Briefly about me: “at the sound of a flute, he loses his will when he hears about black holes and other things in space.” Unfortunately, I did not receive my education at the physics department, so I am talking about the book exclusively as a humanist (searching for factual errors and misconceptions in the mod off text).
Writing books about quantum mechanics is now fun. Gluons, quarks, wormholes, hot quark soup, quantum jitters and other terms are playing “stand up kids, stand in a circle”, dancing around the main topic: black holes. Stephen Hawking, a superstar in the world of science, sees black holes as information eaters, not containers in which information is stored until required. The author of the book defends the theory of a container-archive on demand, presenting a black hole as something like a sippy cup inkwell (while Hawking adheres to the shredder theory). How heavily archived can information going into black holes be? Susskind writes that even a one-kilogram brick is mostly empty space that can be compacted to the size of a pinhead or even the size of a virus. Black holes are not only extremely tightly compressed stars, but also the ultimate reservoirs for information, where all the information is tightly packed, like cannonballs stacked in rows (except thirty-four orders of magnitude smaller). It is around this - densely packed information and entropy - that all quantum gravity revolves.
For a long time, physicists believed that black holes are eternal, like diamonds, motionless and work only to receive information. But Susskind cites arguments from various scientists who, one after another, refute many of the usual facts about black holes. A scientist like Dennis Sciama concluded that black holes evaporate: electromagnetic radiation carries away part of the black hole's mass. Bekenstein guessed that black holes have entropy, and Hawking guessed that they have temperature. Another property of black holes is that they themselves are capable of moving. If you place a blackhole in the gravitational field of another mass, it will accelerate like any other massive object. It could even fall into a larger black hole. Who even called them holes? John Wheeler. Before him, the phenomenon was called dark (black) stars.
Any name unfamiliar to the reader will be commented on by the author in a very direct manner, for example: “The charming Dane Aage, before moving to the United States, was Niels Bohr's assistant in Copenhagen. He loved quantum mechanics and lived and breathed Bohr’s philosophy.” Susskind will share observations about which physicists at seventy years old preferred to contemplate girls in bikinis instead of talking about science, and who behaved how. For example, about Feynman: “I met a lion, and he did not disappoint me” and “Feynman had a brutal ego, but he was a lot of fun to be around.”
The advantages of Susskind's book are that he allows himself not to stand on ceremony with his words, can say that the scientific picture of the world of the eighteenth century was rather dull, the uncertainty principle is a strange and daring statement, and an ideal crystal, like an ideal BMW, has no entropy at all. The imagery and expressiveness of his text are valuable, however there are a couple of facts that define the significance of the book. The first is a small thing, an “Easter egg”: without quotes there is a very vivid direct quote from Hawking “I was strongly advised to limit myself to one single formula: E = mc2. I was told that with each additional equation, book sales would drop by ten thousand copies.” And the second is a little more serious: after reading the text, you are left with the feeling that Susskind, who entered the battle with Hawking, never really discussed with him, “fighting” only in his imagination.
Chapter by chapter, Susskind talks about how his thoughts rarely strayed from the person of Stephen Hawking, the story increasingly looks like an obsession, parallels are drawn with the novel “Moby Dick”, only unlike Ahab’s obsession, Susskind’s obsession was not a hundred-ton whale, but “ a hundred-pound theoretical physicist in a chair with a motor.” Attached is a scan of a document confirming the fact that Hawking had a dispute with a third party on a topic similar to the Hawking/Susskind “confrontation” (and in the end Hawking admitted defeat). Well, if you forgive the scientist for his frantic fandom, you can glean a lot of interesting information from the book about black holes, string theory and quantum mechanics.
“Today it is incorrect to say that black holes do not emit any light. Take a smoked pot, heat it to several hundred degrees, and it will begin to glow red. Any hotter and the glow will turn orange, then yellow and finally a bright bluish-white. It is curious that, according to the definition of physicists, the Sun is a black body. How strange, you say: it is difficult to imagine something further from black than the Sun. Indeed, the surface of the Sun emits a huge amount of light, but it does not reflect anything. This makes it a black body to a physicist.”
P.S. I first learned that entropy is growing from the song “Civil Defense”; If I had read more encyclopedias, I would have known more about the “black color of the sun” (see the quote “the sun is a black body” above).
What happens when an object falls into a black hole? Does he disappear without a trace? About thirty years ago, one of the leading researchers of the phenomenon of black holes, the now famous British physicist Stephen Hawking, said that this is exactly what is happening. But it turns out that such an answer threatens everything we know about physics and the fundamental laws of the Universe. The author of this book, the outstanding American physicist Leonard Susskind, argued with Stephen Hawking about the nature of black holes for many years, until, finally, in 2004, he admitted his mistake. Brilliant and remarkably readable, the book tells the fascinating story of this decades-long scientific battle that radically changed the way physicists think about the nature of reality. The new paradigm has led to the stunning conclusion that everything in our world - this book, your house, you yourself - is just a kind of hologram projected from the edges of the Universe. The book is included in the Dynasty Foundation Library. The Dynasty Foundation for Non-Profit Programs was founded in 2001 by Dmitry Borisovich Zimin, honorary president of VimpelCom. The Foundation's priority areas of activity are support for fundamental science and education in Russia, popularization of science and education. “The Library of the Dynasty Foundation” is a project of the Foundation to publish modern popular science books selected by scientific experts.
Part 1: The Gathering Storm
1. First thunder
San Francisco, 1983.
By the day the first skirmish took place in the attic of Jack Rosenberg's mansion, the ominous clouds of war had been gathering for more than 80 years. Jack, also known as Werner Erhard, was a guru, a shrewd huckster and a bit of a con artist. Until the early 1970s, he was simply Jack Rosenberg, an encyclopedia salesman. But one day, as he was driving across the Golden Gate Bridge, he had a revelation. He will save the world and become enormously rich because of it. All it takes is a cool name and a new approach to business. The name should be Werner (after Werner Heisenberg) Erhard (after the German politician Ludwig Erhard), and the new approach would be Erhard Training Seminars, EST. And he succeeded, if not in saving the world, then at least in getting rich. Thousands of shy, insecure people paid hundreds of dollars for grueling rants during sixteen-hour motivational seminars by Werner himself or one of his many students, during which (it was rumored) they were forbidden even to go to the toilet.
It was much cheaper and faster than psychotherapy and somehow it worked. People came shy and unsure, but after the seminars they looked strong, confident and friendly - just like Werner: It doesn’t matter that sometimes they seemed like robotic maniacs with shaking hands. They felt better. “Training” even became the theme of the very funny film “Semi-Tough” by Burt Reynolds. Werner was constantly surrounded by frenzied ECT fans. “Slaves” is perhaps too strong a word; let’s call them volunteers. EST-trained chefs prepared his meals, chauffeurs drove him around the city, and his mansion was filled with a variety of servants. But, ironically, Werner himself was also a rabid fan - a fan of physics.
Download the e-book for free in a convenient format, watch and read:
Download the book The Battle of the Black Hole, my battle with Stephen Hawking for a world safe for quantum mechanics, Susskind L. - fileskachat.com, fast and free download.
Download file No. 1 - fb2
Download file No. 2 - rtf
Below you can buy this book at the best price with a discount with delivery throughout Russia.
Leonard Susskind
Battle of the Black Hole
My battle with Stephen Hawking for a world safe for quantum mechanics
What breathes life into these equations and creates the Universe they could describe?
- Stephen Hawking
Introduction
There was so much to grok, but we had to start almost from scratch.
- Robert Heinlein. Stranger in the land of strangers
Somewhere on the East African savannah, a middle-aged lioness is stalking her dinner. She would prefer the slow-moving prey of old age, but all there is is a young, agile antelope. The victim's attentive eyes are ideally placed on the sides of its head to keep the entire surrounding area under surveillance in anticipation of an attack. The predator's eyes look straight ahead, focusing on the prey and assessing the distance.
This time, the antelope’s “wide-angle scanners” missed the predator, which came within throwing distance. The lioness's strong hind legs push her towards her terrified prey. The eternal chase begins again.
Although burdened by years, the big cat is an excellent sprinter. At first, the gap narrows, but due to sudden movements, the lioness’s powerful muscles experience oxygen starvation and gradually weaken. Soon the antelope’s natural endurance wins out: at some point, the relative speed of the cat and its prey changes sign, and the gap that was previously decreasing begins to grow. The lioness feels that her fortune has changed, Her Royal Majesty admits defeat and returns to her ambush in the bushes.
Fifty thousand years ago, a tired hunter finds the entrance to a cave blocked with stones. If you move away a heavy obstacle, you will have a safe place to rest. Unlike his ape-like ancestors, the hunter stands erect. But in this position he pushes the boulder unsuccessfully. Choosing a more suitable angle, he moves his legs further away. When the position of his body is almost horizontal, the main component of the applied force begins to act in the desired direction. The stone moves.
Distance? Speed? Change of sign? Corner? Force? Component? What kind of incredibly complex calculations go on in the brain of a hunter, not to mention a cat? These technical concepts are commonly found in high school physics textbooks. Where did a cat learn to measure not only prey speed, but more importantly, relative speed? Did the hunter take physics classes to understand the concept of force? And more trigonometry to use sines and cosines to calculate components?
The truth, of course, is that all complex life forms have built-in instinctive ideas about physics that are hardwired by evolution into their nervous systems. Without this pre-installed physical “software” it would be impossible to survive. Mutations and natural selection have made us all physicists, even animals. The large volume of the human brain has allowed these instincts to develop into concepts that we operate consciously.
Self-flashing
In fact, we are all classic physicists. We “gut feel” force, speed and acceleration. Robert Heinlein, in his science fiction novel Stranger in the Land of Strangers (1961), coined the word “grok” to express this deeply intuitive, almost physiological understanding of the phenomenon. I rock power, speed and acceleration. I'm rocking three-dimensional space. I grokk the time and the number 5. The trajectories of a stone or arrow lend themselves to grokk. But my standard built-in grokker breaks down when I try to apply it to ten-dimensional spacetime, or to the number 10 1000, or, worse, to the world of electrons and the Heisenberg Uncertainty Principle.
With the advent of the 20th century, our intuition suffered a colossal accident; physics suddenly found itself bewildered by completely unfamiliar phenomena. My paternal grandfather was already ten years old when Albert Michelson and Edward Morley discovered that the orbital motion of the Earth through a hypothetical ether could not be detected. The electron was discovered when my grandfather was in his twenties; When he turned thirty, Albert Einstein's theory of special relativity was published, and when he crossed the threshold of middle age, Heisenberg discovered the uncertainty principle. There is no way that the evolutionary pressure could lead to the development of an intuitive understanding of worlds so radically different from the one we are familiar with. But something in our nervous systems, at least for some of us, turned out to be ready for a fantastic rewiring, allowing us not only to be interested in obscure phenomena, but also to create mathematical abstractions, sometimes completely counterintuitive, to explain and manipulate these phenomena.
Speed first caused the need for re-flashing - enormous speed, rivaling light itself. No animal before the twentieth century moved faster than a hundred miles per hour (160 km/h), and even by today's standards the speed of light is so fast that to all but scientists it appears as if it is not moving at all, but simply appearing instantly. when it is turned on. Ancient people did not require firmware to operate at ultra-high speeds such as the speed of light.
The change in the speed issue happened suddenly. Einstein was not a mutant; for ten years, in complete obscurity, he struggled to replace his old Newtonian firmware. But to the physicists of that time, it must have seemed that a new type of person had suddenly appeared among them - someone capable of seeing the world not as a three-dimensional space, but as a four-dimensional one. space-time.
Einstein then fought for another ten years, this time in full view of all physicists, to unite what he called the special theory of relativity with Newton's theory of gravity. The result of these efforts was the general theory of relativity, which profoundly changed all our traditional ideas about geometry. Space-time has become plastic, capable of bending and folding. It reacts to the presence of matter somewhat like a rubber sheet bending under load. Previously, space-time was passive, its geometric properties were unchanged. In general relativity, spacetime becomes an active player: it can be deformed by massive objects such as planets and stars, but this is impossible to imagine without complex additional mathematics.
In 1900, five years before Einstein appeared on the scene, another, even more astonishing paradigm shift began with the discovery that light is made up of particles called photons or, sometimes, light quanta. The photon theory of light was only a harbinger of the coming revolution; the mental exercises along this path turned out to be much more abstract than anything encountered before. Quantum mechanics is more than a new law of nature. It caused a change in the rules of classical logic, that is, the usual rules of thinking that every sane person uses in reasoning. She seemed crazy. But crazy or not, physicists have been able to rewire themselves according to a new logic called quantum. In Chapter 4, I'll explain everything you need to know about quantum mechanics. Prepare to be confused. It happens to everyone.
Relativity and quantum mechanics disliked each other from the very beginning. Attempts to forcibly “marry” them had disastrous consequences - for every question asked by physicists, mathematics produced monstrous infinities. It took half a century to reconcile quantum mechanics with special relativity, but eventually the mathematical incompatibilities were resolved. By the early 1950s, Richard Feynman, Julian Schwinger, Shinichiro Tomonaga and Freeman Dyson had laid the groundwork for unification special theory of relativity and quantum mechanics, called quantum field theory. However general the theory of relativity (Einstein's synthesis of special relativity with Newton's theory of gravity) and quantum mechanics remained irreconcilable, and clearly not for lack of peacemaking efforts. Feynman, Steven Weinberg, Bryce DeWitt and John Wheeler tried to quantize Einstein's equations, but all ended up with only mathematical absurdity. Perhaps this was not surprising. Quantum mechanics ruled the world of very light objects. Gravity, on the contrary, seemed significant only for very heavy accumulations of matter. There seemed to be nothing light enough for quantum mechanics to matter, and yet heavy enough for gravity to be taken into account. As a result, many physicists in the second half of the twentieth century considered the search for such a unified theory to be a futile exercise, fit only for mad scientists and philosophers.
Leonard Susskind
Battle of the Black Hole
My battle with Stephen Hawking for a world safe for quantum mechanics
What breathes life into these equations and creates the Universe they could describe?
- Stephen Hawking
Introduction
There was so much to grok, but we had to start almost from scratch.
- Robert Heinlein. Stranger in the land of strangers
Somewhere on the East African savannah, a middle-aged lioness is stalking her dinner. She would prefer the slow-moving prey of old age, but all there is is a young, agile antelope. The victim's attentive eyes are ideally placed on the sides of its head to keep the entire surrounding area under surveillance in anticipation of an attack. The predator's eyes look straight ahead, focusing on the prey and assessing the distance.
This time, the antelope’s “wide-angle scanners” missed the predator, which came within throwing distance. The lioness's strong hind legs push her towards her terrified prey. The eternal chase begins again.
Although burdened by years, the big cat is an excellent sprinter. At first, the gap narrows, but due to sudden movements, the lioness’s powerful muscles experience oxygen starvation and gradually weaken. Soon the antelope’s natural endurance wins out: at some point, the relative speed of the cat and its prey changes sign, and the gap that was previously decreasing begins to grow. The lioness feels that her fortune has changed, Her Royal Majesty admits defeat and returns to her ambush in the bushes.
Fifty thousand years ago, a tired hunter finds the entrance to a cave blocked with stones. If you move away a heavy obstacle, you will have a safe place to rest. Unlike his ape-like ancestors, the hunter stands erect. But in this position he pushes the boulder unsuccessfully. Choosing a more suitable angle, he moves his legs further away. When the position of his body is almost horizontal, the main component of the applied force begins to act in the desired direction. The stone moves.
Distance? Speed? Change of sign? Corner? Force? Component? What kind of incredibly complex calculations go on in the brain of a hunter, not to mention a cat? These technical concepts are commonly found in high school physics textbooks. Where did a cat learn to measure not only prey speed, but more importantly, relative speed? Did the hunter take physics classes to understand the concept of force? And more trigonometry to use sines and cosines to calculate components?
The truth, of course, is that all complex life forms have built-in instinctual understandings of physics that are evolutionarily hard-wired into their nervous systems. Without this pre-installed physical “software” it would be impossible to survive. Mutations and natural selection have made us all physicists, even animals. The large volume of the human brain has allowed these instincts to develop into concepts that we operate consciously.
Self-flashing
In fact, we are all classic physicists. We “gut feel” force, speed and acceleration. Robert Heinlein, in his science fiction novel Stranger in the Land of Strangers (1961), coined the word “grok” to express this deeply intuitive, almost physiological understanding of the phenomenon. I rock power, speed and acceleration. I'm rocking three-dimensional space. I grokk the time and the number 5. The trajectories of a stone or arrow lend themselves to grokk. But my standard built-in grokker breaks down when I try to apply it to ten-dimensional spacetime, or to the number 101000, or, worse, to the world of electrons and the Heisenberg Uncertainty Principle.
With the advent of the 20th century, our intuition suffered a colossal accident; physics suddenly found itself bewildered by completely unfamiliar phenomena. My paternal grandfather was already ten years old when Albert Michelson and Edward Morley discovered that the orbital motion of the Earth through a hypothetical ether could not be detected. The electron was discovered when my grandfather was in his twenties; When he turned thirty, Albert Einstein's theory of special relativity was published, and when he crossed the threshold of middle age, Heisenberg discovered the uncertainty principle. There is no way that the evolutionary pressure could lead to the development of an intuitive understanding of worlds so radically different from the one we are familiar with. But something in our nervous systems, at least for some of us, turned out to be ready for a fantastic rewiring, allowing us not only to be interested in obscure phenomena, but also to create mathematical abstractions, sometimes completely counterintuitive, to explain and manipulate these phenomena.
Speed first caused the need for re-flashing - enormous speed, rivaling light itself. No animal before the twentieth century moved faster than a hundred miles per hour (160 km/h), and even by today's standards the speed of light is so fast that to all but scientists it appears as if it is not moving at all, but simply appearing instantly. when it is turned on. Ancient people did not require firmware to operate at ultra-high speeds such as the speed of light.
The change in the speed issue happened suddenly. Einstein was not a mutant; for ten years, in complete obscurity, he struggled to replace his old Newtonian firmware. But to the physicists of that time, it must have seemed that a new type of person had suddenly appeared among them - someone capable of seeing the world not as a three-dimensional space, but as a four-dimensional one. space-time.
Einstein then fought for another ten years, this time in full view of all physicists, to unite what he called the special theory of relativity with Newton's theory of gravity. The result of these efforts was the general theory of relativity, which profoundly changed all our traditional ideas about geometry. Space-time has become plastic, capable of bending and folding. It reacts to the presence of matter somewhat like a rubber sheet bending under load. Previously, space-time was passive, its geometric properties were unchanged. In general relativity, spacetime becomes an active player: it can be deformed by massive objects such as planets and stars, but this is impossible to imagine without complex additional mathematics.
In 1900, five years before Einstein appeared on the scene, another, even more astonishing paradigm shift began with the discovery that light is made up of particles called photons or, sometimes, light quanta. The photon theory of light was only a harbinger of the coming revolution; the mental exercises along this path turned out to be much more abstract than anything encountered before. Quantum mechanics is more than a new law of nature. It caused a change in the rules of classical logic, that is, the usual rules of thinking that every sane person uses in reasoning. She seemed crazy. But crazy or not, physicists have been able to rewire themselves according to a new logic called quantum. In Chapter 4, I'll explain everything you need to know about quantum mechanics. Prepare to be confused. It happens to everyone.
Relativity and quantum mechanics disliked each other from the very beginning. Attempts to forcibly “marry” them had disastrous consequences - for every question asked by physicists, mathematics produced monstrous infinities. It took half a century to reconcile quantum mechanics with special relativity, but eventually the mathematical incompatibilities were resolved. By the early 1950s, Richard Feynman, Julian Schwinger, Shinichiro Tomonaga and Freeman Dyson had laid the groundwork for unification special theory of relativity and quantum mechanics, called quantum field theory. However general the theory of relativity (Einstein's synthesis of special relativity with Newton's theory of gravity) and quantum mechanics remained irreconcilable, and clearly not for lack of peacemaking efforts. Feynman, Steven Weinberg, Bryce DeWitt and John Wheeler tried to quantize Einstein's equations, but all ended up with only mathematical absurdity. Perhaps this was not surprising. Quantum mechanics ruled the world of very light objects. Gravity, on the contrary, seemed significant only for very heavy accumulations of matter. There seemed to be nothing light enough for quantum mechanics to matter, and yet heavy enough for gravity to be taken into account. As a result, many physicists in the second half of the twentieth century considered the search for such a unified theory to be a futile exercise, fit only for mad scientists and philosophers.
Horatio, - in heaven and earth
There are many things that we never even dreamed of
Science.
The first hint of something like a black hole appeared at the end of the 18th century, when the great French physicist Pierre-Simon de Laplace and the English cleric John Mitchell expressed the same remarkable idea. All physicists of those days were seriously interested in astronomy. Everything that was known about the celestial bodies was revealed by the light that they emitted or, as in the case of the Moon and planets, reflected. Although by the time of Mitchell and Laplace half a century had passed since the death of Isaac Newton, he still remained the most influential figure in physics. Newton believed that light was made up of tiny particles - corpuscles, as he called them - and if so, why shouldn't light be affected by gravity? Laplace and Mitchell wondered whether there could be a star so massive and dense that light could not overcome its gravitational pull. Should such stars, if they exist, be completely dark and therefore invisible?
Let's temporarily call any massive celestial body a star, be it a planet, an asteroid or a real star. The Earth is just a small star, the Moon is an even smaller star, etc. According to Newton's law of gravity, the gravitational influence of a star is proportional to its mass, so it is quite natural that the escape velocity also depends on the mass of the star. But mass is only half the battle. The other half is the radius of the star. Imagine that you are standing on the earth's surface and at this time a certain force begins to compress the Earth, reducing its size, but without losing mass. If you remain on the surface, the compression will bring you closer to each and every atom of the Earth. When approaching a mass, the effect of its gravity intensifies. Your weight - a function of gravity - will increase, and, as you might guess, it will be increasingly difficult to overcome gravity. This example illustrates a fundamental physical law: compression of a star (without loss of mass) increases its escape velocity.
Now imagine the exact opposite situation. For some reason the Earth is expanding, so you are moving away from the mass. Gravity on the surface will become weaker, which means it will be easier to escape from it. The question posed by Mitchell and Laplace was whether a star could have such a large mass and such a small size that its escape velocity would exceed the speed of light.
When Mitchell and Laplace first expressed these prophetic thoughts, the speed of light (denoted by the letter c) has been known for over a hundred years. Danish astronomer Ole Roemer in 1676 determined that it was a colossal value - 300,000 km (that's about seven revolutions around the Earth) in one second:
c= 300,000 km/s.
At such colossal speeds, it would require an extremely large or extremely concentrated mass to contain light, but there is no apparent reason why one could not exist. Mitchell's report to the Royal Society made the first mention of objects that John Wheeler would later call black holes.
It may surprise you that among all forces, gravity is considered extremely weak. Although an obese lifter and a high jumper may feel differently, there is a simple experiment that demonstrates how weak gravity really is. Let's start with a small weight: let it be a small ball of foam. In one way or another we will give it a static electric charge. (You can just rub it on your sweater.) Now hang it from the ceiling on a thread. When it stops spinning, the thread will hang vertically. Now bring another similar charged object to the hanging ball. The electrostatic force will push away the suspended weight, causing the thread to tilt.
The same effect can be achieved using a magnet if the hanging weight is made of iron.
Now remove the electrical charge or magnet and try to deflect the suspended load by bringing very heavy objects towards it. Their gravity will attract the load, but the effect will be so weak that it cannot be noticed. Gravity is extremely weak compared to electrical and magnetic forces.
But if gravity is so weak, why can't we jump to the moon? The fact is that the huge mass of the Earth, 6·10 24 kg, easily compensates for the weakness of gravity. But even with such a mass, the speed of escape from the surface of the Earth is less than one ten thousandth the speed of light. To increase the escape speed c, the dark star invented by Mitchell and Laplace must be stunningly massive and stunningly dense.
To get a feel for the scale of the magnitudes, let's look at the escape velocities for different celestial bodies. To leave the Earth's surface, an initial speed of about 11 km/s is needed, which, as already noted, is approximately 40,000 km/h. By earthly standards this is very fast, but compared to the speed of light it is similar to the movement of a snail.
On an asteroid you would have a much better chance of leaving the surface than on Earth. An asteroid with a radius of 1.5 km has an escape velocity of about 2 m/s: just jump. On the other hand, the Sun is much larger than the Earth, both in size and mass. These two factors act in opposite directions. A large mass makes it difficult to leave the surface of the Sun, but a large radius, on the contrary, makes it easier. Mass, however, wins out, and the escape velocity for the solar surface is about fifty times greater than for the Earth's. But it still remains much below the speed of light.
But the Sun will not remain its current size forever. Eventually the star will run out of fuel, and the pressure that pushes it, supported by internal heat, will weaken. Like a giant vice, gravity will begin to compress the star to a small fraction of its original size. In about five billion years, the Sun will burn out and collapse into the so-called white dwarf with a radius approximately the same as that of the Earth. To leave its surface, you will need a speed of 6400 km/s - this is a lot, but still only 2% of the speed of light.
If the Sun were a little - one and a half times - heavier, the additional mass would squeeze it more tightly than to the state of a white dwarf. The electrons in the star would be pressed into the protons, forming an incredibly dense ball of neutrons. A neutron star is so dense that just one teaspoon of its material weighs several billion tons. But the neutron star is not yet the desired dark one; the speed of escape from its surface is already close to the speed of light (about 80% c), but still not equal to it.
If the collapsing star is even heavier, say five times as massive as the Sun, then even a dense ball of neutrons will not be able to resist the compressive gravitational pull. As a result of the final inward explosion, the star will shrink into singularity - a point of almost infinite density and destructive power. The escape velocity for this tiny nucleus is many times greater than the speed of light. This is how a dark star appears, or, as we say today, a black hole.
Einstein was so displeased with the idea of black holes that he denied the possibility of their existence, arguing that they could never form. But whether Einstein likes it or not, black holes are real. Today, astronomers easily study them, not only single collapsed stars, but also black giants located in the centers of galaxies, formed by the merger of millions and even billions of stars.
The sun is not massive enough to collapse into a black hole on its own, but if it were helped by being squeezed in a cosmic vice to a radius of 3 km, it would become a black hole. You might think that if you then loosen the grip, it will swell again, say, to 100 km, but in reality it will be too late: the matter of the Sun will go into a state of some kind of free fall. The surface will quickly cover a radius of one mile, one meter, one centimeter. No stops are possible until a singularity is formed, and this collapse is irreversible.
Imagine that we are close to a black hole, but at a point other than the singularity. Will the light leaving this point be able to leave the black hole? The answer depends both on the mass of the black hole and on the specific location from which the light begins to travel. An imaginary sphere called horizon, divides the Universe into two parts. Light that comes from inside the horizon will inevitably be pulled into the black hole, but light coming from outside the horizon can escape the black hole. If the Sun one day became a black hole, the radius of its horizon would be about 3 km.
The radius of the horizon is called Schwarzschild radius part of the astronomer Karl Schwarzschild, who was the first to study the mathematics of black holes. The Schwarzschild radius depends on the mass of the black hole; in fact, it is directly proportional to it. For example, if the mass of the Sun is replaced by a thousand solar masses, a light beam emitted from a distance of 3 or 5 km will have no chance to escape, since the radius of the horizon will increase a thousandfold, to three thousand kilometers.
The proportionality between mass and Schwarzschild radius is the first thing physicists learned about black holes. The Earth is about a million times less massive than the Sun, so its Schwarzschild radius is a million times smaller than the Sun's. To turn into a dark star, it would have to be compressed to the size of a cranberry. For comparison: in the center of our Galaxy lurks a giant black hole with a Schwarzschild radius of about 150,000,000 km - approximately the same as the Earth’s orbit around the Sun. And in other corners of the Universe there are even larger monsters.
Tides and the 2000 Mile Man
What makes the seas rise and recede as if they were taking two deep breaths every day? The point, of course, is the Moon, but how does she do it and why twice a day? I'll explain now, but first I'll talk about the fall of the 2000-mile man.
Imagine a giant, 2,000 miles (3,200 km) tall from crown to toe, falling feet first from space to Earth.
Far out in outer space, gravity is weak, so weak that he feels nothing. However, as he approaches the Earth, a strange sensation arises in his long body: but this is not a feeling of falling, but a feeling of tension.
It's not a matter of the giant accelerating towards the Earth. The reason for his discomfort is that gravity in space is not uniform. Far from Earth it is almost completely absent. But as it gets closer, gravity increases. For a 2,000-mile man, this causes trouble even when he is in free fall. The poor fellow is so tall that his legs are pulled in much more strongly than his head. The resulting effect is an unpleasant feeling, as if his legs and head are being pulled in opposite directions.
Perhaps he could avoid the sprain by falling horizontally, with his legs and head at the same height. But when the giant tries this, he will encounter another inconvenience: the feeling of tension is replaced by an equal feeling of compression. He feels his head being pressed against his legs.
To understand why this happens, let's imagine for a moment that the Earth is flat. Vertical lines with arrows indicate the direction of gravitational forces, naturally pulling straight down.
Moreover, the force of gravitational attraction is exactly the same. A 2,000-mile man would have no problem in such conditions whether he fell vertically or horizontally—at least until he reached the ground.
But the Earth is not flat. Both the strength and the direction of its gravity change. Instead of pulling in one direction, gravity pulls straight towards the center of the planet, as shown here:
This creates new problems for the giant as he falls horizontally. The forces acting on his head and legs will not be the same, since gravity pulling them towards the center of the Earth will press his head towards his legs, causing a strange squeezing sensation.
Let's return to the issue of ocean tides. The reason for the twice daily rise and fall of the sea is the same thing that causes discomfort to a 2,000-mile man: the inhomogeneity of gravity. Only in this case it is lunar gravity, not terrestrial gravity. The lunar gravity is strongest on the oceans on the side of the Earth that faces the Moon, and weakest on the opposite side. It may seem that the Moon should produce a single ocean hump on its near side, but this is a mistake. For the same reason that a tall man's head is pulled away from his feet, water on both sides of the Earth - near and far - bulges above its surface. One way to understand this is to consider that on the near side the Moon pulls water away from the Earth, and on the far side it pulls the Earth away from the water. The result is two humps on opposite sides of the Earth, facing towards and away from the Moon. While the Earth makes one revolution under these humps, each point on its surface experiences two tides.
Deforming forces caused by changes in the magnitude and direction of gravitational attraction are called tidal forces, be they caused by the Moon, Earth, Sun or any other massive celestial body. Can a normal-sized person feel tidal forces, for example, when jumping from a diving board into water? No, but only because we are so small that the earth's gravitational field practically does not change within the body.
Descent into the Underworld
Descended along a wooded path into the darkness of the abyss.
- Dante. The Divine Comedy
For a person falling into a solar mass black hole, the tidal forces will no longer be so weak. The enormous mass compressed into the tiny volume of the black hole makes gravity near the horizon not only very strong, but also extremely heterogeneous. Long before approaching the Schwarzschild radius, at a distance of more than 100,000 km from the black hole, tidal forces will cause severe discomfort. Like a 2,000-mile man, you will find yourself too large for the black hole's rapidly changing gravitational field. By the time you approach the horizon, you are deformed - almost like toothpaste being squeezed out of a tube.
There are two ways to deal with tidal forces on the horizon of a black hole: make yourself smaller or make the black hole bigger. A bacterium wouldn't notice tidal forces on the horizon of a solar-mass black hole, but you wouldn't feel tidal forces on the horizon of a million-solar-mass black hole. This may seem strange, since the gravity of a more massive black hole is stronger. But this judgment ignores an important fact: the horizon of a large black hole is so large that it will appear almost flat. Near the horizon, the gravitational field will be very strong, but almost uniform.
If you know a little about Newton's theory of gravity, you can calculate the tidal forces on the horizon of a dark star. And then it turns out that the larger and more massive it is, the less tidal forces on the horizon. Therefore, crossing the horizon of a very large black hole would be an unremarkable event. But in the end, even the greatest of black holes cannot escape tidal forces. Its size will only delay the inevitable. In the end, the inevitable fall to the singularity will be as terrible as any torture invented by Dante or used by Torquemada in the trials of the Spanish Inquisition. (The rack comes to mind.) Even the smallest bacterium will be torn apart along the vertical axis and flattened along the horizontal axis. Small molecules will live longer than bacteria, and atoms will live a little longer. But sooner or later the singularity will prevail even over an individual proton. I don’t know if Dante is right when he claims that no sinner will escape the torments of hell, but I am absolutely sure that nothing can withstand the monstrous tidal forces near the singularity of a black hole.
But, despite all the alienness and brutality of the properties of the singularity, it does not contain the deepest mysteries of the black hole. We know what happens to any object that manages to fall into a black hole - its fate is unenviable. However, whether we like the singularity or not, it does not come close to the horizon in terms of paradox. In modern physics, almost nothing has caused more confusion than the question of what happens to matter as it falls through the horizon? Any answer you give will probably be wrong.
Mitchell and Laplace lived long before Einstein was born and could not have known about the two discoveries he made in 1905. The first of these was the special theory of relativity, which is based on the principle: nothing - neither light nor anything else can ever exceed the speed of light. Mitchell and Laplace understood that light could not escape from a dark star, but they had no idea that this was impossible for anything else.
Einstein's second discovery, made in 1905, was that light really consists of particles. Soon after Mitchell and Laplace put forward their ideas about dark stars, Newton's corpuscular theory of light fell into disgrace. Evidence has accumulated that light is made of waves, like sound waves or those that travel along the surface of the sea. By 1865, James Clerk Maxwell showed that light consists of oscillating electric and magnetic fields, which propagate through space at the speed of light, and the corpuscular theory has completely ceased to show signs of life. No one seemed to realize that electromagnetic waves could also be attracted by gravity, so dark stars were forgotten.
Forgotten until, in 1917, astronomer Karl Schwarzschild solved the equations of Einstein's new, general theory of relativity and rediscovered dark stars.
Equivalence principle
Like most of Einstein's work, general relativity was complex and sophisticated, but it was based on extremely simple observations. In fact, they are so basic that they were available to everyone, but no one made them.
It was Einstein's style to draw far-reaching conclusions from the simplest thought experiments. (Personally, I admire this way of thinking more than any other.) In the case of general relativity, the thought experiment involved an observer in an elevator. Textbooks often modernize experiments by replacing the elevator with a rocket, but in Einstein's era elevators were an exciting new technology. He was the first to imagine an elevator floating freely in outer space, far from any gravitating objects. Anyone in such an elevator will experience complete weightlessness, and the projectiles will fly past in perfectly straight trajectories at a constant speed. The same thing will happen with light rays, but, of course, at the speed of light.
Einstein then imagined what would happen if he began to accelerate the elevator upward, say, with the help of a cable attached to some distant anchor, or by means of rockets mounted under the bottom. Passengers will begin to be pressed to the floor, and the trajectories of the projectiles will begin to bend downward, forming parabolic orbits. Everything will be exactly the same as under the influence of gravity. Everyone has known this since Galileo, but it fell to Einstein to turn this simple fact into a powerful new principle of physics. The equivalence principle states that there is absolutely no difference between the effects of gravity and the effects of acceleration. No experiment carried out inside an elevator will distinguish whether the elevator is at rest in a gravitational field or accelerating in outer space.
This in itself was not surprising, but it had important consequences. At the time Einstein formulated the equivalence principle, very little was known about how gravity affects other phenomena such as the flow of electricity, the behavior of magnets, or the propagation of light. According to Einstein's approach, we should have started by understanding how all these phenomena are affected by acceleration. At the same time, no new physics usually appeared. All Einstein did was imagine what known phenomena would look like in an accelerating elevator. And then the equivalence principle told him what the effect of gravity would be.
The first example examined the behavior of light in a gravitational field. Imagine a beam of light moving horizontally from left to right across an elevator. If the elevator were to move freely, away from any gravitating masses, the light would travel in a perfectly straight horizontal line.
But now let's say that the elevator accelerates upward. The light starts moving from the left side of the elevator in a horizontal direction, but because the elevator is accelerating, by the time it arrives on the other side, the light will have a downward component of motion. From one point of view, the elevator is accelerating upward, but, from another, it seems to its passengers that the light is accelerating downward.
In fact, the light beam is bent in the same way as the trajectory of a very fast particle. This result does not depend in any way on whether the light consists of waves or particles; it is simply an upward acceleration effect. But, Einstein reasoned, if acceleration causes the path of a light beam to bend, gravity should do the same. In fact, we can say that gravity attracts light and causes it to fall. This completely coincides with the guesses of Mitchell and Laplace.
There is, however, another side to the coin: if acceleration can simulate the effect of gravity, then it can destroy it. Imagine the same elevator no longer infinitely far in outer space, but at the top of a skyscraper. If it is stationary, passengers experience all the effects of gravity, including the bending of light rays passing across the elevator. But then the cable snaps and the elevator begins to accelerate towards the ground. During the short time of free fall, gravity inside the elevator appears to have completely disappeared. Passengers float around the cabin, losing the sense of up and down. Particles and beams of light move in perfectly straight lines. This is the flip side of the equivalence principle.
Sewage, blind and black holes
Anyone who tries to describe modern physics without mathematical formulas knows how useful analogies can be. For example, it is very convenient to think of an atom as a miniature planetary system, and using ordinary Newtonian mechanics to describe dark stars helps those who are not ready to dive into the higher mathematics of general relativity. But analogies have their limitations, and a dark star as an analogue of a black hole stops working if you go deep enough. There is another, better analogy. I learned about it from one of the pioneers of quantum mechanics of black holes, Bill Unruh. Perhaps I especially like it because my first profession is a plumber.
Imagine an endless shallow lake. It is only a few feet deep, but it extends indefinitely in the horizontal plane. Blind tadpoles live throughout the lake; they spend their entire lives here, not seeing light, but they make excellent use of sound to locate objects and communicate. There is one inviolable rule: nothing can move in water faster than the speed of sound. For most tasks, this speed limit is not significant, since tadpoles move much more slowly.
But there is danger in the lake. Many tadpoles discover it too late to escape, and no one has ever come back to tell what happened to them. There is a drainage hole in the center of the lake. The water flows through it into an underground cave, where it breaks against deadly sharp rocks.
If you look at the lake from above, you can see that the water is moving towards the drain. Far from it, the speed of the water is undetectably small, but the closer it is, the greater it becomes. Suppose that the drain removes water so quickly that at some distance its speed reaches the speed of sound. Even closer to the outlet, the flow becomes supersonic. This is indeed a very dangerous drain.
Tadpoles swimming in water, familiar only with their liquid habitat, never know how fast they are actually moving; everything around them is pulled down by the water at the same speed. The big danger is that they can get sucked into the drain and die on sharp rocks. In reality, as soon as one of them crosses the radius at which the current speed exceeds sound, it is doomed. Once past this point of no return, he will be unable to overcome the current or even send a warning to others still in the safe area (no acoustic signal can travel faster than sound in water). Unruh names such a waste hole and its point of no return blind hole - deaf in the sense of silent, since no sound can come out of it.
One of the most interesting properties of the point of no return is that an unwary observer passing through it will not initially notice anything unusual. There are no warning signs or sirens, no obstacles to stop him, nothing to alert him to impending danger. At some moment it seems that everything is wonderful, and at the next moment - too. Passing the point of no return is a non-event.
And now a free-driving tadpole named Alice swims towards the drain, singing a song for her friend Bob, who remains in the distance. Like all her blind relatives, Alice has a rather poor repertoire. The only note it can sing is the middle octave "C" at a frequency of 262 vibrations per second, or in technical parlance, 262 hertz (Hz). While Alice is away from the drain, her movement is almost imperceptible. Bob listens to the sound of Alice's voice and hears "C" of the first octave. But when Alice picks up speed, the sound becomes lower, at least in Bob's perception; “do” changes to “si”, then to “a”. This is caused by the so-called Doppler shift, which can be noticed when a fast train passes by with its whistle on. As the train approaches, the sound of the whistle seems higher to you than to the driver in the cab. When the whistle passes you and begins to move away, the sound decreases. Each successive vibration is forced to travel a little further than the previous one, and it reaches your ear with a slight delay. The time between successive sound vibrations increases and you hear a lower frequency. Moreover, if the train picks up speed as it moves away from you, the perceived frequency will become lower and lower.
The same thing happens to Alice's musical note as she approaches the point of no return. Bob first hears a frequency of 262 Hz. Then it drops to 200 Hz, then to 100 Hz, to 50 Hz, etc. Sound emitted very close to the point of no return will take a very long time to travel away; the movement of water almost completely dampens the outward speed of sound, slowing it down almost to a stop. Soon the sound becomes so low that without special equipment Bob can no longer hear it.
Bob may have special equipment that allows him to focus sound waves and capture images of Alice as she approaches the point of no return. But successive sound waves take longer and longer to travel to Bob, causing everything about Alice to appear slow. Her voice gets lower; the movements of her paws slow down almost to a complete stop. The very last swing that Bob sees stretches out to infinity. In fact, Bob thinks it will take Alice forever to reach the point of no return.
Meanwhile, Alice does not notice anything unusual. She drifts serenely beyond the point of no return, feeling no slowdown or acceleration. She realizes the danger only later, already falling onto the deadly rocks. Here we see one of the key features of black holes: different observers paradoxically perceive the same events in completely different ways. To Bob, judging by the sounds coming, it seems that it will take Alice forever to reach the point of no return, but for Alice it can happen in the blink of an eye.
You probably already guessed that the point of no return is an analogue of the horizon of a black hole. Replace sound with light (remember, nothing can travel faster than light), and you get a very accurate illustration of the properties of a Schwarzschild black hole. As with the drain hole, anything that has crossed the horizon can no longer escape back or even remain at rest. The danger in a black hole is not the sharp rocks, but the singularity located in the center. All matter within the horizon is pulled towards a singularity, where it will be compressed to infinite pressure and density.
Armed with the analogy of a blind hole, you can clarify for yourself many of the paradoxical properties of black holes. Let, for example, Bob is no longer a tadpole, but an astronaut on a space station orbiting a black hole at a safe distance. Alice, falling towards the horizon, does not sing - there is no air in outer space to carry her voice - but gives signals with a blue flashlight. As it falls, Bob sees the light shift in frequency from blue to red, then to infrared, to microwaves, and finally to low-frequency radio waves. Alice herself looks more and more lethargic, slowing down almost to a complete stop. Bob will never see her cross the horizon; from his point of view, it will take Alice an infinite amount of time to reach the point of no return. But Alice, in her frame of reference, calmly falls through the horizon and begins to feel something strange only as she approaches the singularity.
The horizon of a Schwarzschild black hole is located at the Schwarzschild radius. Although Alice is doomed after crossing it, she still has, like the tadpoles, a little time before she dies in the singularity. But how much exactly? It depends on the size, that is, on the mass, of the black hole. The greater the mass, the greater the Schwarzschild radius and the more time Alice has. In a black hole with the mass of the Sun, it would only have ten microseconds. In a black hole, which is located at the center of the galaxy and can have a billion times more mass, Alice would have a billion microseconds, or about half an hour. One can imagine an even larger black hole, in which Alice could live her entire life and perhaps even several generations of her descendants would have time to grow old and die before being destroyed by the singularity.
Of course, according to Bob's observations, Alice will never reach the horizon. So who is right? Will it reach the horizon or not? What's really happening? AND really is this? After all, physics is an observational and experimental science, so one might give preference to Bob's reliable observations, even if they are in obvious contradiction with Alice's description of events. (We'll return to Alice and Bob after we discuss the amazing quantum properties of black holes discovered by Jacob Bekenstein and Stephen Hawking.)
The drain analogy is good for many purposes, but like all analogies, it has its limits. For example, when an object falls through the horizon, its mass is added to the mass of the black hole. Increasing mass means expanding the horizon. This can certainly be modeled in analogy with a waste outlet, say by installing a pump in it to control the flow. Every time something falls into the drain, the pump must increase power a little, speeding up the flow and pushing the point of no return a little further. But such a model quickly loses its simplicity.
Another property of black holes is that they themselves are capable of moving. If you place a black hole in the gravitational field of another mass, it will accelerate like any other massive object. It could even fall into a larger black hole. If you try to capture all these properties of real black holes in a sewer analogy, it becomes more complex than the mathematics it avoids. But despite these limitations, sink is a very useful concept for understanding the basic properties of black holes without mastering the equations of general relativity.
A few formulas for those who love them
I wrote this book for non-mathematical readers, but for those who like a little math, here are a few formulas and what they mean. If you're not interested, just move on to the next chapter. This is not an exam.
According to Newton's law of gravity, every object in the Universe attracts all other objects, and the force of gravity is proportional to the product of their masses and inversely proportional to the square of the distance between them:
This is one of the most famous equations in physics, almost as widely known as E= mc 2 (this famous equation relates energy E with mass m and the speed of light c).
There is strength on the left side F, acting between two masses, such as the Moon and the Earth or the Earth and the Sun. There is a large mass on the right side M and less weight m. For example, the mass of the Earth is 6·10 24 kg, and the mass of the Moon is 7·10 22 kg. The distance between the masses is indicated D. The distance from the Earth to the Moon is about 4·10 8 m.
The last notation in the equation, G, is a numerical constant called Newton's gravitational constant. This value cannot be derived purely mathematically. To find its value, it is necessary to measure the force of attraction between two known masses located at some known distance. Once this is done, the force acting between any two masses at any distance can be calculated. Ironically, Newton never learned the value of his own constant. The fact is that gravity is so weak, and the magnitude G, accordingly, is so small that it was not possible to measure it until the end of the 19th century. By that time, the English physicist Henry Cavendish had developed an ingenious way to measure extremely small forces. Cavendish discovered that the force acting between a pair of kilogram masses separated by one meter was approximately 6.7 10 -11 newtons. (A newton is a unit of force in the metric C system. It is approximately a tenth of the weight of one kilogram.) Thus, the value of the gravitational constant in the C system is:
G= 6.7×10 –11.
While studying the consequences of his theory, Newton made one important discovery concerning the special properties of the inverse square law. When you measure your own weight, part of the gravitational force pulling you towards the Earth is due to the mass directly under your feet, another part is due to the mass deep inside the Earth, and part is due to the contribution of masses on the opposite side of the Earth 12.5 thousand away kilometers. But thanks to a mathematical miracle, it can be considered that all the mass is concentrated at one point directly in the geometric center of the planet.
This convenient fact allowed Newton to calculate the escape velocity of a large object by replacing its extended mass with a tiny massive point. And here is the result:
Note translation ), and the following note is given to it: “The American Heritage Dictionary of the English Language (4th ed.) defines projectile as “an object shot, thrown, or otherwise set in motion, such as a bullet, that does not have the power of self-propulsion.” Can a projectile be a single particle of light? According to Mitchell and Laplace, the answer is yes.
The escape velocity is also called the second cosmic velocity. The first escape velocity is considered to be the one that is sufficient to enter a circular orbit near the Earth's surface. - Note translation
The idea of escape velocity is an idealization that neglects effects such as, say, air resistance, which would cause the object to require much higher speed.
The mass of the Sun is about 210 30 kg. This is about a million times the mass of the Earth. The radius of the Sun is about 70,000 km, that is, about a hundred on Earth.
Professor George Ellis reminded me of a subtlety associated with variable flow. In this case, the point of no return does not coincide exactly with the point where the speed of water matches the speed of sound. In the case of black holes, there is a similar subtle difference between the apparent horizon of visibility and the true one.