The universe in a nutshell epub download

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: 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. 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 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.

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: p-branes are created e q u a l! 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.

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: 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. 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. 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.

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: Prometheus. 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. W h a t Left: 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. Read Online Download. Great book, The Universe in a Nutshell pdf is enough to raise the goose bumps alone. Add a review Your Rating: Your Comment:.

The Grand Design by Stephen Hawking. Professor Hawking has combined many perspectives to show how Einstein's special and, The Universe in a Nutshell is an updated work of popular physics which informs the reader of advances in theoretical physics since his previous writings.

Written in , Hawking is able to take the reader through far more sophisticated attempts to unite science's two most successful theories, quantum mechanics and quantum gravity.. As with the earlier book, Nutshell is very ambitious, seeking to acquaint the reader with modern and highly mathematical theories on the fundamental nature of matter..

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Version of PDF eBook and the name of writer and number pages in ebook every information is given inside our post. Hawking's theory. Main menu. As with the earlier book, Nutshell is very ambitious, seeking to acquaint the reader with modern and highly mathematical theories on the fundamental nature of matter.

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