The Universe in a Nutshell ALSO A BLACK HOLES BY STEPHEN BRIEF AND HISTORY BABY HAWKING OF T I M E U N I V E R S E S AND O T H E R ESSAYS. Stephen Hawking's A Brief History of Time was a publishing phenomenon. Now, in The Universe in a Nutshell, Stephen Hawking brings us fully up-to-date with the advances in scientific thinking. Beautifully illustrated throughout, with original artwork commissioned for this project. Brinson Lecture. History of the Universe in a Nutshell: From the Big Bang to Life and the End of Time. John Mather. Nobel Laureate and NASA.
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Reading 'The Universe in a Nutshell' the other day, I came to a few realisations about the nature of gravity. I was already aware of the basic ideas, but I hadn't. In this new book Hawking takes us to the cutting edge of theoretical physics, where truth is often stranger than fiction, to explain in laymen's terms the principles. Stephen Hawking's phenomenal, multimillion-copy bestseller, A Brief History of Time, introduced the ideas of this brilliant theoretical physicist.
For time is not anything yet switch. The Quantum Story: A history in 40 moments The 20 th century was once outlined by means of physics. From the minds of the world's top physicists there flowed a river of rules that might delivery mankind to the top of wonderment and to the very depths of human melancholy. This was once a century that started with the certainties of absolute wisdom and ended with the data of absolute uncertainty. I beat all of them, yet regrettably there has been a crimson alert, so I by no means amassed my winnings.
The final will not be tough. That means that quite a lot of things which should be explained are skimped. When he writes, for example, that "we have come to recognise that this standing still of real and imaginary time means that spacetime has a temperature", you expect an account of how "we" came to this realisation. But none appears. There is a deeper problem, though.
The developments in theory that have taken place since the earlier book have just made things less comprehensible - whether explained by Hawking or anyone else.
Strings, for example, are no longer strings but a subset of a much larger range of "branes", which can extend in any number of dimensions - 10 or 11 are the hot bets. But when a caption alongside an abstract depiction of some wavy-looking, textured sheets in shades of brown simply says that "Black holes can be thought of as the intersections of p-branes in the extra dimensions of spacetime", neither words nor images yield any real download on the theory.
The fact is that p-branes make a lay reader feel like a pea-brain because they can only properly be thought of in mathematical terms. Words don't make it. These objects if objects they are have no correlates in our familiar world that we can sensibly say they are like, and diagrams tend to be bad at representing 10 dimensions.
Hawking offers a reason not to care. He is, he says several times, a positivist, so is concerned only with whether mathematical models with extra dimensions provide a good description of the universe, not with whether they have any real meaning.
This is little comfort if the reader does not share this curiously old-fashioned philosophy of science. But even writers who have tried to convey the nature of these theories at much greater length have not been much help.
I would mention in particular Thomas Hertog and Neel Shearer, for assistance with the figures, captions, and boxes, Ann Harris and Kitty Ferguson, who edited the manuscript or, more accurately, the computer files, because everything I write is electronic , Philip Dunn of the Book Laboratory and Moonrunner Design, who created the illustrations.
But beyond that, I want to thank all those who have made it possible for me to lead a fairly normal life and carry on scientific research.
Without them this book could not have been written. Stephen Hawking Cambridge, May 2, 2 0 0 1. Albert was no child prodigy, but claims that he did poorly at school seem to be an exaggeration. In 1 8 9 4 his father's business failed and the family moved to Milan. His parents decided he should stay behind to finish school, but he did not like its authoritarianism, and within months he left to join his family in Italy.
He later completed his education in Zurich, graduating from the prestigious Federal Polytechnical School, known as the ETH, in 1 9 0 0. His argumentative nature and dislike of authority did not endear him to the professors at the ETH and none of them offered him the position of assistant, which was the normal route to an academic career. Two years later, he finally managed to get a junior post at the Swiss patent office in Bern.
It was while he held this job that in 1 9 0 5 he wrote three papers that both established him as one of the world's leading scientists and started two conceptual revolutions—revolutions that changed our understanding of time, space, and reality itself. Toward the end of the nineteenth century, scientists believed they were close to a complete description of the universe. They imagined that space was filled by a continuous medium called the "ether. All that was needed for a complete theory were careful measurements of the elastic properties of the ether.
In fact, anticipating such measurements, the Jefferson Lab at Harvard University was built entirely without iron nails so as not to interfere with delicate magnetic measurements. However, the planners forgot that the reddish brown bricks of which the lab and most of Harvard are built contain large amounts of iron.
The building is still in use today, although Harvard is still not sure how much weight a library floor without iron nails will support.
It was expected that light would travel at a If light were a wave in an elastic mate- fixed speed through the ether but that if you were traveling through rial called ether, the speed of light the ether in the same direction as the light, its speed would appear should appear higher to someone on a spaceship a moving toward it, and lower on a spaceship b traveling in the same direction as the light.
Yet a series of experiments failed to support this idea. The most careful and accurate of these experiments was carried out by FIG. They compared the speed of light in the direction of the speed of light in two beams at right angles to each other. As the Earth's orbit and in a direction at right angles to it. Earth rotates on its axis and orbits the Sun, the apparatus moves through the ether with varying speed and direction Fig. But Michelson and Morley found no daily or yearly differences between the two beams of light.
It was as if light always traveled at the same speed relative to where one was, no matter how fast and in which direction one was moving Fig. Based on the Michelson-Morley experiment, the Irish physicist George FitzGerald and the Dutch physicist Hendrik Lorentz suggested that bodies moving through the ether would contract and that clocks would slow down.
This contraction and the slowing down of clocks would be such that people would all measure the same speed for light, no matter how they were moving with respect to the ether. FitzGerald and Lorentz still regarded ether as a real substance. Flying from west to east pointed out that if one could not detect whether or not one was FIG.
O n e version Instead, he started from the postulate that the laws of science should appear the same to all freely moving observers. In particular, they should all measure the same speed for light, no matter how fast they were moving. The speed of light is independent of their motion and is the same in all directions. This required abandoning the idea that there is a universal Fig. W h e n they met up again the clock that flew toward the east had recorded slightly less time.
Instead, everyone would have his or her own personal time. The times of two people would agree if the people were at rest with respect to each other, but not if they were moving. This has been confirmed by a number of experiments, including one in which two accurate clocks were flown in opposite directions around the world and returned showing very slightly different times Fig. This might suggest that if one wanted to live longer, one should keep flying to the east so that the plane's speed is added to the earth's rotation.
However, the tiny fraction of a second one would gain would be more than canceled by eating airline meals.
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Its beauty and simplicity convinced many thinkers, but there remained a lot of opposition. Einstein had overthrown two of the absolutes of nineteenth-century science: Many people found this an unsettling concept. Did it imply, they asked, that everything was relative, that there were no absolute moral standards? This unease continued throughout the 1 9 2 0 s and 1 9 3 0 s. When Einstein was awarded the Nobel Prize in 1 9 2 1 , the citation was for important but by his standard comparatively minor work also carried out in 1 9 0 5.
It made no mention of relativity, which was considered too controversial. I still get two or three letters a week telling me Einstein was wrong. Nevertheless, the theory of relativity is now completely accepted by the scientific community, and its predictions have been verified in countless applications.
Einstein's postulate that the speed of light should appear the same to everyone implied that nothing could be moving faster than light.
What happens is that as one uses energy to accelerate anything, whether a particle or a spaceship, its mass increases, making it harder to accelerate it further. To accelerate a particle to the speed of light would be impossible because it would take an infinite amount of energy. This is probably the only equation in physics to have recognition on the street. Among its consequences was the realization that if the nucleus of a uranium atom fissions into two nuclei with slightly less total mass, this will release a tremendous amount of energy see pages , Fig.
This led to the Manhattan Project and ultimately to the bombs that exploded over Hiroshima and Nagasaki in 1 9 4 5. Some people have blamed the atom bomb on Einstein because he discovered the relationship between mass and energy; but that is like blaming Newton for causing airplanes to crash because he discovered gravity.
Einstein himself took no part in the Manhattan Project and was horrified by the dropping of the bomb. After his groundbreaking papers in 1 9 0 5 , Einstein's scientific reputation was established. But it was not until 1 9 0 9 that he was offered a position at the University of Zurich that enabled him to leave the Swiss patent office.
Despite the anti-Semitism that was common in much of Europe, even in the universities, he was now an academic hot property.
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He moved to Berlin in April and was joined shortly after by his wife and two sons. The marriage had been in a bad way for some time, however, and his family soon returned to Zurich. Although he visited them occasionally, he and his wife were eventually divorced. Einstein later married his cousin Elsa, who lived in Berlin.
The fact that he spent the war years as a bachelor, without domestic commitments, may be one reason why this period was so productive for him scientifically. Although the theory of relativity fit well with the laws that governed electricity and magnetism, it was not compatible with Newton's law of gravity.
This law said that if one changed the distribution of matter in one region of space, the change in the gravitational field would be felt instantaneously everywhere else in the universe. Not only would this mean one could send signals faster than light something that was forbidden by relativity ; in order to know what instantaneous meant, it also required the existence of absolute or universal time, which relativity had abolished in favor of personal time.
This causes it to fission in turn, and a chain reaction of further collisions begins. If the reaction sustains itself it is called "critical" and the mass of U is said to be a "critical mass.
The Universe in a Nutshell by Stephen Hawking PDF Book Download
He realized that there is a close relationship between acceleration and a gravitational field. Someone inside a closed box, such as an elevator, could not tell whether the box was at rest in the Earth's gravitational field or was being accelerated by a rocket in free space.
Of course, this was before the age of Star Trek, and so Einstein thought of people in elevators rather than spaceships. But one cannot accelerate or fall freely very far in an elevator before disaster strikes Fig. This equivalence between acceleration and gravity didn't seem to work for a round Earth, however—people on the opposite sides of the world would have to be accelerating in opposite directions but staying at a constant distance from each other Fig. But on his return to Zurich in Einstein had the brain wave of realizing that the equivalence would work if the geometry of Newton's head because of gravity or that the Earth and Newton were accelerating upward.
T h i s equivalence didn't work for a spherical Earth FIG. I I because people on opposite sides of the world would be getting farther away from each other Einstein overcame this difficulty by making space and time curved. Objects such as apples or planets alent only if a massive body curves would try to move in straight lines through spacetime, but their spacetime, thereby bending the paths of objects in its neighborhood.
With the help of his friend Marcel Grossmann, Einstein studied the theory of curved spaces and surfaces that had been developed earlier by Georg Friedrich Riemann. However, Riemann thought only of space being curved.
It took Einstein to realize that it is spacetime which is curved. However, because of a mistake by Einstein who was quite human and fallible , they weren't able to find the equations that related the curvature of spacetime to the mass and energy in it. Einstein continued to work on the problem in Berlin, undisturbed by domestic matters and largely unaffected by the war, until he finally found the right equations in November He had discussed his ideas with the mathematician David Hilbert during a visit to the University of Gottingen in the summer of , and Hilbert independently found the same equations a few days before Einstein.
Nevertheless, as Hilbert himself admitted, the credit for the new theory belonged to Einstein. It was his idea to relate gravity to the warping of spacetime. It is a tribute to the civilized state of Germany at this period that such scientific discussions and exchanges could go on undisturbed even in wartime.
It was a sharp contrast to the Nazi era twenty years later. The new theory of curved spacetime was called general relativity to distinguish it from the original theory without gravity, which was now known as special relativity. This produces a slight shift in the apparent position of the star as seen from the Earth b.
This can be observed during an eclipse. Einstein found that his e q u a tions didn't have a solution that described a static universe, u n c h a n g i n g in t i m e. T h e universe is e x p a n d ing, with t h e distance b e t w e e n any two galaxies steadily increasing with time Fig. A static universe could have existed forever or could have been created in its present form at some time in the past. However, if galaxies are moving apart now, it means that they must have been closer together in the past.
About fifteen billion years ago, they would all have been on top of each other and the density would have been very large.
This state was called the "primeval atom" by the Catholic priest Georges Lemaitre, who was the first to investigate the origin of the universe that we now call the big bang.
Einstein seems never to have taken the big bang seriously. He apparently thought that the simple model of a uniformly expanding universe would break down if one followed the motions of the galaxies back in time, and that the small sideways velocities of the galaxies would cause them to miss each other.
He thought the universe might have had a previous contracting phase, with a bounce into the present expansion at a fairly moderate density. Further, observations of the microwave background indicate that the density was probably once a trillion trillion trillion trillion trillion trillion 1 with 72 zeros after it tons per cubic inch.
We also now know that Einstein's general theory of relativity does not allow the universe to bounce from a contracting phase to the present expansion. As will be discussed in Chapter 2, Roger Penrose and I were able to show that general relativity predicts that the universe began in the big bang.
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So Einstein's theory does imply that time has a beginning, although he was never happy with the idea. Einstein was even more reluctant to admit that general relativity predicted that time would come to an end for massive stars when they reached the end of their life and no longer generated enough heat to balance the force of their own gravity, which was trying to make them smaller.
Einstein thought that such stars would settle down to some 23 T H E U a massive star exhausts its nuclear fuel, it will lose heat and contract. The warping of spacetime will b e c o m e so great that a black hole will be created from which light cannot escape. Inside the black hole time will c o m e to an end. Such stars will continue to shrink until they become black holes, regions of spacetime that are so warped that light cannot escape from them Fig.
Penrose and I showed that general relativity predicted that time would come to an end inside a black hole, both for the star and for any unfortunate astronaut who happened to fall into it. But both the beginning and the end of time would be places where the equations of general relativity could not be defined. Thus the theory could not predict what should emerge from the big bang. Some saw this as an indication of Cod's freedom to start the universe off in any way God wanted, but others including myself felt that the beginning of the universe should be governed by the same laws that held at other times.
We have made some progress toward this goal, as will be described in Chapter 3, but we don't yet have a complete understanding of the origin of the universe. The reason general relativity broke down at the big bang was that it was not compatible with quantum theory, the other great conceptual revolution of the early twentieth century.
The first step toward quantum theory had come in , when Max Planck in Berlin discovered that the radiation from a body that was glowing red-hot was explainable if light could be emitted or absorbed only if it came in discrete packets, called quanta. In one of his groundbreaking papers, written in when he was at the patent office, Einstein showed that Planck's quantum hypothesis could explain what is called the photoelectric effect, the way certain metals give off electrons when light falls on them.
This is the basis of modern light detectors and television cameras, and it was for this work that Einstein was awarded the Nobel Prize for physics. Einstein continued to work on the quantum idea into the s, but he was deeply disturbed by the work of Werner Heisenberg in Copenhagen, Paul Dirac in Cambridge, and Erwin Schrodinger in Zurich, who developed a new picture of reality called quantum mechanics.
Instead, the more accurately one determined a particle's position, the less accurately one could determine its speed, and vice versa. Einstein was horrified by this random, unpredictable element in the basic laws and never fully accepted quantum mechanics. His feelings were expressed in his famous dictum "God does not play dice. They are the basis of modern developments in chemistry, molecular biology, and electronics, and the foundation for the technology that has transformed the world in the last fifty years.
In December 1 9 3 2 , aware that the Nazis and Hitler were about to come to power, Einstein left Germany and four months later renounced his citizenship, spending the last twenty years of his life at the Institute for Advanced Study in Princeton, New Jersey. In Germany, the Nazis launched a campaign against "Jewish science" and the many German scientists who were Jews; this is part of the reason that Germany was not able to build an atomic bomb.
Albert Einstein with a puppet of Einstein and relativity were principal targets of this campaign.
Einstein, he replied: If I were wrong, one would have been enough. In 1 9 4 8 , he was offered the presidency of the new state of Israel but turned it down. He once said: They should last as long as the universe.
The world has changed far more in the last hundred years than in any previous century. The reason has not been new political or economic doctrines but the vast developments in technology made possible by advances in basic science.
W h o better symbolizes those advances than Albert Einstein? How this can be reconciled with quantum theory. Or is it a railroad track? Maybe it has loops and branches, so you can keep going forward and yet return to an earlier station on the line Fig.
The nineteenth-century author Charles Lamb wrote: And yet nothing troubles me less than time and space, because I never think of them. Any sound scientific theory, whether of time or of any other concept, should in my opinion be based on the most workable philosophy of science: According to this way of thinking, a scientific theory is a mathematical model that describes and codifies the observations we make.
A good theory will describe a large range of phenomena on the basis of a few simple postulates and will make definite predictions that can be tested. If the predictions agree with the observations, the theory survives that test, though it can never be proved to be correct. On the other hand, if the observations disagree with the predictions, one has to discard or modify the theory. At least, that is what is supposed to happen. In practice, people often question the accuracy of the observations and the reliability and moral character of those making the observations.
If one takes the positivist position, as I do, one cannot say what time actually is. All one can do is describe what has been found to be a very good mathematical model for time and say what predictions it makes. Isaac Newton gave us the first mathematical model for time and space in his Principia Mathematica, published in Newton occupied the Lucasian chair at Cambridge that I now hold, though it wasn't electrically operated in his time. In Newton's model, time and space were a background in which events took place but which weren't affected by them.
Time was separate from space and was considered to be a single line, or railroad track, that was infinite in both directions Fig. Time itself was considered eternal, in the sense that it had existed, and would exist, forever. By contrast, most people thought the physical universe had been created more or less in its present state only a few thousand years ago. This worried Isaac Newton published his mathematical model of time and space over 3 0 0 years ago. If the universe had indeed been created, why had there been an infinite wait before the creation?
On the other hand, if the universe had existed forever, why hadn't everything that was going to happen already happened, meaning that history was over? In particular, why hadn't the universe reached thermal equilibrium, with everything at the same temperature?
T h e large ball in the center represents But it was a contradiction only within the context of the Newtonian a massive body such as a star mathematical model, in which time was an infinite line, independent Its weight curves the sheet near it T h e ball bearings rolling on the sheet are deflected by this curvature and go of what was happening in the universe. However, as we saw in Chapter 1, in 1 9 1 5 a completely new mathematical model was put around the large ball, in the same way forward by Einstein: In the years that planets in the gravitational field of since Einstein's paper, we have added a few ribbons and bows, but a star can orbit it.
This and the following chapters will describe how our ideas have developed in the years since Einstein's revolutionary paper. It has been a success story of the work of a large number of people, and I'm proud to have made a small contribution. The theory incorporates the effect of gravity by saying that the distribution of matter and energy in the universe warps and distorts spacetime, so that it is not flat. Objects in this spacetime try to move in straight lines, but because spacetime is curved, their paths appear bent.
They move as if affected by a gravitational field.
As a rough analogy, not to be taken too literally, imagine a sheet of rubber. One can place a large ball on the sheet to represent the Sun. The weight of the ball will depress the sheet and cause it to be curved near the Sun. If one now rolls little ball bearings on the sheet, they won't roll straight across to the other side but instead will go around the heavy weight, like planets orbiting the Sun Fig. The analogy is incomplete because in it only a two-dimensional section of space the surface of the rubber sheet is curved, and time is left undisturbed, as it is in Newtonian theory.
However, in the theory of relativity, which agrees with a large number of experiments, time and space are inextricably tangled up. One cannot curve space without involving time as well. Thus time has a shape. By curving space and time, general relativity changes them from being a passive background against which events take place to being active, dynamic participants in what happens. In Newtonian theory, where time existed independently of anything else, one could ask: What did God do before He created the universe?
As Saint Augustine said, one should not joke about this, as did a man who said, "He was preparing Hell for those who pry too deep. According to Saint Augustine, before God made heaven and earth, He did not make anything at all. In fact, this is very close to modern ideas. In general relativity, on the other hand, time and space do not exist independently of the universe or of each other.
They are defined by measurements within the universe, such as the number of vibrations of a quartz crystal in a clock or the length of a ruler. It is quite conceivable that time defined in this way, within the universe, should have a minimum or maximum value—in other words, a beginning or an end.
It would make no sense to ask what happened before the beginning or after the end, because such times would not be defined. The general prejudice among theoretical physicists, including Einstein, held that time should be infinite in both directions.
Otherwise, there were awkward questions about the creation of the universe, which seemed to be out- Galaxies as they appeared recently Galaxies as they appeared 5 billion years ago side the realm of science.
Solutions of the Einstein equations were known in which time had a beginning or end, but these were all The background radiation very special, with a large amount of symmetry. It was thought that in a real body, collapsing under its own gravity pressure or sideways velocities would prevent all the matter falling together to the same point, where the density would be infinite.
Similarly, if one traced the expansion of the universe back in time, one would find that the matter of the universe didn't all emerge from a point of infinite density.
Such a point of infinite density was called a singularity and would be a beginning or an end of time. In 1 9 6 3 , two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, claimed to have proved that solutions of the Einstein equations with a singularity all had a special arrangement of matter and velocities. The chances that the solution representing the universe would have this special arrangement were practically zero.
Almost all solutions that could represent the universe would avoid having a singularity of infinite density: Before the era during which the universe has been expanding, there must have been a previous contracting phase during which matter fell together but missed colliding with itself, moving apart again in the present expanding phase. If this were the case, time would continue on forever, from the infinite past to the infinite future.
Not everyone was convinced by the arguments of Lifshitz and Khalatnikov. Instead, Roger Penrose and I adopted a different approach, based not on a detailed study of solutions but on the global structure of spacetime. In general relativity, spacetime is FIG. If we represent time by the it. Energy is always positive, so it gives spacetime a curvature that vertical direction and represent two bends the paths of light rays toward each other.
Now consider our past light cone Fig.
In a diagram with time plotted upward and FIG. Because the universe has been expanding and everything used to be much closer together, as we characteristic of that from a hot body. We observe a faint background of microwave radia- equilibrium, matter must have scat- tion that propagates to us along our past light cone from a much tered it many times. T h i s indicates that there must have been sufficient matter earlier time, when the universe was much denser and hotter than it in our past light cone to cause it to is now.
By tuning receivers to different frequencies of microwaves, bend in. This microwave radiation is not much good always warps spacetime so that light for defrosting frozen pizza, but the fact that the spectrum agrees so rays bend toward each other.
Thus we can conclude that our past light cone must pass through a certain amount of matter as one follows it back. This amount of matter is enough to curve spacetime, so the light rays in our past light cone are bent back toward each other Fig. Our past is pear-shaped Fig. As one follows our past light cone back still further, the positive energy density of matter causes the light rays to bend toward each other more strongly.
The cross section of the light cone will shrink to zero size in a finite time. This means that all the matter inside our past light cone is trapped in a region whose boundary shrinks to zero. It is therefore not very surprising that Penrose and I could prove that in the mathematical model of general relativity, time must have a beginning in what is called the big bang.
Similar arguments show that time would have an end, when stars or galaxies collapse under their own gravity to form black holes. We had sidestepped Kant's antimony of pure reason by dropping his implicit assumption that time had a meaning independent of the universe. I don't think the other prize essays that year have shown much enduring value. There were various reactions to our work.
It upset many physicists, but it delighted those religious leaders who believed in an act of creation, for here was scientific proof. Meanwhile, Lifshitz and Khalatnikov were in an awkward position. They couldn't argue with the mathematical theorems that we had proved, but under the Soviet system they couldn't admit they had been wrong and Western science had been right.
However, they saved the situation by finding a more general family of solutions with a singularity, which weren't special in the way their previous solutions had been. This enabled them to claim singularities, and the beginning or end of time, as a Soviet discovery. The whole universe we observe is contained within a region whose boundary shrinks to zero at the big bang. T h i s would be a singularity, a place where the density of matter would be infinite and classical general relativity would break down.
T h e longer the wavelength used to The shorter the wavelength used to observe a particle, the greater the observe a particle, the greater the uncertainty of its position.
They therefore pointed out that the mathematical model might not be expected to be a good description of spacetime near a singularity. The reason is that general relativity, which describes the gravitational force, is a classical theory, as noted in Chapter 1, and does not incorporate the uncertainty of quantum theory that governs all other forces we know. This inconsistency does not matter in most of the universe most of the time, because the scale on which spacetime is curved is very large and the scale on which quantum effects are important is very small.
But near a singularity, the two scales would be comparable, and quantum gravitational effects would be important.
So what the singularity theorems of Penrose and myself really established is that our classical region of spacetime is bounded to the past, and possibly to the future, by regions in which quantum gravity is important.
To understand the origin and fate of the universe, we need a quantum theory of gravity, and this will be the subject of most of this book. Quantum theories of systems such as atoms, with a finite number of particles, were formulated in the s, by Heisenberg, Schrodinger, and Dirac. Dirac was another previous holder of my chair in Cambridge, but it still wasn't motorized. However, people encountered difficulties when they tried to extend quantum ideas to the Maxwell field, which describes electricity, magnetism, and light.
One can think o f the Maxwell field as being made up o f waves of different wavelengths the distance between o ne wave crest and the next. In a wave, the field will swing fro m o ne value to ano ther 2. According to FIG.
That wo uld have bo th a definite to the wave's direction of motion. The position and a definite velo city, zero. Instead, even in its ground state a pendulum or any oscillating system must have a certain minimum amount of what are called zero point fluctuations. These mean that the pendulum won't necessarily be pointing straight down but will also have a probability of being found at a FIG. Instead quantum theory small angle to the vertical Fig. Similarly, even in the vacuum predicts that, even in its lowest energy or lowest energy state, the waves in the Maxwell field won't be state, the pendulum must have a min- exactly zero but can have small sizes.
The higher the frequency imum amount of fluctuations. T h i s means that the pendulum's posi- the number of swings per minute of the pendulum or wave, the tion will be given by a probability distri- higher the energy of the ground state.
In its ground state, the most Calculations of the ground state fluctuations in the Maxwell and electron fields made the apparent mass and charge of the elec- likely position is pointing straight down, but it has also a probability of being found at a small angle to the vertical. Nevertheless, the ground state fluctuations still caused small effects that could be measured and that agreed well with experiment.
Similar subtraction schemes for removing infinities worked for the Yang-Mills field in the theory put forward by Chen Ning Yang and Robert Mills. Yang-Mills theory is an extension of Maxwell theory that describes interactions in two other forces called the weak and strong nuclear forces.
However, ground state fluctuations have a much more serious effect in a quantum theory of gravity. Again, each wavelength would have a ground state energy. Since there is no limit to how short the wavelengths of the Maxwell field can be, there are an infinite number of different wavelengths in any region of spacetime and an infinite amount of ground state energy. Because energy density is, like matter, a source of gravity, this infinite energy density ought to mean there is enough gravitational attraction in the universe to curl spacetime into a single point, which obviously hasn't happened.
One might hope to solve the problem of this seeming contradiction between observation and theory by saying that the ground state fluctuations have no gravitational effect, but this would not work. One can detect the energy of ground state fluctuations by the Casimir effect. If you place a pair of metal plates parallel to each other and close together, the effect of the plates is to reduce slightly the number of wavelengths that fit between the plates relative to the number outside.
This means that the energy density of ground state fluctuations between the plates, although still infinite, is less than the energy density outside by a finite amount Fig. This difference in energy density gives rise to a force pulling the plates together, and this force has been observed experimentally.
Forces are a source of gravity in general relativity, just as matter is, so it would not be consistent to ignore the gravitational effect of this energy difference. Reduced number of wavelengths that can fit between the plates The energy density of ground state The energy density of ground fluctuations between the plates is state fluctuations is greater less than the density outside, caus- outside the plates.
If this constant had an infinite negative value, it could exactly cancel the infinite positive value of the ground state energies in free space, but this cosmological constant seems very ad hoc, and it would have to be tuned to extraordinary accuracy. Fortunately, a totally new kind of symmetry was discovered in the s that provides a natural physical mechanism to cancel the infinities arising from ground state fluctuations.
Supersymmetry is a feature of our modern mathematical models that can be described in various ways. One way is to say that spacetime has extra dimensions besides the dimensions we experience. These are called Grassmann dimensions, because they are measured in numbers known as Grassmann variables rather than in ordinary real numbers.
Ordinary numbers commute; that is, it does not matter in which order you multiply them: But Grassmann variables anticommute: Supersymmetry was first considered for removing infinities in matter fields and Yang-Mills fields in a spacetime where both the ordinary number dimensions and the Grassmann dimensions were flat, not curved.
But it was natural to extend it to ordinary numbers and Grassmann dimensions that were curved. This led to a number of theories called supergravity, with different amounts of supersymmetry. In doing so they briefly annihilate one another in a frantic burst of energy, creating a photon.
T h i s then releases its energy, producing another electron-positron pair. T h i s still appears as if they are just deflected into new trajectories. Then, when they collide and annihilate one another, they create a new string with a different vibrational pattern. Releasing energy, it divides into two strings continuing along new trajectories.
Because there are equal numbers point in space, but one-dimensional strings. These strings may have ends or they may join up with themselves in of bosons and fermions, the biggest infinities cancel in supergravity theories see Fig 2.
There remained the possibility that there might be smaller but closed loops. Just like the strings on a violin, the strings in string theory support certain vibrational patterns, or resonant still infinite quantities left over.
The Universe in a Nutshell - Chapter 1, A Brief History of Relativity Summary & Analysis
No one had the patience needed to calculate whether these theories were actually completely finite.For these classes, the p-brane model predicts exactly the same rate of emission that the virtual-particle pair model predicts. If one now rolls little ball bearings on the sheet, they won't roll straight across to the other side but instead will go around the heavy weight, like planets orbiting the Sun Fig. But I have come to realize that there is room for a different kind of book that might be easier to understand.
Worst luck, it takes time and energy. Einstein continued to work on the quantum idea into the s, but he was deeply disturbed by the work of Werner Heisenberg in Copenhagen, Paul Dirac in Cambridge, and Erwin Schrodinger in Zurich, who developed a new picture of reality called quantum mechanics. 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.
T h i s means that it has a gravitational effect on the expansion flicker their fuel.
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