"Battle of the Black Hole". Chapter from a book

briefly about me: "at the sound of a flute, he loses his will when he hears about black holes and other cosmos." Unfortunately, I did not receive education at the Faculty of Physics, so I talk about the book exclusively as a humanist (search for factual errors and misconceptions in the text of the mod off).

Writing books about quantum mechanics can now be fun. Gluons, quarks, wormholes, hot quark soup, quantum shivers and other terms play “stand up children, stand in a circle”, arranging a round dance around main topic: black holes. Stephen Hawking, a superstar in the world of science, sees black holes as information eaters, not receptacles in which information is stored on demand. The author of the book defends the theory of storage-archive on demand, presenting black hole something like a non-spill inkwell (while Hawking adheres to the shredder theory). How heavily archived can information fall into black holes? Susskind writes that even a one-kilogram brick is mostly a void that can be compacted to the size of a pinhead and even to the size of a virus. Black holes are not only extremely compressed stars, but also the ultimate reservoirs for information, where all information is densely packed, like cannonballs stacked in rows (except smaller size thirty-four orders of magnitude). 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 the arguments of various scientists who, one after another, refute many of the usual facts about black holes. A scientist such as Dennis Skiama concluded that black holes evaporate: electromagnetic radiation carries away some 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 able to move. If you place a blackhole in the gravitational field of another mass, it will accelerate like any other massive object. It may 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 adored quantum mechanics and lived and breathed Bohr's philosophy." Susskind will share his observations about which of the physicists at the age of seventy preferred to contemplate girls in bikinis instead of talking about science, and how they behaved. For example, about Feynman: "I met a lion, and he did not disappoint me" and "Feynman's ego was brutal, but next to him it was a lot of fun."

The advantage of Susskind's book is that he allows himself not to stand on ceremony with words, can say that the scientific picture of the world of the eighteenth century was rather dull, the uncertainty principle is a strange and audacious statement, and an ideal crystal, like an ideal BMW, has no entropy at all. The imagery and expressiveness of his text is valuable, however there are a couple of facts denominating the significance of the book. The first is a trifle, an “easter egg”: without quotes, there is a very bright direct quote from Hawking “I was strongly advised to limit myself to a single formula: E = mc2. I was told that with each additional equation, sales of the book would fall by ten thousand copies. And the second one is a little more serious: after reading the text, there is a feeling that Susskind, who entered the battle with Hawking, never once had a real discussion with him, “fighting” only in his imagination.

Chapter after chapter, Susskind talks about how his thoughts rarely moved away from the person of Stephen Hawking, the story is more and more 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 was " hundred pound theoretical physicist in a chair with a motor. In the attachment there is a scan of a document confirming the fact of Hawking's dispute with a third party on a topic similar to the "confrontation" Hawking / Susskind (and in the end Hawking admitted defeat). Well, if you forgive the scientist for his frantic fanaticism, you can learn 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 smoky pot, heat it up to a few hundred degrees, and it will begin to glow red. Still 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 will say: it is difficult to imagine anything further from black than the Sun. Indeed, the surface of the Sun emits great amount light, but it does not reflect anything. This makes it a blackbody for a physicist."

P.S. I first learned about the fact that entropy is growing from the song "Civil Defense"; if I read more encyclopedias, then I would have known more subtext about the "black color of the sun" (see the quote "the sun is black body" higher).

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 black hole phenomenon, the now famous British physicist Stephen Hawking, stated that this is exactly what happens. 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 for many years with Stephen Hawking about the nature of black holes, until, finally, in 2004, he admitted his mistake. Brilliant and remarkably easy to read, this book tells the compelling story of this decades-long scientific controversy that has radically changed the way physicists view the nature of reality. The new paradigm led to the stunning conclusion that everything in our world - this book, your home, yourself - is just a kind of hologram projected from the edges of the universe. The book is included in the Library of the Dynasty Foundation. The Dynasty Foundation for Non-Commercial Programs was founded in 2001 by Dmitry Borisovich Zimin, Honorary President of Vimpelcom. Priority directions The activities of the Foundation 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 for the publication of modern popular science books selected by expert scientists.

Part 1. The coming storm
1. First thunder

San Francisco, 1983.

By the time the first skirmish took place in the attic of Jack Rosenberg's mansion, the menacing clouds of war had been gathering for more than 80 years. Jack, also known as Werner Erhard, was a guru, a slick shopkeeper, and a bit of a swindler. Until the early 1970s, he was just Jack Rosenberg, an encyclopedia salesman. But one day, as he was driving across the Golden Gate Bridge, a revelation came upon him. He will save the world and, thanks to this, will become enormously rich. All it takes is a cool name and new approach to the point. The name would be Werner (after Werner Heisenberg) Erhard (after the German politician Ludwig Erhard), and the new approach would be Erhard's Training Seminars, est. And he succeeded, if not in saving the world, at least in getting rich. Thousands of shy, insecure people paid hundreds of dollars for exhausting rants at sixteen-hour motivational seminars by Werner himself or one of his many students, during which (according to rumors) it was forbidden even to go to the toilet.

It was much cheaper and faster than psychotherapy, and somehow it worked. People came in shy and insecure, and after the seminars they looked strong, confident and friendly - just like Werner: Never mind that sometimes they seemed like maniac robots with shaky hands. They did feel better. "Training" even became the subject of a very funny film "Semi-Tough" by Burt Reynolds. Werner was constantly surrounded by frenzied EST fans. "Slaves" is perhaps too much strong word Let's call them volunteers. ECT-trained cooks cooked his meals, chauffeurs drove him around the city, his mansion was filled with all sorts of servants. But, ironically, Werner himself was also a rabid fan - a physics fan.

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Leonard Susskind

Black Hole Battle

My battle with Stephen Hawking for a world safe for quantum mechanics

What breathes life into these equations and creates the universe that they could describe?

- Stephen Hawking

Introduction

So much to grok, and had to start almost from scratch.

- Robert Heinlein. Stranger in the land of strangers

Somewhere in the East African savannah, a middle-aged lioness hunts down her dinner. She would have preferred slow prey of old age, but all that is there is only a young frisky antelope. The attentive eyes of the victim are ideally placed on the sides of his head, so that in anticipation of an attack, keep under observation the entire surrounding area. The eyes of a predator, on the other hand, look straight ahead, focusing on the prey and estimating the distance.

This time, the antelope's "wide-angle scanners" missed a predator that got within throwing distance. The strong hind legs of the lioness push her towards the frightened prey. The eternal chase begins again.

Although burdened by years, the big cat is an excellent sprinter. At first, the gap is reduced, but from sudden movements, the powerful muscles of the lioness experience oxygen starvation and gradually weaken. Soon, the natural endurance of the antelope wins: at some point, the relative speed of the cat and its prey changes sign, the lag that was shrinking before begins to grow. The lioness feels that her fortune has betrayed her, Her Royal Majesty admits defeat and returns to her ambush in the bushes.

Fifty thousand years ago, a tired hunter finds a stone-filled entrance to a cave. If you move a heavy obstacle, you get a safe place to rest. Unlike its ape-like ancestors, the hunter stands upright. But in this position, he unsuccessfully pushes the boulder. Choosing a more suitable angle, he puts 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 right direction. The stone is moving.

Distance? Speed? Sign change? Injection? Force? component? What incredibly complex calculations are going on in the brain of a hunter, let alone a cat? These technical concepts are commonly found in high school physics textbooks. Where did the cat learn to measure not only prey speed but, more importantly, relative speed? Did the hunter take physics lessons to understand the concept of force? And more trigonometry to use sines and cosines to calculate the components?

The truth, of course, is that all complex life forms have built-in instinctive concepts of physics that are hard-wired 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 size of the brain in humans has allowed these instincts to develop into concepts that we operate consciously.

Self-flashing

In fact, we are all classic physicists. We “feel” force, speed and acceleration. Robert Heinlein, in the science fiction novel Alien in Alien Land (1961), coined the word "grok" to express this deeply intuitive, almost physiological understanding of the phenomenon. I play strength, speed and acceleration. I'm groking 3D space. I grok the time and the number 5. The trajectories of a stone or an arrow lend themselves to grok. But my standard built-in groker 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 Heisenberg's uncertainty principle.

With the advent of the 20th century, our intuition has fallen into 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 Earth's orbital motion through a hypothetical ether could not be registered. Electron was discovered when my grandfather was in his twenties; when he turned thirty, was published special theory relativity of Albert Einstein, and when he crossed the threshold of middle age, Heisenberg discovered the uncertainty principle. No way could the evolutionary press lead to the development of an intuitive understanding of worlds so radically different from what we are used to. But something in our nervous systems, at least for some of us, turned out to be ready for a fantastic flashing, allowing not only to be interested in obscure phenomena, but also to create mathematical abstractions, sometimes completely counterintuitive, to explain and manipulate these phenomena.

The speed of the first caused the need for flashing - tremendous speed competing with 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 great that for everyone except scientists, it does not seem to move at all, but simply appears instantly, when it is turned on. Ancient people did not need firmware to operate at ultra-high speeds, such as the speed of light.

Flashing in the question of speed occurred suddenly. Einstein was not a mutant; For ten years, in complete obscurity, he struggled to replace his old Newtonian firmware. But it must have seemed to the physicists of that time that a new type of person suddenly appeared among them - someone capable of seeing the world not as a three-dimensional space, but as a four-dimensional one. space-time.

Then Einstein fought for another ten years, this time in full view of all physicists, to unify what he called special 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, able to bend and fold. It reacts to the presence of matter somewhat like a rubber sheet that sags under load. Formerly space-time was passive, its geometric properties- unchanged. AT general theory In 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 amazing paradigm shift began with the discovery that light is made up of particles called photons, or sometimes light quanta. Photon theory light was only a harbinger of the coming revolution; mental exercises on this path proved to be much more abstract than anything that had ever been encountered before. Quantum mechanics is more than new law nature. It caused a change in the rules of classical logic, that is, the usual rules of thought that every sane person uses in reasoning. She seemed insane. But crazy or not, physicists have been able to reflash themselves in accordance with the new logic, which is called quantum. In Chapter 4, I will explain everything you need to know about quantum mechanics. Get ready to be knocked down. It happens to everyone.

Relativity and quantum mechanics have taken a dislike to each other from the very beginning. Attempts to forcibly "marry" them had disastrous consequences - for every question asked by physicists, mathematics gave out monstrous infinities. It took half a century to reconcile quantum mechanics with special relativity, but in the end the mathematical incompatibilities were eliminated. By the early 1950s, Richard Feynman, Julian Schwinger, Shinichiro Tomonaga, and Freeman Dyson laid the groundwork for the unification special theory of relativity and quantum mechanics, called quantum theory fields. However general the theory of relativity (Einstein's synthesis of the special theory of relativity with Newton's theory of gravity) and quantum mechanics remained irreconcilable, and obviously not from a lack of peacemaking efforts. Feynman, Steven Weinberg, Bryce De Witt, and John Wheeler tried to quantize Einstein's equations, but all ended up with mathematical absurdity. Perhaps this was not surprising. Quantum mechanics ruled the world of very light objects. Gravity, on the contrary, seemed to be significant only for very heavy accumulations of matter. It seemed that there was nothing light enough for quantum mechanics to be essential, and at the same time, nothing 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, suitable only for mad scientists and philosophers.

Leonard Susskind

Black Hole Battle

My battle with Stephen Hawking for a world safe for quantum mechanics

What breathes life into these equations and creates the universe that they could describe?

- Stephen Hawking

Introduction

So much to grok, and had to start almost from scratch.

- Robert Heinlein. Stranger in the land of strangers

Somewhere in the East African savannah, a middle-aged lioness hunts down her dinner. She would have preferred slow prey of old age, but all that is there is only a young frisky antelope. The attentive eyes of the victim are ideally placed on the sides of his head, in order to keep the entire surrounding area under observation in anticipation of an attack. The eyes of a predator, on the other hand, look straight ahead, focusing on the prey and estimating the distance.

The truth, of course, is that all complex life forms have built-in instinctive ideas about physics that are hard-wired 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 size of the brain in humans has allowed these instincts to develop into concepts that we operate consciously.

Self-flashing

In fact, we are all classic physicists. We “feel” force, speed and acceleration. Robert Heinlein, in the science fiction novel Alien in Alien Land (1961), coined the word "grok" to express this deeply intuitive, almost physiological understanding of the phenomenon. I play strength, speed and acceleration. I'm groking 3D space. I grok the time and the number 5. The trajectories of a stone or an arrow lend themselves to grok. But my standard built-in groker 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 Heisenberg's uncertainty principle.

With the advent of the 20th century, our intuition has fallen into 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 Earth's orbital motion through a hypothetical ether could not be registered. Electron was discovered when my grandfather was in his twenties; when he turned thirty, Albert Einstein's special theory of relativity was published, and when he crossed the threshold of middle age, Heisenberg discovered the uncertainty principle. No way could the evolutionary press lead to the development of an intuitive understanding of worlds so radically different from what we are used to. But something in our nervous systems, at least some of us, turned out to be ready for a fantastic rewiring, allowing not only to be interested in obscure phenomena, but also to create mathematical abstractions, sometimes completely counterintuitive, to explain and manipulate these phenomena.

The speed of the first caused the need for flashing - a tremendous speed that rivals 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 great that for everyone except scientists, it does not seem to move at all, but simply appears instantly, when it is turned on. Ancient people did not need firmware to operate at ultra-high speeds, such as the speed of light.

Then Einstein fought for another ten years, this time in full view of all physicists, to unify what he called special 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, able to bend and fold. It reacts to the presence of matter somewhat like a rubber sheet that sags under load. Previously, space-time was passive, its geometric properties 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 complicated additional mathematics.

In 1900, five years before Einstein appeared on the scene, another even more amazing 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; mental exercises on this path proved to be much more abstract than anything that had ever been 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 thought that every sane person uses in reasoning. She seemed insane. But crazy or not, physicists have been able to reflash themselves in accordance with the new logic, which is called quantum. In Chapter 4, I will explain everything you need to know about quantum mechanics. Get ready to be knocked down. It happens to everyone.

Relativity and quantum mechanics have taken a dislike to each other from the very beginning. Attempts to forcibly "marry" them had disastrous consequences - for every question asked by physicists, mathematics gave out monstrous infinities. It took half a century to reconcile quantum mechanics with special relativity, but in the end the mathematical incompatibilities were eliminated. By the early 1950s, Richard Feynman, Julian Schwinger, Shinichiro Tomonaga, and Freeman Dyson laid the groundwork for the unification special theory of relativity and quantum mechanics, called quantum field theory. However general the theory of relativity (Einstein's synthesis of the special theory of relativity with Newton's theory of gravity) and quantum mechanics remained irreconcilable, and obviously not from a lack of peacemaking efforts. Feynman, Steven Weinberg, Bryce De Witt, and John Wheeler tried to quantize Einstein's equations, but all ended up with mathematical absurdity. Perhaps this was not surprising. Quantum mechanics ruled the world of very light objects. Gravity, on the contrary, seemed to be significant only for very heavy accumulations of matter. It seemed that there was nothing light enough for quantum mechanics to be essential, and at the same time, nothing 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, suitable only for mad scientists and philosophers.

Horatio - in heaven and earth
There are many things that you 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 the physicists of those days were seriously interested in astronomy. Everything that was known about the celestial bodies was revealed by the light 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 experience the action of gravity? Laplace and Mitchell wondered if there could be a star so massive and dense that light couldn't overcome its gravitational pull. Must such stars, if they exist, be absolutely 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, and so on. According to Newton's law of gravity, the gravitational force of a star is proportional to its mass, so it is only natural that the escape velocity also depends on the star's mass. But mass is only half the battle. The other half is the radius of the star. Imagine that you are standing on earth's surface and at this time a certain force begins to compress the Earth, reducing its size, but without losing mass. If you stay on the surface, then the compression will bring you closer to all the atoms of the Earth without exception. When approaching a mass, the effect of its gravity increases. Your weight - a function of gravity - will increase, and, as you might guess, it will become increasingly difficult to overcome the earth's gravity. This example illustrates a fundamental physical pattern: the contraction of a star (without loss of mass) increases the escape velocity.

Now imagine the exact opposite situation. For some reason, the Earth is expanding so you are moving away from the mass. The gravity on the surface will become weaker, which means it will be easier to break out of it. The question posed by Mitchell and Laplace was whether a star could have such a large mass and such a small size that the escape velocity exceeded 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 Römer in 1676 determined that it is a colossal amount - 300,000 km (that's about seven revolutions around the Earth) in one second:

c= 300,000 km/s.

At such a colossal speed, an extremely large or extremely concentrated mass is required to hold light, but there is no apparent reason why such a thing could not exist. In the Mitchell report Royal Society the first mention of objects that John Wheeler would later call black holes.

It may surprise you that among all the forces, gravity is considered to be 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 light weight: let it be a small ball of styrofoam. In one way or another, we will give it a static electric charge. (You can just rub it on a 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 repel the suspended load, causing the string to tilt.

The same effect can be achieved with a magnet if the hanging weight is made of iron.

Now remove the electric charge or magnet and try to deflect the suspended load by bringing very heavy objects towards it. Their gravity will pull the load, but the effect will be so weak that it cannot be noticed. Gravity is extremely weak compared to electric and magnetic forces.

But if gravity is so weak, why can't you 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 this mass, the speed of escape from the surface of the Earth is less than one ten-thousandth of the speed of light. To increase the speed of escape c, invented by Mitchell and Laplace dark Star should be stunningly massive and stunningly dense.

To get a feel for the scale of the magnitudes, let's look at escape velocities for different celestial bodies. To leave the Earth's surface starting speed about 11 km / s, 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 like 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 jumping is enough. On the other hand, the sun is more earth both in terms of size and weight. These two factors operate in opposite directions. A large mass makes it difficult to leave the surface of the Sun, and a large radius, on the contrary, makes it easier. The mass, however, wins, and the escape velocity for solar surface about fifty times more than for the earth. But it still remains much lower than the speed of light.

But the Sun will not remain at its current size forever. Eventually, the star will run out of fuel, and the pressure that bulges it, supported by internal heat, will weaken. Like a giant vise, gravity will begin to compress the star to a fraction of its original size. Somewhere in five billion years, the Sun will burn out and collapse into the so-called white dwarf with a radius about the same as that of the Earth. To leave its surface would require a speed of 6400 km/s - 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 strongly than before the state of a white dwarf. The electrons in the star would squash into the protons, forming an incredibly dense ball of neutrons. A neutron star is so dense that just one teaspoon of its matter weighs several billion tons. But also neutron star not yet desired dark; escape velocity 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 the mass of the Sun, then even a dense neutron ball cannot resist the compressive gravitational pull. As a result of the final inward explosion, the star will collapse into singularity - point of almost infinite density and destructive force. The escape velocity for this tiny nucleus is many times the speed of light. This is how a dark star appears, or, as we say today, a black hole.

Einstein disliked the idea of black holes so much that he denied the possibility of their existence, arguing that they could never form. But like it Einstein or not, black holes are a reality. 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 you help it by squeezing it in a cosmic grip to a radius of 3 km, it would become a black hole. You might think that if you later loosen the grip, it will inflate again, say, to 100 km, but in reality it will be too late: the Sun’s substance will go into a state of a kind free fall. The surface will quickly overcome 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 near 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 its journey. An imaginary sphere called horizon, divides the universe into two parts. Light coming from inside the horizon will inevitably be sucked into the black hole, but light coming from outside the horizon can leave the black hole. If the Sun were to become a black hole one day, its horizon radius would be about 3 km.

The horizon radius 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 not have a chance to escape, since the radius of the horizon will increase a thousand times, 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. 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 - about the same as earth orbit around the sun. And in other parts of the universe there are even larger monsters.

Tides and the 2000 Mile Man

What makes the seas rise and fall, as if they take 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 2,000-mile man.

Imagine a giant, 2,000 miles (3,200 km) tall from crown to toe, falling feet first from space to Earth.

far in open space gravity is weak, so weak that he can't feel anything. However, as it approaches the Earth, a strange sensation arises in its long body: but this is not a feeling of falling, but a feeling of tension.

It's not about the acceleration of the giant in the direction of the Earth. The reason for his discomfort is that gravity in space is not uniform. Far from the 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 much more strongly than his head. The net effect is an unpleasant feeling, as if his legs and head are being pulled in opposite directions.

Perhaps he could have avoided the strain by falling horizontally with his feet and head at the same height. But when the giant tries it, he will face another inconvenience: the feeling of tension is replaced by an equal feeling of constriction. He feels his head pressed against his legs.

To understand why this happens, imagine for a moment that the Earth is flat. The vertical lines with arrows indicate the direction of the gravitational forces, pulling naturally straight down.

Moreover, the force of gravitational attraction is exactly the same. A 2,000-mile man in such conditions would have no problem falling vertically or horizontally—at least until he hits the ground.

But the earth is not flat. Both the force 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 when it falls horizontally. The forces acting on his head and legs will not be the same, as gravity pulling them toward the center of the earth will press his head against his legs, causing a strange squeezing sensation.

Let us return to the question of ocean tides. The cause of the twice daily rise and fall of the sea is the same that causes discomfort to a 2000-mile man: the non-uniformity of gravity. Only in this case It's lunar gravity, not Earth gravity. moon attraction it has the strongest effect on the oceans on the side of the Earth that faces the moon, and the weakest on opposite side. It may seem that the Moon should spawn a single ocean hump on the near side, but this is a mistake. For the same reason that the head tall man is pulled away from his feet, water from two sides of the Earth - near and far - protrudes above its surface. One way to understand this is to think that on the near side, the Moon is pulling water away from the Earth, and on the far side, the Earth is pulling 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.

The deforming forces caused by changes in the magnitude and direction of gravitational attraction are called tidal forces, whether caused by the Moon, the Earth, the Sun, or any other massive celestial body. Can a person of normal size feel tidal forces, for example, when jumping off a springboard into the water? No, but only because we are so small that the terrestrial gravitational field practically does not change within the body.

Descent into the underworld

He descended through the 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 huge mass compressed into the tiny volume of a black hole makes gravity near the horizon not only very strong, but also extremely inhomogeneous. Long before approaching the Schwarzschild radius, more than 100,000 km from the black hole, tidal forces will cause extreme discomfort. Like a 2,000-mile man, you will be too big for the rapidly changing gravitational field of a black hole. By the time you approach the horizon, you are deformed - almost like toothpaste squeezed out of the tube.

There are two ways to deal with tidal forces at the horizon of a black hole: shrink yourself, or make the black hole bigger. A bacterium wouldn't notice tidal forces at the horizon of a solar-mass black hole, but you wouldn't feel tidal forces at the horizon of a million-solar-mass black hole either. This may seem strange, since the effect of 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 are somewhat familiar with Newtonian gravity theory, you can calculate the tidal forces at 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 in the greatest of black holes, there is no escape from 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 processes of the Spanish Inquisition. (Memory pops up.) Even the smallest bacterium will be torn apart along vertical axis and flattened horizontally. Small molecules will live longer than bacteria, and atoms a little longer. But sooner or later the singularity will prevail even over a single proton. I don't know if Dante is right when he says that no sinner will escape the torments of hell, but I am quite sure that nothing can withstand the monstrous tidal forces near the singularity of a black hole.

But, despite all the strangeness and brutality of the properties of the singularity, it does not contain the deepest mysteries of a 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 even come close to the horizon in terms of paradoxicality. In modern physics, almost nothing has caused more confusion than the question of what happens to matter when it falls through the horizon? Any of your answers 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. Mitchel and Laplace understood that light could not escape from a dark star, but they did not realize that this was impossible for anything else.

Einstein's second discovery, in 1905, was that light really is made up of particles. Shortly after Mitchell and Laplace advanced their ideas about dark stars, Newton's corpuscular theory of light fell into disgrace. Evidence has accumulated that light is made up of waves like sound waves or those that run across the surface of the sea. By 1865, James Clerk Maxwell had shown that light was made up 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. It seems that no one thought that electromagnetic waves can also be attracted by gravity, so dark stars were forgotten.

Forgotten until astronomer Karl Schwarzschild solved the equations of Einstein's new, general theory of relativity in 1917 and rediscovered dark stars.

Principle of equivalence

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 elementary 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 the Einstein era, elevators were exciting. new technology. He was the first to imagine an elevator floating freely in outer space, away from any gravitating objects. Anyone who is in such an elevator will experience complete weightlessness, and the projectiles will fly past in perfectly straight trajectories with 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 the elevator were to be accelerated upwards, say, by means of a cable attached to some distant anchor, or by means of rockets fixed under the bottom. Passengers will begin to be pressed to the floor, and the trajectories of the projectiles will begin to bend down, forming parabolic orbits. Everything will be exactly the same as under the influence of gravity. Everyone has known about this since the days of Galileo, but it fell to Einstein to turn this simple fact into a powerful new one. physical principle. The principle of equivalence states that there is absolutely no difference between the effect of gravity and the effect of acceleration. No experiment carried out inside an elevator will make it possible to distinguish whether an elevator is at rest in a gravitational field or is 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 the Einsteinian approach, one should have started by understanding how all these phenomena are affected by acceleration. At the same time, there usually did not appear any new physics. All Einstein did was imagine what known phenomena would look like in an accelerating elevator. And then the principle of equivalence told him what the effect of gravity would be.

The first example considered the behavior of light in a gravitational field. Imagine a light beam moving horizontally from left to right across an elevator. If the elevator were free to move away from any gravitating masses, the light would travel in a perfectly straight horizontal line.

But now suppose that the elevator is accelerating upwards. The light starts 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 motion component. From one point of view, the elevator is accelerating upward, but, on the other hand, it seems to its passengers that the light is accelerating downward.

In fact, the light beam curves in the same way as the trajectory of a very fast particle. This result does not depend in any way on whether light consists of waves or of particles; it is simply the effect of upward acceleration. But, Einstein reasoned, if acceleration causes the path of a light beam to bend, so should gravity. 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 of the coin: if acceleration can simulate the effects of gravity, then it can destroy it. Imagine the same elevator no longer infinitely far away in outer space, but at the top of a skyscraper. If it is standing, the passengers observe all the effects of gravity, including the bending of the rays of light going across the elevator. But then the cable breaks, and the elevator begins to accelerate towards the ground. For a short time of free fall, it seems that gravity inside the elevator has completely disappeared. Passengers float around the cabin, having lost the sense of up and down. Particles and beams of light move in perfectly straight lines. This is the other side of the equivalence principle.

Waste, 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 that an atom is a miniature planetary system, and using ordinary Newtonian mechanics to describe dark stars helps those who are not ready to dive into higher mathematics general theory of relativity. But analogies have their limitations, and a dark star as a black hole analogy stops working if you go deep enough. There is another, better analogy. I learned about it from one of the pioneers of quantum black hole mechanics, Bill Unruh. Perhaps I especially like her because I am a plumber by my first specialty.

Imagine an endless shallow lake. Its depth is only a few feet, but it extends indefinitely into horizontal plane. Blind tadpoles live all over the lake, they spend their whole lives here without seeing the light, but they perfectly use sound to locate objects and communicate. There is one unbreakable rule: nothing can move faster in water than at 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 yet come back to tell what happened to him. There is a sewer in the center of the lake. Water through it enters an underground cave, where it breaks on deadly sharp rocks.

If you look at the lake from above, you can see that the water is moving towards the drain. Away from it, the speed of water is undetectable, but the closer it gets, the faster it becomes. Let us assume that the drain drains the water so fast that at some distance its speed reaches the speed of sound. Even closer to the drain, the flow becomes supersonic. This is indeed a very dangerous stock.

Water-swimming tadpoles, familiar only with their liquid habitat, never know how fast they actually move; everything around them is being pulled by the water at the same speed. The big danger is that they can be pulled into the drain and die on sharp stones. In fact, as soon as one of them crosses the radius at which the current speed exceeds the sound speed, it is doomed. Having passed this point of no return, he will not be able to overcome the current, nor even send a warning to others who are still in it. safe area(no acoustic signal can travel faster than sound in water). Unruh names such a sewer 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 a careless observer swimming through it will not notice anything out of the ordinary at first. There are no warning signs or sirens, no obstacles to stop him, nothing to tell him of impending danger. At some point, everything seems to be wonderful, and the next moment, too. Passing the point of no return is a non-event.

And now a free-drifting tadpole named Alice is swimming towards the drain, singing a song for her friend Bob, who has remained at a distance. Like all her blind relatives, Alice has a rather poor repertoire. The only note she can sing is the middle octave C at 262 vibrations per second, or, on technical language, 262 hertz (Hz) . As long as 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 as Alice picks up speed, the sound gets lower, at least in Bob's mind; “do” changes to “si”, then to “la”. This is caused by the so-called Doppler shift, you can see it when it passes by Express train with whistle on. As the train approaches, the sound of the whistle sounds higher to you than to the driver in the cab. When the whistle passes you and starts to move away, the sound goes down. Each successive vibration is forced to travel a little longer than the previous one, and it reaches your ear with a slight delay. 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, then the perceived frequency will become lower and lower.

The same thing happens with Alice's musical note as it approaches the point of no return. First, Bob hears a frequency of 262 Hz. Then it drops to 200 Hz, then to 100 Hz, to 50 Hz, and so on. A sound emitted very close to the point of no return will take a very long time to go away; the movement of the water almost completely dampens the outward speed of sound, slowing it almost to a halt. Soon the sound becomes so low that, without special equipment, Bob can no longer hear it.

Bob may have special equipment to focus sound waves and capture images of Alice as she approaches the point of no return. But consistent sound waves it takes longer and longer to get to Bob, making everything about Alice look slow. Her voice is getting lower; the movements of her paws slow down almost to a complete stop. The very last stroke Bob saw stretches out to infinity. In fact, it seems to Bob that it will take Alice forever to reach the point of no return.

Meanwhile, Alice does not notice anything unusual. She drifts serenely past the point of no return, feeling no slowdown or speedup. She realizes the danger only later, already falling on the deadly rocks. Here we see one of key features black holes: different observers, paradoxically, perceive the same events in completely different ways. Bob, judging by the incoming sounds, it seems that it will take Alice an eternity to reach the point of no return, but for Alice it can happen in the blink of an eye.

You have 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 move faster than light), and you get a very accurate illustration of the properties of a Schwarzschild black hole. As with the sewer, anything that has crossed the horizon can no longer escape or even remain still. The danger in a black hole is not sharp rocks, but a singularity in the center. All matter within the horizon is contracted to the singularity, where it will be compressed to infinite pressure and density.

Armed with the dead hole analogy, many of the paradoxical properties of black holes can be clarified. Let, for example, Bob is no longer a tadpole, but an astronaut on space station orbiting at a safe distance around the black hole. 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, 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 would 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 approaching 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 larger the mass, the larger the Schwarzschild radius and the more time Alice has left. In a black hole with the mass of the Sun, it would have only ten microseconds. In a black hole, which is located in the center of the galaxy and can have a mass of a billion times more, Alice will have a billion microseconds, that is, about half an hour. One can imagine an even larger black hole in which Alice could live her whole life and perhaps even several generations of her descendants have time to grow old and die before they are 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 is really happening? And really whether it? After all, physics is observational and experimental science, so one might prefer Bob's reliable observations, even if they are in apparent conflict with Alice's account of events. (We will return to Alice and Bob after we discuss the amazing quantum properties of black holes discovered by Jacob Bekenstein and Stephen Hawking.)

The sink 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. An increase in mass means an expansion of the horizon. This can certainly be modeled in the analogy of a drain, say by installing a pump in it to control the flow. Every time something falls into the drain, the pump should increase the 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 able to move. If you put a black hole in the gravitational field of another mass, it will accelerate like any other massive object. It may even fall into a larger black hole. If you try to capture all these properties of real black holes in the sewer analogy, it becomes more complicated than the mathematics it avoids. But despite these limitations, the stock is a very useful representation to understand basic properties black holes without mastering the equations of general relativity.

A few formulas for those who love them

I wrote this book for non-math readers, but for those who like a bit of math, here are a few formulas and their meaning explained. If you are not interested, just go to next chapter. It's not an exam.

According to Newton's law of gravity, every object in the universe attracts all other objects, and the force of gravity 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 physical equations, it is almost as widely known as E= mc 2 (this famous equation relates the energy E with mass m and the speed of light c).

Power is on the left F acting between two masses, such as the Moon and the Earth or the Earth and the Sun. On the right side there is a large mass 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 the Newtonian 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 at some known distance. Once this is done, the force acting between any two masses at any distance can be calculated. Ironically, Newton never knew the value of his own constant. The fact is that gravity is so weak, and the magnitude G, respectively, is so small that it could not be measured until late XIX centuries. By that time English physicist Henry Cavendish developed an ingenious way to measure extremely small forces. Cavendish found that the force acting between a pair of kilogram masses separated by one meter is approximately 6.7 x 10 -11 newtons. (Newton is the unit of force in metric system Si. It is about a tenth of the weight of one kilogram.) Thus, the value of the gravitational constant in the C system is:

G\u003d 6.7 × 10 -11.

While studying the consequences of his theory, Newton made one important discovery regarding the special properties of the inverse square law. When you measure your own weight, part gravitational force pulling you towards the Earth is due to the mass right under your feet, part is due to the mass deep inside the Earth, and part is the contribution of the masses on the opposite side of the Earth at a distance of 12.5 thousand kilometers. But thanks to a mathematical miracle, we can assume that the entire 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 dot. And here is the result:

Note. transl. ), and the following note is given to it: "The American Heritage Dictionary of the English language(4th ed.) defines a projectile as "a shot, thrown, or otherwise propelled object, such as a bullet, that has no self-propelling capability." 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. First space speed it is considered that which is enough to enter a circular orbit near the surface of the Earth. - Note. transl.

The notion of escape velocity is an idealization that ignores effects such as, say, air resistance, which would require an object to go much faster.

The mass of the Sun is about 210 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 terrestrial.

Professor George Ellis reminded me of a subtlety about variable flow. In this case, the point of no return does not coincide exactly with the place where the speed of water coincides with 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.