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.
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 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.
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 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 this period, in 1905, that he wrote three papers that not only made Einstein one of the world's leading scientists, but also marked the beginning of two scientific revolutions - revolutions that changed our ideas about time, space and reality itself.
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.
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 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.
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 a normal life and engage in scientific research. Without them this book would not have been written.
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 smartest people living on our planet today. 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 are 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 kindly 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 pity 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 understand in general terms 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 the basic concepts that school teachers tried to give us is 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 Universe we observe, 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 space-time 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 be embroidered with a message appropriate to the occasion.
My friend and colleague Kip Thorne, with whom I have made many bets (still active), is not one of those who follows the conventional 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 general relativity, anyone's personal time, as measured by a wristwatch, will always increase, just as in Newton's theory or in the flat spacetime 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 reformulate the question in technical terms: can there be closed time-like curves in space-time, that is, those that return again and again to their starting point? 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).
Note that since the surface of the cone is still the same flat piece of paper we started with (minus the sector removed), 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 a good illustration of this. 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 this time machine criterion, there is a wonderful opportunity to 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. One might hope 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 it is possible to 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. The other is a 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 - this is another equivalent treatment 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 recent years we have discovered 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, it is a useful framework for discussing 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 off 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 Since 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 travel 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? Perhaps you are 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.
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 smartest people living on our planet today. 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 are 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 kindly 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 pity 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 understand in general terms 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 the basic concepts that school teachers tried to give us is 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”).
