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The Universe in a Nutshell ALSOA BLACKHOLESBY STEPHENBRIEFANDHISTORYBABYHAWKINGOF T I M EU N I V. CHAPTER 3 ~ page 6 7. The Universe in a Nutshell. The universe has multiple histories, each of which is determined by a tiny nut. CHAPTER 4 ~ page Read Download The Universe in a Nutshell |PDF books PDF Free Download Here: raudone.info?book=X.
Motionless, unable to react to Thor drowning in grief. They kept watching as Thor bent over the dead body, his fingers grazing over the black hair. With obvious care Thor picked him up, cradled his dead brother against his chest and walked out of this laboratory where they had probably planned to cut him into pieces. It took Steve over an hour to talk him into letting go of the body.
Tony sent me a picture. At least he was dead before they cut him up. And what they had been looking for during the autopsy.
The Illustrated A Brief History of Time / The Universe in a Nutshell by Stephen Hawking
Bruce desperately hoped that they would be done quickly, so he could get out of this lab. How was he supposed to do anything when one of them was going through such a nightmare? Loki had always been their enemy, a danger to every living, breathing person on this planet. But to Thor he would always be his little brother. Who had been murdered by Hydra. None of them had ever seen Thor in this state.
Struck down by this immense loss, barely able to stand on his own feet. Clearing his throat and hopefully his own thoughts Bruce continued to go through the data on the computer which was a deep, bottomless, black hole. Bruce lost track of time and was unable to tell how long he had been sitting here until Natasha, who had gone off scanning the rest of the base, gave him a call. Looking back up Bruce stared at Natasha who was white as a sheet. Tony reminded himself to break this story down into the simplest words he could come up with.
It was mind-blowing enough that idiots like Hydra had been able to succeed at something as revolutionary as this. By now he was knee-deep into the data and it got more twisted with every line that he read.
Even Tony knew that one had to be careful what to tell somebody who was completely grief-struck. Also Tony had no idea if Thor would comprehend the matter.
The body you found is a clone. It was my brother. No magic involved. Only science. He probably would have liked to do this himself, but Steve knew about cloning exactly as much as Thor.
Well, Hydra did. They got his DNA like this and disgusting assholes that they are they wanted to use it to find a way to recreate his powers. To use them for themselves and to weaponize them. Yes, he was all for people not getting murdered by Hydra, but Loki still out and about was immensely dangerous. None of them had ever seen him in such a state of distress and now they were able to relieve him of that. The sparks disappeared and Thor looked so hopeful that Tony thought his old, worn-out heart might break any second.
Your brother is still out and about. Probably perfectly fine. What did they do?
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Worked out examples have been presented after discussing each theory. Practice problems have also been included to enrich the learning experience of the students and professionals. PSpice and Multisim software packages have been included for simulation of different electrical circuit parameters. A number of exercise problems have been included in the book to aid faculty members.
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.
The Universe in a Nutshell by Stephen Hawking PDF Book Download
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. 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. 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. It is a matter of c o m m o n experience that we live in three-dimensional space. But w h y is space three-dimensional? W h y isn't it two, or four, or some o t h e r number of dimensions, as in science fiction?
In M-theory, space has nine or ten dimensions, but it is thought that six or seven of the directions are curled up very small, leaving three dimensions that are large and nearly flat Fig. W h y don't we live in a history in w h i c h eight of the dimensions are curled up small, leaving o n l y two dimensions that we n o t i c e?
If it had a gut that w e n t right through it, it would divide the animal in two, and the p o o r creature would fall apart. On the o t h e r hand, if there were four or m o r e nearly flat directions, the gravitational force b e t w e e n two bodies would increase m o r e rapidly as t h e y a p p r o a c h e d each other. T h i s would mean that FIG. T h u s , although the idea of multiple histories would allow any n u m b e r of nearly flat directions, time that expands in an inflationary o n l y histories with three flat directions will contain intelligent manner.
O n l y in such histories will the question be asked, " W h y does space have three dimensions? It determines a history of the universe in the real time that we experience, in which the universe is the same at every point of space and is expanding in time. In these respects, it is like the universe we live in.
But the rate of expansion is very rapid, and it keeps on getting faster. Such accelerating expansion is called inflation, because it is like the way prices go up and up at an ever-increasing rate.
W h i l e t h e universe is inflating, matter could n o t fall 9! T h u s a l t h o u g h histories of t h e universe INFLATION in imaginary time that are perfectly round spheres are allowed by the notion of multiple histories, t h e y are not of m u c h interest. However, histories in imaginary time that are slightly flattened at the south pole of the spheres are m u c h m o r e relevant Fig.
In this case, the corresponding history in real time will expand in an accelerated, inflationary manner at first. But then the expansion 3. After July the phase of hyperinflation began.
All confidence in money vanished and the price index rose faster and faster for will begin to slow down, and galaxies can form. In order for intelli- fifteen months, outpacing the printing gent life to be able to develop, the flattening at the S o u t h Pole must presses, which be very slight. T h i s will mean that the universe will expand initially could not produce money as fast as it was depreciating. By late , 3 0 0 paper mills were by an enormous amount.
T h e record level of m o n e t a r y inflation working at top speed and printing occurred in G e r m a n y between the world wars, when prices rose bil- companies had 2, presses running lions of t i m e s — b u t the amount of inflation that must have occurred day and night turning out currency.
Instead, the histories in imaginary time will be a w h o l e family of slightly deformed spheres, each of w h i c h corresponds to a history in real time in which the universe inflates for a long time but not indefinitely. We can then Although slightly irregular histories ask w h i c h of these allowable histories is the most probable.
It turns b and c are each less probable, out that t h e most p r o b a b l e histories are not c o m p l e t e l y smooth but there are such a large number of have tiny ups and downs Fig.
T h e ripples on the most prob- them that the likely histories of the universe will have small departures from smoothness.
T h e departures from smoothness are of the order of o n e part in a hundred thousand. Nevertheless, although t h e y are e x t r e m e l y small, we have managed to observe them as small variations in the microwaves that c o m e to us from different directions in space. T h e C o s m i c Background Explorer satellite was launched in 1 9 8 9 and made a map of the sky in microwaves.
T h e different colors indicate different temperatures, but the whole range from red to blue is only about a ten-thousandth of a degree. So in principle, at least, the instrument, time. C O B E map is the blueprint for all the structures in the universe. T h e r e seem to be various possibilities, d e p e n d ing on the amount of matter in the universe. If there is m o r e than a certain critical amount, the gravitational attraction b e t w e e n the galaxies will slow them down and will eventually stop them from flying apart.
S o , again, things will c o m e to an end, but in a the big crunch in which all matter will be sucked back into a vast cataclysmic gravity well. Either way, the universe will last a g o o d few billion years m o r e Fig. As well as matter, the universe may contain what is called "vac- FIG, 3. T h i s means that it has a gravitational effect on the expansion flicker their fuel. But, remarkably e n o u g h , the effect of vacuum energy is the opposite of that of matter.
M a t t e r causes the expansion to slow down and can eventually stop and reverse it. On the other hand, vacuum e n e r g y causes the expansion to accelerate, as in inflation. However, it may not have been a mistake at all.The density of galaxies appears to drop off at very clear view on either side of that plane.
T h a t is w h y casino operators are so rich. Views Total views. Therefore, one could not use the tivity is flat. Fundamentals of Electrical Circuit Analysis.
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