all the matter falling together to the same point, where the density would be infinite. Similarly, if one traced the expansion of the universe back in time, one would find that the matter of the universe didn’t all emerge from a point of infinite density. Such a point of infinite density was called a singularity and would be a beginning or an end of time.

In 1963, two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, claimed to have proved that solutions of the Einstein equations with a singularity all had a special arrangement of matter and velocities. The chances that the solution representing the universe would have this special arrangement were practically zero. Almost all solutions that could represent the universe would avoid having a singularity of infinite density:

Before the era during which the universe has been expanding, there must have been a previous contracting phase during which matter fell together but missed colliding with itself, moving apart again in the present expanding phase. If this were the case, time would continue on forever, from the infinite past to the infinite future.

Not everyone was convinced by the arguments of Lifshitz and Khalatnikov. Instead, Roger Penrose and I adopted a different approach, based not on a detailed study of solutions but on the global structure of spacetime. In general relativity, spacetime is curved not only by massive objects in it but also by the energy in it. Energy is always positive, so it gives spacetime a curvature that bends the paths of light rays toward each other.

Now consider our past light cone, that is, the paths through spacetime of the light rays from distant galaxies that reach us at the present time. In a diagram with time plotted upward and space plotted sideways, this is a cone with its vertex, or point, at us.

As we go toward the past, down the cone from the vertex, we see galaxies at earlier and earlier times. Because the universe has been expanding and everything used to be much closer together, as we look back further we are looking back through regions of higher matter density. We observe a faint background of microwave radiation that propagates to us along our past light cone from a much earlier time, when the universe was much denser and hotter than it is now. By tuning receivers to different frequencies of microwaves, we can measure the spectrum (the distribution of power arranged by frequency) of this radiation. We find a spectrum that is characteristic of radiation from a body at a temperature of 2.7 degrees above absolute zero. This microwave radiation is not much good for defrosting frozen pizza, but the fact that the spectrum agrees so exactly with that of radiation from a body at 2.7 degrees tells us that the radiation must have come from regions that are opaque to microwaves.

Thus we can conclude that our past light cone must pass through a certain amount of matter as one follows it back. This amount of matter is enough to curve spacetime, so the light rays in our past light cone are bent back toward each other.

As one goes back in time, the cross sections of our past light cone reach a maximum size and begin to get smaller again. Our past is pear-shaped.

As one follows our past light cone back still further, the positive energy density of matter causes the light rays to bend toward each other more strongly. The cross section of the light cone will shrink to zero size in a finite time. This means that all the matter inside our past light cone is trapped in a region whose boundary shrinks to zero. It is therefore not very surprising that Penrose and I could prove that in the mathematical model of general relativity, time must have a beginning in what is called the big bang. Similar arguments show that time would have an end, when stars or galaxies collapse under their own gravity to form black holes. We had sidestepped Kant’s antimony of pure reason by dropping his implicit assumption that time had a meaning independent of the universe. Our paper, proving time had a beginning, won the second prize in the competition sponsored by the Gravity Research Foundation in 1968, and Roger and I shared the princely sum of $300. I don’t think the other prize essays that year have shown much enduring value.

There were various reactions to our work. It upset many physicists, but it delighted those religious leaders who believed in an act of creation, for here was scientific proof. Meanwhile, Lifshitz and Khalatnikov were in an awkward position. They couldn’t argue with the mathematical theorems that we had proved, but under the Soviet system they couldn’t admit they had been wrong and Western science had been right. However, they saved the situation by finding a more general family of solutions with a singularity, which weren’t special in the way their previous solutions had been. This enabled them to claim singularities, and the beginning or end of time, as a Soviet discovery.

Most physicists still instinctively disliked the idea of time having a beginning or end. They therefore pointed out that the mathematical model might not be expected to be a good description of spacetime near a singularity. The reason is that general relativity, which describes the gravitational force, is a classical theory, as noted in Chapter 1, and does not incorporate the uncertainty of quantum theory that governs all other forces we know.

This inconsistency does not matter in most of the universe most of the time, because the scale on which spacetime is curved is very large and the scale on which quantum effects are important is very small. But near a singularity, the two scales would be comparable, and quantum gravitational effects would be important. So what the singularity theorems of Penrose and myself really established is that our classical region of spacetime is bounded to the past, and possibly to the future, by regions in which quantum gravity is important. To understand the origin and fate of the universe, we need a quantum theory of gravity, and this will be the subject of most of this book.

Quantum theories of systems such as atoms, with a finite number of particles, were formulated in the 1920s, by Heisenberg, Schrödinger, and Dirac. (Dirac was another previous holder of my chair in Cambridge, but it still wasn’t motorized.) However, people encountered difficulties when they tried to extend quantum ideas to the Maxwell field, which describes electricity, magnetism, and light.

One can think of the Maxwell field as being made up of waves of different wavelengths (the distance between one wave crest and the next). In a wave, the field will swing from one value to another like a pendulum.

According to quantum theory, the ground state, or lowest energy state, of a pendulum is not just sitting at the lowest energy point, pointing straight down. That would have both a definite position and a definite velocity, zero. This would be a violation of the uncertainty principle, which forbids the precise measurement of both position and velocity at the same time. The uncertainty in the position multiplied by the uncertainty in the momentum must be greater than a certain quantity, known as Planck’s constant—a number that is too long to keep writing down, so we use a symbol for it:

So the ground state, or lowest energy state, of a pendulum does not have zero energy, as one might expect. Instead, even in its ground state a pendulum or any oscillating system must have a certain minimum amount of what are called zero point fluctuations. These mean that the pendulum won’t necessarily be pointing straight down but will also have a probability of being found at a small angle to the vertical. Similarly, even in the vacuum or lowest energy state, the waves in the Maxwell field won’t be exactly zero but can have small sizes. The higher the frequency (the number of swings per minute) of the pendulum or wave, the higher the energy of the ground state.

Calculations of the ground state fluctuations in the Maxwell and electron fields made the apparent mass and charge of the electron infinite, which is not what observations show. However, in the 1940s the physicists Richard Feynman, Julian Schwinger, and Shin‘ichiro Tomonaga developed a consistent way of removing or “subtracting out” these infinities and dealing only with the finite observed values of the mass and charge. Nevertheless, the ground state fluctuations still caused small effects that could be measured and that agreed well with experiment. Similar subtraction schemes for removing infinities worked for the Yang-Mills field in the theory put forward by Chen Ning Yang and Robert Mills. Yang-Mills theory is an extension of Maxwell theory that describes interactions in two other forces called the weak and strong nuclear forces. However, ground state fluctuations have a much more serious effect in a quantum theory of gravity. Again, each wavelength would have a ground state energy. Since there is no limit to how short the wavelengths of the Maxwell field can be, there are an infinite number of different wavelengths in any region of spacetime and an infinite amount of ground state energy.

Because energy density is, like matter, a source of gravity, this infinite energy density ought to mean there is enough gravitational attraction in the universe to curl spacetime into a single point, which obviously hasn’t happened.

One might hope to solve the problem of this seeming contradiction between observation and theory by saying that the ground state fluctuations have no gravitational effect, but this would not work. One can detect the energy of ground state fluctuations by the Casimir effect. If you place a pair of metal plates parallel to each other and close together, the effect of the plates is to reduce slightly the number of wavelengths that fit between the plates relative to the number outside. This means that the energy density of ground state fluctuations between the plates, although still infinite, is less than the energy density outside by a finite amount. This difference in energy density gives rise to a force pulling the plates together, and this force has been observed experimentally.

Forces are a source of gravity in general relativity, just as matter is, so it would not be consistent to ignore the gravitational effect of this energy difference.

Another possible solution to the problem might be to suppose there was a cosmological constant such as Einstein introduced in an attempt to have a static model of the universe. If this constant had an infinite negative value, it could exactly cancel the infinite positive value of the ground state energies in free space, but this cosmological constant seems very ad hoc, and it would have to be tuned to extraordinary accuracy.

Fortunately, a totally new kind of symmetry was discovered in the 1970s that provides a natural physical mechanism to cancel the infinities arising from ground state fluctuations.

Supersymmetry is a feature of our modern mathematical models that can be described in various ways. One way is to say that spacetime has extra dimensions besides the dimensions we experience. These are called Grassmann dimensions, because they are measured in numbers known as Grassmann variables rather than in ordinary real numbers. Ordinary numbers commute; that is, it does not matter in which order you multiply them: 6 times 4 is the same as 4 times 6. But Grassmann variables anticommute: x times y is the same as –y times x.

Supersymmetry was first considered for removing infinities in matter fields and Yang-Mills fields in a spacetime where both the ordinary number dimensions and the Grassmann dimensions were flat, not curved. But it was natural to extend it to ordinary numbers and Grassmann dimensions that were curved. This led to a number of theories called supergravity, with different amounts of supersymmetry. One consequence of supersymmetry is that every field or particle should have a “superpartner” with a spin that is either 1/2 greater than its own or 1/2 less.

The ground state energies of bosons, fields whose spin is a whole number (0, 1, 2 , etc.), are positive. On the other hand, the ground state energies of fermions, fields whose spin is a half number (1/2, 3/2 , etc.), are negative. Because there are equal numbers of bosons and fermions, the biggest infinities cancel in supergravity theories.

There remained the possibility that there might be smaller but still infinite quantities left over. No one had the patience needed to calculate whether these theories were actually completely finite. It was reckoned it would take a good student two hundred years, and how would you know he hadn’t made a mistake on the second page? Still, up to 1985, most people believed that most supersymmetric supergravity theories would be free of infinities.
Then suddenly the fashion changed. People declared there was no reason not to expect infinities in supergravity theories, and this was taken to mean they were fatally flawed as theories. Instead, it was claimed that a theory named supersymmetric string theory was the only way to combine gravity with quantum theory. Strings, like their namesakes in everyday experience, are one-dimensional extended objects. They have only length. Strings in string theory move through a background spacetime. Ripples on the string are interpreted as particles.

If the strings have Grassmann dimensions as well as their ordinary number dimensions, the ripples will correspond to bosons and fermions. In this case, the positive and negative ground state energies will cancel so exactly that there will be no infinities even of the smaller sort. Superstrings, it was claimed, were the TOE, the Theory of Everything.

Historians of science in the future will find it interesting to chart the changing tide of opinion among theoretical physicists. For a few years, strings reigned supreme and supergravity was dismissed as just an approximate theory, valid at low energy. The qualification “low energy” was considered particularly damning, even though in this context low energies meant particles with energies of less than a billion billion times those of particles in a TNT explosion. If supergravity was only a low energy approximation, it could not claim to be the fundamental theory of the universe. Instead, the underlying theory was supposed to be one of five possible superstring theories. But which of the five string theories described our universe? And how could string theory be formulated, beyond the approximation in which strings were pictured as surfaces with one space dimension and one time dimension moving through a flat background spacetime? Wouldn’t the strings curve the background spacetime?

In the years after 1985, it gradually became apparent that string theory wasn’t the complete picture. To start with, it was realized that strings are just one member of a wide class of objects that can be extended in more than one dimension. Paul Townsend, who, like me, is a member of the Department of Applied Mathematics and Theoretical Physics at Cambridge, and who did much of the fundamental work on these objects, gave them the name “p-branes.” A p-brane has length in p directions. Thus a p=1 brane is a string, a p=2 brane is a surface or membrane, and so on.There seems no reason to favor the p=1 string case over other possible values of p. Instead, we should adopt the principle of p-brane democracy: all p-branes are created equal.

All the p-branes could be found as solutions of the equations of supergravity theories in 10 or 11 dimensions. While 10 or 11 dimensions doesn’t sound much like the spacetime we experience, the idea was that the other 6 or 7 dimensions are curled up so small that we don’t notice them; we are only aware of the remaining 4 large and nearly flat dimensions.

I must say that personally, I have been reluctant to believe in extra dimensions. But as I am a positivist, the question “Do extra dimensions really exist?” has no meaning. All one can ask is whether mathematical models with extra dimensions provide a good description of the universe. We do not yet have any observations that require extra dimensions for their explanation. However, there is a possibility we may observe them in the Large Hadron Collider in Geneva. But what has convinced many people, including myself, that one should take models with extra dimensions seriously is that there is a web of unexpected relationships, called dualities, between the models. These dualities show that the models are all essentially equivalent; that is, they are just different aspects of the same underlying theory, which has been given the name M-theory. Not to take this web of dualities as a sign we are on the right track would be a bit like believing that God put fossils into the rocks in order to mislead Darwin about the evolution of life.

These dualities show that the five superstring theories all describe the same physics and that they are also physically equivalent to supergravity. One cannot say that superstrings are more fundamental than supergravity, or vice versa. Rather, they are different expressions of the same underlying theory, each useful for calculations in different kinds of situations. Because string theories don’t have any infinities, they are good for calculating what happens when a few high energy particles collide and scatter off each other. However, they are not of much use for describing how the energy of a very large number of particles curves the universe or forms a bound state, like a black hole. For these situations, one needs supergravity, which is basically Einstein’s theory of curved spacetime with some extra kinds of matter. It is this picture that I shall mainly use in what follows.

To describe how quantum theory shapes time and space, it is helpful to introduce the idea of imaginary time. Imaginary time sounds like something from science fiction, but it is a well-defined mathematical concept: time measured in what are called imaginary numbers. One can think of ordinary real numbers such as 1, 2, -3.5, and so on as corresponding to positions on a line stretching from left to right: zero in the middle, positive real numbers on the right, and negative real numbers on the left.
Imaginary numbers can then be represented as corresponding to positions on a vertical line: zero is again in the middle, positive imaginary numbers plotted upward, and negative imaginary numbers plotted downward. Thus imaginary numbers can be thought of as a new kind of number at right angles to ordinary real numbers. Because they are a mathematical construct, they don’t need a physical realization; one can’t have an imaginary number of oranges or an imaginary credit card bill.

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

Einstein’s classical (i.e., nonquantum) general theory of relativity combined real time and the three dimensions of space into a four-dimensional spacetime. But the real time direction was distinguished from the three spatial directions; the world line or history of an observer always increased in the real time direction (that is, time always moved from past to future), but it could increase or decrease in any of the three spatial directions. In other words, one could reverse direction in space, but not in time.

On the other hand, because imaginary time is at right angles to real time, it behaves like a fourth spatial direction. It can therefore have a much richer range of possibilities than the railroad track of ordinary real time, which can only have a beginning or an end or go around in circles. It is in this imaginary sense that time has a shape.

To see some of the possibilities, consider an imaginary time spacetime that is a sphere, like the surface of the Earth. Suppose that imaginary time was degrees of latitude. Then the history of the universe in imaginary time would begin at the South Pole. It would make no sense to ask, “What happened before the beginning?” Such times are simply not defined, any more than there are points south of the South Pole. The South Pole is a perfectly regular point of the Earth’s surface, and the same laws hold there as at other points. This suggests that the beginning of the universe in imaginary time can be a regular point of spacetime, and that the same laws can hold at the beginning as in the rest of the universe. (The quantum origin and evolution of the universe will be discussed in the next chapter.)

Another possible behavior is illustrated by taking imaginary time to be degrees of longitude on the Earth. All the lines of longitude meet at the North and South Poles. Thus time stands still there, in the sense that an increase of imaginary time, or of degrees of longitude, leaves one in the same spot. This is very similar to the way that ordinary time appears to stand still on the horizon of a black hole. We have come to recognize that this standing still of real and imaginary time (either both stand still or neither does) means that the spacetime has a temperature, as I discovered for black holes.

Not only does a black hole have a temperature, it also behaves as if it has a quantity called entropy. The entropy is a measure of the number of internal states (ways it could be configured on the inside) that the black hole could have without looking any different to an outside observer, who can only observe its mass, rotation, and charge. This black hole entropy is given by a very simple formula I discovered in 1974. It equals the area of the horizon of the black hole: there is one bit of information about the internal state of the black hole for each fundamental unit of area of the horizon. This shows that there is a deep connection between quantum gravity and thermodynamics, the science of heat (which includes the study of entropy). It also suggests that quantum gravity may exhibit what is called holography.

Information about the quantum states in a region of spacetime may be somehow coded on the boundary of the region, which has two dimensions less. This is like the way that a hologram carries a three-dimensional image on a two-dimensional surface. If quantum gravity incorporates the holographic principle, it may mean that we can keep track of what is inside black holes. This is essential if we are to be able to predict the radiation that comes out of black holes. If we can’t do that, we won’t be able to predict the future as fully as we thought. This is discussed in Chapter 4. Holography is discussed again in Chapter 7. It seems we may live on a 3-brane—a four-dimensional (three space plus one time) surface that is the boundary of a five-dimensional region, with the remaining dimensions curled up very small. The state of the world on a brane encodes what is happening in the five-dimensional region.


From the Audio CD (Unabridged) edition.

Copyright 2001 by Stephen Hawking
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Table of Contents

Foreword
Ch. 1 A Brief History of Relativity 3
Ch. 2 The Shape of Time 29
Ch. 3 The Universe in a Nutshell 67
Ch. 4 Predicting the Future 101
Ch. 5 Protecting the Past 131
Ch. 6 Our Future? Star Trek or Not? 155
Ch. 7 Brane New World 173
Glossary
Suggested further readings
Acknowledgments
Index
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Customer Reviews

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See All Sort by: Showing 1 – 20 of 38 Customer Reviews
  • Posted February 2, 2009

    more from this reviewer

    The Big Physics Questions Made Comprehensible

    Stephen Hawking's book, THE UNIVERSE IN A NUTSHELL, succeeds in making some of the newest theories in physics understandable to everyday people. Until reading this book, I hadn't considered what conditions would be necessary in order for our night-time sky to look completely white with stars, nor had I seen such a gorgeous depiction of the micro and macro-cosmic universe in a nutshell (cover illustration). Hawking carefully examines time-travel, predicting the future, and the shape of time after starting the book with an overview of the theory of relativity. Hawking saves his biggest question for last, to leave readers wondering 'Do we live on a brane, or are we just holograms?' (A brane is something like a membrane.) Thanks to stunning color illustrations and fascinating questions and ideas gracing almost every page, THE UNIVERSE IN A NUTSHELL accesses both the rational and intuitive hemispheres of the reader's brain. It's the perfect book to unwind with after a long day -- allowing the exotic images and ideas to percolate in your mind like a delicious cup of your favorite hot beverage -- opening your mind to whole new worlds of possibility. Those seeking mathematical equations to accompany their theoretical physics will likely be disappointed by this coffee-table masterpiece, as will readers who prefer to read ground-breaking books which describe entirely new theories in physics. Pretty much everyone else will be thrilled to take a peek at the 'big' questions and ideas being contemplated by the world's most famous physicist.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted March 19, 2012

    This book is a very successful popular science book. Prof Stephe

    This book is a very successful popular science book. Prof Stephen Hawking uses very simple language to explain complicated physics. However, the M-Theory or superstring theory may not be the ultimate grand unified theory. Go to read a book entitled "Theories of Everything by logic" by Wan-Jiung Hu. He proposes a grand unified theory by explaining the origin of dark matter and dark energy.

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  • Posted May 3, 2011

    Check it out!

    The book The Universe in a Nutshell is a book of crazy wild and exciting theories that explain ideas that many people have wondered about. The theories are all very convincing in many ways due to Hawking's great use of supporting evidence along with illustrations which really help the reader thoroughly understand the meaning of the theory and why it would actually be true. Hawking covers the past, present, and future, which definitely helps the reader, have an idea in their head of how all of the theories came to be and were evolved. Hawking takes complex ideas and breaks them down to be simple so that the audience can work their mind and figure out the point he is trying to get across. Examples of material Hawking covers include; black holes, worm holes, time and space, time travel, particles, history of particles, futuristic research, etc. Not to worry though this book is interesting and not your everyday science text book. The book can change the way you as a person look at different things in the world and universe and that is a really cool thing to do. Stephen Hawking did a fabulous job writing this book and I hope many people decide to read it as it is a neat book and very knowledgeable. Hawking is known to be one of the greatest thinkers of our time and it's amazing to hear his thoughts on the universe. All in all, the book changes your point of view and may open your mind to new things you have never thought of before.

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  • Anonymous

    Posted March 28, 2008

    A reviewer

    This Book MUST be read by all Physicist, Scientist, or religious zealots. This is THE ultimate guide for all mankind. I highly recommend the illustrated version as unless you are already familiar, the concepts can be hard to visualize.

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  • Anonymous

    Posted January 18, 2008

    Among the deepest, borderline-philosophical questions in modern physics is that of the origin and formation of the Universe

    Earlier attempts to formulate an answer that takes into account existing theories and observations have failed because of obstacles posed by gravity. The Nature of Space and Time pitts two heavy weights trying to provide a loop quantum gravitational model that successfully merges current ideas, and which may enable us to overcome such difficulties. Stephen Hawking shot to fame in the world of physics when he provided a mathematical proof for the Big Bang theory. This theory showed that the entire universe exploded from a singularity, an infinitely small point with infinite density and infinite gravity. Hawking was able to come to his proof using mathematical techniques that had been developed by Roger Penrose. These techniques were however developed to deal not with the beginning of the Universe but with black holes.......................Science had long predicted that if a sufficiently large star collapsed at the end of its life, all the matter left in the star would be crushed into an infinitely small point with infinite gravity and infinite density...a singularity. Hawking realized that the Universe was, in effect, a black hole in reverse. Instead of matter being crushed into a singularity, the Universe began when a singularity expanded to form everything we see around us today, from stars to planets to people. Hawking realized that to come to a complete understanding of the Universe he would have to unravel the mysteries of the black hole....................Hawking and his fellow physicists embarked on an extraordinary intellectual expedition to tame the black hole. Slowly physicists were coming to understand this most destructive force of nature. But Hawking realized that there was something missing from the emerging picture. All work on black holes to that point used the physics of the large-scale Universe, the physics of gravity first developed by Newton and then refined by Einstein's theories of general and special relativity. Hawking realized that to come to a full understanding of black holes, physicists would also have to use the physics of the small-scale Universe, (the physics that had been developed to explain the movements of atoms and sub-atomic particles, known as quantum mechanics.) The problem was that no one had ever combined these two areas of physics before. But that didn't deter Hawking. He set about developing a new way to force the physics of quantum mechanics to co-exist with Einstein's relativity within the intense gravity of a black hole....................After months of work Hawking came up with a remarkable result. His equations were showing him that something was coming out of the black hole. This was supposed to be impossible. The one thing that everyone thought they knew about black holes was that things went in but nothing, not even light itself, could escape. But the more Hawking checked, the more he was convinced he was right. He could see radiation coming out of the black hole. Hawking then realized that this radiation (Hawking Radiation) would cause the black hole to evaporate and eventually disappear. Although Hawking's theories about black hole evaporation were revolutionary, they soon came to be widely accepted. But Hawking knew that this work had far more fundamental consequences. In 1976 he published a paper called 'The Breakdown of Predictability in Gravitational Collapse'. In it he argued that it wasn't just the black hole that disappeared. All the information about everything that had ever been inside the black hole disappeared too......................There are limits to what science can know. For many years no one took much notice of Hawking's ideas until a fateful meeting in San Francisco. Hawking presented his ideas to some of the world's leading physicists. In the audience were Gerad t'Hooft and Leonard Susskind, two leading particle physicists. They were shocked. Both realized that Hawking's 'breakdown of predictability' applied not only to black holes but to all processes i

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  • Anonymous

    Posted January 9, 2007

    Fascinating book -- please do not disrespect this forum with blind faith.

    This book is an excellent book. It is not enough, but that is how it should be. Hawking was trying to inspire the average reader, give them the seed of curiosity, giving them incentive to find out the rest of the details for themselves. And oh yes, I am extremely grateful I live in a time where the answers are so readily available. In response to the reader who wrote 'Hawking's Search for the Revealed' and then complained about how he did not mention a seed theory: You are free to write as you wish. However, keep in mind that your theories are founded in a whimsical religious desire to define your existence in a much simpler way than Hawking, or any of us, can, because it is just not that simple. I am glad the meaning of life is not simple. This makes life that much more fun, fills it with things for us to discover. Please do not read a book of science and then judge it with religion. That is like reading Hawking's book, and then saying it is horrible because it does not agree with the religious idea that the Earth is 5000 years old. Faith is ok, but blind faith will get you in trouble. It strips away your ability to think. Please do not bring blind faith to this forum.

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  • Anonymous

    Posted November 13, 2005

    Work of a Genius

    This was my first time reading a book of this level and theme. However I ended up actually enjoying the book quite a bit. It opened my mind to new ideas and to things that I never even knew existed. The book was written in a level that was understandable yet contained very complex ideas.

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  • Anonymous

    Posted November 24, 2004

    Excellent but incomplete picture of the universe

    This book is a must read for everyone who loves science. One has to feel discomfort from the incompleteness of the big bang universe and its inefficiency to explain the growing number of observations. It is quite uncertain what was before the big bang. That is why new theories that incorporate the progress of experimental science from the last few decades should be considered.

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  • Anonymous

    Posted August 1, 2004

    Profound

    Excellent! Stephen Hawking out does himself and presents his theories to the limit of the universe..

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  • Anonymous

    Posted November 11, 2003

    Ok however...

    I found this book to be okay however I still prefer M. R. Franks' The Universe and Multiple Reality.

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  • Anonymous

    Posted August 15, 2003

    A book for every mind - a Scientist for our time

    Nothing happens out of chance. Professor Hawking is the Scientist who chose to be in our Planet Earth at this point and time. He is our messenger of Light for this time and age, scientifically speaking. There are messengers for all walks of life, and he holds that position in the scientific circles 'where truth is often stranger than fiction.'

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  • Anonymous

    Posted November 8, 2002

    Nobody could do it better

    I can't imagine anyone writing about physics and cosmology more clearly than Stephen Hawking. If you want to know the state of those fields today, and how they got where they are, this book is ideal. Several things set it apart from Hawking's bestseller, A Brief History of Time. In The Universe in a Nutshell, he provides more of the history of cosmological thinking, and goes on to give sparklingly clear descriptions of some more recent developments, such as branes (lower-dimensional spaces that are subsets of higher-dimensional universes) and M-theory, a meta-theory that unites supergravity and string theories. In the current book, Hawking also makes frequent and interesting use of the anthropic principle, which limits our universe in certain ways since if it were significantly different galaxies, stars, planets, and humans could not have appeared. I was surprised and pleased to find Hawking taking time to speculate on the future of humanity given our ability to create increasingly complex organisms, and electronic systems. And, the book is full of colorful and helpful illustrations. Like A Brief History of Time, The Universe in a Nutshell is full of Hawking's witty asides. My favorite was, "Newton occupied the Lucasian chair at Cambridge that I now hold, though it wasn't electrically operated at that time." I found the book to be a delightful and of course informative read. Robert Adler, author of Science Firsts: From the Creation of Science to the Science of Creation

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  • Anonymous

    Posted July 13, 2002

    An excellent book for understanding the cosmos

    This book is incredibly fascinating, and Stephen Hawking writes it in the clearest, most easy to read English ever. Hawking talks about black holes, the fate of the universe, and about the quest for the Theory of Everything. An excellent read for the average person.

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  • Anonymous

    Posted July 17, 2002

    Better than a brief history of time

    I found this book to be better than his ealier book, a brief history of time. The pictures helped a lot and generally it was easier to understand. Overall, a very good book by one of the leading scientists.

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  • Anonymous

    Posted May 21, 2002

    Interesting digest of modern cosmology for the layman

    This book has the strengths (and a few weaknesses) of books for the layman on very technical subjects. The ideas are exciting, and when well-described (Hawking is an excellent writer) thrilling to read about. The lay reader is left with a lingering concern that he has not quite understood what is really going on. This is hardly a surprise, for the technical basis of the ideas described is fiendishly difficult (Hawking himself is resposible for some of the most remarkable, but difficult, discoveries in this area). Hawking does as good a job as anyone could, but if you come away with the feeling that you haven't quite understood it, you are right. There really is no shortcut.

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  • Anonymous

    Posted July 28, 2002

    An easy-to-read book about a challenging subject.

    Stephen Hawking tops a Brief History of Time in this new book. If you know not much about quantum physics or if you are experienced in the field, this new book will catch your attention. The added help of illustrations and charts make this book even better. Have fun reading it!

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  • Anonymous

    Posted May 13, 2002

    Hawking's Search for the Revealed

    Stephen Hawking's The Universe in a Nutshell describes and illustrates many divorced-from-reality cosmological ideas. Consequently it does not really come as a surprise that he failed to mention the Holy Grail of Science, namely the theory that a cosmic seed of human life generated the universe for the production of human beings in its own image, just as a seed generates a tree for the production of seeds in its own image. The seed of the universe or 'Unbegotten Father' is considered to be immortal, because the universe has no power over the cause of its own origin, just as a tree has no power over the seed of its own origin. Considering that the birth of the universe from an everlasting human seed or genome is in line with the principle of biogenesis, as well as with the observations that the universe is tailor-made for the production of human beings (anthropic principle), The Universe in a Nutshell should read: The Universe in a Seed of Human Life. Just in case Professor Hawking failed to notice, in the Bhagavad-Gita Krishna revealed: 'O Arjuna, I am the divine seed of all lives. In this world, nothing animate or inanimate exists without me.' The Zohar also implies that the human genome is the microcosm or store-house of all the seeds of life, because 'As soon as man appeared, everything was complete ... for everything is comprised in man. He unites in himself all forms.' Finally in John 10:30 Christ said: 'I and my Father are one,¿ and in Revelation 22:13 he declared: 'I am Alpha and Omega, the beginning and the end, the first and the last.¿ So by still searching for the Holy Grail of Science Hawking and the rest of the researchers only reveal their ignorance, for to the wise it is known that the human genome is a seed from which a universe may come into existence.

    0 out of 3 people found this review helpful.

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  • Anonymous

    Posted April 23, 2002

    Very good book but with two minor mistakes

    I loved the book, of course. One of the best ones I have ever read in my life. It is very interesting! I cannot add anything new to what has already been said. But has anyone realised what happens to figures 4.1 and 4.3? In Figure 4.1 (p.103), on the top, numbers 3 and 4 are swoped. In Figure 4.3 (p.104) the butterfly is flapping his wings in Central Park (NY) and the storm takes place in Tokyo, but the text says exactly the opposite. I think these minor errors could be arranged in future editions, Yours sincerely,

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  • Anonymous

    Posted April 3, 2002

    OUTSTANDING

    It is written for everyone. You don't need to know math. He easily describes concepts and complex theories in your everyday language. There is also a lot of information for the advanced reader who deals with physics and math.

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  • Anonymous

    Posted June 26, 2002

    Great Illustrations!

    The best part about this book is the illustrations. Nearly every page is filled with pictures and diagrams which can make even a dry book entertaining. A few things in this book are merely re-hashes from his old books, but most of the content is fresh.

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