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Loved each and every part of this book. I will definitely recommend this book to science, non fiction lovers. Your Rating:. Due to a regretful glitch in the publishing process, the answers to the etudes were never published. The main characters of this science, childrens story are ,. The illustrated theory of everything. A brilliant theoretical physicist whose work helped to reconfigure models of the universe and to redefine whats in it.
This public document was automatically mirrored from pdfy. Kids coloring books for minecrafters Disappointing in some ways, i. These books cost money to buy, but you can get them free for review! Get free access to the library by create an account, fast download and ads free. The origin and fate of universe , stephen hawking. I am deeply sorry about this, and have made these available for you now in pdf form. Michio kaku, renowned theoretical physicist and 1 new york times bestselling author of the future of the mind and the future of humanity, tells the story of the greatest quest in all of science.
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This book assumes some familiarity with the special theory of relativity. The origin and fate of the universe pdf epub book. Instead, there must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of a field. One can think of these fluctuations as pairs of particles of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other.
These particles are called virtual particles. However, their indirect effects, such as small changes in the energy of electron orbits and atoms, can be measured and agree with the theoretical predictions to a remarkable degree of accuracy. By conservation of energy, one of the partners in a virtual particle pair will have positive energy and the other partner will have negative energy.
The one with negative energy is condemned to be a short-lived virtual particle. This is because real particles always have positive energy in normal situations.
It must therefore seek out its partner and annihilate it. However, the gravitational field inside a black hole is so strong that even a real particle can have negative energy there.
It is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle. In this case it no longer has to annihilate its partner; its forsaken partner may fall into the black hole as well. But because it has positive energy, it is also possible for it to escape to infinity as a real particle.
To an observer at a distance, it will appear to have been emitted from the black hole. The smaller the black hole, the less far the particle with negative energy will have to go before it becomes a real particle.
Thus, the rate of emission will be greater, and the apparent tem- perature of the black hole will be higher. A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so the second law is never violated. So as the black hole loses mass, its temperature and rate of emission increase.
It there- fore loses mass more quickly. What happens when the mass of the black hole eventually becomes extremely small is not quite clear. The most reasonable guess is that it would disappear completely in a tremendous final burst of emis- sion, equivalent to the explosion of millions of H-bombs.
A black hole with a mass a few times that of the sun would have a tempera- ture of only one ten-millionth of a degree above absolute zero. This is much less than the temperature of the microwave radiation that fills the universe, about 2.
The hole will then absorb less than it emits and will begin to lose mass. But, even then, its temperature is so low that it would take about years to evaporate completely. This is much longer than the age of the universe, which is only about years. On the other hand, as we learned in the last lecture, there might be primor- dial black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of the universe.
Such black holes would have a much higher temperature and would be emitting radiation at a much greater rate. A primordial black hole with an initial mass of a thousand mil- lion tons would have a lifetime roughly equal to the age of the universe. Primordial black holes with initial masses less than this figure would already have completely evaporated. However, those with slightly greater masses would still be emitting radiation in the form of X rays and gamma rays.
These are like waves of light, but with a much shorter wavelength. Such holes hardly deserve the epithet black.
They really are white hot, and are emitting energy at the rate of about ten thousand megawatts. One such black hole could run ten large power stations, if only we could har- ness its output. This would be rather difficult, however. If you had one of these black holes on the surface of the Earth, there would be no way to stop it falling through the floor to the center of the Earth.
It would oscillate through the Earth and back, until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the energy that it emitted, would be in orbit around the Earth. And the only way that one could get it to orbit the Earth would be to attract it there by towing a large mass in front of it, rather like a carrot in front of a donkey.
This does not sound like a very practical proposition, at least not in the immediate future. We could look for the gamma rays that the primordial black holes emit during most of their lifetime. Although the radiation from most would be very weak because they are far away, the total from all of them might be detectable. We do, indeed, observe such a background of gamma rays.
However, this background was probably generated by processes other than primordial black holes. But they tell us that, on average, there cannot be more than three hundred little black holes in every cubic light-year in the universe.
This limit means that primordial black holes could make up at most one mil- lionth of the average mass density in the universe. With primordial black holes being so scarce, it might seem unlikely that there would be one that was near enough for us to observe on its own.
But since gravity would draw primordial black holes toward any matter, they should be much more common in galaxies. If they were, say, a million times more com- mon in galaxies, then the nearest black hole to us would probably be at a distance of about a thousand million kilometers, or about as far as Pluto, the farthest known planet. At this distance it would still be very difficult to detect the steady emission of a black hole even if it was ten thousand megawatts.
In order to observe a primordial black hole, one would have to detect several gamma ray quanta coming from the same direction within a reasonable space of time, such as a week. Otherwise, they might simply be part of the background. So to radiate even ten thou- sand megawatts would not take many quanta. Moreover, the detector would have to be in space, because gamma rays cannot penetrate the atmosphere.
Of course, if a black hole as close as Pluto were to reach the end of its life and blow up, it would be easy to detect the final burst of emission. But if the black hole has been emitting for the last ten or twenty thousand million years, the chances of it reaching the end of its life within the next few years are really rather small.
It might equally well be a few million years in the past or future. So in order to have a reasonable chance of seeing an explosion before your research grant ran out, you would have to find a way to detect any explosions within a distance of about one light-year.
You would still have the problem of needing a large gamma ray detector to observe several gamma ray quanta from the explosion. However, in this case, it would not be necessary to determine that all the quanta came from the same direction. It would be enough to observe that they all arrived within a very short time interval to be reasonably confident that they were coming from the same burst.
We are, in any case, unlikely to be able to build a larger detector. When a high-energy gamma ray quantum hits the atoms in our atmosphere, it creates pairs of electrons and positrons.
So one gets what is called an electron shower. The result is a form of light called Cerenkov radiation. One can therefore detect gamma ray bursts by looking for flashes of light in the night sky. Of course, there are a number of other phenomena, such as lightning, which can also give flashes in the sky. However, one could distinguish gamma ray bursts from such effects by observing flashes simultaneously at two or more thoroughly widely separated locations.
A search like this has been carried out by two scientists from Dublin, Neil Porter and Trevor Weekes, using telescopes in Arizona. They found a number of flashes but none that could be definitely ascribed to gamma ray bursts from primordial black holes.
Even if the search for primordial black holes proves negative, as it seems it may, it will still give us important information about the very early stages of the universe. If the early universe had been chaotic or irregular, or if the pres- sure of matter had been low, one would have expected it to produce many more primordial black holes than the limit set by our observations of the gamma ray background.
It is only if the early universe was very smooth and uniform, and with a high pressure, that one can explain the absence of observable numbers of primordial black holes. At the end of my talk the chair- man of the session, John G. Taylor from Kings College, London, claimed it was all nonsense. He even wrote a paper to that effect. However, in the end most people, including John Taylor, have come to the conclusion that black holes must radiate like hot bodies if our other ideas about general relativity and quantum mechanics are correct.
Thus even though we have not yet managed to find a primordial black hole, there is fairly general agreement that if we did, it would have to be emitting a lot of gamma and X rays.
If we do find one, I will get the Nobel Prize. The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as we once thought. If an astronaut falls into a black hole, its mass will increase. Thus, in a sense, the astronaut will be recycled. It would be a poor sort of immortal- ity, however, because any personal concept of time for the astronaut would almost certainly come to an end as he was crushed out of existence inside the black hole.
Even the types of particle that were eventually emitted by the black hole would in general be different from those that made up the astro- naut. The only feature of the astronaut that would survive would be his mass or energy. The approximations I used to derive the emission from black holes should work well when the black hole has a mass greater than a fraction of a gram.
However, they will break down at the end of the black hole's life, when its mass gets very small. The most likely outcome seems to be that the black hole would just disappear, at least from our region of the universe.
It would take with it the astronaut and any singularity there might be inside the black hole. This was the first indication that quantum mechanics might remove the sin- gularities that were predicted by classical general relativity.
However, the methods that I and other people were using in to study the quantum effects of gravity were not able to answer questions such as whether singulari- ties would occur in quantum gravity. The answers that this approach suggests for the origin and fate of the universe will be described in the next two lectures. We shall see that quantum mechanics allows the universe to have a beginning that is not a singularity. This means that the laws of physics need not break down at the origin of the universe.
The state of the universe and its contents, like ourselves, are completely deter- mined by the laws of physics, up to the limit set by the uncertainty principle. So much for free will. However, in my interest in questions about the origin of the universe was reawakened when I attended a conference on cosmology in the Vatican. The Catholic church had made a bad mistake with Galileo when it tried to lay down the law on a question of science, declaring that the sun went around the Earth.
Now, centuries later, it had decided it would be better to invite a num- ber of experts to advise it on cosmology. At the end of the conference the participants were granted an audience with the pope. He told us that it was okay to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of creation and therefore the work of God.
I was glad then that he did not know the subject of the talk I had just given at the conference. I had no desire to share the fate of Galileo; I have a lot of sym- pathy with Galileo, partly because I was born exactly three hundred years after his death. In such models one finds that as the uni- verse expands, the temperature of the matter and radiation in it will go down.
Since temperature is simply a measure of the average energy of the particles, this cooling of the universe will have a major effect on the matter in it. At very high temperatures, particles will be moving around so fast that they can escape any attraction toward each other caused by the nuclear or electromagnetic forces.
But as they cooled off, one would expect particles that attract each other to start to clump together. At the big bang itself, the universe had zero size and so must have been infi- nitely hot. But as the universe expanded, the temperature of the radiation would have decreased. One second after the big bang it would have fallen to about ten thousand million degrees.
This is about a thousand times the tem- perature at the center of the sun, but temperatures as high as this are reached in H-bomb explosions.
At this time the universe would have contained mostly photons, electrons, and neutrinos and their antiparticles, together with some protons and neutrons. As the universe continued to expand and the temperature to drop, the rate at which electrons and the electron pairs were being produced in collisions would have fallen below the rate at which they were being destroyed by annihilation.
About one hundred seconds after the big bang, the temperature would have fallen to one thousand million degrees, the temperature inside the hottest stars. At this temperature, protons and neutrons would no longer have suffi- cient energy to escape the attraction of the strong nuclear force. They would start to combine together to produce the nuclei of atoms of deuterium, or heavy hydrogen, which contain one proton and one neutron.
The deuterium nuclei would then have combined with more protons and neutrons to make helium nuclei, which contained two protons and two neutrons. There would also be small amounts of a couple of heavier elements, lithium and beryllium.
One can calculate that in the hot big bang model about a quarter of the pro- tons and neutrons would have been converted into helium nuclei, along with a small amount of heavy hydrogen and other elements. The remaining neu- trons would have decayed into protons, which are the nuclei of ordinary hydrogen atoms. These predictions agree very well with what is observed.
The hot big bang model also predicts that we should be able to observe the radiation left over from the hot early stages. This is the explanation of the microwave background of radiation that was discovered by Penzias and Wilson in We are therefore thoroughly confident that we have the right picture, at least back to about one second after the big bang. Within only a few hours of the big bang, the production of helium and other elements would have stopped.
And after that, for the next million years or so, the universe would have just continued expanding, without anything much happening. Eventually, once the tempera- ture had dropped to a few thousand degrees, the electrons and nuclei would no longer have had enough energy to overcome the electromagnetic attraction between them. They would then have started combining to form atoms.
The universe as a whole would have continued expanding and cooling. However, in regions that were slightly denser than average, the expansion would have been slowed down by extra gravitational attraction. This would eventually stop expansion in some regions and cause them to start to recol- lapse. As they were collapsing, the gravitational pull of matter outside these regions might start them rotating slightly.
As the collapsing region got smaller, it would spin faster—just as skaters spinning on ice spin faster as the draw in their arms. Eventually, when the region got small enough, it would be spinning fast enough to balance the attraction of gravity. In this way, disklike rotating galaxies were born. As these contracted, the temper- ature of the gas would increase until it became hot enough to start nuclear reactions.
These would convert the hydrogen into more helium, and the heat given off would raise the pressure, and so stop the clouds from contracting any further.
They would remain in this state for a long time as stars like our sun, burning hydrogen into helium and radiating the energy as heat and light. More massive stars would need to be hotter to balance their stronger gravita- tional attraction.
This would make the nuclear fusion reactions proceed so much more rapidly that they would use up their hydrogen in as little as a hun- dred million years.
They would then contract slightly and, as they heated up further, would start to convert helium into heavier elements like carbon or oxygen. This, however, would not release much more energy, so a crisis would occur, as I described in my lecture on black holes. What happens next is not completely clear, but it seems likely that the central regions of the star would collapse to a very dense state, such as a neutron star or black hole.
The outer regions of the star may get blown off in a tremendous explosion called a supernova, which would outshine all the other stars in the galaxy. They would provide some of the raw material for the next generation of stars.
Our own sun contains about 2 percent of these heavier elements because it is a second— or third—generation star. It was formed some five thousand million years ago out of a cloud of rotating gas containing the debris of earlier super- novas.
Most of the gas in that cloud went to form the sun or got blown away. However, a small amount of the heavier elements collected together to form the bodies that now orbit the sun as planets like the Earth. Nevertheless, it leaves a number of important questions unanswered.
First, why was the early universe so hot? Second, why is the universe so uniform on a large scale—why does it look the same at all points of space and in all directions?
Third, why did the universe start out with so nearly the critical rate of expan- sion to just avoid recollapse? On the other hand, if the expansion rate at one second had been larger by the same amount, the universe would have expanded so much that it would be effectively empty now. Fourth, despite the fact that the universe is so uniform and homogenous on a large scale, it contains local lumps such as stars and galaxies. These are thought to have developed from small differences in the density of the early universe from one region to another.
What was the origin of these density fluctuations? The general theory of relativity, on its own, cannot explain these features or answer these questions. This is because it predicts that the universe started off with infinite density at the big bang singularity. At the singularity, general rel- ativity and all other physical laws would break down.
One cannot predict what would come out of the singularity. As I explained before, this means that one might as well cut any events before the big bang out of the theory, because they can have no effect on what we observe. Space—time would have a boundary— a beginning at the big bang.
Why should the universe have started off at the big bang in just such a way as to lead to the state we observe today? Why is the universe so uniform, and expanding at just the critical rate to avoid recollapse? One would feel happier about this if one could show that quite a number of different initial configurations for the universe would have evolved to produce a universe like the one we observe. There might also be regions that were very different. However, these regions would probably not be suitable for the formation of galaxies and stars.
These are essential prerequisites for the development of intelligent life, at least as we know it. Thus, these regions would not contain any beings to observe that they were different. When one considers cosmology, one has to take into account the selection principle that we live in a region of the universe that is suitable for intelligent life. This fairly obvious and elementary consideration is sometimes called the anthropic principle. Suppose, on the other hand, that the initial state of the universe had to be chosen extremely carefully to lead to something like what we see around us.
Then the universe would be unlikely to contain any region in which life would appear. In the hot big bang model that I described earlier, there was not enough time in the early universe for heat to have flowed from one region to another.
This means that different regions of the universe would have had to have started out with exactly the same temperature in order to account for the fact that the microwave background has the same temperature in every direction we look. This means that the ini- tial state of the universe must have been very carefully chosen indeed if the hot big bang model was correct right back to the beginning of time. It would be very difficult to explain why the universe should have begun in just this way, except as the act of a God who intended to create beings like us.
In this, many different initial configurations could have evolved to something like the present universe. He suggested that the early universe might have had a period of very rapid, or exponential, expansion. This expansion is said to be inflationary—an analogy with the inflation in prices that occurs to a greater or lesser degree in every country.
The world record for price inflation was probably in Germany after the first war, when the price of a loaf of bread went from under a mark to millions of marks in a few months. But the inflation we think may have occurred in the size of the universe was much greater even than that—a million million million million million times in only a tiny frac- tion of a second.
Of course, that was before the present government. One would expect that at such high temperatures, the strong and weak nuclear forces and the electromagnetic force would all be unified into a single force. As the universe expanded, it would cool, and particle energies would go down.
Eventually there would be what is called a phase transition, and the symmetry between the forces would be broken. The strong force would become different from the weak and electromagnetic forces. One common example of a phase transition is the freezing of water when you cool it down. Liquid water is sym- metrical, the same at every point and in every direction.
However, when ice crystals form, they will have definite positions and will be lined up in some direction. This breaks the symmetry of the water.
That is, one can reduce the temperature below the freezing point—0 degrees centigrade—with- out ice forming. Guth suggested that the universe might behave in a similar way: The temperature might drop below the critical value without the symme- try between the forces being broken.
If this happened, the universe would be in an unstable state, with more energy than if the symmetry had been broken. This special extra energy can be shown to have an antigravitational effect.
It would act just like a cosmological constant. However,in this case, the universe would already be expanding. The repulsive effect of this cosmo- logical constant would therefore have made the universe expand at an ever- increasing rate.
Even in regions where there were more matter particles than average, the gravitational attraction of the matter would have been out- weighed by the repulsion of the effective cosmological constant. Thus, these regions would also expand in an accelerating inflationary manner. As the universe expanded, the matter particles got farther apart. One would be left with an expanding universe that contained hardly any particles.
It would still be in the supercooled state, in which the symmetry between the forces is not broken. Any irregularities in the universe would simply have been smoothed out by the expansion, as the wrinkles in a balloon are smoothed away when you blow it up. Thus, the present smooth and uniform state of the universe could have evolved from many different nonuniform initial states.
The rate of expansion would also tend toward just the critical rate needed to avoid recollapse. Moreover, the idea of inflation could also explain why there is so much matter in the universe. There are something like 1, particles in the region of the universe that we can observe. Where did they all come from? But that just raises the question of where the energy came from. The answer is that the total energy of the universe is exactly zero.
The matter in the universe is made out of positive energy. However, the mat- ter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart. This is because you have to expend energy to separate them. You have to pull against the gravitational force attracting them together. Thus, in a sense, the gravita- tional field has negative energy. In the case of the whole universe, one can show that this negative gravitational energy exactly cancels the positive ener- gy of the matter.
So the total energy of the universe is zero. Now, twice zero is also zero. Thus, the universe can double the amount of pos- itive matter energy and also double the negative gravitational energy without violation of the conservation of energy. This does not happen in the normal expansion of the universe in which the matter energy density goes down as the universe gets bigger. It does happen, however, in the inflationary expansion, because the energy density of the supercooled state remains constant while the universe expands.
When the universe doubles in size, the positive matter ener- gy and the negative gravitational energy both double, so the total energy remains zero. Thus, the total amount of energy available to make parti- cles becomes very large. But the universe is the ultimate free lunch. Thus, there had to be some mechanism that would eliminate the very large effective cosmolog- ical constant. This would change the rate of expansion from an accelerated one to one that is slowed down by gravity, as we have today.
As the universe expanded and cooled, one might expect that eventually the symmetry between the forces would be broken, just as supercooled water always freezes in the end. The extra energy of the unbroken symmetry state would then be released and would reheat the universe. The universe would then go on to expand and cool, just like the hot big bang model. However, there would now be an explanation of why the universe was expanding at exactly the critical rate and why differ- ent regions had the same temperature.
The trouble was, as I and several other people pointed out, the universe was expanding so fast that the bubbles would be moving away from each other too rapidly to join up. The universe would be left in a very nonuniform state, with some regions having symmetry between the different forces.
Such a model of the universe would not correspond to what we see. In October I went to Moscow for a conference on quantum gravity. After the conference, I gave a seminar on the inflationary model and its problems at the Sternberg Astronomical Institute.
In the audience was a young Russian, Andrei Linde. He said that the difficulty with the bubbles not joining up could be avoided if the bubbles were very big. In this case, our region of the universe could be contained inside a single bubble. In order for this to work, the change from symmetry to broken symmetry must have taken place very slowly inside the bubble, but this is quite possible according to grand unified theories.
I showed that instead the symmetry would have broken everywhere at the same time, rather than just inside bubbles. This would lead to a uniform universe, like we observe.
However, I and several other people showed that it predicted much greater variations in the microwave background radiation than are observed. Also, later work cast doubt on whether there would have been the right kind of phase transition in the early universe. A better model, called the chaotic inflationary model, was introduced by Linde in The infla- tionary model showed that the present state of the universe could have arisen from quite a large number of different initial configurations.
It cannot be the case, however, that every initial configuration would have led to a universe like the one we observe. So even the inflationary model does not tell us why the initial configuration was such as to produce what we observe. Must we turn to the anthropic principle for an explanation? Was it all just a lucky chance? That would seem a counsel of despair, a negation of all our hopes of under- standing the underlying order of the universe.
If the classical theory of general relativity was correct, the singularity theorem showed that the beginning of time would have been a point of infinite density and curvature. One might suppose that there were new laws that held at singularities, but it would be very difficult even to formulate laws at such badly behaved points and we would have no guide from observations as to what those laws might be.
However, what the singularity theorems really indicate is that the gravitational field becomes so strong that quantum gravita- tional effects become important: Classical theory is no longer a good descrip- tion of the universe.
So one has to use a quantum theory of gravity to discuss the very early stages of the universe. As we shall see, it is possible in the quan- tum theory for the ordinary laws of science to hold everywhere, including at the beginning of time.
It is not necessary to postulate new laws for singularities, because there need not be any singularities in the quantum theory. However, we are thoroughly certain of some features that such a unified theory should have. In this approach, a particle going from A to B does not have just a single history as it would in a classical theory. Instead, it is supposed to follow every possible path in space—time. With each of these histories, there are associated a couple of numbers, one representing the size of a wave and the other repre- senting its position in the cycle—its phase.
When one actually tries to perform these sums, however, one runs into severe technical problems. The only way around these is the following peculiar prescription: One must add up the waves for particle histories that are not in the real time that you and I experience but take place in imaginary time. Imaginary time may sound like science fiction, but it is in fact a well—defined mathematical concept.
This has an interesting effect on space—time: The distinction between time and space disappears completely. A space—time in which events have imaginary values of the time coordinate is said to be Euclidean because the metric is positive definite. In Euclidean space-time there is no difference between the time direction and directions in space. On the other hand, in real space-time, in which events are labeled by real values of the time coordinate, it is easy to tell the difference.
The time direction lies within the light cone, and space directions lie outside. One can regard the use of imaginary time as merely a mathematical device—or trick—to calculate answers about real space-time. However, there may be more to it than that. It may be that Euclidean space-time is the fundamental concept and what we think of as real space-time is just a figment of our imagination.
For the technical reasons mentioned above, these curved space—times must be taken to be Euclidean. That is, time is imaginary and is indistinguishable from directions in space.
To calculate the probability of finding a real space-time with some certain property, one adds up the waves associated with all the histories in imaginary time that have that property.
One can then work out what the probable history of the universe would be in real time. Either it has existed for an infi- nite time, or else it had a beginning at a singularity at some finite time in the past. In fact, the singularity theorems show it must be the second possibility.
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