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The Universe in a Nutshell ALSO A BLACK HOLES BY STEPHEN BRIEF AND HISTORY BABY HAWKING OF T I M E U N I V E R S E S AND O T H E R ESSAYS. The Universe in a Nutshell. Page 4. ALSO BY STEPHEN HAWKING. A BRIEF The right of Stephen Hawking to be identified as the author of this work has. The Universe in a Nutshell | 𝗥𝗲𝗾𝘂𝗲𝘀𝘁 𝗣𝗗𝗙 on ResearchGate | The Universe in a Nutshell | Stephen Hawking's A Brief History of Time was a publishing.

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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. Reading 'The Universe in a Nutshell' the other day, I came to a few realisations other than a series of events), but Stephen Hawking compared spacetime to a. Stephen Hawking's first popular book, A brief history of time, first published in The universe in a nutshell is billed as "the inspiring sequel to A brief history of.

What happens is that as one uses energy to accelerate anything, whether a particle or a spaceship, its mass increases, making it harder to accelerate it further. To accelerate a particle to the speed of light would be impossible because it would take an infinite amount of energy.

This is probably the only equation in physics to have recognition on the street. Among its consequences was the realization that if the nucleus of a uranium atom fissions into two nuclei with slightly less total mass, this will release a tremendous amount of energy see pages , Fig. This led to the Manhattan Project and ultimately to the bombs that exploded over Hiroshima and Nagasaki in 1 9 4 5. Some people have blamed the atom bomb on Einstein because he discovered the relationship between mass and energy; but that is like blaming Newton for causing airplanes to crash because he discovered gravity.

Einstein himself took no part in the Manhattan Project and was horrified by the dropping of the bomb. After his groundbreaking papers in 1 9 0 5 , Einstein's scientific reputation was established. But it was not until 1 9 0 9 that he was offered a position at the University of Zurich that enabled him to leave the Swiss patent office. Despite the anti-Semitism that was common in much of Europe, even in the universities, he was now an academic hot property.

He moved to Berlin in April and was joined shortly after by his wife and two sons. The marriage had been in a bad way for some time, however, and his family soon returned to Zurich. Although he visited them occasionally, he and his wife were eventually divorced. Einstein later married his cousin Elsa, who lived in Berlin.

The fact that he spent the war years as a bachelor, without domestic commitments, may be one reason why this period was so productive for him scientifically. Although the theory of relativity fit well with the laws that governed electricity and magnetism, it was not compatible with Newton's law of gravity. This law said that if one changed the distribution of matter in one region of space, the change in the gravitational field would be felt instantaneously everywhere else in the universe.

Not only would this mean one could send signals faster than light something that was forbidden by relativity ; in order to know what instantaneous meant, it also required the existence of absolute or universal time, which relativity had abolished in favor of personal time.

Strung out

This causes it to fission in turn, and a chain reaction of further collisions begins. If the reaction sustains itself it is called "critical" and the mass of U is said to be a "critical mass. He realized that there is a close relationship between acceleration and a gravitational field. Someone inside a closed box, such as an elevator, could not tell whether the box was at rest in the Earth's gravitational field or was being accelerated by a rocket in free space. Of course, this was before the age of Star Trek, and so Einstein thought of people in elevators rather than spaceships.

But one cannot accelerate or fall freely very far in an elevator before disaster strikes Fig. This equivalence between acceleration and gravity didn't seem to work for a round Earth, however—people on the opposite sides of the world would have to be accelerating in opposite directions but staying at a constant distance from each other Fig.

But on his return to Zurich in Einstein had the brain wave of realizing that the equivalence would work if the geometry of Newton's head because of gravity or that the Earth and Newton were accelerating upward. T h i s equivalence didn't work for a spherical Earth FIG. I I because people on opposite sides of the world would be getting farther away from each other Einstein overcame this difficulty by making space and time curved.

Objects such as apples or planets alent only if a massive body curves would try to move in straight lines through spacetime, but their spacetime, thereby bending the paths of objects in its neighborhood.

With the help of his friend Marcel Grossmann, Einstein studied the theory of curved spaces and surfaces that had been developed earlier by Georg Friedrich Riemann. However, Riemann thought only of space being curved.

It took Einstein to realize that it is spacetime which is curved. However, because of a mistake by Einstein who was quite human and fallible , they weren't able to find the equations that related the curvature of spacetime to the mass and energy in it. Einstein continued to work on the problem in Berlin, undisturbed by domestic matters and largely unaffected by the war, until he finally found the right equations in November He had discussed his ideas with the mathematician David Hilbert during a visit to the University of Gottingen in the summer of , and Hilbert independently found the same equations a few days before Einstein.

Nevertheless, as Hilbert himself admitted, the credit for the new theory belonged to Einstein. It was his idea to relate gravity to the warping of spacetime. It is a tribute to the civilized state of Germany at this period that such scientific discussions and exchanges could go on undisturbed even in wartime.

It was a sharp contrast to the Nazi era twenty years later. The new theory of curved spacetime was called general relativity to distinguish it from the original theory without gravity, which was now known as special relativity. This produces a slight shift in the apparent position of the star as seen from the Earth b. This can be observed during an eclipse. Einstein found that his e q u a tions didn't have a solution that described a static universe, u n c h a n g i n g in t i m e.

T h e universe is e x p a n d ing, with t h e distance b e t w e e n any two galaxies steadily increasing with time Fig. A static universe could have existed forever or could have been created in its present form at some time in the past.

However, if galaxies are moving apart now, it means that they must have been closer together in the past. About fifteen billion years ago, they would all have been on top of each other and the density would have been very large. This state was called the "primeval atom" by the Catholic priest Georges Lemaitre, who was the first to investigate the origin of the universe that we now call the big bang.

Einstein seems never to have taken the big bang seriously. He apparently thought that the simple model of a uniformly expanding universe would break down if one followed the motions of the galaxies back in time, and that the small sideways velocities of the galaxies would cause them to miss each other.

He thought the universe might have had a previous contracting phase, with a bounce into the present expansion at a fairly moderate density.

Further, observations of the microwave background indicate that the density was probably once a trillion trillion trillion trillion trillion trillion 1 with 72 zeros after it tons per cubic inch. We also now know that Einstein's general theory of relativity does not allow the universe to bounce from a contracting phase to the present expansion. As will be discussed in Chapter 2, Roger Penrose and I were able to show that general relativity predicts that the universe began in the big bang.

So Einstein's theory does imply that time has a beginning, although he was never happy with the idea. Einstein was even more reluctant to admit that general relativity predicted that time would come to an end for massive stars when they reached the end of their life and no longer generated enough heat to balance the force of their own gravity, which was trying to make them smaller. Einstein thought that such stars would settle down to some 23 T H E U a massive star exhausts its nuclear fuel, it will lose heat and contract.

The warping of spacetime will b e c o m e so great that a black hole will be created from which light cannot escape.

Inside the black hole time will c o m e to an end. Such stars will continue to shrink until they become black holes, regions of spacetime that are so warped that light cannot escape from them Fig. Penrose and I showed that general relativity predicted that time would come to an end inside a black hole, both for the star and for any unfortunate astronaut who happened to fall into it.

But both the beginning and the end of time would be places where the equations of general relativity could not be defined.

Thus the theory could not predict what should emerge from the big bang. Some saw this as an indication of Cod's freedom to start the universe off in any way God wanted, but others including myself felt that the beginning of the universe should be governed by the same laws that held at other times. We have made some progress toward this goal, as will be described in Chapter 3, but we don't yet have a complete understanding of the origin of the universe.

The reason general relativity broke down at the big bang was that it was not compatible with quantum theory, the other great conceptual revolution of the early twentieth century. The first step toward quantum theory had come in , when Max Planck in Berlin discovered that the radiation from a body that was glowing red-hot was explainable if light could be emitted or absorbed only if it came in discrete packets, called quanta.

In one of his groundbreaking papers, written in when he was at the patent office, Einstein showed that Planck's quantum hypothesis could explain what is called the photoelectric effect, the way certain metals give off electrons when light falls on them. This is the basis of modern light detectors and television cameras, and it was for this work that Einstein was awarded the Nobel Prize for physics.

Einstein continued to work on the quantum idea into the s, but he was deeply disturbed by the work of Werner Heisenberg in Copenhagen, Paul Dirac in Cambridge, and Erwin Schrodinger in Zurich, who developed a new picture of reality called quantum mechanics. Instead, the more accurately one determined a particle's position, the less accurately one could determine its speed, and vice versa.

Einstein was horrified by this random, unpredictable element in the basic laws and never fully accepted quantum mechanics. His feelings were expressed in his famous dictum "God does not play dice. They are the basis of modern developments in chemistry, molecular biology, and electronics, and the foundation for the technology that has transformed the world in the last fifty years. In December 1 9 3 2 , aware that the Nazis and Hitler were about to come to power, Einstein left Germany and four months later renounced his citizenship, spending the last twenty years of his life at the Institute for Advanced Study in Princeton, New Jersey.

In Germany, the Nazis launched a campaign against "Jewish science" and the many German scientists who were Jews; this is part of the reason that Germany was not able to build an atomic bomb.

Albert Einstein with a puppet of Einstein and relativity were principal targets of this campaign. Einstein, he replied: If I were wrong, one would have been enough. In 1 9 4 8 , he was offered the presidency of the new state of Israel but turned it down. He once said: They should last as long as the universe.

The world has changed far more in the last hundred years than in any previous century. The reason has not been new political or economic doctrines but the vast developments in technology made possible by advances in basic science.

W h o better symbolizes those advances than Albert Einstein? How this can be reconciled with quantum theory. 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. The nineteenth-century author Charles Lamb wrote: And yet nothing troubles me less than time and space, because I never think of them.

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: 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 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. 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 Isaac Newton published his mathematical model of time and space over 3 0 0 years ago. 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? T h e large ball in the center represents But it was a contradiction only within the context of the Newtonian a massive body such as a star mathematical model, in which time was an infinite line, independent Its weight curves the sheet near it T h e ball bearings rolling on the sheet are deflected by this curvature and go of what was happening in the universe.

However, as we saw in Chapter 1, in 1 9 1 5 a completely new mathematical model was put around the large ball, in the same way forward by Einstein: In the years that planets in the gravitational field of since Einstein's paper, we have added a few ribbons and bows, but a star can orbit it. 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.

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.

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.

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. 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 out- Galaxies as they appeared recently Galaxies as they appeared 5 billion years ago side the realm of science. Solutions of the Einstein equations were known in which time had a beginning or end, but these were all The background radiation 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 1 9 6 3 , 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 FIG. If we represent time by the it. Energy is always positive, so it gives spacetime a curvature that vertical direction and represent two bends the paths of light rays toward each other. Now consider our past light cone Fig.

In a diagram with time plotted upward and FIG. Because the universe has been expanding and everything used to be much closer together, as we characteristic of that from a hot body. We observe a faint background of microwave radia- equilibrium, matter must have scat- tion that propagates to us along our past light cone from a much tered it many times. T h i s indicates that there must have been sufficient matter earlier time, when the universe was much denser and hotter than it in our past light cone to cause it to is now.

By tuning receivers to different frequencies of microwaves, bend in. This microwave radiation is not much good always warps spacetime so that light for defrosting frozen pizza, but the fact that the spectrum agrees so rays bend toward each other. 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. Our past is pear-shaped Fig.

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.

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. The whole universe we observe is contained within a region whose boundary shrinks to zero at the big bang.

T h i s would be a singularity, a place where the density of matter would be infinite and classical general relativity would break down. T h e longer the wavelength used to The shorter the wavelength used to observe a particle, the greater the observe a particle, the greater the uncertainty of its position.

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 s, by Heisenberg, Schrodinger, 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 o f the Maxwell field as being made up o f waves of different wavelengths the distance between o ne wave crest and the next. In a wave, the field will swing fro m o ne value to ano ther 2. According to FIG.

That wo uld have bo th a definite to the wave's direction of motion. The position and a definite velo city, zero. 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 FIG.

Instead quantum theory small angle to the vertical Fig. Similarly, even in the vacuum predicts that, even in its lowest energy or lowest energy state, the waves in the Maxwell field won't be state, the pendulum must have a min- exactly zero but can have small sizes. The higher the frequency imum amount of fluctuations. T h i s means that the pendulum's posi- the number of swings per minute of the pendulum or wave, the tion will be given by a probability distri- higher the energy of the ground state.

In its ground state, the most Calculations of the ground state fluctuations in the Maxwell and electron fields made the apparent mass and charge of the elec- likely position is pointing straight down, but it has also a probability of being found at a small angle to the vertical. 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.

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. Reduced number of wavelengths that can fit between the plates The energy density of ground state The energy density of ground fluctuations between the plates is state fluctuations is greater less than the density outside, caus- outside the plates.

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 s 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: But Grassmann variables anticommute: 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. In doing so they briefly annihilate one another in a frantic burst of energy, creating a photon.

T h i s then releases its energy, producing another electron-positron pair. T h i s still appears as if they are just deflected into new trajectories. Then, when they collide and annihilate one another, they create a new string with a different vibrational pattern.

Releasing energy, it divides into two strings continuing along new trajectories. Because there are equal numbers point in space, but one-dimensional strings. These strings may have ends or they may join up with themselves in of bosons and fermions, the biggest infinities cancel in supergravity theories see Fig 2.

There remained the possibility that there might be smaller but closed loops. Just like the strings on a violin, the strings in string theory support certain vibrational patterns, or resonant still infinite quantities left over. No one had the patience needed to calculate whether these theories were actually completely finite. It frequencies, whose wavelengths fit was reckoned it would take a good student two hundred years, and precisely between the two ends.

But while the different resonant frequencies of a violin's strings give rise to different musical notes, the different oscillations of a string give rise to different masses and force charges, which are interpreted as fundamental particles. Roughly speaking, the short- Still, up to 1 9 8 5 , 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, er the wavelength of the oscillation on it was claimed that a theory named supersymmetric string theory the string, the greater the mass of the was the only way to combine gravity with quantum theory.

Strings, particle. They have only length. Strings in string theory move through a background spacetime. Ripples on the string are interpreted as particles Fig. 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. 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. 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? 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.

Instead, we should adopt the principle of p-brane democracy: 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.

Special cases are I must say that personally, I have been reluctant to believe in extra dimensions. But as I am a positivist, the question "Do extra mem- dimensions really exist? Often, some or all of the p-dimensions are curled up like a torus.

We hold these truths to be All self-evident: The membranes can be seen better if they string curled up curled up into a torus are curled up. The dualities suggest that the different string theories are just different expressions of the same underlying theory, which has been named M-theory. 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. These dualities show that the five superstring theories all describe the same physics and that they are also physically equivalent to supergravity Fig.

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 theo- Heterotic-0 Heterotic-E ries don't have any infinities, they are good for calculating what happens when a few high energy particles collide and scatter off M-theory unites the five string theories within a single theoretical 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 framework, but many of its prop- forms a bound state, like a black hole. For these situations, one erties have yet to be understood.

It is this picture that I shall mainly use in what follows. The model has rules that determine the history in imaginary time in terms of the history in real time, and vice versa.

Imaginary time sounds like something from science fiction, but it is a well-defined mathematical concept: You can't have an imaginary number credit card bill. One can think of ordinary real numbers such as 1 , 2 , - 3. Imaginary numbers can then be represented as corresponding to positions on a vertical line: 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.

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? But the real time direction was distin- from the space directions because it guished from t h e three spatial directions; the world line or history increases only along the history of an observer unlike the space directions, of an observer always increased in t h e real time direction that is, which can increase or decrease along time always m o v e d from past to future , but it could increase or that history.

The imaginary time direc- decrease in any of t h e three spatial directions. In o t h e r words, one tion of quantum theory, on the other hand, is like another space direction, so can increase or decrease. On the o t h e r hand, because imaginary time is at right angles to real time, it behaves like a fourth spatial direction. As one moves north, the circles of latitude at constant distances from the South Pole become bigger corresponding to the universe expanding with imaginary time.

The universe would reach maximum size at the equator and then contract again with increasing imaginary time to a single point at the North Pole. Even though the universe would have zero size at the poles, these points would not be singularities, just as the North and South Poles on the Earth's surface are perfectly regular points.

This suggests that the origin of the universe in imaginary time can be a regular point in spacetime. Because all the lines of longitude meet at the North and South Poles, time is standing still at the poles; an increase of imaginary time leaves one on the same spot, just as going west on the North Pole of the Earth still leaves one on the North Pole.

Imaginary time as degrees of longitude which meet at the North and South Poles 61 T H E U N I V E R S E Information falling into black hole T h e area formula for the e n t r o p y — o r number of internal s t a t e s — o f a black hole suggests that information about what falls into a black hole may be stored like that on a record, and played back as the black hole evaporates.

It is in this imaginary sense that time has a shape.

The Illustrated A Brief History of Time / The Universe in a Nutshell pdf free

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. T h e n the history of the universe in imaginary time would begin at the South Pole. It would make no sense to ask, " W h a t h a p p e n e d before the beginning? T h e South Pole is a perfectly regular point of the Earth's surface, and the same laws hold there as at other points.

T h i s suggests that the b e g i n n i n g 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.

T h e quantum origin and evolution of the universe will be discussed in the next chapter. A n o t h e r possible b e h a v i o r is illustrated by taking imaginary time to be degrees of longitude on the Earth. All the lines of longitude meet at the N o r t h and S o u t h Poles Fig. T h i s is very similar to the way that ordinary time appears to stand still on the horizon of a b l a c k h o l e. We have c o m e to r e c o g n i z e that this standing still of real and imaginary time either b o t h stand still or neither does means that the s p a c e t i m e has a temperature, as I discovered for black holes.

N o t o n l y does a b l a c k h o l e have a t e m perature, it also behaves as if it has a quantity called entropy. T h e entropy is a measure of t h e n u m b e r of internal states ways it c o u l d be configured on the inside that the black h o l e c o u l d have w i t h o u t looking any different to an outside observer, w h o can o n l y observe its mass, rotation, and c h a r g e. It equals t h e area of the horizon of the black h o l e: Information a b o u t the quantum states in a region of spacetime may be s o m e h o w c o d e d on t h e boundary of the region, which has t w o dimensions less.

T h i s is like t h e way that a hologram carries a t h r e e - d i m e n s i o n a l image on a two-dimensional surface. T h i s is essential if we are to be able to predict the radiation that c o m e s out of black holes. If we can't do that, we won't be able to predict the future as fully as we t h o u g h t.

It seems we may live on a 3 - b r a n e — a four-dimensional three space plus o n e time surface that is the b o u n d a r y of a five-dimensional region, with the remaining dimensions curled up very small. T h e state of the world on a brane e n c o d e s what is h a p p e n i n g in the five-dimensional region. Is the universe actually infinite or just very large? And is it everlasting or just long-lived? Isn't it presumptuous of us even to make the attempt?

Despite this cautionary tale, I believe we can and should try to understand the universe. We have already made remarkable progress Above: Etruscan vase painting, 6th century B. We don't yet have a c o m p l e t e picture, but this may not be far off. Hubble space telescope lens and mirrors being upgraded by a space shuttle mission.

Australia can be seen below. Galaxies can have various shapes and sizes; they can be either elliptical or spiral, like our own Milky Way. The dust in the spiral arms blocks our view of the universe in FIG. We find that the galaxies are distributed the outer region of the spiral Milky Way galaxy.

T h e stellar dust in the spiral arms blocks our view within the roughly uniformly throughout space, with some local concentra- plane of the galaxy but we have a tions and voids. The density of galaxies appears to drop off at very clear view on either side of that plane. As far as we can tell, the universe goes on in space forever see page 7 2 , Fig. Although the universe seems to be much the same at each position in space, it is definitely changing in time.

This was not realized until the early years of the twentieth century. Up to then, it was thought the universe was essentially constant in time. It might have existed for an infinite time, but that seemed to lead to absurd conclusions. If stars had been radiating for an infinite time, they would have heated up the universe to their temperature.

T h e observation that we have all made, that the sky at night is dark, is very important. It implies that the universe c a n n o t have existed forever in the state we see today. S o m e t h i n g must have happ e n e d in the past to make the stars light up a finite time ago, which means that t h e light from very distant stars has not had time to reach us yet.

T h i s would explain why the sky at night isn't glowing in every d i r e c t i o n. However, discrepancies with this idea b e g a n to appear with the observations by V e s t o S l i p h e r and Edwin H u b b l e in t h e s e c o n d decade o f the twentieth century.

In T h e Doppler effect is also true of light order for them to appear so small and faint, the distances had to be so great that light from them would have taken millions or even billions of years to reach us. This indicated that the beginning of the universe couldn't have been just a few thousand years ago. But the second thing Hubble discovered was even more remarkable. Astronomers had learned that by analyzing the light from other galaxies, it was possible to measure whether they are moving toward us or away from us Fig.

To their great surprise, they had found that nearly all galaxies are moving away. Moreover, waves. If a galaxy were to remain at a constant distance from Earth, characteristic lines in the spectrum would appear in a normal or standard position. However, if the galaxy is moving away from us, the waves will appear elongated or stretched and the characteristic lines will be shifted toward the red right. If the galaxy is moving toward us then the waves will appear to be compressed, and the lines will be blue-shifted left.

It was Hubble who recognized the dramatic implications of this discovery: The universe is expanding Fig. The discovery of the expansion of the universe was one of the great intellectual revolutions of the twentieth century. It came as a total surprise, and it completely changed the discussion of the origin of the universe.

If the galaxies are moving apart, they must have been closer together in the past. From the present rate of expansion, we can estimate that they must have been very close together indeed ten to fifteen billion years ago. As described in the last chapter, Roger Penrose and I were able to show that Einstein's general theory of relativity implied that the universe and time itself must have had a beginning in a tremendous explosion. We are used to the idea that events are caused by earlier events, w h i c h in turn are caused by still earlier events.

W h a t caused it? T h i s was not a question that m a n y scientists w a n t e d to address. T h e y tried to avoid it, either by claiming, like t h e Russians, that t h e universe didn't have a b e g i n n i n g or by maintaining that t h e origin of the universe did not lie within the realm of s c i e n c e but b e l o n g e d to metaphysics or religion. In my opinion, this is n o t a position a n y true scientist should take. We must try to understand the beginning of the universe on the basis of science.

It may he a task beyond our powers, hut we should at least make the attempt.

The Universe in a Nutshell

W h i l e the t h e o r e m s that Penrose and I proved s h o w e d that the universe must have had a beginning, t h e y didn't give much information about the nature of that b e g i n n i n g. T h e y indicated that the universe began in a big bang, a point where the w h o l e universe, and everything in it, was scrunched up into a single point of infinite density. At this point, Einstein's general t h e o r y of relativity would have broken down, so it c a n n o t be used to predict in what m a n n e r t h e universe began.

O n e is left with the origin of the universe apparently being b e y o n d the scope of s c i e n c e. T h i s was not a conclusion that scientists should be happy with. As Chapters 1 and 2 point out, the reason general relativity b r o k e down near the big bang is that it did not incorporate the uncertainty principle, the random element of quantum theory that Einstein had o b j e c t e d to on the grounds that G o d does not play dice.

However, all the evidence is that G o d is quite a gambler. You might think that operating a casino is a very c h a n c y business, because you risk losing m o n e y each time dice are thrown or the wheel is spun. But over a large number of bets, the gains and losses average out to a result that can be predicted, even though the result of any particular bet c a n n o t be predicted Fig.

T h e casino operators make sure the odds average out in their favor. T h a t is w h y casino operators are so rich. T h e o n l y c h a n c e you have of winning against them is to stake all your m o n e y on a few rolls of the dice or spins of the wheel. It is the same with the universe. W h e n the universe is big, as it is today, there are a very large number of rolls of the dice, and the results FIG.

T h a t is why classical laws If a gambler bets on red for a large work for large systems. But when the universe is very small, as it was near in time to the big bang, there are only a small number of rolls of the dice, and the uncertainty principle is very important. Because the universe keeps on rolling t h e dice to see what happens next, it doesn't have just a single history, as o n e m i g h t have t h o u g h t.

Instead, t h e universe must have every possible history, e a c h with its own probability. If t h e frontier of t h e universe was just at a normal point of space and time, we c o u l d go past it and claim t h e territory b e y o n d as part of the universe. On the o t h e r hand, if the b o u n d a r y of the 80 number of rolls of the dice, one can fairly accurately predict his return because the results of the single rolls average out. On the other hand, it is impossible to predict the outcome of any particular bet.

However, a colleague named Jim Hartle and I realized there was a third possibility.

M a y b e the universe has no boundary in space and time. At first sight, this seems to be in direct contradiction with the theorems that Penrose and I proved, which showed that the universe must have had a beginning, a boundary in time. However, as explained in C h a p t e r 2, there is another kind of time, called imaginary time, that is at right angles to the ordinary real time that we feel going by. In particular, the universe need have no beginning or end in imaginary time.

Imaginary time behaves just like a n o t h e r direction in space. T h u s , the histories of the universe in imaginary time can be thought of as curved surfaces, like a ball, a plane, or a saddle shape, but with four dimensions instead of two see Fig. If the histories of the universe went off to infinity like a saddle or a plane, o n e would have the p r o b l e m of specifying w h a t the boundary c o n d i t i o n s were at infinity.

But o n e can avoid having to specify boundary c o n d i t i o n s at all if the histories of the universe in imaginary time are closed surfaces, like the surface of the Earth. T h e surface of the Earth doesn't have any boundaries or e d g e s.

T h e r e are no reliable reports of p e o p l e falling off. T h e universe would be entirely s e l f - c o n t a i n e d ; it wouldn't need wind the up anything clockwork outside and set to it going. Instead, e v e r y t h i n g in the universe would be d e t e r m i n e d by t h e laws of science and by rolls of the dice within the universe. T h i s may sound presumptuous, but it is what I and m a n y o t h e r scientists believe.

Even if the boundary condition of the universe is that it has no boundary, it won't have just a single history. It will have multiple histories, as suggested by Feynman. T h e r e will be a history in imaginary time corresponding to every possible closed surface, and each history in imaginary time will determine a history in real time. T h u s we have a superabundance of possibilities for the universe.

W h a t picks out the particular universe that we live in from the set of all possible universes? O n e point we can notice is that many of the possible histories of the universe won't go through the sequence of forming galaxies and stars that was essential to our own development.

W h i l e it may be that intelligent beings can evolve without galaxies and stars, this seems unlikely. The surface of the Earth doesn't have T h u s , the very fact that we exist as beings w h o can any boundaries or edges. Reports of ask the question " W h y is the universe the way it is? It implies it is o n e of the minority of histories that have galaxies and stars.

On the far right are those open universes b that will continue expanding forever Those critical universes that are balanced between falling back on themselves and continuing to expand like cl or the double might inflation of c2 harbor intelligent life. Our own universe d is poised The double inflation could T h e inflation of our own universe to continue expanding for now.

M a n y scientists dislike the anthropic principle because it seems rather vague and does not appear to have much predictive power. But the anthropic principle can be given a precise formulation, and it seems to be essential when dealing with the origin of the universe. M - t h e o ry, described in C h a p t e r 2, allows a very large number of possible histories for the universe.

M o s t of these histories are not suitable for the development of intelligent life; either they are empty, last for t o o short a time, are too highly curved, or w r o n g in some o t h e r way. Yet according to Richard Feynman's idea of multiple histories, these uninhabited histories can have quite a high probability see page 8 4. In fact, it doesn't really matter h o w many histories there may be that don't contain intelligent beings.

We are interested o n l y in the subset of histories in w h i c h intelligent life develops. T h i s intelligent life need not be anything like humans. Little green aliens would do as well. In fact, t h e y might do rather better. T h e human race does not have a very g o o d record of intelligent behavior. As an example of the power of the a n t h r o p i c principle, consider the number of directions in space.

Nov 06, Pages Buy. Nov 06, Minutes Buy. Nov 06, Pages. Nov 06, Minutes. 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.

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.

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.

He involves us in the attempts at uncovering its secrets-from supergravity to supersymmetry, from quantum theory to M-theory, from holography to duality, and now, at the very frontiers of science, superstring theory and p-branes.

From the Hardcover edition. Stephen Hawking was the Lucasian Professor of Mathematics at the University of Cambridge for thirty years and the recipient of numerous awards and honors including the Presidential Medal of Freedom. And he leavens it further with occasional wry humor. Best of all, the book is liberally sprinkled with well-conceived, gorgeously rendered and frequently whimsical illustrations.

Join Reader Rewards and earn your way to a free book! Join Reader Rewards and earn points when you purchase this book from your favorite retailer. Read An Excerpt.

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Science Category: Science Audiobooks Category:Albert Einstein with a puppet of Einstein and relativity were principal targets of this campaign. The spectrum of a black hole is exactly what we would expect from a hot body, with a temperature proportional to the gravitational field on the horizon—the boundary—of the black hole. Thus, according to the p-brane model, we can use the Schrodinger equation to calculate what the wave function will be at later times.

Meanwhile, Lifshitz andKhalatnikov were in an awkward position. My seminar fell rather flat because at that time almost no one in Paris believed in black holes. He takes us to the wild frontiers of science, where superstring theory and p-branes may hold the final clue to the puzzle.

LAURICE from Michigan
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