Dear Dr. Bee,
Why physicists are so worried about the disappearance of information in a black hole, because there are other irreversible processes, and a fairly routine property. One obvious example is the increase in entropy in an isolated system, the other is a measurement in quantum mechanics.
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 does not really understand this problem, and he does not just have a doctorate in physics, he also endured my chatter about this issue for 15 years!
So I’m happy to explain why the theorists are so worried about because of the information and BH. This problem has two aspects: scientific and social. Let’s start with the scientific.
In the classical general theory of relativity, BHs do not pose any particular problems. Of course, they contain a singularity in which the curvature turns into infinity – and this is considered contrary to the spirit of physics – but the black hole hides it beyond the horizon of events, as a result of which it does not harm anyone.
But, as Stephen Hawking pointed out, If we take into account that the Universe, including the vacuum, is filled with quantum material fields, you will be able to calculate that black holes emit particles; This process is now called “Hawking radiation”. This combination of unquantized gravity with quantum material fields is known as “semiclassical” gravity, and should serve as a good approximation until the quantum gravity effects can be neglected, that is, until you are very close to the singularity.
Radiation Hawking consists of pairs of entangled particles. In each pair, one particle falls into the black hole, and the other runs away. This leads to a loss of BH mass, that is, BH is compressed. Eventually, it completely loses mass, and as a result only Hawking radiation particles scattered everywhere are left.
The problem is that the runaway particles do not contain any information that they formed a black hole. Moreover, the information of the partners of these particles that have fallen in the BH is also lost. If we study the side effects of BH evaporation, we can not say what the initial state was; You can only calculate the total mass, charge and angular momentum – three “hair” of black holes (and one qubit). It turns out that evaporation of BH is irreversible.
But in quantum field theory (KTP) irreversible processes do not exist. Speaking in technical jargon, black holes turn pure states into mixed states, which does not happen at all. Therefore, evaporation of BH leads to internal contradictions: you combine KTP with GRT, but the result turns out to be incompatible with QFT.
Answering the questions: increasing entropy does not usually imply 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 must be reversible: breaking eggs, kneading flour, burning books – the reverse processes are easy to describe mathematically. We simply do not observe them, since such an event would require extremely fine-tuned initial states. A strong increase in entropy makes the process irreversible in practice, but reversible theoretically.
And this is true for any processes other than evaporation of black holes. No fine tuning will return information lost in 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 are worried.
Irreversibility in quantum mechanics, which you mentioned in the question, comes from the measurement process, but BH evaporation is irreversible even before the measurements were taken. Of course, one can argue – why worry so much, if all that we can observe, still have to be measured? Yes, such an objection is possible, and it has already been applied. But in itself it does not eliminate contradictions. Still need to show how you can reconcile two mathematical platforms.
This problem attracted such attention, because its mathematics are very clear, and the consequences are global. Hawking 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 customary to assume that the quantification of space-time is necessary to eliminate contradictions. In the process of solving the problem with 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 sociology. You might have noticed that this problem is not so new. It appeared before my birth. During my life, thousands of works have been written on it, and hundreds of solutions have been proposed, but theorists can not agree on any of them. All because they do not have to do this: after all, for those black holes that we can observe (for example, in the center of our Galaxy), the temperature of Hawking radiation is so small that we can not measure the departing particles in any way. Therefore, black hole evaporation is an ideal sandbox for mathematical reflections.
There is an obvious solution to the problem of information loss, which has been pointed out for a long time. The black holes destroy information, because everything that gets to the horizon turns into a singularity and is destroyed. But the singularity is considered a mathematical artifact, which in the theory of quantum gravity should not be. Indeed, Hawking’s calculations stop working when the black hole loses nearly its entire 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, because if you do not know what is happening near the singularity and in cases with a strong Curvature, nothing can be calculated, for this will require quantum gravity. So this idea is not very fruitful. Few scientific works can be written with its help, and few people have written about it. It is much more fruitful to assume that Hawking’s calculations are incorrect elsewhere.
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 is rejected, you will find , That this justification is mainly social, not scientific.
If the information is delayed for a long time in the BH, this means that small BHs should contain a lot of different combinations of information. Several papers state that such BHs should emit information slowly, which means that small BHs should behave in practice as an infinite number of particles. In this case, the authors of the works assert, they should 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 an unreasonable assumption of The fact that the BH interior has a small volume. But in general relativity there is no obvious relationship between surface area and volume, since space can be bent. The assumption that small black holes, for which quantum gravity is strong, can be described as particles, is also devoid of grounds.
As a result, Leonard Susskind wrote a work that rejects the idea that information remains in the BH for a long time and is emitted at the end of their life. This made it possible for all the rest to say that the obvious solution does not work and start releasing countless new works with their reasoning.
Forgive me for skepticism, but this is how I assess this situation. I even admit that I myself put my hand to this mountain of papers, because the learned world works just like this. 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 works on it, And since there are so many people working on this subject, there are no problems with quotes either.