Theoretical physicists Stephen Hawking, Malcolm Perry and Andrew Strominger have proposed a solution to the information loss paradox in black holes. This problem is considered by many scientists to be one of the most important in physics, since it is associated with the determinism of the world - how the past, present and future influence each other. "Lenta.ru" tells the details of the study.

The essence of the problem of the information paradox of black holes is as follows. According to the simplest version of the no-hair theorem, uncharged and non-rotating black holes described in Schwarzschild space-time are characterized by only one parameter - mass. The word "hair" in this case is used as a metaphor for other parameters and was suggested by the physicist John Wheeler.

The paradox means that there is no way to tell black holes of equal masses apart from each other. Matter that enters the black hole subsequently evaporates due to Hawking radiation, and it is unclear what happens to the information it previously carried. Broadly speaking, this can mean, as Strominger pointed out in an interview with editor Seth Fletcher for Scientific American, the world is indeterminate: the present does not define the future and cannot be used to completely reconstruct the past.

Hawking first announced the new discovery on August 25, 2015, speaking at a conference at the Royal Institute of Technology in Stockholm. Then he intrigued the scientific community with an upcoming article devoted to solving the black hole paradox. “Information is not stored inside, as one might expect, but on the event horizon of a black hole,” the scientist said at the time. He also mentioned the super-broadcasts used by the authors in the work (more on them below), the research of which Strominger inspired Hawking to write the article. “The idea is that super broadcasts are a hologram of falling particles,” Hawking said. "They contain all information that might otherwise have been lost." The scientist also spoke about the prospects for using information from black holes. “For all practical purposes, information is lost,” Hawking said. According to him,black holes return information in a "chaotic and useless form."

In his lecture a day earlier, on August 24, Hawking talked about black holes as tunnels to other universes. “If a black hole is big enough and rotates, it could be a bridge to another universe. But after passing through it, you will not return to ours,”said the physicist. Hawking presented his ideas at the conference on September 3 in a preprint on the arXiv.org website. Hawking's work itself, co-authored with Perry and Strominger, was published there on January 5, 2016.

Malcolm Perry, Andrew Strominger and Stephen Hawking (left to right)

Photo: Anna N. Zytkow / scientificamerican.com

Earlier (since the mid-1970s) Hawking believed that information is not stored in black holes. On this issue, in 1997, he and Kip Thorne entered into a bet with American theoretical physicist John Preskill. Hawking's view of the black hole information paradox has changed with advances in string theory.

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In 1996, in the framework of string theory, Strominger and Kumrun Wafa demonstrated the derivation of an expression for the entropy of black holes, first obtained thermodynamically by the Israeli physicist Jacob Bekenstein in 1973. Their conclusion indicates that the evaporation of black holes preserves the unitarity of quantum mechanics (associated with a consistent interpretation of probability), which Hawking previously questioned.

In a work published in 2005, the British scientist tried to qualitatively explain the conservation of information in a black hole using the functional integral technique taken over a space with a trivial topology. The same results followed from the idea of the AdS / CFT correspondence proposed in 1998 by Juan Maldacena in the framework of string theory. It, in turn, is based on the holographic principle proposed in 1993 by the Dutch theoretical physicist Gerard t'Hooft (this scientist published a preprint on September 5, 2015 with an alternative way of storing information by a black hole).

In the new work, the scientists build on research from the 1960s. Then physicists Steven Weinberg and others proposed the concept of super translations (they should not be confused with the term of the same name used in super mathematics). In addition, the authors used the results of Strominger and co-authors, from which it followed that the black hole has so-called soft hair. Strominger used soft photons known from quantum electrodynamics - quanta of electromagnetic radiation of long wavelengths used in renormalizations (procedures for eliminating divergences in quantum field theory). Such particles have low energy and, when describing the vacuum state (with the lowest energy), lead to the appearance of a new quantum state characterized by angular momentum (since the photon has one).

Strominger became interested in the question of whether the initial quantum state of the system would be different from the next one if we set the photon's wavelength to be infinite (that is, to count its energy as zero). Calculations have shown that the quantum state of the system will change in this case. Soft gravitons and photons in the limit of infinite wavelength exist at the boundaries of space-time. Applied to black holes, it turns out that soft particles are localized on the event horizon - a three-dimensional hologram of a four-dimensional space-time hole.

When they talk about super broadcasts, scientists mean transformations of identical light beams that exist on the black hole's event horizon. In the 1960s, super translations were used to describe rays of light at infinity in spacetime, rather than the event horizon of black holes. Strominger explained the idea of super broadcasting using the example of a collection of infinitely long and identical straws. If one of them is moved up or down relative to the others, can such a movement be considered real? Research by scientists has given a positive answer to this question.

Gerard t'Hooft and Stephen Hawking

Photo: Håkan Lindgren / kth.se

“If you compare two black holes that differ only in the addition of a soft photon that does not change energy, you get different black holes. And then you let them evaporate. In this case, they must evaporate into something different from each other. We give the exact formula, which is one of the main results of our work, describing the differences in the quantum state of a black hole, to which a soft photon was or was not added,”Strominger told Scientific American.

The physicist noted that in the course of the research he was able to formulate 35 promising problems, the solution of each of which can take up to several months. “If we have all the ingredients to understand the quantum dynamics of black holes, it makes it possible to count the number of holographic pixels,” he said. In the future, Strominger and co-authors are going to study not super-translations, but super-rotations. Using the analogy with identical infinitely long straws, we can say that in this case the latter exchange places with each other (one straw rotates around the other).

“They (super-rotations) are another kind of symmetry at infinity, where you don't just move the light rays up and down, but you allow them to move relative to each other,” Strominger said. Scientists began to study such transformations about ten years ago, and progress in understanding them has been achieved only in the last two years. Hawking, who celebrated his 74th birthday on January 8, will present his vision of his new work in lectures that will be broadcast on January 26 and February 2 by BBC Radio 4.

Andrey Borisov