The Universe in a Nutshell

The Universe in a Nutshell

by Stephen Hawking

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Overview

Einstein said that the most incomprehensible thing about the universe is that it is comprehensible. But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists—Stephen Hawking (A Brief History of Time) and Roger Penrose (The Emperor's New Mind and Shadows of the Mind)—disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.

How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?

In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.

Product Details

ISBN-13: 9780553802023
Publisher: Random House Publishing Group
Publication date: 11/28/2001
Edition description: Reissue
Pages: 224
Sales rank: 98,832
Product dimensions: 7.80(w) x 10.16(h) x 0.81(d)

About the Author

Stephen Hawking is Lucasian Professor of Mathematics at the University of Cambridge. Roger Penrose is the Rouse Ball Professor of Mathematics at the University of Oxford. Michael Atiyah, Master of Trinity College Cambridge, and former President of the Royal Society, has written a foreword for this book.

Hometown:

Cambridge, England

Date of Birth:

January 8, 1942

Date of Death:

March 14, 2018

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 (Fig. 2.1).

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 takes the 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 (Fig. 2.2). 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 (see page 33, Fig. 2.3). 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 (Fig. 2.4).

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 (Fig. 2.5), 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 (Fig. 2.6).

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 (Fig. 2.7).

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 (Fig. 2.8).

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 (Fig. 2.9).

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 (Fig. 2.10). 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 (Fig. 2.11). 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 (Fig 2.12).

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 (see Fig 2.13, page 50).

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 (Fig. 2.14).

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 (Fig. 2.15). 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 (Fig. 2.16). 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 (Fig. 2.17).

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 (Fig. 2.18).

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 (Fig. 2.19).

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 (Fig. 2.20, see page 61). 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 (Fig. 2.21, see page 61) 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 (Fig. 2.22).

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.

Table of Contents

  • Classical Theory (Hawking)
  • Structure of Spacetime Singularities (Penrose)
  • Quantum Black Holes (Hawking)
  • Quantum Theory and Spacetime (Penrose)
  • Quantum Cosmology (Hawking)
  • The Twistor View of Spacetime (Penrose)
  • The Debate (Hawking and Penrose)

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The Universe in a Nutshell 4.5 out of 5 based on 0 ratings. 50 reviews.
CynthiaSueLarson More than 1 year ago
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.
Anonymous More than 1 year ago
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.
ToriBentley More than 1 year ago
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.
Guest More than 1 year ago
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.
Guest More than 1 year ago
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
Guest More than 1 year ago
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.
Guest More than 1 year ago
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.
Guest More than 1 year ago
Excellent! Stephen Hawking out does himself and presents his theories to the limit of the universe..
Guest More than 1 year ago
I found this book to be okay however I still prefer M. R. Franks' The Universe and Multiple Reality.
Guest More than 1 year ago
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.'
Guest More than 1 year ago
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
Guest More than 1 year ago
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!
Guest More than 1 year ago
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.
Guest More than 1 year ago
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.
Guest More than 1 year ago
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.
Guest More than 1 year ago
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.
Guest More than 1 year ago
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,
Guest More than 1 year ago
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.
Jewsbury on LibraryThing More than 1 year ago
This is an interesting book because it exposes part of the undercurrent of troubles in modern physics. Indeed it should be commended for not glossing over the issues. Regrettably though, this book is only really accessible to those who already have a good background in general relativity. However, this restriction does not appear to have been the intention, as (for the most part) the chapters present general overviews without technical derivations. Thus readers without an adequate background will lament the lack of an adequate introduction to place the set of presentations in their wider context. At its heart, this book demonstrates the contrast between a mathematical and a scientific approach to understanding nature. Penrose presents the mathematical viewpoint. He favours formal precise mathematics which he assumes will mirror reality. Hawking bats for the scientists. He starts with physically accessible conceptual representations with presumed mathematical approximations. Thus Hawking goes for physically reasonable methods, Penrose for mathematically realistic methods. Inevitably Penrose questions aspects of Hawking¿s mathematics; Hawking questions Penrose¿s relevance to physical reality. Both are trapped by their unexpressed belief that the laws of nature must be regulated by mathematics. In this context Hawking calls himself a positivist (reality=observation), and he calls Penrose a Platonist (reality=rational). However, Penrose prefers the moniker realist (reality=definite). Now, the book explores our current understanding of gravity, which is separable from spacetime. Regrettably it is almost impossible to solve the equations of general relativity for the cosmos without making approximations eg spherical symmetry, flat-space boundaries, uniform distribution of matter or even no matter. It goes without saying that when we make approximations, we cannot be sure that the derived conclusions will apply to reality. Thus another approach is to seek some general theorems about the nature of spacetime. Hence the book starts with the classical picture of spacetime as a continuum. The gravitational field (a distortion of spacetime) has energy, thus it cooks up a distortion of spacetime. Consequently spacetime can go haywire and introduce singularities ¿ places where the spatial curvature becomes infinite. The book discusses the rules for singularities and their encapsulating space. What makes this extra awkward is that singularities will only appear in the rather limited classical theory. Quantum gravity should avoid singularities. The quantum nature will not just smooth out the classical theory, it should actually replace our notion of spacetime on the small scale. Hence even these general rules might not apply to the real cosmos. Then the book moves on to discuss black holes. Hawking explains how black bodies take on a thermodynamic appearance with a temperature and entropy in the quantum theory. Indeed as thermodynamic entities, they become indistinguishable from white holes and they are fully time-reversal symmetric. In contrast classical general relativity distinguishes black and white holes (a white hole being the time-reverse of a black hole). Hawking claims that this matter-space interaction generates a new source of indeterminism in nature. Nevertheless that comment is debatable. This black-hole thermodynamics is probably the only sure thing in the book. Hence one has to wonder whether the claims are correct that field of cosmology has become a science. The rigorously derived mathematical results push physical credulity too far; hence most results are of uncertain relevance. On the other hand, physically reasonable arguments are generally forced to use questionable mathematical techniques. Only occasionally in this intellectual minefield is a probable result found eg the thermodynamic behaviour of black holes. Put simply, it appears that the cosmos is too complex for our theories and mathematics to get a proper grip. I am
Pompeia on LibraryThing More than 1 year ago
I read Stephen Hawking's previous book, A Brief History of Time when I was about 16 years old. That book was great and pretty easy to understand even though I didn't know much about physics back then. Now, ten years later, having spent five of those years studying physics at university level, I can't find much enjoyment in this book. Admittedly, it could be a question of my taste changing while growing up - but I still enjoy A Brief History of Time. Although there were many new tidbits for me (I'm by no means an astrophysicist) and I enjoyed reading the book, the sense of wonder was not there. The "plot" of the book was hard to follow since the book wasn't as well structured as ABHoT. Also, I have a feeling that if I had read this book back when I was 16, I might not have understood very much of it, so I'm not sure that this book is as suitable to someone who has never studied physics.All in all, a good book if you enjoy physics without the equations every once in a while, but not something I would recommend as a must read for a beginner.
melydia on LibraryThing More than 1 year ago
As with A Brief History of Time, I was frequently caught off guard by Hawking's sense of humor. His witty comments brighten up what could have been rather dry material. This is another I listened to on audiobook, read by Simon Prebble. The narrator was good and the subject matter interesting, but I think this would be better read in paper form, if only for the added benefit of diagrams. I had a lot of trouble following some of the more mind-bending notions in theoretical physics.
carterchristian1 on LibraryThing More than 1 year ago
When Amazon has over 150 glowing reviews of a book it says something. This is clearly the book I need to help with History of Physics, but have it tucked away in Box 5 in the basement. Must retrieve it soon as I plan to advance my science education, so neglected in high school and college.
dwarfplanet9 on LibraryThing More than 1 year ago
I read this book while in rehab, during my recover from total paralysis caused by Guillain-Barré Syndrome. I could not turn the pages myself, so I made a pest of myself by calling out to whatever staff member was walking by my hospital room. On night, I called Shirley, who worked mostly in the kitchen, as she walked by my room. Before she got to my bedside, I managed to turn the page by myself. We both were amazed and happy! This was a big milestone in my recovery, and I will never forget it. I finished the book pretty quickly after that.
bragan on LibraryThing More than 1 year ago
I was kind of unimpressed by Hawking's latest book, The Grand Design (co-authored with Leonard Mlodinow), which I read a few months ago. But it did remind me that I still had this book sitting on my To-Read Pile, getting more and more out of date by the minute, so I figured I'd better pick it up and give it a shot. In a way, this one gave me some of what I'd been hoping for from The Grand Design, as it touches a little more on topics such as M-theory, which I am very, very fuzzy on and quite interested in learning more about, instead of concentrating mainly on the basic concepts of modern physics. So I found parts of it interesting and reasonably rewarding. On the other hand, I do think I can make some of the same complaints about it as I did about The Grand Design, namely that it's often rather too abstruse and lacking in explanatory background to make sense to the complete layman, but also frequently lacks the technical detail that might help make it more understandable to, say, someone with a decent but slightly rusty undergraduate-level background in physics and astrophysics like yours truly. Admittedly, this is a problem any popularizer is going to run into when dealing with a field like this in which it's essentially impossible to grasp certain ideas without an understanding of advanced mathematics, but I know I've seen other writers do it somewhat better.At least the illustrations make the book very attractive, and, unlike those in The Grand Design, they tend to actually be relevant and sometimes even useful, if also a little distracting.
jaimelesmaths on LibraryThing More than 1 year ago
With humor and pretty pictures, Stephen Hawking describes the current theories about the universe as we know it. Definitely more approachable if you have some mathematics or physics background, but appreciable by a layperson as well.