Ask Ethan # 103: have we decided the information paradox?

Apparently, Einstein was wrong twice when he said that God does not play dice. God not only uniquely plays them, but sometimes also confuses us, throwing them where we cannot see them.
- Stephen Hawking

Every week I look at the questions you sent, and I prefer those that support us through Patreon crowdfunding, especially when their questions are good. A week before the article was written, an announcement that Stephen Hawking decided to solve the information paradox of black holes, although the work has not yet been published. Our reader and sponsor Denier wants to know:

How does Hawking's theory of black hole storage of information on the shell of an event horizon differ from what Susskind said many years ago? Can it be that Hawking behaved like Steve Jobs and declared new what appeared on Android long ago? Or is it really something new?

Black holes (BHs) are interesting objects, so let's go back to the beginning and talk about what this paradox represents.
')


On the one hand, BH, in theory, is quite easy to create. You just need to put enough mass (or energy equivalent, according to E = mc ² ) in a fairly small area of ​​space, and here it is! Usually a massive star with a collapsing core, unable to restrain itself under the influence of gravity, is the best way to do it. If you start with a star 20 times more massive than the Sun, then when it finishes its existence in a supernova type II explosion, the BH will remain from it.



Over time, BHs can either absorb more substance, or combine with other objects (including BH) and grow. Some galaxies, in particular, ours, have in the center a BH of millions of solar masses, and the largest of them can reach billions or even tens of billions of solar masses.



But looking at the BH outside, we cannot find out how it appeared. As far as we know, BH can distinguish very few properties:

• Mass,
• Electric charge,
• angular momentum (spin).

And that's it!



It can alert you. If a BH is made only from neutrons, its information must differ from a BH made of antineutrons, or from that which consists of a mixture of electrons and positrons. After all, the “baryon number” is an important part of the information of the quantum world, and if the BH baryon number is 10 ⁵⁸ , the other has zero, the third has –10 ⁵⁸ , this information should remain somewhere.

In fact, there is a chance to save it. Imagine that you have a BH, and something has fallen into it. Proton, antiproton, photon, two photons ... Maybe even a man!



While falling, this thing increases the BH mass, and its information is encoded on the surface of the BH event horizon. Although the observer (particle, photon, person), falling into the hole, will not notice the intersection of the horizon, the casual observer will see his increasing red shift, he will become darker and redder, but the horizon will never cross. Instead, their information is encoded on the surface of the BH, where it is probably preserved forever.

So, if BH were eternal, there would be no informational paradox. Something falls inside, and the information about what it was is encoded on the surface of the BH.



But then you need to turn to the quantum world, where the problem was born. You see, BHs are the sources of the strongest gravity, since their entire mass is packed in a small volume. As a result, the space around the BH is extremely curved, and the quantum universe behaves in a curved space differently than in a flat one.

In particular, one of the properties of flat space is non-zero quantum energy: particle-antiparticle pairs appear and disappear. Under normal conditions, they exist for a very short time, and then reannigulate and disappear in a vacuum. A comparison of the “before” and “after” states will not reveal a difference. But in a curved space, such particle-antiparticle pairs can occur on different sides of the event horizon. Under the right conditions — rare, but possible — you will get a small low-energy quantum of radiation emitted as a result of this, while a particle from one virtual pair annihilates with an antiparticle from another pair, which results in black body radiation.



The process is slow and long: for the evaporation of the BH of the solar mass it will take 10 ⁶⁷ , and for the supermassive - 10 ¹⁰⁰ years, but the Universe is patient and it has enough time. As a result, nothing will remain of the BH, only a sea of ​​black body heat radiation. Thanks to this radiation - Hawking radiation - BH disappears.

But worst of all, this radiation is missing information that fell in the BH. This is the paradox of BH information: information gets into BH, but over time it is lost. Since information should not just disappear, we have a paradox.



It is usually assumed that the information is stored. Until now, no one knew exactly how, although the ideas were. It was assumed that information from the BH surface was somehow encoded in Hawking's outgoing radiation. Stephen Hawking, together with Malcolm Perry and Andrew Strominger, suggested that it was all about one of the properties of string theory, called over-broadcasting.

Outer translation, in simple terms, is based on the fact that the classical vacuum in the general theory of relativity is strongly degenerate. There may be different vacuum states with identical properties, that is, indistinguishable from each other. Different vacuums corresponding to different states correlate with each other with the help of broken symmetry defined by Bondi, van der Burg and Metzer in 1962. These broken symmetries are the supertranslations studied by Strominger, and they can describe the propagation of changes in the gravitational field.



In April 2014, Hawking heard the Strominger report, and decided that it follows from it that particles falling on the horizon of black holes cause supertranslations, and these supertranslations can be displayed on Hawking's outgoing radiation. This will be described in the work.



But there is a big difference between having an idea and recognizing that idea as a solution to a problem, and so far we only have an idea. For example, some new clarifications have appeared:

• The paper describes a classical picture that does not take into account such quantum information as baryon numbers.
• An infinite number of charges is assumed, and not their actual amount for a BH, resulting from the Beckenstein-Hawking entropy.
• There is no quantum version of the mentioned symmetries or supertranslations.
• There is no quantum version of information transfer to outgoing radiation - this is just an idea.

In addition, Sabine Hossenfelder, working on quantum gravity in warped spaces, is concerned about:

My concern is that if you look at the picture from a quantum point of view, BMS-charges (Bondi-Metzner-Sachs) at infinity will be entangled with charges falling in a BH, as a result of which the BH information paradox will reappear.



So, yes, Denier, Hawking came up with a new thing about the BH information paradox. But this can hardly be called a solution to the paradox. Therefore, it cannot be said that the paradox is resolved. It may be noted that a new idea of ​​its resolution was proposed, which is in an embryonic state.

In my opinion, if this idea was proposed by a person who was not called Stephen Hawking, very few people would have paid attention to it, since for the time being it can only be called an embryo, a spark of opportunity. But it is worth further research - although most of these ideas are not justified as a result. It is possible that something will grow out of it, but until someone works out the entire theoretical part from beginning to end, it makes no sense to think that the paradox will be finished in the foreseeable future.