Stephen Hawking - the world in a nutshell.

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Lively and intriguing. Hawking has a natural gift for teaching and explaining, and humorously illustrating extremely complex concepts with analogies from everyday life.

New York Times

This book weds childhood wonders to genius intellects. We travel through Hawking's universe, transported by the power of his mind.

Sunday Times

Lively and witty... Allows the general reader to draw deep scientific truths from the original source.

New Yorker

Stephen Hawking is a master of clarity... It is difficult to imagine that anyone else alive today has more clearly presented mathematical calculations that frighten the layman.

Chicago Tribune

Probably the best popular science book. A masterful summary of what modern physicists know about astrophysics. Thank you Dr. Hawking! thinking about the universe and how it came to be this way.

Wall Street journal

In 1988, Stephen Hawking's book Short story time,” which broke sales records, introduced readers around the world to the ideas of this remarkable theoretical physicist. And here's a new important event: Hawking is back! The superbly illustrated sequel, The World in a Nutshell, reveals the scientific discoveries that have been made since the publication of his first, widely acclaimed book.

One of the most brilliant scientists of our time, renowned not only for the boldness of his ideas but also for the clarity and wit of his expression, Hawking takes us to the cutting edge of research where truth seems stranger than fiction to explain in simple words principles that govern the universe. Like many theoretical physicists, Hawking longs to find the Holy Grail of science - the Theory of Everything, which lies at the foundation of the cosmos. It allows us to touch the secrets of the universe: from supergravity to supersymmetry, from quantum theory to M-theory, from holography to dualities. We go on an exciting adventure with him as he talks about his attempts to build on Einstein's general theory of relativity and Richard Feynman's idea of multiple histories into a complete unified theory that would describe everything that happens in the Universe.

We accompany him on an extraordinary journey through space-time, and magnificent color illustrations serve as landmarks on this journey through a surreal Wonderland, where particles, membranes and strings move in eleven dimensions, where black holes evaporate, taking their secrets with them, and where the cosmic seed from which our Universe grew was a tiny nut.

Stephen Hawking holds the Lucasian Professorship of Mathematics at Cambridge University, succeeding Isaac Newton and Paul Dirac in this post. He is considered one of the most prominent theoretical physicists since Einstein.

Preface

I didn't expect my non-fiction book, A Brief History of Time, to be so successful. It remained on the London Sunday Times bestseller list for more than four years - longer than any other book, which is especially surprising for a publication about science, because they usually don’t sell out very quickly. Then people started asking when to expect a sequel. I was reluctant, I didn't want to write something like "Continuation of a short story" or "A little longer history of time." I was also busy with research. But gradually it became clear that another book could be written, which had a chance of being easier to understand. “A Brief History of Time” was structured according to a linear pattern: in most cases, each subsequent chapter is logically connected with the previous ones. Some readers loved it, but others got stuck in the early chapters and never got to more. interesting topics. This book is structured differently - it is more like a tree: chapters 1 and 2 form a trunk, from which the branches of the remaining chapters extend.

These “branches” are largely independent of each other, and, having gained an idea of the “trunk,” the reader can get acquainted with them in any order. They relate to areas in which I have worked or thought about since the publication of A Brief History of Time. That is, they reflect the most actively developing areas of modern research. Within each chapter I have also tried to move away from a linear structure. Illustrations and captions point the reader along an alternative route, as in An Illustrated Brief History of Time, published in 1996. Sidebars and marginal notes allow some topics to be addressed in greater depth than is possible in the main text.

In 1988, when A Brief History of Time was first published, the impression was that the final Theory of Everything was just barely looming on the horizon. How has the situation changed since then? Are we any closer to our goal? As you will learn in this book, the progress has been dramatic. But the journey is still ongoing, and there is no end in sight. As they say, it is better to continue on the path with hope than to arrive at the goal." Our searches and discoveries fuel creativity in all areas, not just in science. If we reach the end of the road, the human spirit will wither and die. But I don’t think we we will ever stop: we will move, if not in depth, then towards complexity, always remaining in the center of the expanding horizon of possibilities.

I had many helpers while working on this book. I would especially like to acknowledge Thomas Hertog and Neil Shearer for their help with figures, captions and sidebars, Anne Harris and Kitty Fergusson who edited the manuscript (or more accurately the computer files, since everything I write appears in electronic form), Philip Dunn of Book Laboratory and Moonrunner Design, who created the illustrations. But also, I want to thank all those who gave me the opportunity to lead normal life and engage in scientific research. Without them this book would not have been written.

Stephen Hawking

"WORLD IN A NUTSHELL"

Lively and intriguing. Hawking has a natural gift for teaching and explaining, and humorously illustrating extremely complex concepts with analogies from everyday life.

New York Times

This book weds childhood wonders to genius intellects. We travel through Hawking's universe, transported by the power of his mind.

Sunday Times

Lively and witty... Allows the general reader to draw deep scientific truths from the original source.

New Yorker

Stephen Hawking is a master of clarity... It is difficult to imagine that anyone else alive today has more clearly presented mathematical calculations that frighten the layman.

Chicago Tribune

Probably the best popular science book. A masterful summary of what modern physicists know about astrophysics. Thank you Dr. Hawking! thinking about the universe and how it came to be this way.

Wall Street journal

In 1988, Stephen Hawking's record-breaking book A Brief History of Time introduced readers around the world to the ideas of this remarkable theoretical physicist. And here's a new important event: Hawking is back! The superbly illustrated sequel, The World in a Nutshell, reveals the scientific discoveries that have been made since the publication of his first, widely acclaimed book.

One of the most brilliant scientists of our time, known not only for the boldness of his ideas but also for the clarity and wit of his expression, Hawking takes us to the cutting edge of research, where truth seems stranger than fiction, to explain in simple terms the principles that govern the universe. Like many theoretical physicists, Hawking longs to find the Holy Grail of science - the Theory of Everything, which lies at the foundation of the cosmos. It allows us to touch the secrets of the universe: from supergravity to supersymmetry, from quantum theory to M-theory, from holography to dualities. We go on an exciting adventure with him as he talks about his attempts to build on Einstein's general theory of relativity and Richard Feynman's idea of multiple histories into a complete unified theory that would describe everything that happens in the Universe.

Stephen Hawking holds the Lucasian Professorship of Mathematics at the University of Cambridge, succeeding Isaac Newton and Paul Dirac. He is considered one of the most prominent theoretical physicists since Einstein.

Preface

I didn't expect my non-fiction book, A Brief History of Time, to be so successful. It remained on the London Sunday Times bestseller list for more than four years - longer than any other book, which is especially surprising for a publication about science, because they usually don’t sell out very quickly. Then people started asking when to expect a sequel. I was reluctant, I didn't want to write something like "Continuation of a short story" or "A little longer history of time." I was also busy with research. But gradually it became clear that another book could be written, which had a chance of being easier to understand. “A Brief History of Time” was structured according to a linear pattern: in most cases, each subsequent chapter is logically connected with the previous ones. Some readers loved it, but others got stuck in the early chapters and never got to the more interesting topics. This book is structured differently - it is more like a tree: chapters 1 and 2 form a trunk, from which the branches of the remaining chapters extend.

I had many helpers while working on this book. I would especially like to acknowledge Thomas Hertog and Neil Shearer for their help with figures, captions and sidebars, Anne Harris and Kitty Fergusson who edited the manuscript (or more accurately the computer files, since everything I write appears in electronic form), Philip Dunn of Book Laboratory and Moonrunner Design, who created the illustrations. But also, I want to thank all those who gave me the opportunity to lead a normal life and engage in scientific research. Without them this book would not have been written.

Chapter 1. A Brief History of Relativity

How Einstein laid the foundations for two fundamental theories of the 20th century: general relativity and quantum mechanics

Albert Einstein, the creator of the special and general theories of relativity, was born in 1879 in the German city of Ulm; the family later moved to Munich, where the father of the future scientist, Hermann, and his uncle, Jacob, had a small and not very successful electrical engineering company. Albert was not a child prodigy, but claims that he failed at school seem to be an exaggeration. In 1894, his father's business failed and the family moved to Milan. His parents decided to leave Albert in Germany until he finished school, but he could not stand German authoritarianism and after a few months he left school, going to Italy to join his family. He later completed his education in Zurich, receiving a diploma from the prestigious Polytechnic (ETN) in 1900. Einstein's tendency to argue and dislike his superiors prevented him from establishing relationships with ETH professors, so none of them offered him the position of assistant, which usually began his academic career. Only two years later, the young man finally managed to get a job as a junior clerk at the Swiss Patent Office in Bern. It was during that period, in 1905, that he wrote three articles that not only made Einstein one of the leading world scientists, but also laid the foundation for two scientific revolutions- revolutions that changed our ideas about time, space and reality itself.

Transcript

1 Downloaded from the website Stephen Hawking “THE WORLD IN A NUTSHELL” Lively and intriguing. Hawking has a natural gift for teaching and explaining, and humorously illustrating extremely complex concepts with analogies from everyday life. New York Times where particles, membranes and strings move in eleven dimensions, where black holes evaporate, taking their secrets with them, and where the cosmic seed from which our Universe grew was a tiny nut. Stephen Hawking holds the Lucasian Professorship of Mathematics at the University of Cambridge, succeeding Isaac Newton and Paul Dirac. He is considered one of the most prominent theoretical physicists since Einstein. Preface This book weds childhood wonders to genius intellects. We travel through Hawking's universe, transported by the power of his mind. Sunday Times Lively and witty Allows the general reader to glean deep scientific truths from the source. New Yorker Stephen Hawking is a master of clarity. It is difficult to imagine that anyone living today has more clearly outlined mathematical calculations that frighten the layman. Chicago Tribune Probably the best popular science book. A masterful summary of what modern physicists know about astrophysics. Thank you Dr. Hawking! thinking about the universe and how it came to be this way. Wall Street journal In 1988, Stephen Hawking's record-breaking book A Brief History of Time introduced readers around the world to the ideas of this remarkable theoretical physicist. And here's a new important event: Hawking is back! The beautifully illustrated sequel, The World in a Nutshell, reveals the scientific discoveries that have been made since the publication of his first, widely acclaimed book. One of the most brilliant scientists of our time, known not only for the boldness of his ideas but also for the clarity and wit of his expression, Hawking takes us to the cutting edge of research, where truth seems stranger than fiction, to explain in simple terms the principles that govern the universe. Like many theoretical physicists, Hawking longs to find the Holy Grail of science, the Theory of Everything, which lies at the foundation of the cosmos. It allows us to touch the secrets of the universe: from supergravity to supersymmetry, from quantum theory to M-theory, from holography to dualities. We go on an exciting adventure with him as he talks about his attempts to build on Einstein's general theory of relativity and Richard Feynman's idea of multiple histories into a complete unified theory that would describe everything that happens in the Universe. We accompany him on an extraordinary journey through space-time, and gorgeous color illustrations serve as milestones on his journey through a surreal Wonderland. I did not expect my non-fiction book, A Brief History of Time, to be so successful. It stayed on the London Sunday Times bestseller list for more than four years longer than any other book, which is especially surprising for a science publication, since they usually don't sell out very quickly. Then people started asking when to expect a sequel. I was reluctant, I didn't want to write something like "Continuation of a short story" or "A little longer history of time." I was also busy with research. But gradually it became clear that another book could be written, which had a chance of being easier to understand. “A Brief History of Time” was structured according to a linear pattern: in most cases, each subsequent chapter is logically connected with the previous ones. Some readers loved it, but others got stuck in the early chapters and never got to the more interesting topics. This book is structured differently; it is more like a tree: chapters 1 and 2 form a trunk, from which the branches of the remaining chapters extend. These “branches” are largely independent of each other, and, having gained an idea of the “trunk,” the reader can get acquainted with them in any order. They relate to areas in which I have worked or thought about since the publication of A Brief History of Time. That is, they reflect the most actively developing areas of modern research. Within each chapter I have also tried to move away from a linear structure. Illustrations and captions point the reader along an alternative route, as in An Illustrated Brief History of Time, published in 1996. Sidebars and marginal notes allow some topics to be addressed in greater depth than is possible in the main text. In 1988, when A Brief History of Time was first published, the impression was that the final Theory of Everything was just barely looming on the horizon. How has the situation changed since then? Are we any closer to our goal? As you will learn in this book, the progress has been significant. But the journey is still ongoing, and there is no end in sight. As they say, better

3 If light were a wave in an elastic substance called ether, its speed would appear faster to someone moving in a spaceship towards it (a), and slower to someone moving in the same direction as the light (b). No differences were found between the speed of light in the direction of the Earth's orbit and the speed of light in the perpendicular direction. Towards the end of the century, the concept of an all-pervasive ether began to encounter difficulties. Light was expected to travel through the ether at a fixed speed, but if you yourself were moving through the ether in the same direction as the light, the speed of light should appear slower, and if you were moving in the opposite direction, the speed of light would appear to be faster (Figure 1.1). ). However, in a number of experiments these ideas could not be confirmed. The most accurate and correct of them was carried out in 1887 by Albert Michelson and Edward Morley at the Case School of Applied Sciences, Cleveland, Ohio. They compared the speed of light in two beams traveling at right angles to each other. As the Earth rotates on its axis and revolves around the Sun, the speed and direction of movement of the equipment through the ether changes (Fig. 1.2). But Michelson and Morley found no daily or annual differences in the speed of light in the two beams. It turned out that light always moved relative to you at the same speed, no matter how fast and in what direction you were moving (Fig. 1.3). Fig. Measuring the speed of light In the Michelson Morley interferometer, the light from the source was split into two beams by a translucent mirror. The rays moved perpendicular to each other, and then united again, falling on a translucent mirror. The difference in the speed of light rays moving in two directions could lead to the fact that the crests of the waves of one ray would arrive simultaneously with the troughs of the waves of the other and cancel each other out. Based on Michelson Morley's experiment, Irish physicist George Fitzgerald and Dutch physicist Hendrik Lorentz proposed that bodies moving through the ether should contract and clocks would slow down. This compression and deceleration are such that people will always measure the same speed of light regardless of how they move relative to the ether. (Fitzgerald and Lorentz still considered the ether to be a real substance.) However, in a paper written in June 1905, Einstein noted that if no one can determine whether he is moving through the ether or not, then the very concept of an ether becomes redundant. Instead, he began with the postulate that the laws of physics must be the same for all freely moving observers. In particular, all of them, measuring the speed of light, should receive the same value, no matter how fast they themselves move. The speed of light is independent of their movements and is the same in all directions. But this requires discarding the idea that there is a single quantity for all, called time, which is measured by any clock. Instead, everyone should have their own, personal time. The time of two people will coincide only if they are at rest relative to each other, but not if they are moving. This has been confirmed by a number of experiments. In one, two very precise timekeepers were sent around the world in opposite directions, and when they returned, their readings were slightly different (Figure 1.4). From this we can conclude that, 3

4, wanting to extend your life, you must constantly fly east so that the speed of the plane is added to the speed of rotation of the Earth. However, the gain will be only a fraction of a second and will be completely negated by the quality of the food that the airline passengers are fed. Rice. 1.5 Twin Paradox Fig. Experimental design reconstructed from an illustration that appeared in Scientific American magazine in 1887. One version of the Twin Paradox (see Fig. 1.5) was tested experimentally by sending two high-precision chronometers around the world in opposite directions. At the meeting, the readings of the watches that were flying east turned out to be slightly smaller. According to the theory of relativity, each observer has his own measure of time. This can lead to the so-called twin paradox. One of the twins (a) goes on a space journey, during which he moves at near-light speed (c), while his brother (b) remains on Earth. Due to the movement in the spacecraft, time passes slower for the traveler (a) than for his twin (b) on Earth. Therefore, upon returning, the space traveler (a2) will find that his brother (b2) has aged more than himself. Although it seems counterintuitive, a number of experiments confirm that in this scenario the traveling twin will indeed be younger. A spaceship flies past Earth at four-fifths the speed of light. A pulse of light is emitted at one end of the cabin and reflected back at the other (a). The light is monitored by people on Earth and on the ship. Due to the motion of the spacecraft, they will differ in their estimate of the path traveled by the light (b). They must also differ in their estimates of the time it took light to travel back and forth, since according to Einstein's postulate, the speed of light is constant for all freely moving observers. 4

5 Fig. 1.6 Einstein's postulate that the laws of nature should be the same for all freely moving observers became the basis of the theory of relativity, which received this name because only relative movements matter. Its beauty and simplicity are recognized by many thinkers, but there are still many who think differently. Einstein rejected two absolutes of 19th century science: absolute rest, represented by the ether, and absolute universal time, which all clocks measure. Many people are uneasy about this concept. Doesn't it imply, they ask, that everything in the world is relative, so that there are no longer absolute moral standards? This unease was felt throughout the 1920s and 1930s. When Einstein was awarded the Nobel Prize in 1921, they cited an important, but (in terms of its scope) relatively small work, also completed in 1905. The theory of relativity was not even mentioned, since it was considered too controversial. (I still receive letters two or three times a week telling me that Einstein was wrong.) Despite this, the theory of relativity is now fully accepted by the scientific community, and its predictions have been tested in countless experiments. A very important consequence of the theory relativity became the connection between mass and energy. From Einstein's postulate that the speed of light should be the same for everyone, it follows that it is impossible to move faster than light. If you use energy to accelerate an object, be it an elementary particle or a spaceship, its mass will increase, making further acceleration increasingly difficult. It will be impossible to accelerate a particle to the speed of light, since this will require an infinite amount of energy. Mass and energy are equivalent, as expressed by Einstein’s famous formula E = mc 2. This is probably the only physical formula that is recognized on the streets (Fig. 1.7). One of its consequences was the understanding that if the nucleus of a uranium atom decays into two nuclei with a slightly smaller total mass, then a huge amount of energy should be released (Fig. 1.8). Rice. 1.8 Nuclear Communication Energy In 1939, as the prospect of a new world war became apparent, a group of scientists who understood its consequences persuaded Einstein to overcome his pacifist doubts and lend his authority to an appeal to President Roosevelt calling on the United States to begin a nuclear research program. Prophetic letter sent by Einstein to President Roosevelt in 1939 “During the last four months, thanks to the work of Joliot in France, and Fermi and Szilard in America, it has probably become possible to start a nuclear chain reaction in a large mass of uranium, as a result of which enormous energy can be released and a large number of elements like radium. It can be considered almost certain that this will be realized in the near future. This new phenomenon could also lead to the creation of bombs and, perhaps, although less certain, exceptionally powerful new types of bombs.” Rice

6 the ability to transmit signals at superluminal speeds (which is prohibited by the theory of relativity), but to give meaning to the concept of “instantaneous” also requires the existence of absolute or universal time, which the theory of relativity abandoned in favor of individual time. Einstein had been aware of this difficulty since 1907, when he was still working at the Berne patent office, but it was not until 1911 in Prague that he began to think seriously about the problem. He realized that there is a close connection between acceleration and the gravitational field. When you are in a small enclosed space, such as an elevator, you cannot tell whether it is at rest in the earth's gravitational field or being accelerated by a rocket in outer space. (Of course, this was long before the appearance of the series " Star Trek"3, and Einstein rather imagined people in an elevator than in a spaceship.) But in an elevator you cannot accelerate or fall freely for a long time: everything will quickly end in disaster (Fig. 1.9). This led to the Manhattan Project and ultimately the bombs that exploded over Hiroshima and Nagasaki in 1945. Some people blame Einstein for the atomic bomb because he discovered the relationship between mass and energy, but just as well blame Newton for crashing planes because he discovered gravity. Einstein himself took no part in the Manhattan Project and was horrified by the bombing. After his pioneering papers in 1905, Einstein gained respect in the scientific community. But it was only in 1909 that he was offered a position at the University of Zurich, which allowed him to part ways with the Swiss Patent Office. Two years later he moved to the German University in Prague, but in 1912 he returned to Zurich, this time to the ETH. Despite the anti-Semitism that then gripped much of Europe and even penetrated the universities, Einstein was now very highly rated as a scientist. He received offers from Vienna and Utrecht, but decided to give preference to a position as a researcher at the Prussian Academy of Sciences in Berlin, since it freed him from teaching duties. He moved to Berlin in April 1914 and was soon joined by his wife and two sons. But family life things didn’t work out, and quite quickly the scientist’s family returned to Zurich. Despite his occasional visits to his wife, they eventually divorced. Einstein later married his cousin Elsa, who lived in Berlin. However, throughout the years of the First World War he remained free from family ties, which is perhaps why this period of his life turned out to be so fruitful for science. Nuclei are made up of protons and neutrons that are held together by the strong force. But the mass of the nucleus is always less than the total mass of protons and neutrons of which it consists. The difference serves as a measure of the nuclear binding energy that holds particles in the nucleus. The binding energy can be calculated using Einstein's formula Amc 2, where Am is the difference between the mass of the nucleus and the sum of the masses of the particles included in it; with the speed of light. It is the release of this potential energy that generates the destructive power of nuclear devices. Although the theory of relativity is fully consistent with the laws that govern electricity and magnetism, it is incompatible with Newton's law of gravity. This latter says that if you change the distribution of matter in one place in space, then changes in the gravitational field will instantly appear everywhere in the Universe. This not only means Fig. 1.9 An observer in a container does not perceive the difference between being in a stationary elevator on Earth (a) and moving in a rocket moving with acceleration in free space (b). The rocket engine shutting down (c) would feel exactly the same as the elevator free falling to the bottom of the shaft (d). 3 This famous American science fiction series tells about the adventures of the exploration starship Enterprise, capable of moving many times faster than light with the help of warp engines that bend space (from the English warp curvature). Filming began in 1966 and continues intermittently to the present day. 6

7 If the Earth were flat (Fig. 1.10), we could equally say that the apple fell on Newton’s head under the influence of gravity, and that the Earth, together with Newton, moved upward with acceleration. This equivalence does not work for a spherical Earth (Figure 1.11), since people on opposite sides of the globe must move away from each other. Einstein got around this obstacle by introducing curved space-time. If the Earth were flat, we could equally attribute the fall of the apple on Newton's head to both gravity and the fact that Newton, along with the surface of the Earth, was accelerating upward (Fig. 1.10). Such equivalence between acceleration and gravity is not observed, however, in round earth: People on opposite sides of the globe would have to accelerate in different directions while remaining a constant distance from each other (Figure 1.11). But by the time he returned to Zurich in 1912, Einstein had already formed the understanding that the equivalence should work if space-time turned out to be curved, and not flat, as was believed in the past. The idea was that mass and energy should bend spacetime, but exactly how this was to be determined. Objects like apples or planets should tend to move through spacetime in straight lines, but their paths appear to be curved by the gravitational field because spacetime itself is curved (Figure 1.12). Fig Curvature of space-time Acceleration and gravity can be equivalent only if a massive body bends space-time, thereby bending the trajectories of objects in its vicinity. With the help of his friend Marcel Grossmann, Einstein studied the theory of curved spaces and surfaces, which had been developed earlier by Georg Friedrich Riemann. But Riemann thought only of curved space. Einstein realized that space-time is curved. In 1913, Einstein and Grossman jointly wrote a paper in which they put forward the idea that the force we think of as gravity is just a manifestation of the fact that spacetime is curved. However, because Einstein made mistakes (and he, like all of us, was prone to making mistakes), they were unable to find equations that relate the curvature of space-time to the mass and energy found in it. Einstein continued to work on the problem in Berlin, where he was undisturbed by domestic affairs and largely unaffected by the war, and eventually found the correct equations in November 1915. During a trip to the University of Göttingen in the summer of 1915, he discussed his ideas with the mathematician David Hilbert, who independently derived the same equations several days before Einstein. Nevertheless, Hilbert himself admitted that the honor of creating a new theory belongs to Einstein. It was the latter's idea to connect gravity with the curvature of space-time. And we must pay tribute to the civility of the then German state, for the fact that scientific discussions and the exchange of ideas could continue without hindrance even in war time. What a contrast with the Nazi era that came twenty years later! The new theory of curved spacetime was called general relativity to distinguish it from the original theory, which did not include gravity and is now known as special relativity. It received very dramatic confirmation in 1919, when a British expedition observed in West Africa a slight bending of starlight passing near the Sun during an eclipse (Fig. 1.13). This was direct evidence that space and time are curved, and stimulated the most profound revision of ideas about the universe in which we live since Euclid wrote his Elements around 300 AD. e. 7

8 Fig Observations of galaxies indicate that the Universe is expanding: the distances between almost any pair of galaxies are increasing. Fig. Bending of light The light of a star passes near the Sun and is deflected because the Sun bends space-time (a). This leads to a slight shift in the apparent position of the star when observed from Earth (b). You can see this during an eclipse. Einstein's general theory of relativity transformed space and time from a passive background against which events unfold into active participants in dynamic processes in the Universe. And from here grew a great problem that remains at the forefront of physics in the 21st century. The universe is filled with matter, and this matter bends space-time in such a way that bodies fall on top of each other. Einstein discovered that his equations had no solution that described a static, time-invariant Universe. Rather than abandon the kind of eternal universe that he and most other people believed in, Einstein tweaked his equations by adding a term called the cosmological constant, which curved space in the opposite way so that bodies flew apart. The repulsive effect of the cosmological constant could balance the effect of the attraction of matter, thereby allowing a static solution for the Universe. This was one of the greatest missed opportunities in theoretical physics. If Einstein had kept the original equations, he could have predicted that the Universe must either expand or contract. In fact, the possibility of a time-varying universe was not seriously considered until observations made in the 1920s. on the 100-inch telescope at Mount Wilson Observatory. These observations revealed that the further away another galaxy is, the faster it is moving away from us. The Universe is expanding in such a way that the distance between any two galaxies is constantly increasing over time (Fig. 1.14). This discovery made unnecessary the cosmological constant, introduced to provide a static solution for the Universe. Einstein later called the cosmological constant the greatest mistake of his life. However, it appears that this was not a mistake at all: recent observations, described in Chapter 3, suggest that the cosmological constant may actually have a small non-zero value. The general theory of relativity radically changed the content of discussions about the origin and fate of the Universe. A static universe may exist forever, or it may have been created in its current form some time ago. However, if the galaxies are now moving apart, this means that in the past they should have been closer. About 15 billion years ago they were literally sitting on top of each other and the density was very high. This was the state of the “primary atom,” as it was called by the Catholic priest Georges Lemaitre, who was the first to study the birth of the Universe, which we now call the Big Bang. Einstein apparently never took the Big Bang seriously. He seemed to believe that the simple model of the uniform expansion of the Universe should break down if one tried to trace the movements of galaxies back in time, and that the small lateral velocities of the galaxies would result in them not colliding. He believed that previously the Universe could have been in a compression phase, but still at a very moderate density experience reflection and move on to the current expansion. However, as we now know, in order for nuclear reactions in the early Universe to produce the amount of light elements that we observe, the density had to reach at least a ton per cubic centimeter, and the temperature must have reached ten billion degrees. Moreover, observations of the cosmic microwave background indicate that the density was likely as high as a trillion trillion trillion trillion trillion trillion (1 followed by 72 zeros) tons per cubic centimeter. We also know that Einstein's general theory of relativity does not allow the Universe to be reflected, passing from a contraction phase to an expansion phase. As will be discussed in Chapter 2, Roger Penrose and I were able to show that general relativity implies that the universe began with big bang. So Einstein's theory does indeed predict that time has a beginning, although he himself never liked the idea. Einstein was even less willing to accept the prediction of general relativity that time should cease to flow for massive stars when their lives end and they can no longer generate enough heat to contain their own gravitational pull, which tends to shrink their size. Einstein believed that such stars should come to an equilibrium final state, but we now know that for stars twice the mass of the Sun, such a final state does not exist. Such stars will shrink until 8

9 will become black holes about blasts of space-time, so curved that light cannot escape from them (Fig. 1.15). Fig. 100-inch Hooker Telescope at Mount Wilson Observatory When a massive star runs out of nuclear fuel, it loses heat and contracts. The curvature of space-time becomes so strong that a black hole appears from which light cannot escape. Inside a black hole, time is ending. with quantum theory, another great revolutionary concept of the 20th century. The first step towards quantum theory was made in 1900, when Max Planck in Berlin discovered that the glow of a red-hot body can be explained if light is emitted and absorbed only in discrete portions of quanta. In one of his seminal papers, written in 1905 while working in the patent office, Einstein showed that Planck's quantum hypothesis could explain the so-called photoelectric effect, the ability of metals to emit electrons when light shines on them. Modern light detectors and television cameras are based on this, and it was for this work that Einstein was awarded the Nobel Prize in Physics. Einstein continued to work on the quantum idea in the 1920s, but he was deeply disturbed by the work of Werner Heisenberg in Copenhagen, Paul Dirac in Cambridge and Erwin Schrödinger in Zurich, who developed new picture physical reality, called quantum mechanics. Tiny particles lost their definite position and speed. The more accurately we determine the position of a particle, the less accurately we can measure its speed, and vice versa. Einstein was horrified by this randomness and unpredictability in fundamental laws and never fully accepted quantum mechanics. His feelings were expressed in the famous saying: “God does not play dice.” Meanwhile, most other scientists agreed on the correctness of the new quantum laws, which were in excellent agreement with observations and provided explanations for a number of previously inexplicable phenomena. These laws underlie modern achievements chemistry, molecular biology and electronics technologies that have transformed the world over the past half century. In December 1932, realizing that the Nazis were about to come to power, Einstein left Germany and four months later renounced his German citizenship. He spent the remaining 20 years of his life in the United States, in Princeton, New Jersey, where he worked at the Institute for Advanced Study. As Penrose and I showed, the general theory of relativity implies that inside a black hole, time ends, both for the star itself and for the unfortunate astronaut who happens to fall into it. However, both the beginning and the end of time will be points at which the equations of general relativity break down. In particular, the theory cannot predict what will emerge from the Big Bang. Some see this as a manifestation of divine freedom, the ability to launch the development of the Universe in any way pleasing to God, but others (including me) feel that at the initial moment the Universe should be governed by the same laws as at other times. Chapter 3 describes some of the progress that has been made toward this goal, but we do not yet have a complete understanding of the origins of the universe. The reason general relativity breaks down at the Big Bang is because it is incompatible. Many German scientists were Jewish, and the Nazis launched a campaign against “Jewish science,” which, among other reasons, prevented Germany from building the atomic bomb. Einstein and his theory of relativity were the main targets of this campaign. A book “One Hundred Authors Against Einstein” was even published, to which the latter remarked: “Why a hundred? If I were wrong, one would be enough.” After World War II, he insisted that the Allies establish a world government to control nuclear weapons. In 1952, he was offered to become president of the State of Israel, but Einstein rejected this offer. He once said: “Politics is for the moment, but equations are for eternity.” Einstein's equations of general relativity are the best epitaph and monument for him. They will last as long as the Universe. Over the last century, the world has changed much more than in all previous centuries. The reason for this was not new political or economic doctrines, but technological advances that 9

10 became possible thanks to the progress of basic sciences. And who better to symbolize this progress than Albert Einstein? Rice. 2.1 Model of time as railway tracks Chapter 2. The form of time About the fact that the theory of relativity gives time a form and how this can be reconciled with quantum theory What is time? Is it the ever-rolling stream that washes away all our dreams, as the old psalm says? 4 Or is it a rut railway? It may have loops and rings so that you can continue forward and return to the station you have already passed (Figure 2.1). 4 This refers to the lines from the 90th Psalm of I Sahak Watsa (): “Time, like an ever-rolling skein, // washes away all its children; // They fly forgotten, like dreams, // Dying as the day begins" (Time, like ever-rolling stream // Bears all their sons away; // They fly, forgotten, as a dream, // Dies at the op" ning day).Charles Lamb wrote in the 19th century: “Nothing puzzles me more than time and space. And nothing troubles me less than time and space, because I never think about them.” Most of us almost never worries about time and space, whatever they are; but we all sometimes wonder what time is, where it comes from, and where it is leading us. Any reasonable scientific theory, whether it concerns time or any other subject, must, in my opinion , be based on the most workable philosophy of science, the positivist approach, which was developed by Karl Popper and others. According to this way of thinking, a scientific theory is a mathematical model that describes and systematizes the observations we make. A good theory describes a wide range of phenomena based on a few simple postulates and makes clear, testable predictions. If the predictions agree with the observations, the theory passes the test, although it can never be proven correct. On the other hand, if observations do not correspond to predictions, the theory will have to be either discarded or modified. (At least, this is supposed to be the case. In practice, people often question the accuracy of the observations and the reliability and moral character of those who made them.) If one accepts positivist principles, as I do, then it is impossible to say that actually represents time. In the Newtonian model, time and space were the background against which events unfolded, but which they did not affect. Time was separated from space and was seen as a single line, a railway track, endless in both directions (Fig. 2.2). 10

11 Fig. 2.2 All we can do is describe what we know is a very good mathematical model for time and list the predictions it makes. Isaac Newton gave us the first mathematical model of time and space in his work Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687. Newton held the Lucasian Professorship of Mathematics at Cambridge, which I now hold, although in his it didn't have time electronic control. 6 It is impossible to bend space without affecting time. Therefore time has a form. However, it still moves in one direction, like the locomotives in this picture. Rice. 2.4 Rubber sheet analogy The large ball in the center represents a massive body, such as a star. Under the influence of the body's weight, the leaf near it bends. A ball rolling on a sheet is deflected by this curvature and moves around the large ball, just as planets in the gravitational field of a star orbit around it. Einstein's theory of relativity, which is consistent with a large number experiments, says that time and space are inseparably intertwined. 5 It's about about the department of mathematics, founded in 1663 by Henry Lucas with the condition that the professor occupying it should not participate in the activities of the church. In 1980, Stephen Hawking became the 17th Lucas Professor. 6 Hawking alludes to the wheelchair in which he is forced to move due to a serious illness. He likes to make fun of his physical condition. Time itself was considered eternal in the sense that it existed and will always exist. In contrast, most people believed that the physical world was created in more or less modern form just a few thousand years ago. This worried philosophers such as the German thinker Immanuel Kant. If the universe was truly created, then why did it take forever to create it? On the other hand, if the Universe exists forever, then why hasn't everything that should happen happened yet, in other words, why hasn't history ended yet? And in particular, why has the Universe not yet reached thermodynamic equilibrium with the same temperature everywhere? Kant called this problem the “antinomy of pure reason” because it seemed to him a logical contradiction; she had no solution. But this was a contradiction only in the context of Newton's mathematical model, in which time was 11

12 an endless line, independent of what happens in the Universe. Meanwhile, as was shown in Chapter 1, Einstein in 1915 put forward a completely new mathematical model, the general theory of relativity. Over the years since Einstein's paper appeared, we have added some details to it, but overall our model is still based on what Einstein proposed. This and subsequent chapters will describe how our understanding has developed since the publication of Einstein's revolutionary paper. That was the story successful work a large number of people, and I am proud that I was able to make my small contribution to it. General relativity combines the time dimension with the three dimensions of space to form what we call spacetime (Figure 2.3). The theory includes the action of gravity, arguing that the matter and energy filling the Universe bend and deform space-time so that it ceases to be flat. Objects in spacetime tend to move in straight lines, but because spacetime itself is curved, their paths appear curved. They move as if they are being affected by a gravitational field. As a rough analogy that should not be taken literally, imagine a sheet of rubber. You can put a large ball on it, which will represent the Sun. The weight of the ball will push the sheet and cause it to bend near the Sun. If you now run a small ball across the sheet, it will not roll straight from one edge to the other, but instead will move around a large mass, just as the planets orbit around the Sun (Figure 2.4). This analogy is incomplete, since in it only a two-dimensional section of space (the surface of a rubber sheet) is curved, and time remains completely unaffected, as in Newtonian mechanics. However, in the theory of relativity, which is consistent with a large number of experiments, time and space are inextricably linked with each other. You cannot achieve the curvature of space without also involving time. It turns out that time has a form. Thanks to curvatures, space and time in the general theory of relativity turn from a passive background against which events develop into dynamic participants in what is happening. In Newton's theory, where time exists independently of everything else, one might ask: what was God doing before He created the Universe? As St. Augustine said, this topic should not be reduced to jokes, following the example of the man who said: “He prepared hell for the overly curious.” This is a very serious question that people have been pondering for centuries. According to St. Augustine, before God created the heavens and the earth, He did nothing at all. In fact, this is very close to modern ideas. On the one hand, in the general theory of relativity, time and space do not exist independently of the Universe and each other. They are determined by measurements made within the universe, such as the number of vibrations of a quartz crystal in a watch or the length of a ruler. And it is absolutely clear that since time is defined in this way within the Universe, then it must have a minimum and maximum reference, in other words, a beginning and an end. It makes no sense to ask what happened before the beginning or after the end, since such points in time cannot be specified. It seems important to understand whether the mathematical model of general relativity actually predicts that the universe and time itself must have a beginning and an end. A common preconception among theoretical physicists, including Einstein, was that time should be infinite in both directions. On the other hand, there were inconvenient questions about the creation of the world, which seemed to be beyond the purview of science. Such solutions of Einstein's equations, in which time had a beginning or an end, were known, but they were obtained in very special, highly symmetrical particular cases. It was believed that for a real body collapsing under the influence of its own gravity, pressure and lateral velocities should prevent all matter from falling to one point, at which the density increases to infinity. Likewise, if we traced the expansion of the universe back in time, it might turn out that matter was not ejected at all from a single point of infinite density, called a singularity, which can serve as the beginning or end of time. In 1963, two Soviet scientists, Evgeniy Lifshits and Isaac Khalatnikov, announced that they had proof that all solutions to Einstein's equations with a singularity have a special distribution of matter and velocities. The probability that a solution representing our Universe had such a special distribution was practically zero. Almost all solutions that can correspond to our Universe must do without an infinite-density singularity. The era during which the solution representing our Universe has such a special distribution was practically zero. Almost all solutions that can correspond to our Universe must do without an infinite-density singularity. The era during which the Universe expanded must have been preceded by a contraction phase, during which matter fell on itself, but avoided collision, scattering again in the modern expansion phase. If this were the case, then time could last forever from the endless past to the endless future. Not everyone agreed with the arguments of Lifshits and Khalat Niko-va. Roger Penrose and I took a different approach, based not on detailed study of solutions, but on the global structure of spacetime. In general relativity, spacetime is curved not only by the massive objects in it, but also by energy. Energy is always positive, so it always gives space-time a curvature that brings the rays closer to each other. Let's consider the light cone of the past (Fig. 2.5), which represents the paths through space-time of light rays from distant galaxies coming to us at the present time. In a diagram where time is directed upward and space is directed to the sides, a cone is obtained with the apex in which we are located. As we move into the past, from 12

13 vertices down the cone, we see galaxies at earlier and earlier times. Rice. 2.6 Fig. Light cone of our past The observer looks back through time Galaxies, how they looked recently Galaxies, how they looked 5 billion years ago. Because gravity causes attraction, matter always bends spacetime so that light rays bend toward each other. So we can conclude that our past light cone, if we trace it back, passes through a certain amount of matter. This amount is enough to bend space-time in such a way that the rays of light in our light cone bend towards each other (Fig. 2.7). When we look at distant galaxies, we see the Universe as it was in the past, because light travels at a finite speed. If we imagine time as the vertical axis and the two spatial dimensions as the horizontal axes, then the light that now reaches us at the top moves towards us along the surface of the cone. The spectrum of cosmic microwave radiation, that is, the distribution of its intensity over frequencies, is characteristic of a heated body. In order for radiation to reach thermal equilibrium, it must be scattered repeatedly by the substance. This indicates that there must have been enough matter in the light cone of our past to cause it to contract. As the Universe expands and all objects become much closer to each other, our gaze passes through regions with increasing density of matter. We are seeing a faint background of microwave radiation coming to us along the past light cone from a much earlier time when the Universe was much denser and hotter than it is now. By tuning the receiver to different microwave frequencies, we can measure the radiation spectrum (energy distribution across frequencies). We discovered a spectrum that is characteristic of radiation from a body with a temperature of 2.7 degrees above absolute zero. This microwave radiation is of little use for defrosting pizza, but the fact that its spectrum so closely matches the radiation of a body with a temperature of 2.7 degrees Kelvin suggests that it must come from a region opaque to microwaves (Fig. 2.6). Rice. 2.7 As we move back in time, the cross-section of the past light cone will reach its maximum size and begin to decrease again. Our past is pear-shaped (Fig. 2.8). 13

14 Fig Pear-Shaped Time Following further along the light cone of our past, we will discover that the positive energy density of matter causes the rays of light to bend towards each other even more. The cross section of the light cone shrinks to zero size in a finite time. This means that all the matter inside the light cone of the past is driven into a region whose boundary is shrinking to zero. Not surprisingly, Penrose and I were able to prove that in the mathematical model of general relativity, time must have a beginning in what we call the Big Bang. Similar arguments show that time will come to an end when a star or galaxy collapses under its own gravity and forms a black hole. We have bypassed the paradox of Kant's pure reason by discarding his implicit assumption that time has meaning independently of the universe. Our paper proving that time had a beginning won second place in a competition sponsored by the Gravity Research Foundation in 1968, and Roger and I shared a generous $300 prize. I don’t think that any other work submitted to the competition that year had such lasting value. If we trace the light cone of our past back in time, in the early Universe it will be compressed by matter. The entire Universe that is accessible to our observations is contained in a region whose boundaries are compressed to zero at the moment of the Big Bang. This will be a singularity, a place where the density of matter must increase to infinity, and the classical general theory of relativity ceases to work. An important step The discovery of quantum theory was the assumption made in 1900 by Max Planck that light always exists in the form of small packets, which he called quanta. But although Planck's quantum hypothesis fully explained the observed pattern of radiation from hot bodies, the full extent of its consequences was not realized until the mid-1920s, when the German physicist Werner Heisenberg formulated his famous uncertainty principle. He noticed that according to Planck's hypothesis, the more accurately we try to measure the position of a particle, the less accurately we can measure its speed, and vice versa. More rigorously, he showed that the uncertainty of a particle's position, multiplied by the uncertainty of its momentum, must always be greater than Planck's constant, the numerical value of which is closely related to the energy transferred by one quantum of light. Form of time Our article evoked a variety of responses. It upset many physicists, but it pleased those religious leaders who believed in the act of Creation; here there was its scientific proof. Meanwhile, Lifshits and Khalatnikov found themselves in an awkward position. They could neither challenge the mathematical theorem that we had proved, nor admit, under the Soviet system, that they were wrong and Western scientists were right. Yet they saved face by finding a more general family of solutions with a singularity that was not special in the sense that their previous solutions were. The latter allowed them to declare singularities, as well as the beginning and end of time, to be a Soviet discovery. Most physicists still instinctively dislike the idea that time has a beginning or an end. Therefore, they note that this mathematical model cannot be considered a good description of space-time near a singularity. The reason is that general relativity, which describes the force of gravity, is, as noted in Chapter 1, a classical theory and does not take into account the uncertainties of quantum theory, which governs all other forces we know. 14

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Oh, Stephen Hawking has already been posted on Funlab. It’s very unexpected, but since he’s here, I can’t remain silent.

First, a little about the author himself: Stephen Hawking is the clearest example of the strength of the human spirit. Finding yourself paralyzed and unable to speak - what could be worse than this fate? But his spirit and Titan's mind overcame his physical weakness. And how we won! Hawking is one of the the smartest people that live on our planet now. If anyone needs proof of the primacy of the spirit over the body, then here is the proof. Those who complain about their minor problems or sores - here is an example of a REAL problem and REAL physical weakness. Actually, Stephen Hawking himself is Science Fiction. A man-ascetic, a man-martyr, a man-symbol. :pray:

About the book: I read (or rather, I’m still reading, because things are going very slowly) only one book. The thing is absolutely gorgeous! And like any luxury item, it is quite rare. The book's circulation is 7,000 copies, so it is hardly possible to find it on the shelves of bookstores in small towns. I personally ordered this book via the Internet, on the website www.urss.ru (I ask moderators not to delete the link, since this store distributes exclusively scientific or scientific-educational literature, which often cannot be found anywhere else). An excellent edition in a dust jacket and hardcover on luxurious coated paper (god, how different this is from the cheap and grayish paper that has already become familiar!). Excellent printing, the text is not smudged anywhere. Excellent color drawings that perfectly complement the rather complex text, clearly showing the course of the author's thoughts. In general, it’s not a shame to pay your hard-earned six hundred rubles + pay for delivery by mail for this book.

As for the text itself, it is quite complex. But it is complicated not because the author expresses his thoughts poorly or because he abuses terminology or scary formulas, but because he is trying to explain the most complex and interesting problems that modern physics is struggling to solve. For his part (i.e., on the part of the popular scientist), Hawking did everything he could, but the reader must make a lot of effort to at least general outline understand what the author is talking about.

In this book, unlike, for example, another best-selling non-fiction book by Brian Greene, “The Elegant Universe,” there are no chapters to refresh your memory of the physical laws of the macro- and microworld. If Brian Greene spent half a book to prepare the reader for the theory of Superstrings and the eleven-dimensional dimension in which they exist, then Stephen Hawking preferred to take the bull by the horns and from the second chapter began to talk about the form of Time, simultaneously recalling the basics of his science. So unprepared people (like me, for example) can sometimes lose the thread of the author's reasoning. However, is it the author’s fault that they taught physics poorly at school? Nothing more than basic concepts What school teachers tried to give us is not required here.

I hasten to please fans of Nick Perumov! The Multiverse, which Hawking talks about in one of the chapters of the book, is very similar (how similar, one to one, even if you announce a “find ten differences” competition) to the Ordered One. So we can say that fantasy operates with modern physical theories.

Of course, the content of the book does not end there and the Author talks about absolutely fantastic things. For example, about the possibility of time travel. Or about those very “wormholes” that are talked about a lot, but few people know.

Bottom line: I can’t raise my hand to give this book less than ten points. Before us is a masterpiece, yes, a masterpiece of popular science literature in the field of physics. Moreover, for once, the masterpiece received a worthy design in the form of an ideal edition (how Brian Greene’s book “The Elegant Universe” lacks this!) Anyone who is at least a little interested in what the best minds of our time are struggling with is a must-read.

Rating: 10

The book is good, but not as good as “A Brief History of Time,” which at one time made a splash in popular science literature.

There are a lot of large, colorful drawings, no complicated formulas, everything can be chewed literally on your fingers. The ideas are indeed very complex and it is not always possible to express them in simple words like this... nevertheless, the author tries to do it. In my opinion, oversimplification of the material significantly damaged the book in terms of information content. Many questions remain for people who want to get to the bottom of the truth on their own, so, ultimately, they have to buy additional literature: Brian Greene, Weinberg, Penrose. Separately, I would like to note the works published by Amphora on Einstein’s theory of relativity (the series is called the “Stephen Hawking Library”).

In 1988, Stephen Hawking's record-breaking book A Brief History of Time introduced the ideas of this remarkable theoretical physicist to readers around the world. And here's a new important event: Hawking is back! The beautifully illustrated sequel, The World in a Nutshell, reveals the scientific discoveries that have been made since the publication of his first, widely acclaimed book.

One of the most brilliant scientists of our time, known not only for the boldness of his ideas but also for the clarity and wit of his expression, Hawking takes us to the cutting edge of research, where truth seems stranger than fiction, to explain in simple terms the principles that govern the universe.

Like many theoretical physicists, Hawking longs to find the Holy Grail of science - the Theory of Everything, which lies at the foundation of the cosmos. It allows us to touch the secrets of the universe: from supergravity to supersymmetry, from quantum theory to M-theory, from holography to dualities. Together we embark on a fascinating adventure as he talks about his attempts to create, based on Einstein's general theory of relativity and Richard Feynman's idea of multiple histories, a complete unified theory that would describe everything that happens in the Universe.

We accompany him on an extraordinary journey through space-time, and magnificent color illustrations serve as landmarks on this journey through a surreal Wonderland, where particles, membranes and strings move in eleven dimensions, where black holes evaporate, taking their secrets with them, and where the cosmic seed from which our Universe grew was a tiny nut.

STEPHEN HAWKING
The Universe in a Nutshell
Translated from English by A. G. Sergeev
The publication was prepared with the support of Dmitry Zimin’s Dynasty Foundation
SPb: Amphora. TID Amphora, 2007. - 218 p.

Chapter 5. Protecting the Past

About whether time travel is possible and whether a highly developed civilization, returning to the past, is capable of changing it

Because Stephen Hawking (who lost a previous bet on this issue by making his demands too general) remains firmly convinced that naked singularities are cursed and should be prohibited by the laws of classical physics, and because John Preskill and Kip Thorne (who won the previous bet) - still believe that naked singularities as quantum gravitational objects can exist, without being covered by the horizon, in the observable Universe, Hawking proposed, and Preskill/Thorne accepted the following bet:

Since any form of classical matter or field that is unable to become singular in flat spacetime obeys the classical equations of Einstein's general theory of relativity, dynamical evolution from any initial conditions (that is, from any open set of initial data) can never generate a naked singularity (incomplete zero geodesic from I + with end point in the past).

The loser rewards the winner with clothing so that he can cover his nakedness. The clothing must have an appropriate message embroidered on it.

My friend and colleague Kip Thorne, with whom I have made many bets (still active), is not one of those who follows the generally accepted line in physics just because everyone else does. Therefore, he became the first serious scientist who dared to discuss time travel as a practical possibility.

Talking openly about time travel is a very sensitive matter. You risk being led astray either by loud calls to invest budget money in some absurdity, or by demands to classify research for military purposes. Really, how can we protect ourselves from someone with a time machine? After all, he is able to change history itself and rule the world. Few of us are foolhardy enough to work on a question that is considered so politically incorrect among physicists. We disguise this fact with technical terms that encode time travel.

The basis of all modern discussions about time travel is Einstein's general theory of relativity. As seen in previous chapters, Einstein's equations make space and time dynamic by describing how they are bent and distorted by matter and energy in the Universe. In the general theory of relativity, anyone's personal time, measured by wristwatch, will always increase, just as in Newton's theory or in the flat space-time of special relativity. But perhaps space-time will be so twisted that you will be able to fly away on a starship and return before your departure (Fig. 5.1).

For example, this can happen if there are wormholes - the space-time tubes mentioned in Chapter 4 that connect different regions of it. The idea is to send a starship into one mouth of a wormhole and emerge from another in a completely different place and time (Fig. 5.2).

Wormholes, if they exist, could solve the problem of the speed limit in space: according to the theory of relativity, it takes tens of thousands of years to cross the Galaxy. But through a wormhole you can fly to the other side of the Galaxy and return back during dinner. Meanwhile, it is easy to show that if wormholes exist, they can be used to find yourself in the past.

So it’s worth thinking about what will happen if you manage, for example, to blow up your rocket on the launch pad in order to prevent your own flight. This is a variation of the famous paradox: what would happen if you went back in time and killed your own grandfather before he could conceive your father (Figure 5.3)?

Of course, the paradox here arises only if we assume that, once in the past, you can do whatever you want. This book is not the place for philosophical discussions about free will. Instead, we'll focus on whether the laws of physics allow spacetime to be twisted so that a macroscopic body like a spaceship can return to its past. According to Einstein's theory, a spacecraft always moves at a speed that is less than the local speed of light in space-time, and follows the so-called timelike world line. This allows us to rephrase the question into technical terms: Can closed timelike curves exist in space-time, that is, those that return to their starting point again and again? I will call such trajectories “temporal s mi loops.”

You can look for an answer to the question posed at three levels. The first is the level of Einstein's general theory of relativity, which implies that the Universe has a clearly defined history without any uncertainty. For this classical theory we have a complete picture. However, as we have seen, such a theory cannot be absolutely accurate, since, according to observations, matter is subject to uncertainty and quantum fluctuations.

Therefore, we can ask the question about time travel at the second level - for the case of semi-classical theories. Now we consider the behavior of matter according to quantum theory with uncertainties and quantum fluctuations, but we consider space-time to be well defined and classical. This picture is not as complete, but it at least gives some idea of how to proceed.

Finally, there is an approach from the standpoint of a complete quantum theory of gravity, whatever that turns out to be. In this theory, where not only matter, but also time and space themselves are subject to uncertainty and fluctuate, it is not even entirely clear how to pose the question of the possibility of time travel. Perhaps the best that can be done is to ask people in regions where spacetime is nearly classical and free of uncertainties to interpret their measurements. Will they experience time travel in regions with strong gravity and large quantum fluctuations?

Let's start with the classical theory: the flat space-time of the special theory of relativity (without gravity) does not allow time travel; this is also impossible in those curved versions of space-time that were studied at first. Einstein was literally shocked when in 1949 Kurt Gödel, the same one who proved Gödel's famous theorem, discovered that space-time in a universe entirely filled with rotating matter has a temporary at th loop at each point (Fig. 5.4).

Gödel's solution required the introduction of a cosmological constant, which may not exist in reality, but later similar solutions were found without a cosmological constant. A particularly interesting case is when two cosmic strings move past each other at high speed.

Cosmic strings should not be confused with the elementary objects of string theory, with which they are completely unrelated. Such objects have extension, but at the same time have a tiny cross section. Their existence is predicted in some theories of elementary particles. Spacetime outside a single cosmic string is flat. However, this flat space-time has a wedge-shaped cutout, the top of which lies just on the string. It is similar to a cone: take a large circle of paper and cut out a sector from it, like a piece of pie, the top of which is located in the center of the circle. After removing the cut piece, glue the edges of the cut to the remaining part - you will get a cone. It depicts the space-time in which the cosmic string exists (Fig. 5.5).

Please note, since the surface of the cone is still the same flat sheet paper with which we started (minus the removed sector), it can still be considered flat, except for the top. The presence of curvature at the vertex can be revealed by the fact that the circles described around it are shorter than the circles that are the same distance from the center on the original round sheet of paper. In other words, the circle around the vertex is shorter than a circle of the same radius should be in flat space due to the missing sector (Fig. 5.6).

Likewise, a sector removed from flat spacetime shortens the circles around the cosmic string, but does not affect the time or distance along it. This means that the space-time around an individual cosmic string does not contain time s x loops, and therefore travel to the past is impossible. However, if there is a second cosmic string that moves relative to the first, its time direction will be a combination of the time and spatial changes of the first. This means that the sector that is cut by the second string will reduce both distances in space and time intervals for the observer who moves along with the first string (Fig. 5.7). If the strings are moving relative to each other at near the speed of light, the reduction in time to go around both strings can be so significant that you end up back before you started. In other words, there are temporary s e loops along which you can travel into the past.

Cosmic strings contain matter that has a positive energy density, which is consistent with known physics today. However, the twisting of space, which gives rise to temporary s e loops, stretches to infinity in space and to the endless past in time. So such space-time structures initially, by construction, allow for the possibility of time travel. There is no reason to believe that our own Universe is tailored according to such a perverted style; we have no reliable evidence of the appearance of guests from the future. (I'm not counting the conspiracy theories that UFOs are coming from the future and the government knows about it but is hiding the truth. They usually hide things that aren't so great.) So I'm going to assume that temporary s x loops did not exist in the distant past, or more precisely, in the past relative to some surface in space-time, which I will denote S. Question: can a highly developed civilization build a time machine? That is, can it change space-time in the future relative to S(above surface S on the diagram) so that loops appear only in the finite size area? I say a finite area because no matter how advanced a civilization is, it appears to be able to control only a limited portion of the universe. In science, correctly formulating a problem often means finding the key to its solution, and the case we are considering is good for that illustration. For the definition of a finite time machine, I will turn to one of my old works. Time travel is possible in some region of space-time where there are temporary s e loops, that is, trajectories with sub-light speed of movement, which nevertheless manage to return to the original place and time due to the curvature of space-time. Since I assumed that in the distant past temporary s x there were no loops, there must exist, as I call it, a “time travel horizon” - a boundary that separates the area containing time s e loops, from the area where they are not (Fig. 5.8).

The horizon of time travel is quite similar to the horizon of a black hole. While the latter is formed by light rays that are just a little short of escape from a black hole, the horizon of time travel is defined by rays that are on the verge of meeting themselves. Further, I will consider the criterion of a time machine to be the presence of a so-called finitely generated horizon, that is, formed by light rays that are emitted from a region of limited size. In other words, they should not come from infinity or singularity, but only from a finite region containing temporary at th loop, such an area that we assume our highly developed civilization will be able to create.

With the adoption of such a criterion, a time machine appears great opportunity use the methods that Roger Penrose and I developed to study singularities and black holes. Even without using Einstein's equations, I can show that, in general, a finitely generated horizon will contain light rays that meet themselves, continuing to return to the same point again and again. As it circles, the light will experience more and more blue shift each time, and the images will become bluer and bluer. The humps of waves in the beam will begin to move closer and closer to each other, and the intervals through which the light returns will become shorter and shorter. In fact, a particle of light will have a finite history when considered in its own time, even though it runs circles in a finite region and does not hit the singular point of curvature.

The fact that a particle of light will exhaust its history in a finite time may seem unimportant. But I can also prove the possibility of the existence of world lines, the speed of movement along which is less than light, and the duration is finite. These could be stories of observers who are caught in a finite region before the horizon and move around, around and around, faster and faster, until they reach the speed of light in a finite amount of time. So, if a beautiful alien from a flying saucer invites you into her time machine, be careful. You can fall into the trap of repeating stories with a finite total duration (Figure 5.9).

These results do not depend on Einstein's equation, but only on the way in which spacetime is twisted to produce time. O th loops in the final region. But still, what kind of material could a highly developed civilization use to build a time machine of finite dimensions? Could it have a positive energy density everywhere, as is the case with the cosmic string space-time described above? The cosmic string does not satisfy my requirement that s e loops appeared only in the final region. But one might think that this is due only to the fact that the strings have an infinite length. Someone might be hoping to build a finite time machine using finite loops of cosmic strings that have positive energy densities throughout. Sorry to disappoint people who, like Kip, want to go back in time, but this cannot be done while maintaining positive energy density throughout. I can prove that to build the ultimate time machine you will need negative energy.

In classical theory, the energy density is always positive, so the existence of a finite time machine at this level is excluded. But the situation changes in semiclassical theory, where the behavior of matter is considered in accordance with quantum theory, and space-time is considered to be well-defined, classical. As we have seen, the uncertainty principle in quantum theory means that fields always fluctuate up and down, even in seemingly empty space, and have an infinite energy density. After all, only by subtracting an infinite value do we obtain the finite energy density that we observe in the Universe. This subtraction can also produce a negative energy density, at least locally. Even in flat space, one can find quantum states in which the energy density is locally negative, although the overall energy is positive. I wonder if these negative values actually cause space-time to bend so that a finite time machine arises? It looks like they should lead to this. As is clear from Chapter 4, quantum fluctuations mean that even seemingly empty space is filled with pairs of virtual particles that appear together, fly apart, and then converge again and annihilate each other (Fig. 5.10). One of the elements of the virtual pair will have positive energy, and the other will have negative energy. If there is a black hole, a particle with negative energy can fall into it, and a particle with positive energy can fly off to infinity, where it will appear as radiation carrying positive energy away from the black hole. And particles with negative energy, falling into a black hole, will lead to a decrease in its mass and slow evaporation, accompanied by a decrease in the size of the horizon (Fig. 5.11).

Ordinary matter with a positive energy density generates an attractive gravitational force and bends spacetime so that the rays turn towards each other, just like the ball on the rubber sheet in Chapter 2 always turns the little ball towards itself and never away.

It follows that the area of the black hole horizon only increases over time and never decreases. For a black hole's horizon to shrink, the energy density at the horizon must be negative, and spacetime must cause the light rays to diverge. I first realized this one night while going to bed, shortly after my daughter was born. I won’t say exactly how long ago it was, but now I already have a grandson.

The evaporation of black holes shows that at the quantum level, energy density can sometimes be negative and bend space-time in the direction that would be needed to build a time machine. So one can imagine a civilization at such a high stage of development that it is able to achieve a sufficiently large negative energy density to obtain a time machine that would be suitable for macroscopic objects like spaceships. However, there is a significant difference between the horizon of a black hole, which is formed by rays of light that just keep moving, and the horizon in a time machine, which contains closed rays of light that just keep going in circles. A virtual particle moving over and over again along such a closed path would bring its ground state energy to the same point. Therefore, we should expect that on the horizon, that is, on the border of the time machine - the area in which you can travel into the past - the energy density will be infinite. This is confirmed by exact calculations in a number of special cases, which are simple enough to allow an exact solution to be obtained. It turns out that a person or a space probe that tries to cross the horizon and get into the time machine will be completely destroyed by the curtain of radiation (Fig. 5.12). So the future of time travel looks pretty bleak (or should we say blindingly bright?).

The energy density of a substance depends on the state in which it is located, so perhaps a highly developed civilization will be able to make the energy density at the edge of the time machine finite by “freezing” or removing virtual particles that move round and round in a closed loop. There is no certainty, however, that such a time machine will be stable: the slightest disturbance, for example someone crossing the horizon to enter the time machine, can start the circulation of virtual particles and cause incinerating lightning. Physicists should discuss this issue freely, without fear of contemptuous ridicule. Even if it turns out that time travel is impossible, we will understand why it is impossible, and this is important.

In order to answer the question under discussion with certainty, we must consider quantum fluctuations not only of material fields, but also of space-time itself. This can be expected to cause some blurring in the paths of the light rays and in the chronological ordering principle in general. In fact, we can think of the black hole's radiation as a leak caused by quantum fluctuations in spacetime, which indicate that the horizon is not well defined. Since we don't yet have a ready-made theory of quantum gravity, it's hard to say what the effect of spacetime fluctuations should be. Even so, we can hope to gain some clues from Feynman's story summation described in Chapter 3.

Each story will be a curved space-time with material fields in it. Since we are going to sum over all possible histories, and not just those that satisfy some equations, the sum must also include those spacetimes that are twisted enough to allow travel into the past (Figure 5.13). The question then arises: why don’t such trips happen everywhere? The answer is that time travel actually occurs on a microscopic scale, but we don't notice it. If we apply Feynman's idea of summation over histories to a single particle, then we must include histories in which it moves faster than light and even backwards in time. In particular, there will be stories in which the particle moves round and round in a closed loop in time and space. Like in the movie “Groundhog Day”, where the reporter lives the same days over and over again (Fig. 5. 14).

Particles with such closed-loop histories cannot be observed at accelerators. However, their side effects can be measured by observing a number of experimental effects. One is a slight shift in the radiation emitted by hydrogen atoms, which is caused by electrons moving in closed loops. Another - small force, acting between parallel metal plates and caused by the fact that slightly fewer closed loops are placed between them than in the outer regions is another equivalent interpretation of the Casimir effect. Thus, the existence of stories closed in a loop is confirmed by experiment (Fig. 5.15).

It is debatable whether such looped histories of particles have anything to do with the curvature of spacetime, since they appear even against such an unchanging background as flat space. But in last years we have found that physical phenomena often have equally valid dual descriptions. It is equally possible to say that particles move in closed loops against a constant background, or that they remain motionless while space-time fluctuates around them. It comes down to the question: do you want to sum over particle trajectories first and then over curved spacetimes, or vice versa?

Thus, quantum theory appears to allow time travel on a microscopic scale. But for sci-fi purposes like going back in time and killing your grandfather, this is of little use. Therefore, the question remains: can the probability, when summed over histories, reach a maximum on spacetimes with macroscopic time loops?

This question can be explored by considering sums over the histories of material fields on a sequence of background spacetimes that are getting closer and closer to allowing time loops. It would be natural to expect that at the moment when temporary A I the loop appears for the first time, something significant is about to happen. This is exactly what happened in a simple example I studied with my student Michael Cassidy.

The background spacetimes we studied were closely related to the so-called Einstein universe, a spacetime that Einstein proposed when he still believed that the universe was static and unchanging in time, neither expanding nor contracting (see Chapter 1) . In Einstein's universe, time moves from an infinite past to an infinite future. But spatial dimensions are finite and closed on themselves, like the surface of the Earth, but only with one more dimension. Such space-time can be depicted as a cylinder, the longitudinal axis of which will be time, and the cross-section will be space with three dimensions (Fig. 5.16).

Since Einstein's universe is not expanding, it does not correspond to the universe in which we live. However, this comfortable base for a discussion of time travel because it is simple enough that summation across stories can be done. Let's forget about time travel for a moment and consider matter in Einstein's universe, which rotates around a certain axis. If you find yourself on this axis, you will remain at the same point in space, as if you were standing in the center of a children's carousel. But by positioning yourself away from the axis, you will move in space around it. The farther you are from the axis, the faster your movement will be (Fig. 5.17). So, if the universe is infinite in space, points far enough from the axis will rotate at superluminal speeds. But since Einstein's universe is finite in spatial dimensions, there is a critical rotation speed at which no part of it will yet rotate faster than light.

Now consider the sum over the histories of a particle in Einstein's rotating universe. When the rotation is slow, there are many paths a particle can take for a given amount of energy. Therefore, summation over all histories of a particle against such a background gives a large amplitude. This means that the probability of such a background when summed over all histories of curved space-time will be high, that is, it is one of the more probable histories. However, as the speed of rotation of Einstein's universe approaches a critical point, and the speed of movement of its outer regions tends to the speed of light, there is only one path left that is allowed And m for classical particles at the edge of the universe, namely movement at the speed of light. This means that the sum over the histories of the particle will be small, which means that the probabilities of such spatiotemporal s x backgrounds in total for all histories of curved space-time will be low. That is, they will be the least likely.

But what does time travel have to do with s m loops have Einstein's spinning universes? The answer is that they are mathematically equivalent to other backgrounds in which time loops are possible. These other backgrounds are universes that expand in two spatial directions. Such universes do not expand in the third spatial direction, which is periodic. That is, if you walk a certain distance in this direction, you will end up where you started. However, with each circle in this direction, your speed in the first and second directions will increase (Fig. 5.18).

If the acceleration is small, then temporarily s x loops do not exist. Consider, however, a sequence of backgrounds with all b O greater increase in speed. Time loops appear at a certain critical acceleration value. It is not surprising that this critical acceleration corresponds to the critical speed of rotation of Einstein's universes. Since the calculation of the sum over the histories on both of these backgrounds is mathematically equivalent, we can conclude that the probability of such backgrounds tends to zero as we approach the curvature required to obtain time loops. In other words, the probability of warping enough for a time machine is zero. This confirms what I call the chronology defense hypothesis: the laws of physics are designed to prevent macroscopic objects from moving through time.

Although temporary s Because loops are allowed when summed over histories, their probabilities are extremely low. Based on the duality relationships mentioned above, I estimated the probability that Kip Thorne could travel back in time and kill his grandfather: it was less than one in ten to the power of trillion trillion trillion trillion trillion.

It's just a surprisingly low probability, but if you look closely at Kip's photo, you'll notice a slight haze around the edges. It corresponds to the vanishingly small probability that some rogue from the future will go back in time and kill his grandfather, and therefore Kip is not really here.

Being the gambling types that we are, Kip and I would like to bet on an anomaly like this. The problem, however, is that we cannot do this because we are currently of the same opinion. And I won’t make a bet with anyone else. What if he turns out to be an alien from the future who knows that time travel is possible?

Did you feel like this chapter was written at the behest of the government to hide the reality of time travel? Maybe you're right.

A world line is a path in four-dimensional space-time. Timelike world lines combine movement in space with natural movement forward in time. Only along such lines can material objects follow.

Finite - having finite dimensions.

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