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Read Download The Universe in a Nutshell |PDF books PDF Free Download Here: pabushobupchild.gq?book=X. 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
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.
The Illustrated A Brief History of Time/The Universe in a Nutshell
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. As described in C h a p t e r 2, we now realize that quantum t h e o r y implies that spacetime is filled with quantum fluctuations.
In a supersymmetric theory, the infinite positive and negative energies of these g r o u n d state fluctuations c a n c e l out b e t w e e n particles of different spin. But we wouldn't e x p e c t the positive and negative energies to c a n c e l so c o m p l e t e l y that there wasn't a small, finite a m o u n t of vacuum energy left over, because the universe is not in a supersymmetric state.
M a y b e this is another example of the FIG. A history with a larger vacuum energy would not have formed galaxies, so would not contain beings w h o could ask the question: We can show the well estimated.
T h e dotted line shows t h e boundary of the region in w h i c h intelligent life could d e v e l o p Fig. Fortunately, all three regions have a c o m m o n intersection. If the matter density and vacuum energy lie in this intersection, it means that t h e expansion of the universe has begun to speed up again, after a l o n g period of slowing down. It seems that inflation may be a law of nature.
In this c h a p t e r we have seen h o w the b e h a v i o r of the vast universe can be understood in terms of its history in imaginary time, which is a tiny, slightly flattened sphere. It is like Hamlet's nutshell, yet this nut e n c o d e s e v e r y t h i n g that happens in real time.
So H a m l e t was quite right. We could be b o u n d e d in a nutshell and still count ourselves kings of infinite space. The of the complicated planets in apparent motion the can sky be explained by Newton's laws and has no influence on personal fortunes. T h a t is w h y astrology is so popular. A s t r o l o g y claims that events on Earth are related to the m o t i o n s of the planets across the sky. T h i s is a scientifically testable h y p o t h e s i s , or would be if astrologers stuck their necks out and made definite p r e d i c t i o n s that c o u l d be tested.
S t a t e m e n t s such as "Personal relations may b e c o m e intense" or "You will have a financially rewarding opportunity" can never be proved wrong. W h e n C o p e r n i c u s and G a l i l e o discovered that the planets orbit the Sun rather than the Earth, and N e w t o n discovered the laws that govern their m o tio n, astrology b e c a m e e x t r e m e l y implausible.
W h y should the positions of o t h e r planets against the b a c k g r o u n d sky as seen from Earth have any correlations with the m a c r o m o l e c u l e s on a minor planet that call themselves intelligent life Fig.
Yet this is what astrology would have us believe. T h e success of Newton's laws and o t h e r physical theories led to the idea of scientific determinism, which was first expressed at the beginning of the nineteenth century by the French scientist the Marquis de Laplace.
Laplace suggested that if we knew the positions and velocities of all the particles in the universe at one time, the laws of physics should allow us to predict what the state of the universe would be at any o t h e r time in the past or in the future Fig. In o t h e r words, if scientific determinism holds, we should in principle be able to predict the future and wouldn't need astrology.
Of course, in practice even s o m e t h i n g as simple as Newton's theory of gravity produces e q u a t i o n s that we can't solve exactly for more than t w o particles.
Furthermore, the equations often have a property known as c h a o s , so that a small c h a n g e in position or velocity at o n e time can lead to c o m p l e t e l y different behavior at later times. As t h o s e w h o have seen Jurassic Park know, a tiny disturbance in o n e place can cause a m a j o r c h a n g e in another. T h e trouble is the sequence of events is not repeatable. T h e next time FIG. That is why weather forecasts are so unreliable. Thus, although in principle the laws of quantum electrodynamics should allow us to calculate everything in chemistry and biology, we have not had much success in predicting human behavior from mathematical equations.
Nevertheless, despite these practical difficulties most scientists have comforted themselves with the idea that, again in principle, the future is predictable. At first sight, determinism would also seem to be threatened by the uncertainty principle, which says that we cannot measure accurately both the position and the velocity of a particle at the same time.
The more accurately we measure the position, the less accurately we can determine the velocity, and vice versa. The Laplace version of scientific determinism held that if we knew the positions and velocities of particles at one time, we could determine their positions and velocities at any time in the past or future. But how could we even get started if the uncertainty principle prevented us from knowing accurately both the positions and the velocities at one time?
However good our computer is, if we put lousy data in, we will get lousy predictions out. A wave function is a number at each point of space that gives the probability that the particle is to be found at that position. The rate at which the wave function changes from point to point tells how probable different particle velocities are.
Some wave functions are sharply peaked at a particular point in space. In these cases, there is only a small amount of uncertainty in the position of the particle. That means the probability distribution for the velocity is spread over a wide range. In other words, the uncertainty in the velocity is large. Consider, on the other hand, a continuous train of waves. Now there is a large uncertainty in position but a small uncertainty in velocity. So the description of a particle by a wave function does not have a well-defined position or velocity.
It satisfies the uncertainty principle. We now realize that the wave function is all that can be well defined. We cannot even suppose that the particle has a position and velocity that are known to God but are hidden from us. Such "hidden-variable" theories predict results that are not in agreement with observation.
Even God is bound by the uncertainty principle and cannot know the position and velocity; He can only know the wave function. The rate at which the wave function changes with time is given by what is called the Schrodinger equation Fig.
Therefore, there is still determinism in quantum theory, but it is on a reduced scale. Instead measures of time, but we can use of being able to predict both the positions and the velocities, we can the Schrodinger equation in any of predict only the wave function.
This can allow us to predict either the these times to predict what the wave function will be in the future. Thus in quantum theory the ability to make exact predictions is just half what it was in the classical Laplace worldview.
Nevertheless, within this restricted sense it is still possible to claim that there is determinism. However, the use of the Schrodinger equation to evolve the wave function forward in time that is, to predict what it will be at future times implicitly assumes that time runs on smoothly everywhere, forever. This was certainly true in Newtonian physics.
Time was assumed to be absolute, meaning that each event in the history of the universe was labeled by a number called time, and that a series of time labels ran smoothly from the infinite past to the infinite future. This is what might be called the commonsense view of time, and it is the view of time that most people and even most physicists have at the back of their minds.
However, in 1 9 0 5 , as we have seen, the concept of absolute time was overthrown by the special theory of relativity, in which time was no longer an independent quantity on its own but was just one direction in a four-dimensional continuum called spacetime. However, the spacetime of special rela- where time stood still.
At these points, time would not increase in any direction. Therefore, one could not use the tivity is flat. This means that in special relativity, the time measured Schrodinger equation to predict what by any freely moving observer increases smoothly in spacetime the wave function will be in the future. We can use any of these measures of time in the Schrodinger equation to evolve the wave function.
In special relativity, therefore, we still have the quantum version of determinism. The situation was different in the general theory of relativity, in which spacetime was not flat but curved, and distorted by the matter and energy in it.
In our solar system, the curvature of spacetime is so slight, at least on a macroscopic scale, that it doesn't interfere with our usual idea of time. In this situation, we could still use this time in the Schrodinger equation to get a deterministic evolution of the wave function. However, once we allow spacetime to be curved, the door is opened to the possibility that it may have a structure that doesn't admit a time that increases smoothly for every observer, as we would expect for a reasonable measure of time.
For example, suppose that spacetime was like a vertical cylinder Fig. However, imagine instead that spacetime was like a cylinder with a handle or "wormhole" that branched off and then joined back on. Then any measure of time would necessarily have stagnation points where the handle joined the main cylinder: At these points, time would not increase for any observer. In such a spacetime, we could not use the Schrodinger equation to get a deterministic evolution for the wave function.
Watch out for wormholes: Black holes are the reason we think time will not increase for every observer. The first discussion of black holes appeared in 1 7 8 3. A former Cambridge don, John Michell, presented the following argument. If one fires a particle, such as a cannonball, vertically upward, its ascent will be slowed by gravity, and eventually the particle will stop moving upward and will fall back Fig.
However, if the initial upward velocity is greater than a critical value called the escape velocity, gravity will never be strong enough to stop the particle, and it will get away. The escape velocity is about 12 kilometers per second for the Earth, and about 6 1 8 kilometers per second for the Sun. Thus, light can get away from the Earth or Sun without much difficulty.
The Illustrated A Brief History of Time / The Universe in a Nutshell by Stephen Hawking
However, Michell argued that there could be stars that are much more massive than the Sun and have escape velocities greater than the speed of light Fig. We would not be able to see these stars, because any light they sent out would be dragged back by the gravity of the star.
Thus they would be what Michell called dark stars and we now call black holes. Michell's idea of dark stars was based on Newtonian physics, in which time was absolute and went on regardless of what happened. Thus they didn't affect our ability to predict the future in the classical Newtonian picture. But the situation was very different in the general theory of relativity, in which massive bodies curve spacetime.
In 1 9 1 6 , shortly after the theory was first formulated, Karl Schwarzschild who died soon after of an illness contracted on the Russian front in the First World War found a solution of the field equations of general relativity that represented a black hole.
What Schwarzschild had found wasn't understood or its importance recognized for many years. Matter falling into a black hole seems to be the only mechanism that can account for such a high luminosity. I remember going to Paris to give a seminar on my discovery that quantum theory means that black holes aren't completely black.
My seminar fell rather flat because at that time almost no one in Paris believed in black holes. The French also felt that the name as they translated it, trou noir, had dubious sexual connotations and should be replaced by astre occlu, or "hidden star.
The discovery of quasars in 1 9 6 3 brought forth an outburst of theoretical work on black holes and observational attempts to detect them Fig. Here is the picture that has emerged. Consider what we believe would be the history of a star with a mass twenty times that of the Sun.
Such stars form from clouds of gas, like those in the Orion Nebula Fig. As clouds of gas contract under their own gravity, the gas heats up and eventually becomes hot enough to start the nuclear fusion reaction that converts hydrogen into helium. The heat generated by this process creates a pressure that supports the star against its own gravity and stops it from contracting further. A star will stay in this state for a long time, burning hydrogen and radiating light into space.
The gravitational field of the star will affect the paths of light rays coming from it. One can draw a diagram with time plotted F I G.
In this diagram, the surface of the star is represented by two vertical lines, one on either side of the center. One can choose that time be measured in seconds and distance in lightseconds—the distance light travels in a second.
When we use these units, the speed of light is 1; that is, the speed of light is 1 light-second per second. This means that far from the star and its gravitational field, the path of a light ray on the diagram is a line at a degree angle to the vertical. However, nearer the star, the curvature of spacetime produced by the mass of the star will change the paths of the light rays and cause them to be at a smaller angle to the vertical. This means they can run out of hydrogen in as vertical lines.
Far from the star, the light little as a few hundred million years. After that, such stars face a cri- rays are at 45 degrees to the vertical, sis.
They can burn their helium into heavier elements such as car- but near the star the warping of spacetime by the mass of the star causes light rays to be at a smaller angle to the vertical. Therefore they begin to get smaller. If they FIG.
They will collapse to becomes so large that light rays near the zero size and infinite density to form what is called a singularity surface move inward. A black hole is formed, a region of spacetime from which it is not possible for light to escape. When the star reaches a certain critical radius, the path will be vertical on the diagram, which means that the light will hover at a constant distance from the center of the star, never getting away.
This critical path of light F U T U R E The horizon, the outer boundary of a black hole, is formed by light rays that just fail to get away from the black hole, but stay hovering at a constant distance from the center.
Any light emitted by the star after it passes the event horizon will be bent back inward by the curvature of spacetime. The star will have become one of Michell's dark stars, or, as we say now, a black hole.
How can you detect a black hole if no light can get out of it? The answer is that a black hole still exerts the same gravitational T FIG. If the 4. T h e galaxy N G C Sun were a black hole and had managed to become one without losing any of its mass, the planets would still orbit as they do now.
T h e horizontal line passing One way of searching for a black hole is therefore to look for matter that is orbiting what seems to be an unseen compact massive through the image is from light gener- object. A number of such systems have been observed. Perhaps the ated by the black hole at the center of most impressive are the giant black holes that occur in the centers Right Image showing the velocity of oxygen emissions. All the evidence of galaxies and quasars Fig.
The properties of black holes that have been discussed thus far indicates that N G C contains a don't raise any great problems with determinism. Time will come to black hole about a hundred million an end for an astronaut who falls into a black hole and hits the sin- times the mass of the Sun. However, in general relativity, one is free to measure time at different rates in different places.
One could therefore speed up the FIG. On the time-and-distance diagram Fig. But they would agree with the usual measure of time in the nearly flat spacetime far away from the black hole.
One could use this time in the Schrodinger equation and calculate the wave function at later times if one knew it initially.
Thus one still has determinism. It is worth noting, however, that at late times, part of the wave function is inside the black hole, where it can't be observed by someone outside. Thus an observer who is sensible enough not to fall into a black hole cannot run the Schrodinger equation backward and calculate the wave function at early times. To do that, he or she would need to know the part of the wave function that is inside the black hole.
This is potentially a very large amount of information, because a black hole of a given mass and rate of rotation can be formed from a very large number of different collections of particles; a black hole does not depend on the nature of the body that had collapsed to form it. John Wheeler called this result "a black hole has no hair. The difficulty with determinism arose when I discovered that black holes aren't completely black.
As we saw in Chapter 2, quantum theory means that fields can't be exactly zero even in what is The no-hair result. If they were zero, they would have both an exact value or position at zero and an exact rate of change or velocity that was also zero. This would be a violation of the uncertainty principle, which says that the position and velocity can't both be well defined. All fields must instead have a certain amount of what are called vacuum fluctuations in the same way that the pendulum in Chapter 2 had to have zero point fluctuations.
Vacuum fluctuations can be interpreted in several ways that seem different but are in fact mathematically equivalent.
From a positivist viewpoint, one is free to use whatever picture is most useful for the problem in question. In this case it is helpful to think of vacuum fluctuations as pairs of virtual particles that appear together at some point of spacetime, move apart, and come back together and annihilate each other. If a black hole is present, one member of a pair of particles may fall into the black hole, leaving the other member free to escape to infinity Fig. To someone far from the black hole, the escaping particles appear to have been radiated by the black hole.
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. In other words, the temperature of a black hole depends on its size.
A black hole of a few solar masses would have a temperature of about a millionth of a degree above absolute zero, and a larger black hole would have an even lower temperature. O n e of the pair falls into the black hole while its twin is free to escape. From outside the event horizon it appears that the black hole is radiating the particles that escape.
It would be inflationary manner In the diagram possible to detect the radiation from much smaller and hotter black time is shown in the upward and the holes, but there don't seem to be many of them around. That is a size of the universe in the horizontal pity. If one were discovered, I would get a Nobel Prize. However, direction. Spatial distances increase so rapidly that light from distant galaxies never reaches us, and there is an event horizon, a boundary of the region we cannot observe, as in a black hole.
As described in Chapter 3, it is thought that very early in its history, the universe went through an inflationary period during which it expanded at an ever-increasing rate. Thus there would be a horizon in the universe like the horizon of a black hole, separating the region from which light can reach us and the region from which it cannot Fig. Very similar arguments show that there should be thermal radiation from this horizon, as there is from a black hole horizon.
In thermal radiation, we have learned to expect a characteristic spectrum of density fluctuations. In this case, these density fluctuations would have expanded with the universe. When their length scale became longer than the size of the event horizon, they would have become frozen in, so that we can observe them today as small variations in the temperature of the cosmic background radiation left over from the early universe.
The observations of those variations agree with the predictions of thermal fluctuations with remarkable accuracy. Even if the observational evidence for black hole radiation is a bit indirect, everyone who has studied the problem agrees it must occur in order to be consistent with our other observationally tested theories. This has important implications for determinism.
The radiation from a black hole will carry away energy, which must mean that the black hole will lose mass and get smaller. In turn, this will mean that its temperature will rise and the rate of radiation will increase.
Eventually the black hole will get down to zero mass. We don't know how to calculate what happens at this point, but the only natural, reasonable outcome would seem to be that the black hole disappears completely. So what happens then to the part of the wave function inside the black hole and the information it contains about what had fallen into the black hole? The first guess might be that this part of the wave function, and the information it carries, would emerge when the black hole finally disappears.
However, information cannot be carried for free, as one realizes when one gets a telephone bill. Information requires energy to carry it, and there's very little energy left in the final stages of a black hole. However, according to the picture of one member of a virtual-particle pair falling in and loses mass, the temperature of the the other member escaping, one would not expect the escaping par- black hole rises and its rate of radia- ticle to be related to what fell in, or to carry away information about tion increases, so it loses mass more and more quickly.
We don't know what happens if the mass b e c o m e s it. So the only answer would seem to be that the information in the part of the wave function inside the black hole gets lost Fig. To start with, we have noted that even if you knew hole would disappear completely. What that was would depend in part on the bit of the wave function that got lost in the black hole.
We are used to thinking we can know the past exactly. However, if information gets lost in black holes, this is not the case.
Anything could have happened. At first glance, it m i g h t seem that the loss of part of the wave function down the black h o l e would not prevent us from predicting the wave function outside the b l a c k h o l e. Imagine that a radioactive atom decays and sends out two particles in o p p o s i t e directions and with o p p o s i t e spins. But if the o b s e r v e r measures it to be spinning to the right, then he or she can predict with c e r t a i n t y that the o t h e r particle will be spinning to t h e left, and v i c e versa Fig.
Einstein thought that this proved that quantum t h e o r y was ridiculous: However, most other scientists agree that it was tion that predicts that both particles will have opposite spins. But if one Einstein who was confused, not quantum theory. The Einstein- particle falls into the black hole, it is Podolsky-Rosen thought experiment does not show that one is able impossible to predict with certainty to send information faster than light.
That would be the ridiculous the spin of the remaining particle. One cannot choose that one's own particle will be measured to be spinning to the right, so one cannot prescribe that the distant observer's particle should be spinning to the left.
In fact, this thought experiment is exactly what happens with black hole radiation. The virtual-particle pair will have a wave function that predicts that the two members will definitely have opposite spins Fig. What we would like to do is predict the spin and wave function of the outgoing particle, which we could do if we could observe the particle that has fallen in.
Because of this, it is not possible to predict the spin or the FIG. It can have different spins Black holes can be thought of as the and different wave functions, with various probabilities, but it doesn't have a unique spin or wave function. Thus it would seem that our 4. Information about the internal states of black holes power to predict the future would be further reduced. The classical would be stored as waves on the p- idea of Laplace, that one could predict both the positions and the branes.
However, one could still measure the wave function and use the Schrodinger equation to predict what it should be in the future. This would allow one to predict with certainty one combination of position and velocity—which is half of what one could predict according to Laplace's ideas. This means that there isn't any measurement out- A particle falling into a black hole can side the black hole that can be predicted with certainty: It will excite waves in the p-brane 2.
Waves can c o m e together and cause part of the p-brane to break off as a closed string 3. This would be a particle emitted by the black hole. So maybe astrology is no worse at predicting the future than the laws of science.
Many physicists didn't like this reduction in determinism and therefore suggested that information about what is inside can somehow get out of a black hole. For years it was just a pious hope that some way to save the information would be found. But in 1 9 9 6 Andrew Strominger and Cumrun Vafa made an important advance.
They chose to regard a black hole as being made up of a number of building blocks, called p-branes see page 5 4. Recall that one way of thinking about p-branes is as sheets that move through the three dimensions of space and also through seven extra dimensions that we don't notice see Fig.
In certain cases, one can show that the number of waves on the pbranes is the same as the amount of information one would expect the black hole to contain. If particles hit the p-branes, they excite extra waves on the branes. Thus the p-branes can absorb and emit particles like black holes Fig. One can regard the p-branes as an effective theory; that is, while we don't need to believe that there actually are little sheets moving through a flat spacetime, black holes can behave as if they were made up of such sheets.
It is like water, which is made up of billions and billions of H 0 molecules with complicated interactions. The mathematical model of black holes as made of p-branes gives results similar to the virtual-particle pair picture described earlier. Thus from a positivist viewpoint, it is an equally good model, at least for certain classes of black hole. For these classes, the p-brane model predicts exactly the same rate of emission that the virtual-particle pair model predicts.
However, there is one important difference: Instead, the information will eventually emerge from the black hole in the radiation from the p-branes. Thus, according to the p-brane model, we can use the Schrodinger equation to calculate what the wave function will be at later times. Nothing will get lost, and time will roll smoothly on.
We will have complete determinism in the quantum sense. So which of these pictures is correct? Does part of the wave function get lost down black holes, or does all the information get out again, as the p-brane model suggests? This is one of the outstanding questions in theoretical physics today.
Many people believe that recent work shows that information is not lost. The world is safe and predictable, and nothing unexpected will happen. But it's not clear. If one takes Einstein's general theory of relativity seriously, one must allow the possibility that spacetime ties itself in a knot and information gets lost in the folds.
When the starship Enterprise went through a wormhole, something unexpected happened. I know, because I was on board, playing poker with Newton, Einstein, and Data. I had a big surprise. Just look what appeared on my knee. In the future it is proved that the 3 dynamical evolution Stephen Hawking from generic initial signs a sure bet conditions can on 5 February, never produce a This led him to have the courage to be the first serious scientist to discuss time travel as a practical possibility.
It is tricky to speculate openly about time travel. One risks either an outcry at the waste of public money being spent on something so ridiculous or a demand that the research be classified for military purposes. After all, how could we protect ourselves against someone with a time machine?
They might change history and rule the world. There are only a few of us foolhardy enough to work on a subject that is so politically incorrect in physics circles. We dis- Kip Thome guise the fact by using technical terms that are code for time travel. As we have seen in earlier chapters, the Einstein equations made space and time dynamic by describing how they were curved and distorted by the matter and energy in the universe.
In general relativity someone's personal time as measured by their wristwatch would always increase, just as it did in Newtonian theory or the flat spacetime of special relativity. But there was now the possibility that spacetime could be warped so much that you could go off in a spaceship and come back before you set out Fig.
One way this could happen is if there were wormholes, tubes of spacetime mentioned in Chapter 4 that connect different regions of space and time.
The idea is that you steer your spaceship into one mouth of the wormhole and come out of the other mouth in a different place and at a different time Fig. Wormholes, if they exist, would be the solution to the speed limit problem in space: But you might go through a wormhole to the other side of the galaxy and be back in time for dinner. Perfecting Your English Pronunciation, 2nd Edition.
Techlife News - March 24, Overview: A global view of Tech LifeStyle and its influence on our lives. Read the most relevant news of the week about the world of technology and its influence on our lives. New products, Apps, acquisitions in the industry, highlights about the digital world and everything about your favorite iGadgets and upgrades. Everything you need to keep well informed.
A new concept of light, intelligent, innovative reading at your fingertips. 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. Electronica Azi International — N 1, Industrial Automation — February Fundamentals of Electrical Circuit Analysis.
In this Very Short Introduction, Michael Newman seeks to place the idea of socialism in a modern context for today's readers. He explains socialist ideas in the framework of its historical evolution, from the French Revolution to the present day, and examines practical attempts to implement socialism. Not just another history of socialist ideas, this book aims for a different approach that looks at practice as well as theory - centering on the contrast between Communism and Social Democracy.
The relationship between socialism and notions of democracy, freedom, and equality is also discussed. Newman brings the subject entirely up to date by tackling contemporary forms of socialism. While the book's focus is on Europe and the Soviet Union, it is set in a broader geographical context. Newman's fresh approach to the subject enables the reader to re-evaluate socialism. Included are exercises divided according to three levels of increasing difficulty, labeled from A to C; a self-assessment test and full-length practice Reading tests; all questions answered and explained; test taking tips; and extensive vocabulary review.However, if FIG.
The difficult sounds of English consonants and vowels are spoken first in individual words, then phrases, and finally in complete sentences. 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. For a few years, strings reigned supreme and supergravity was dismissed as just an approximate theory, valid at low energy.
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.
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