Doctor of Philosophy (in physics) K. ZLOSCHASTYEV, Department of Gravity and Field Theory, Institute of Nuclear Research, National Autonomous University of Mexico.
On singularity, information, entropy, cosmology and the multidimensional Unified Theory of Interactions in the light of the modern theory of black holes
Science and life // Illustrations
Ill. 1. Near a collapsing star, the trajectory of a light beam is bent by its gravitational field.
Black holes photographed by the Hubble Space Telescope at the centers of six galaxies. They pull in surrounding matter, which forms spiral arms and falls into the black hole, disappearing forever behind the event horizon.
Ill. 2. Light cone.
Nowadays, it is difficult to find a person who has not heard about black holes. At the same time, it is perhaps no less difficult to find someone who could explain what it is. However, for specialists, black holes have already ceased to be science fiction - astronomical observations have long proven the existence of both “small” black holes (with a mass on the order of the Sun), which were formed as a result of the gravitational compression of stars, and supermassive ones (up to 10 9 solar masses), which were generated by the collapse of entire star clusters in the centers of many galaxies, including ours. Currently, microscopic black holes are being searched for in streams of ultra-high-energy cosmic rays (Pierre Auger International Laboratory, Argentina) and it is even proposed to “set up their production” at the Large Hadron Collider (LHC), which is planned to be launched in 2007 at CERN. However, the true role of black holes, their “purpose” for the Universe, lies far beyond the scope of astronomy and particle physics. In their study, researchers have made great progress in the scientific understanding of previously purely philosophical questions - what space and time are, whether there are limits to the knowledge of Nature, what is the connection between matter and information. We will try to cover all the most important things on this topic.
1. Mitchell-Laplace dark stars
The term “black hole” was proposed by J. Wheeler in 1967, but the first predictions of the existence of bodies so massive that even light cannot escape them date back to the 18th century and belong to J. Mitchell and P. Laplace. Their calculations were based on Newton's theory of gravity and the corpuscular nature of light. In the modern version, this problem looks like this: what should the radius R s and mass M of the star be so that its second cosmic velocity (the minimum speed that must be imparted to a body on the surface of the star so that it leaves the sphere of its gravitational action) is equal to the speed of light c? Applying the law of conservation of energy, we obtain the quantity
R s = 2GM/c 2 , (1)
which is known as the Schwarzschild radius, or radius of a spherical black hole (G is the gravitational constant). Despite the fact that Newton’s theory is obviously inapplicable to real black holes, formula (1) itself is correct, which was confirmed by the German astronomer K. Schwarzschild within the framework of Einstein’s general theory of relativity (GTR), created in 1915! In this theory, the formula determines to what size a body must be compressed to form a black hole. If the inequality R/M > 2G/c 2 is satisfied for a body of radius R and mass M, then the body is gravitationally stable, otherwise it collapses (collapses) into a black hole.
2. Black holes from Einstein to Hawking
A truly consistent and consistent theory of black holes, or collapses, is impossible without taking into account the curvature of space-time. Therefore, it is not surprising that they naturally appear as partial solutions of the general relativity equations. According to them, a black hole is an object that bends space-time in its vicinity so much that no signal can be transmitted from its surface or inside, even by a light beam. In other words, the surface of a black hole serves as the boundary of space-time accessible to our observations. Until the early 70s, this was a statement to which it was impossible to add anything significant: black holes seemed to be “a thing in itself” - mysterious objects of the Universe, the internal structure of which is incomprehensible in principle.
Entropy of black holes. In 1972, J. Bekenstein hypothesized that a black hole has entropy proportional to its surface area A (for a spherical hole A = 4pR s 2):
S BH = C A/4, (2)
where C=kc 3 /Gћ is a combination of fundamental constants (k is Boltzmann’s constant and ћ is Planck’s constant). By the way, theorists prefer to work in the Planck system of units, in this case C = 1. Moreover, Bekenstein suggested that for the sum of the entropies of a black hole and ordinary matter, S tot = S matter + S black hole, the generalized second law of thermodynamics holds:
D S tot є (S tot) final - (S tot) initial? 0, (3)
that is, the total entropy of the system cannot decrease. The last formula is also useful because from it one can derive a limitation on the entropy of ordinary matter. Let's consider the so-called Susskind process: there is a spherically symmetric body of “subcritical” mass, that is, one that still satisfies the condition of gravitational stability, but it is enough to add a little energy-mass DE for the body to collapse into a black hole. The body is surrounded by a spherical shell (whose total energy is just equal to DE), which falls on the body. Entropy of the system before the shell falls:
(S tot) initial = S substance + S shell,
(S tot) finite = S BH = A/4.
From (3) and the non-negativity of entropy we obtain the famous upper limit on the entropy of matter:
S substance? A/4. (4)
Formulas (2) and (3), despite their simplicity, gave rise to a mystery that had a huge impact on the development of fundamental science. From the standard course of statistical physics it is known that the entropy of a system is not a primary concept, but a function of the degrees of freedom of the microscopic components of the system - for example, the entropy of a gas is defined as the logarithm of the number of possible microstates of its molecules. Thus, if a black hole has entropy, then it must have internal structure! Only in recent years has there been truly great progress in understanding this structure, and then Bekenstein’s ideas were generally received skeptically by physicists. Stephen Hawking, by his own admission, decided to refute Bekenstein with his own weapon - thermodynamics.
Hawking radiation. Since (2) and (3) are endowed with physical meaning, the first law of thermodynamics dictates that a black hole must have a temperature T. But excuse me, what temperature could it have?! Indeed, in this case, the hole should radiate, which contradicts its main property! Indeed, a classical black hole cannot have a temperature different from absolute zero. However, if we assume that the microstates of a black hole obey the laws of quantum mechanics, which, generally speaking, is practically obvious, then the contradiction can be easily eliminated. According to quantum mechanics, or more precisely, its generalization - quantum field theory, spontaneous birth of particles from a vacuum can occur. In the absence of external fields, the particle-antiparticle pair created in this way annihilates back into the vacuum state. However, if there is a black hole nearby, its field will attract the nearest particle. Then, according to the law of conservation of energy-momentum, another particle will go a greater distance from the black hole, taking with it a “dowry” - part of the energy-mass of the collapsar (sometimes they say that “the black hole spent part of the energy on the birth of a pair,” which is not entirely correct, because not the whole pair survives, but only one particle).
Be that as it may, as a result, a remote observer will detect a stream of all kinds of particles emitted by a black hole, which will spend its mass on the birth of pairs until it completely evaporates, turning into a cloud of radiation. The temperature of a black hole is inversely proportional to its mass, so the more massive ones evaporate more slowly because their lifetime is proportional to the cube of the mass (in four-dimensional spacetime). For example, the lifetime of a black hole with a mass M of the order of the solar exceeds the age of the Universe, while a microhole with M = 1 teraelectronvolt (10 12 eV, approximately 2 . 10 -30 kg) lives for about 10 -27 seconds.
3. Black holes and singularities
In science fiction literature and films, a black hole is usually presented as a kind of cosmic Gargantua, mercilessly devouring passing ships with brave blondes and even entire planets. Alas, if science fiction writers knew a little more about modern physics, they would not be so unfair to black holes. The fact is that collapsars actually protect the Universe from much more formidable monsters...
A singularity is a point in space at which its curvature tends to infinity without limit - space-time seems to break at this point. Modern theory speaks of the existence of singularities as an inevitable fact - from a mathematical point of view, solutions to equations that describe singularities are as equal as all other solutions that describe the more familiar objects of the Universe that we observe.
There is, however, a very serious problem here. The fact is that to describe physical phenomena it is necessary not only to have the appropriate equations, but also to set the boundary and initial conditions. So, at singular points these same conditions cannot be set in principle, which makes a predictive description of subsequent dynamics impossible. Now let’s imagine that at the early stage of the existence of the Universe (when it was quite small and dense) many singularities were formed. Then in the regions that are inside the light cones of these singularities (in other words, causally dependent on them), no deterministic description is possible. We have absolute and structureless chaos, without a hint of any causality. Further, these regions of chaos expand over time as the Universe evolves. As a result, by now the overwhelming majority of the Universe would be completely stochastic (random) and there would be no talk of any “laws of nature.” Not to mention blondes, planets and other heterogeneities like you and me.
Fortunately, the situation is saved by our insatiable gluttons. The mathematical structure of the equations of the fundamental theory and their solutions indicates that in real situations, spatial singularities should not appear on their own, but exclusively inside black holes. How can one not recall the mythological titans who tried to reign Chaos on Earth, but were overthrown by Zeus and Co. into Tartarus and safely imprisoned there forever...
In this way, black holes separate singularities from the rest of the Universe and prevent them from influencing its cause-and-effect relationships. This principle of prohibiting the existence of “naked” singularities, that is, not surrounded by an event horizon, proposed by R. Penrose in 1969, was called the cosmic censorship hypothesis. As is often the case with fundamental principles, it has not been fully proven, but no fundamental violations have been noticed so far - the Cosmic Censor is not planning to retire yet.
4. “Information intensity” of matter and the theory of grand unification
Local quantum theory has proven itself to be excellent in describing all known elementary interactions, except gravitational ones. Therefore, the fundamental quantum theory, taking into account general relativity, also belongs to this type? If we accept this hypothesis, it is not difficult to show that the maximum amount of information S that can be stored in a piece of matter of volume V is equal to V, measured in Planck units of volume V P ~10 -99 cm 3 up to a factor depending on the specific theory:
S substance ~ V. (5)
However, this formula conflicts with (4), since in Planck units A is much less than V for known physical systems (the A/V ratio is about 10 -20 for a proton and 10 -41 for the Earth). So which of the formulas is correct: (4), based on general relativity and the properties of black holes in the semiclassical approximation, or (5), based on extrapolation of ordinary quantum field theory to Planck scales? At present, there are very strong arguments in favor of the fact that formula (5) is “dead” rather than (4).
This, in turn, may mean that a truly fundamental theory of matter is not just another modification of quantum field theory formulated “in volume,” but a certain theory “living” on a certain surface that limits this volume. The hypothesis is called the holographic principle, by analogy with an optical hologram, which, being flat, nevertheless gives a three-dimensional image. The principle immediately aroused great interest, because the theory “on the surface” is something fundamentally new, in addition promising a simplification of the mathematical description: due to the decrease in spatial dimension by one, surfaces have fewer geometric degrees of freedom. The holographic hypothesis has not yet been fully proven, but there are already two generally accepted confirmations - the covariant restriction on the entropy of matter and the AdS/CFT correspondence.
The first gives a recipe for calculating statistical entropy (4) for the general case of a material body, as a certain quantity calculated on light-like world surfaces orthogonal to the surface of the body (may the inexperienced reader forgive me for this phrase). The general idea is as follows. What should be taken as a measure of entropy in curved space-time, that is, how to calculate it correctly?
For example, in the case of distributing a ball into boxes (see “Details for the curious”), the measure of entropy is actually the number of boxes; in the case of an ordinary gas, its volume divided by the average volume of the molecule. But in four-dimensional space-time, the volume of anything is not an absolute value (remember the Lorentz contraction of lengths?). Well, the concept of a “box”, you understand, goes somewhat beyond the scope of the elementary concepts of fundamental science. In general, it is necessary to define a measure of entropy through elementary concepts of differential geometry that are covariant, that is, whose values change depending on the position of the observer in a well-defined way.
The second is the so-called correspondence between anti-de Sitter space (adS) and Conformal Field Theory (CFT) - an implementation of holography for a certain special case of spaces of constant negative curvature, closely related to string theory. The correspondence states that Conformal Field Theory defined at the boundary of anti-de Sitter spacetime (that is, on a space with a dimension one less than the dimension of adS itself) is equivalent to quantum gravity within the anti-de Sitter itself. In fact, this is a proven correspondence between high-energy quantum states in CFT and quantum perturbations of the gravitational field in a spacetime of constant negative curvature. Don't forget that string theory is one of the special cases of two-dimensional conformal field theory, so far-reaching applications arise. At first glance, the AdS/CFT correspondence is not interesting from the point of view of physics: if we assume that globally our Universe is a four-dimensional anti-de Sitter space (adS 4), then it cannot expand, in complete disagreement with astronomical observations dating back to to Hubble. However, there is hope that AdS/CFT compliance itself may still find physical applications. If we assume that our four-dimensional Universe (not necessarily of the anti-De Sitter type) is embedded in, say, a five-dimensional space of negative curvature (AdS 5), then we obtain the so-called cosmological models of “brane-worlds”. Then we kill two birds with one stone: (a) space is multidimensional, as string theory predicts, (b) the AdS/CFT correspondence works, that is, you can calculate something with its help. The latter means that some properties of the Universe (experimentally verifiable) can be predicted through direct calculations, and points (a) and (b) can be confirmed or refuted experimentally.
5. Black holes and the limit of divisibility of matter
At the dawn of the last century, the leader of the world proletariat, probably under the impression of the discoveries of Rutherford and Millikan, gave birth to the famous “the electron is as inexhaustible as the atom.” This slogan hung in the physics classrooms of almost all schools of the Union. Alas, Ilyich’s slogan is as incorrect as some of his political economic views. Indeed, “inexhaustibility” implies the presence of an infinite amount of information in any arbitrarily small volume of substance V. However, the maximum information that V can contain, according to (4), is limited from above.
How should the existence of this limit of “information capacity” manifest itself at the physical level? Let's start a little from afar. What are modern colliders, that is, particle accelerators? Essentially, these are very large microscopes whose task is to increase the resolution along the Dx lengths. How can you improve the resolution? From the Heisenberg uncertainty relation DxDp = const it follows that if you want to reduce Dx, you need to increase the momentum p and, as a consequence, the energy E of the particles. And let’s imagine that someone has a collider of unlimited power at their disposal. Will he be able to endlessly extract information by discovering more and more new particles?
Alas, no: continuously increasing the energy of colliding particles, it will sooner or later reach a stage when the distance between some of them in the collision region becomes comparable to the corresponding Schwarzschild radius, which will immediately lead to the birth of a black hole. From this moment on, all the energy will be absorbed by it, and no matter how much you increase the power, you will no longer receive new information. The black hole itself will begin to evaporate intensively, returning energy to the surrounding space in the form of streams of subatomic particles. Thus, the laws of black holes, coupled with the laws of quantum mechanics, inevitably mean the existence of an experimental limit to the fragmentation of matter.
In this sense, reaching the “black hole” threshold at future colliders will inevitably mean the end of good old particle physics - at least in the form as it is understood now (that is, as the continuous replenishment of the museum of elementary particles with new exhibits). But instead, new perspectives will open up. Accelerators will serve us as a tool for studying quantum gravity and the “geography” of additional dimensions of the Universe (against the existence of which no convincing arguments have yet been put forward).
6. Black hole factories on Earth?
So, we have found that particle accelerators are, in principle, capable of producing microscopic black holes. Question: what kind of energy should they develop in order to receive at least one such event per month? Until recently, it was believed that this energy is extremely high, on the order of 10 16 teraelectronvolts (for comparison, the LHC can produce no more than 15 TeV). However, if it turns out that on small scales (less than 1 mm) our space-time has more than four dimensions, the threshold of required energy decreases significantly and can be achieved already at the LHC. The reason is the strengthening of gravitational interaction, when the supposed additional spatial dimensions not observed under normal conditions come into play. Thus, if the usual force of gravitational attraction between massive bodies in four-dimensional space-time is inversely proportional to the square of the distance between them, then in the presence of n additional compact dimensions it is modified into Fgrav ~ 1/r (2 + n) for r? r n, where r n is the maximum size of these dimensions. Then, with a decrease in r F, the gravity grows much faster than according to the inverse square law, and already at distances of the order of 10 (-17 + 32/n) centimeters it compensates for the force of electrostatic repulsion. But it was precisely this that was the reason for the high threshold energy: in order to overcome the Coulomb forces and bring the colliding particles closer to the required distance r = R s, it was necessary to impart greater kinetic energy to the beam particles. In the case of the existence of additional dimensions, the accelerated growth of F grav saves a significant part of the required energy.
All of the above in no way means that mini-holes will be obtained at the LHC facilities - this will happen only under the most favorable version of the theory that Nature will “choose”. By the way, you should not exaggerate their danger if received - according to the laws of physics, they will quickly evaporate. Otherwise, the solar system would have ceased to exist long ago: for billions of years, the planets are bombarded by cosmic particles with energies many orders of magnitude higher than those achieved in terrestrial accelerators.
7. Black holes and the cosmological structure of the Universe
String theory and most dynamical models of the Universe predict the existence of a special type of fundamental interaction - a global scalar field (GSF). On the scale of the planet and the Solar System, its effects are extremely small and difficult to detect, but on a cosmological scale, the influence of GSP increases immeasurably, since its specific share in the average energy density in the Universe can exceed 72 percent! For example, it determines whether our Universe will expand forever or will eventually shrink to a point. The global scalar field is one of the most likely candidates for the role of “dark energy”, which has been written about so much lately.
Black holes appear in this connection in a very unexpected way. It can be shown that the need for their coexistence with the global scalar field imposes mutual restrictions on the properties of black holes. In particular, the presence of black holes imposes a limit on the upper limit of the effective cosmological constant (the GSP parameter responsible for the expansion of the Universe), while the GSP limits the lower limit of their masses (and therefore entropy and inverse temperature T -1) to a certain positive value. In other words, black holes, being “local” and, by the standards of the Universe, tiny objects, nevertheless, by the very fact of their existence, influence its dynamics and other global characteristics indirectly, through the global scalar field.
Epilogue
Einstein once said that the human mind, once "expanded" by a brilliant idea, can never shrink back to its original state. This will sound a little paradoxical, but the study of the extremely compressed state of matter was, is and for a long time will be one of the main ways and incentives for expanding the boundaries of human intelligence and knowledge of the fundamental laws of the universe.
DETAILS FOR THE CURIOUS
The concept of entropy
According to one legend, when Claude Shannon, a giant of thought and the father of information theory, was tormented by the question of what to call a newly invented concept, he asked the advice of another giant, John von Neumann. The answer was: “Call it entropy - then you will get a solid advantage in discussions - because no one knows what entropy is in principle.” This is how the concept of “Shannon entropy” was born, now widely used in information theory.
Well, levels of ignorance can vary - from complete ignorance to a deep understanding of the complexity of the problem. Let's try to slightly improve our level of ignorance of entropy.
Statistical entropy, introduced by Ludwig Boltzmann in 1877, is, roughly speaking, a measure of the number of possible states of a system. Suppose we have two systems consisting of boxes and one ball in each of them. The first box-plus-ball system has only 1 box, the second has 100 boxes. Question - in which box is the ball located in each system? It is clear that in the first system it can only be in one box. Remember the formula “Entropy is the logarithm of the number of possible states”? Then the entropy of the first system is equal to log1, that is, zero, which reflects the fact of complete certainty (by the way, this is one of the reasons why the logarithm was used in the definition of entropy). As for the second system, here we have uncertainty: the ball can be in any of the 100 boxes. In this case, the entropy is equal to log100, that is, not zero. It is clear that the more boxes there are in the system, the greater its entropy. That's why they often talk about entropy as a measure of uncertainty, because our chances of “fixing” a ball in a specific box decrease as their number increases.
Please note that in this question we are not interested in the physical properties of either the boxes or the ball (color, shape, mass, etc.), that is, entropy is a relational type concept *, universal in its essence and sometimes (but not always) endowed with specific physical meaning. We could replace the balls with electrons and the boxes with vacancies in a solid (or even some abstract categories, such as in information theory), and the concept of entropy would still be applicable and useful.
Thermodynamic entropy, proposed in 1865 by Rudolf Clausius and, as we know from school, given by the formula dS = dQ/T, where dQ is the supply of heat to an element of matter, T is the temperature at which it is located, is a special case of statistical entropy, valid, for example, for heat engines. It was previously thought that thermodynamic entropy could not be applied to black holes, but Bekenstein and Hawking showed that this was not the case by properly defining the concepts of T and S (see Chapter 2).
"Paradoxes" of black holes
I found an interesting statement on the Internet. Its author, Andrei, drew attention to several paradoxical, in his opinion, aspects of black hole physics: “In all books about black holes […] it is said that the time for someone (something) to fall into a black hole is infinite in the reference frame, associated with a remote observer. And the time of evaporation of a black hole in the same reference frame is finite, that is, the one who falls there will not have time to do this, because the black hole will already evaporate […] If bodies fall into a black hole for an infinite time, then a body close in mass to a black hole will also be compressed into a black hole for an infinite amount of time, that is, all black holes […] are located only in the future with respect to a remote observer and their collapse (compression) will be completed only after an infinite amount of time has passed . […] From this statement it follows that there is no information paradox - information will simply be lost after an infinitely long time, but this should not worry us, because this fundamentally cannot be expected...”
This is an excellent illustration of the main dilemma of popular science literature - in an attempt to simplify the presentation, book authors are forced to sacrifice the level of mathematical rigor. Therefore, the phrase on which Andrei bases his conclusions, “the time for someone (something) to fall into a black hole is infinite in the frame of reference associated with a remote observer,” is generally speaking incorrect.
In fact, the physically correct formulation looks like this: “the time of falling of someone (something) into a static black hole is infinite in the reference frame associated with a remote static observer.” In other words, its applicability is limited to the idealized case when the characteristics of the hole are constant over time (that is, certainly not when it grows or evaporates), and any falling body is assumed to be a test body, small enough to neglect the changes in the hole caused by its fall.
In the same physical situations that Andrei talks about, both the hole itself and the space-time in its vicinity cannot be considered static. As a result, static (relative to the hole) observers as such simply do not exist. All observers are moving and all have equal rights, and the “time of falling of someone (something) into a black hole,” measured by their watches, is either finite in their reference frames, or is not defined (for example, when the observer is outside the light cone of the incident body hole).
This is the short answer. To understand such things at a deeper level, you need a serious mathematical apparatus (set out, for example, in the book by Hawking and Ellis): Carter-Penrose diagrams, conformal mappings, topology of manifolds and much more.
Unit systems
In systems of units of physical measurements, some units are taken as basic, and all others become derived from them. For example, in SI the basic units of mechanics are the meter, kilogram and second. A unit of force, newton, has the dimension kg . m/s 2, - derivative from them. The size of the basic units is chosen arbitrarily; their choice determines the magnitude of the coefficients in the equations.
In many areas of physics it is more convenient to use the so-called natural systems of units. In them, fundamental constants are taken as the basic units - the speed of light in vacuum c, the gravitational constant G, Planck's constant ћ, Boltzmann's constant k and others.
In the natural system of Planck units, it is customary to consider c = ћ = G = k = 1. The system is named after the German physicist Max Planck, who proposed it in 1899. It is used in cosmology and is especially useful for describing processes in which both quantum and gravitational effects are simultaneously observed, for example in the theory of black holes and the theory of the early Universe.
Light cone
When a body moves in space from a point with coordinates (x = 0, y = 0) with a constant speed v, the graph of its coordinates versus time (world line) looks like a straight line defined by the equation x = vt.
Since the speed of a body cannot be greater than light speed, this straight line is located no higher than the straight line x = ct (future) and no lower than the straight line x = _ ct (past). When a body moves in the plane (x, y) with speed v, its world line will be written as x 2 + y 2 = (vt) 2, and this is the equation of the cone. That is why they say that the body is located within the light cone, or light-like hypersurface.* By the way, this is why the question “So where is the entropy - in the ball or in the boxes?” meaningless.
Stephen Hawking is best known in the scientific world for his hypothesis that small black holes lose energy and gradually evaporate, emitting Hawking radiation, named after its discoverer. Almost a year ago, the scientist already stated that black holes could be doors to an alternative Universe, but the corresponding scientific work gives this theory, which at first glance seems almost fantastic, a certain weight, writes The Independent.
Before the concept of “Hawking radiation” was proposed, many scientists believed that everything that falls into a black hole disappears into it forever. The hypothetical Hawking radiation, which made it possible to change this idea, at the same time implies that almost all information about the quantum state of particles in black holes, with the exception of their mass, charge and rotation speed, is lost, which does not correspond to modern ideas about the structure of the world. The new theory allows us to resolve this paradox by accepting the assumption that what falls into a black hole leaves it, but in another reality - probably in a parallel Universe. However, according to the new theory, there will be no way back for anyone who ends up in another world with the help of a black hole. “So while I’m excited about space flight, I’m not going to fly into a black hole,” Hawking said, commenting on his research.
Recently, a less famous scientist, Martin Rees, suggested that simultaneously with the Big Bang, which marked the emergence of our world, many similar events could have occurred outside of it, which led to the emergence of the so-called Multiverse, which includes a huge number of parallel realities.
Stephen Hawking disproved the traditional theory of black holes
The famous physicist Stephen Hawking published an article on the website of the Cornell University library (USA), in which he claims that black holes in their current understanding do not exist. This is reported by a scientific journal.
It is traditionally believed that every hole is surrounded by an invisible boundary - an event horizon, which nothing, not even light, can pass. Meanwhile, Hawking proposes replacing the term “event horizon” with the “visible horizon,” which, in his opinion, only temporarily traps matter and energy, after which it releases them again, albeit in a distorted form. And the absence of an event horizon means that black holes do not exist.
Stephen Hawking explains that while according to classical theory there is no way back out of a black hole, if you follow quantum theory, then energy and information are still able to leave the black hole. True, a complete explanation of the process would require the creation of a theory of quantum gravity, unifying quantum mechanics and general relativity, something that physicists have not been able to do for a century. But considering that Stephen Hawking is one of the creators of the theory of black holes, his theory, even if not fully mathematically proven, is worth paying attention to.
Recall that at the end of 2013, the European Research Council issued a grant of 14 million euros to the BlackHoleCam project team, whose goal is to take the world's first photographs of a black hole.
http://www.vokrugsveta.ru/news/14791/
Stephen Hawking posted a preprint of his article on arXiv.org, in which he proposed an explanation for the firewall paradox, or “wall of fire.” From the explanation it follows that black holes in the classical sense of the word do not exist.
According to Hawking, due to disturbances caused by quantum effects, it is impossible in principle to determine the exact boundary of a black hole. In an argument that takes up only two pages of printed text, he proposes replacing the event horizon with the so-called “apparent event horizon.” This horizon is only capable of trapping matter and energy for a time, not forever.
“The absence of an event horizon means that black holes do not exist. At least in the sense of regions of space into which light cannot penetrate,” Hawking concludes.
Physicist Don Page, quoted by Nature News, believes that in Hawking's scheme, over time, the visible horizon of a black hole may disappear altogether. As a result, everything that was in such a hole will be thrown out.
In his work, Hawking also writes that the hole’s radiation will be chaotic (in the mathematical sense) in nature. This means that, despite the fundamental preservation of information, it is not possible to extract it from radiation. In the work, the physicist compares the problem of extracting information with the task of predicting the weather. Chaoticity in this case means such a dependence of the problem on the initial conditions that the slightest inaccuracy in determining these conditions leads to fundamentally different solutions to the problem. The physicist admits that a rigorous mathematical implementation of his ideas has yet to be found.
According to the theory of relativity, if matter reaches a certain critical density, under the influence of its own gravity it collapses into a black hole. This is a region of space in which gravitational forces are so strong that even light cannot escape. The hole is separated from the rest of the Universe by the event horizon - a conditional barrier, permeable only in one direction. In the case of a supermassive black hole of a sufficiently large radius, tidal forces at the event horizon are weak, and a hypothetical observer may not even notice the crossing of this boundary.
In the classical theory of relativity, a black hole could not emit anything (astronomers find holes, for example, by the radiation of matter falling on them). In the mid-20th century, Stephen Hawking discovered that quantum effects near the event horizon cause the hole to actually radiate. However, the spectrum of this radiation turned out to be similar to the spectrum of the radiation of a completely black body. In terms of quantum mechanics, this means that the black hole loses information about what it has absorbed. This effect contradicts the postulate of conservation of information (in a sense, a far-reaching generalization of the law of conservation of energy) and is called the information paradox of black holes.
Developing Hawking's ideas and trying to resolve the paradox, physicist Joe Polchinski and colleagues in 2012described the effect of the so-called “wall of fire”. Its essence is that, andh-for the so-called AdS/CFT duality (about it in detail in an interview with Lenta.ru
told by Brian Greene) instead of the event horizon, the so-calledThe alleged “wall of fire” is a region with particles of colossal energies. This result, in turn, contradicts the theory of relativity, according to which the event horizon isIt is no different from other regions of space in terms of physicalakonov.
The famous British physicist Stephen Hawking revised his previous theories and gave a plausible explanation for the nature of black holes.
It is unknown whether Hawking watched Christopher Nolan's recent blockbuster Interstellar, and if he did, what he thought about the possibility of a father trapped in a black hole sending messages to his daughter through space and time.
However, Hawking's new theory about black holes also addresses the ability of black holes to deal in unusual ways with information that... falls through.
In January 2016, Hawking once again made headlines in the world's leading media. Then he stated that he had found a possible solution to the black hole paradox, i.e. was able to explain how black holes can simultaneously erase information and store it.
Hawking's work was published on ArXiv.org, allowing other physicists to review it and make critical comments. And six months later, without encountering serious resistance from the world's scientific elite, Hawking's theory was published in the authoritative journal Physical Review Letters.
We tried to follow Hawking's train of thought and figure out why his new theory is considered an event in the world of physics.
Everlasting memory?
Current ideas about black holes are formed on the basis of Einstein's general theory of relativity.
According to established beliefs, everything that crosses the event horizon at the edge of a black hole disappears without a trace.
Even light cannot escape such a fate. This is actually why black holes got their name. After all, they absorb light, and we are not able to see them.
However, in the 1970s, British physicist Stephen Hawking suggested that there was something that could “escape” a black hole thanks to the laws of quantum mechanics. This something is radiation.
If we try to retell this Hawking theory in simple language, we get something like this. When a black hole “swallows” one half of a particle-antiparticle pair, the other half returns back into space as a radiation particle, taking with it a small particle of the black hole’s energy.
Water wears away stones, as they say
Therefore, even an insignificant outflow of energy can sooner or later lead to the disappearance of a black hole. And its only trace will be the electromagnetic radiation that this hole emitted. This phenomenon is called “Hawking radiation”.
The problem is that, according to Hawking's calculations, the radiation cannot contain any valuable information about what the black hole “swallowed” during its existence. In other words, all information is lost forever.
And this statement contradicts the ideas of modern physics that time can always be turned back.
At least in theory, all processes in the Universe should look the same, regardless of whether time moves forward or backward.
At first glance, this sounds strange. But if you compare this principle with the principle of operation of a modern computer, then everything becomes extremely clear, explains astrophysicist Dennis Overbye.
“The universe is like a supercomputer,” he says. “And it is supposed to be able to keep a record of everything that happened within its boundaries.”
As an example, he cites logs from road surveillance cameras. They contain records that one of the vehicles passed was a green pickup truck, and the other was a red Porsche. And this information is retained long after both cars have left each other.
In the same way, the Universe remembers that one of the particles consisted of matter, and the second - of antimatter. “Particles can be destroyed, but information about them—about their basic physical attributes—must always exist,” explains Overbye.
Black holes conflict with this fundamental theory of quantum mechanics because they are generally believed to completely destroy all information.
This contradiction is a problem not only for astrophysics, but also for physics in general.
And now, Hawking claims to have found a solution to the problem.
Hair of memory
There may be a kind of halo around a black hole - a glow of soft “hair” that can store information, Hawking suggests.
In fact, “hair” is a metaphor. It describes quantum excitations that carry data about everything that passed through the black hole. And these excitations exist even after the black hole itself disappears.
According to Overbay, these excitations are most easily described as a kind of cosmic analogue of the tracks on the surface of vinyl records. These “tracks” record information about what passed through the event horizon and then disappeared.
Having put forward this hypothesis in January 2016, Hawking admitted the fallacy of his previous calculations, based on which, at one time he assumed that black holes absorb information forever.
Hawking's new hypothesis about “hair” has not gained any serious critics in the six months since its first publication. The researchers note that this elegant explanation of the information paradox seems quite plausible.
Although not entirely exhaustive.
“The hypothesis itself does not provide a complete solution to the problem of information storage by black holes,” explains Gary Horowitz, a physicist at the University of California. “Calculations must also be made for gravitational fields, and not just electromagnetic fields.”
Horowitz is also not sure that these “hairs” are enough to store all the information about what falls into the black hole.
However, Horowitz believes that Hawking's very train of thought could lead to the discovery of new types of information storage in the Universe. And thus, the problem of the information paradox of black holes will eventually be solved, he suggests.
Another Universe
“Black holes are not eternal prisons, as previously thought,” Hawking said when presenting his theory in January. - If you feel like you're in a black hole, don't give up. There is a way out.”
There is some humor in this quote, but overall it brings to mind the main idea that Hawking had hidden in his work.
If destruction of information is possible in principle, Hawking argues, then it can be assumed that it is possible to erase information about the past.
Thus, if black holes could really destroy any information that falls into them without a trace, this would mean that, again, purely theoretically, they could delete pieces of the past.
But it is the past that tells us who we are. “Without a past, we will lose our individuality,” states Hawking.
Therefore, a consequence of the assumption of the “hair” of black holes is the hypothesis of an alternative Universe. Or there are many of them.
Hawking believes that everything that falls into a black hole ends up in another space. At the same time, Hawking is convinced that black holes are a one-way ticket. It is not possible to return to our Universe through a black hole.
Simply put, according to Hawking's theory, the events shown in Interstellar could not have happened. Having fallen into a black hole, the main character would not be able to send messages to his daughter in the past.
“I’m excited about space flight, but I’m not going to fly into a black hole,” Hawking jokes about the ruthlessness of black holes.
According to astrophysicist Stephen Hawking, “black holes” are no longer a cosmic prison for whatever they hold, as we previously believed.
Black holes may, in fact, be working portals to neighboring universes.
During a lecture at the Harvard University Theater, renowned theoretical physicist Stephen Hawking opened up the nature of black holes for open discussion, marking the launch of the Black Hole Initiative.
The scientist’s idea expressed a desire to combine the research of numerous scientists and focus on the scientific point of view of research on “black holes.”
Now, the attitude towards these structures of space is changing by science itself. What science fiction writers have known and talked about for a long time is now confirmed by Professor Hawking: black holes can indeed represent intergalactic portals with access to other worlds.
During the lecture, which took place in the theater at Harvard University, Professor Hawking, who directs the research Center for Theoretical Cosmology at the University of Cambridge in England, said to an audience of more than 1,000 people:
Black holes are not the eternal, inaccessible repositories we once thought, a scientist reminded listeners this week. “Everything can come out of a black hole, both outside and possibly into another universe”... So, if someone is captured by a “black hole”, then do not despair, there is a way out on the other side.
Professor Hawking compared the return of information from a “black hole” to a burnt encyclopedia, where, according to the theory, the information will not be completely destroyed and lost, although it will be quite difficult to decipher it.
Experts now see black holes as having significant implications for star systems, calling for a team of scientists to study the rare cosmic phenomenon, which many researchers say could help understand the basic workings of the universe.
Moreover, Harvard's maturing Black Hole Initiative (sometimes referred to as ““) proposes to cultivate a culture of scientists interested in black hole research,” said Harvard Astronomy Department Chairman Avi Loeb. .
Among other things, at the lecture Professor Hawking spoke about the recent discovery of gravitational waves, which, according to the physicist, under some conditions form part of the solid evidence confirming a new idea in the work of black holes.
A black hole will open an entrance to other worlds, but will also feed the planet with energy
Professor Hawking is one of the few who understands how the “black hole” mechanism works, which was considered a gravitational trap of space with extremely powerful compression. In fact, according to a renowned astrophysicist, we could use "miniature" black holes to our advantage to bring energy to Earth.
If this energy can be brought under control, then mini black holes could provide energy to the entire world in need of it. One mini black hole is believed to emit about 10 million megawatts, as Stephen Hawking said in his lecture on BBC Radio.
Remarks and suggestions about “black holes” were made by the professor during his second lecture. But in fact, it turns out that getting energy from black “mini” holes is not the biggest mystery, because there is a more serious problem, that is, how, as it were, these formations of space.
The theories behind Professor Hawking's groundbreaking proposal for black holes are exciting, and in his latest theory, Professor Hawking claims that so-called "mini-volume black holes" can emit X-rays and gamma rays at staggering speeds in amounting to about 10 million megawatts.According to estimated calculations, these forces are enough to load a ton of electricity onto the planet, ending not only the never-ending demand/supply of energy, but will in turn make our planet much cleaner.
Yes, I agree with those readers who are now wondering: what exactly is the freshness of the theory? The fact that “black holes” are the entrance, and “white holes” the exit to other worlds, was voiced in the last century, and CERN scientists began working in this area not yesterday. Yes, that's all true. But no one has ever proposed connecting energy pipelines to “black holes,” has they?
— By the way, two years ago, astrophysicists “heard” cries for help that came from the outskirts of the Messier 86 galaxy neighboring the Milky Way. The signals were emitted by a dying star being devoured by a black hole. A terrible event in space, and the “cries of pain” of the star were recorded by an international team of scientists observing.
Experts, having studied the information received, found out that the unusually high X-ray activity (that same scream) is nothing more than the signals of a screaming star, which was literally torn into pieces, absorbed by a bottomless black hole.
