Why are physicists so worried about the paradox of the disappearance of information in a black hole

Black hole with jets and accretion disk

Dear Dr. Bee,

Why are physicists so worried about the disappearance of information in a black hole, because there are other irreversible processes, and with a rather routine nature. One obvious example is the increase in entropy in an isolated system, the other is measurements in quantum mechanics.

Sincerely, Petteri.

Dear Petteri,
')
This is a very good question. Confusion is closely related to the information paradox as an accretion disk with a supermassive black hole. A few weeks ago, I discovered that even my husband doesn’t really understand this problem, and he doesn’t just have a PhD in physics, he also endured my chatter about this issue for 15 years!

So I’ll be happy to explain why theorists are so worried about information and BH. This problem has two aspects: scientific and social. Let's start with the scientific.

In the classical general theory of relativity, black holes do not pose any particular problems They, of course, contain a singularity in which the curvature turns into infinity - and this is considered contrary to the spirit of physics - but the BH hide it behind the event horizon, with the result that it does not harm anyone.

But, as Stephen Hawking pointed out, if you consider that the Universe, including the vacuum, is filled with quantum material fields, you can calculate that black holes emit particles; This process is today called Hawking radiation. This combination of non-quantized gravity with quantum material fields is known as "semi-classical" gravity, and should serve as a good approximation until the quantum effects of gravity can be neglected, that is, until you are very close to the singularity.

Hawking radiation consists of pairs of entangled particles. In each of the pairs, one particle falls in the black hole and the other runs away. This leads to a loss of BH mass, that is, BH is compressed. In the end, it completely loses mass, and as a result only Hawking radiation particles scattered everywhere remain.

The problem is that in the runaway particles there is no information about what formed the black hole. Moreover, the information of the partners of these particles that fell in the BH is also lost. If we study the side effects of BH evaporation, we cannot say what the initial state was; you can only calculate the total mass, charge and angular momentum - three “hairs” of black holes ( and one qubit ). It turns out that BH evaporation is irreversible.



But in quantum field theory (QFT) irreversible processes do not exist. Speaking in technical jargon, BH transform pure states into mixed ones, which is not what should happen at all. Therefore, BH evaporation is an internal contradiction: you combine QFT with GR, but the result is incompatible with QFT.

Answering questions: an increase in entropy usually does not imply a fundamental irreversibility, only practical. Entropy increases due to the fact that the probability of seeing the reverse process is small. But in principle, any process should be reversible: breaking eggs, kneading flour, burning books are processes that are inverse of this, it is easy to describe mathematically. We simply do not observe them, since such an event would require extremely finely tuned initial states. A strong increase in entropy makes the process practically irreversible, but theoretically reversible.

And this is true for all processes, except for the evaporation of black holes. No fine adjustment will not return information lost in the BH. This is the only known case of fundamental irreversibility. We know that this is bad, but we do not know what exactly is wrong. Therefore, we worry.

The irreversibility in quantum mechanics, which you talked about in the question, comes from the measurement process, but the BH evaporation is irreversible even before the measurements were taken. Of course, you can argue - why worry so much if everything that we can observe will still have to be measured? Yes, such an objection is possible, and it has already been used. But in itself, it does not eliminate the contradictions. All the same, you need to show how to reconcile the two mathematical platforms.

This problem has attracted such attention, because its mathematics is very clear, and the consequences are global. Hawking's evaporation depends on the quantum properties of material fields, but does not take into account the quantum properties of space and time. Therefore, it is considered that quantification of space-time is necessary to eliminate contradictions. In the process of solving the problem of the disappearance of information, we would learn something new in the field of the theory of quantum gravity. Therefore, the disappearance of information in the BH is an excellent logical puzzle with a huge potential benefit - this makes it so tempting.

Now about the sociology. You may have noticed that this problem is not so new. She appeared before I was born. Over the course of my life, thousands of papers were written on it, and hundreds of solutions were proposed, but theorists cannot agree on any of them. This is because they do not have to do this: for those BHs that we can observe (for example, in the center of our Galaxy), the Hawking radiation temperature is so low that we can’t measure the particles flying away. Therefore, BH evaporation is an ideal sandbox for mathematical thinking.



For the problem of losing information, there is an obvious solution, which has been pointed out for a long time. BH destroy information, because everything that goes beyond the horizon turns out to be in a singularity and destroyed. But the singularity is considered a mathematical artifact, which should not be in the theory of quantum gravity. Remove the singularity - remove the problem.

Indeed, Hawking's calculations stop working when the BH loses almost all of its mass and becomes so small that quantum gravity begins to work. This means that the information will simply break out in the very last phase, the phase of quantum gravity, and no contradiction will happen.

But this obvious solution is also inconvenient, since if one does not know what is happening near the singularity and in cases with strong curvature, nothing can be counted, because this requires quantum gravity. So this idea is not very fruitful. Few scientific works can be written with its help, and few people wrote about it. It is much more fruitful to assume that Hawking's calculations are wrong somewhere else.

Unfortunately, if you dig into the literature and try to find out on what grounds the idea that information comes out in the phase of strong curvature was rejected, you will find that this rationale is mainly social, not scientific.

If information is permanently delayed in BH, this means that small BH must contain many different combinations of information. Several papers state that such BHs should emit information slowly, which means that small BHs should behave in practice like an infinite number of particles. In this case, the authors argue, they must appear in infinite quantities even in weak background fields (for example, near the Earth), which is not observed in reality.

Unfortunately, these arguments are based on the unreasonable assumption that the interior of the BH has a small volume. But in GR, there is no obvious link between surface area and volume, since space can be curved. The assumption that small BHs, for which quantum gravity is strong, can be described as particles, are also devoid of reason .

As a result, Leonard Susskind wrote a work rejecting the idea that information remains in the BH for a long time and is emitted at the end of their lives. This made it possible for everyone else to declare that the obvious solution was not working, and to start releasing countless new works with their reasoning.

Sorry for skepticism, but this is how I assess this situation. I even admit that I myself had a hand in this grief of papers, since the learned world works that way. I also need to live on something.

This is another reason why physicists are so worried about the disappearance of information in BH: since the reasoning on this topic is not limited to experimental data, it is very easy to write papers on it, and since so many people work on this topic, there are no quotes either problems.