Introduction to the Paradox of Information Disappearance in a Black Hole

Original author: Matt Strassler
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This article provides a quick introduction to the paradox of the disappearance of information in a black hole . For brevity, some details are omitted. In addition, it should be noted that the current understanding of the problem is so confusing that the very last part of the article cannot be regarded as reliable or stable.

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Fig. 1

Two conflicting theories


It is believed that the mathematics of quantum theory, sometimes called "quantum mechanics", governs all physical processes in nature. It can be used not to predict specific events, but only to obtain the likelihood that something will happen. But probabilities only make sense if you add up all the probabilities of all the different possible outcomes and get a sum equal to one. A quantum theory in which this is not the case does not make sense. One consequence of this is that in quantum theory, information is never truly lost or copied; in principle, you can always determine where the system started (its initial state), having complete information about what it finished (final state). In fig. 1 shows the collision of two particles and the escape from the place of collision of several particles, bearing, in encrypted form,

The general theory of relativity is Einstein's theory of gravity, in which gravity can be considered as the effect of the curvature of space and time. GR is not a quantum theory. She accurately predicts what will happen, and does not give the likelihood of different outcomes.

From 1915 to 1958, an understanding gradually developed that extremely compact and massive objects turned into black holes. Near them, gravity becomes unusually strong - so much that space-time is extremely distorted, and any object that comes too close to them and crosses the black hole horizon - the surface of no return - cannot escape. In fig. Figure 2 shows the formation of a black hole horizon at the moment when two shells of matter become sufficiently compact. Information about these two shells moves inside the horizon and cannot go outside - in GR.


Fig. 2

Note that it is impossible to correctly draw black holes and the information inside them. My illustrations are unable to demonstrate the curvature of spacetime. For example, for a complete understanding, you would need to take into account that the clock inside the black hole goes completely different than the clock outside the horizon, which, in turn, does not go like a remote clock. Do not take my illustrations too seriously, demonstrating the conceptual, but not technical side of the issue.

The horizon is not an object, but a place beyond which escape becomes impossible. A well-known analogy is a boat approaching a waterfall along an accelerating stream. When the boat passes the curve of no return (Fig. 3), its motor becomes unable to fight the current, and it will inevitably fall. But the captain of the boat will not notice the moment the curve crosses - this is just an ordinary part of the river, whose importance will become clear only when the captain tries to avoid a catastrophe. In the same way, crossing the horizon in GR, you will not notice anything; only when you try to avoid the black hole will you find that - oh - you came too close.


Fig. 3

The paradox of the disappearance of information in a black hole


The paradox arose after Hawking in 1974-1975 showed that a black hole surrounded by quantum fields will emit particles (Hawking radiation) and shrink (Fig. 4), resulting in evaporation. Compare with fig. 2, in which information about two shells is stuck inside a black hole. In fig. 4 black hole disappears. Where did the information go? If it disappeared along with a black hole, this violates quantum theory.


Fig. 4: 1) the shells of matter are compressed; 2) a horizon is formed, and Hawking radiation appears (in the form of particles without mass or small mass, for example, photons, neutrinos or gravitons); 3) Hawking radiation takes away energy, causing the size and mass of the black hole to shrink; 4) in the end, the black hole completely disappears, leaving only the Hawking radiation. Simply put, the information that fell into a black hole disappears, violating the principles of quantum theory. Is it necessary to change quantum theory?

Perhaps the information returned with Hawking radiation? The problem is that information cannot escape from a black hole. She cannot get into Hocknig's radiation, except through copying what remains inside. But having two copies of information, one inside and one outside, also violates quantum theory.


Fig. 5: if information is copied into Hawking radiation, this violates quantum theory.

Of course, the point may be that quantum theory is incomplete, and that black hole physics forces us to expand it, since Einstein expanded Newton's laws with his theory of relativity. That was what Hawking believed in for thirty years.

The principle of complementarity: saving quantum theory


However, others believed that it was not quantum theory that needed to be changed, but the general theory of relativity. In 1992, the "principle of complementarity" was proposed, according to which, information is in a sense, both inside and outside, without violating quantum theory. The assumption was developed by Sasskind and his young colleagues. Specifically, observers who remain outside the black hole see how information accumulates on the horizon, and then flies away with Hawking radiation. Observers falling into a black hole see information inside (Fig. 6). Since these two classes of observers cannot communicate, a paradox does not arise.


Fig. 6: The principle of complementarity says that everything depends on the point of view. The observer outside (2a) sees the information stored outside, and (3a) transmitted to the Hawking radiation. An observer falling inward (2b) sees information inside.

And yet, this assumption is potentially internally contradictory, and requires a few strange things to be true. Among them is what is called “holography,” an idea developed by 't Hooft, and then Sasskind. The idea is that the physics of the three-dimensional content of a black hole, in which gravity obviously works, can be considered, through a mysterious transformation, as physics located directly above the two-dimensional horizon, where it is described by two-dimensional equations in which gravity does not enter at all!


Fig. 7: It is interesting that it is possible to describe the inside of a black hole through its outer part; this was shown in the late 1990s and early 2000s. String theory, which contains a quantum version of GR, can do this in some cases.

Oddly enough, this theory received substantial confirmation in the late 1990s, at least for some situations. In 1997, Muldacena suggested (and hundreds of people tested this assumption in different ways) that under certain conditions , string theory (a quantum generalization of GR, a candidate for the theory of the laws of nature of our Universe) is equivalent to quantum theory (specifically, quantum field theory) without gravity and in fewer measurements. This relationship, known as AdS / CFT or “field / string matching,” deserves a separate article.

The success of holography strengthened the belief in the truth of the principle of complementarity. Moreover, the field / string correspondence made it possible to show quite convincingly that small black holes can form and evaporate in the string theory in a process that can be described by the corresponding quantum field theory (although not in detail) - and therefore this process, like any other the process in quantum theory, occurs with the preservation of information! By 2005, even Hawking accepted this point of view - that, as the principle of complementarity assumes, information is not lost in black holes, and that GR must be changed, not quantum theory.

Firewall and current mess


However, in principle of complementarity there were inconsistencies. The evaporation of black holes is so slow that in quantum theory there are no equations describing this process. In the search for these equations, Almheiri, Morolf, Polchinski, and Sally found that, under reasonable assumptions, the principle of complementarity contains an internal contradiction that manifests itself when the black hole evaporates about halfway. The proof is pretty tricky, it includes quantum entanglement, which Einstein called "creepy", and which is used in quantum computers. Roughly speaking, around the middle of the process, so much information disappears from the black hole through Hawking radiation that it is not enough to display the inside of the black hole on the horizon using holography. Therefore, instead of so that the observer falling inward calmly passes through the harmless horizon, as in Fig. 6, the observer will not find any insides, and very hard - he will fry on a firewall (wall of fire) hanging directly above the horizon (Fig. 8).


Fig. 8 The

possibility of the existence of a firewall would require fundamental changes in GR. In the case of truth, it would turn out that the description of black holes in GR, with a large internal volume, with a horizon representing just a point of no return (as in Fig. 3), and not some special place where something happens, would turn out to be completely wrong after the black hole would substantially evaporate.

So the paradox is back! And even worse. It turns out that if the quantum theory and the principle of complementarity are true, GR should not be partially changed - it must be seriously redone! And no signs of such an alteration are observed in string theory, which offers an example of holography. But the correspondence of fields / strings suggests that quantum theory can describe the formation and evaporation of black holes, so the information does not disappear. Can the principle of complementarity be replaced by anything? Or is any of the arguments creating a paradox wrong?

Everyone is confused. There are many suggestions for solving this puzzle. Most of them do not reach you. The media tells you about Hawking because he is famous, but he is just one of so many voices discussing different ideas. All these ideas suffer from one problem: the lack of equations to prove and explain the details of how they work. And since the lack of equations led to the firewall paradox, one can hardly get out of this situation, relying on another assumption with an insufficient number of equations!

But, although Hawking is just one of many proposers, and although there are not enough equations in his assumption, it will most likely be incomplete, and possibly incorrect - you will probably want to know what he suggested. It is rather difficult to understand this without equations, but here is how I can explain it (Fig. 9). Hawking notes that although the outer part of the black holes is quickly simplified, their insides can be very complex. Complex systems, such as weather, show the properties of chaos, which can make them unpredictable even before using quantum theory. He suggests that this complexity destabilizes the horizon and allows information encrypted inside the black hole to leak out. Since this would violate Hawking's theorems on general relativity, I assume that this means that general relativity must be changed. And since his assumption is based on AdS / CFT (field / string matching), I assume that he believes this should happen in string theory. And since what got into the black hole still comes out of it, these holes are not really black - so call them “gray holes”, or “metastable bound gravitational states”, or “seemingly black holes” "- but" blacks "may not be the right term.


Fig. 9: I apologize to Hawking, because neither I nor anyone in my circle knows exactly what he means. So I had to make a rough sketch of what I think he is trying to propose.

But there are many obvious problems with this proposal, not the least of which is that the mystery of the firewall appears already at the half-vaporized black hole, and not at the end of its life. Therefore, the black hole remains large enough when information already begins to leak out - and it is very difficult to reconcile with Hawking’s proposal. So do not wait for consensus to emerge about Hawking’s proposal, especially without any specific equations to solve.

In any case, everything that you learned about black holes is still essentially true. Astrophysicists do not need to worry about changes in what they think they know about stellar or galactic black holes. At least for large and not very old black holes, Hawking’s proposal will not lead to any measurable changes. And if you fall into a hole, you still can not get out, or send a message to someone outside. So, even if it turns out that strict black holes do not exist, in the center of almost every galaxy in the Universe there will still be a “sufficiently black” hole.

Do not expect this 40-year-old puzzle to be solved soon. Most likely, her decision will be offered by some young physicist, about whom you do not know anything, or even an unborn person.

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