Under the laws of quantum mechanics, information about what has fallen into a black hole cannot be destroyed, and now researchers claim they have figured out how it is preserved.

Black holes have an information problem. According to the laws of quantum mechanics, information about the state of a closed system cannot be destroyed, but black holes seem to obliterate it. Researchers have been trying for decades to solve this problem, called the black hole information paradox, and now one team claims to have finally figured it out.

An artist’s representation of a black hole Shutterstock / Dima Zel |

The black hole information paradox was born in the 1970s when Stephen Hawking calculated that black holes should slowly evaporate by emitting random particles in what is now called Hawking radiation. This suggests that any information-containing matter that falls into a black hole would be destroyed as the black hole eventually shrinks to nothing. The problem there is that the laws of quantum mechanics require that if you know the state of any closed system at one time, you should be able to work out its state forward or backward in time – but if Hawking radiation is indeed random, that becomes impossible.

Xavier Calmet at the University of Sussex in the UK and his colleagues claim that they have solved the problem using a framework called quantum field theory. “We have redone the calculation that Hawking did in the 1970s, but we have taken into account quantum gravity,” says Calmet. “The black hole information paradox is solved now, and we understand the physics of it.”

In earlier work, the researchers found that when they applied quantum mechanical corrections to calculations of stars evolving into black holes, the black holes’ gravitational fields would preserve information about what fell in. Now, they claim to have worked out what happens to that information as the black hole evaporates.

This problem is difficult to solve because of the way the information is distributed as it leaks out. “Imagine your information is made of Lego pieces, and then you’ve got a black hole made of Lego, and then over the course of the age of the universe, piece by piece, individual Lego pieces come out,” says Neil Lambert at King’s College London. “You put a huge amount of information in, and it comes out again so slowly, and in such small pieces, that you have to dig really deep into the theory” to figure out how the information that fell in relates to what is coming out, he says.

Calmet and his team calculated that the gravitational field of the black hole should very slightly modify the energy spectrum of the Hawking radiation that emerges. “It’s a tiny effect, but it means that the spectrum contains information,” he says. Traditionally, Hawking radiation is thought to be random, so any order in its spectrum could allow information to leak out of the black hole as it evaporates and be preserved.

However, some other researchers in the field aren’t satisfied yet. “This doesn’t fix the problem,” says Daniel Harlow at the Massachusetts Institute of Technology. The objections largely boil down to the idea that, ironically, this theory does not have enough information about how exactly the information is preserved, particularly when the black hole evaporates completely. “I don’t think it’s gotten any traction in the community, because I don’t think it’s precise enough,” says Lambert.

“To resolve the black hole information problem requires a major change in our understanding of how space and time emerge from the theory of quantum gravity – I don’t think you’re going to get it by using just the standard laws of physics and quantum field theory,” says Harlow.

Testing this work will be difficult because Hawking radiation is such a minuscule effect. “Practically, honestly, it’s not measurable – we’ve never seen Hawking radiation from a real black hole,” says Calmet. “Hawking radiation will never be measured in astrophysics, I think, but there are ways to build analogues to black holes where you can model Hawking radiation.” Perhaps these analogues will provide resolution, he says.

Journal reference:

Physics Letters BDOI: 10.1016/j.physletb.2023.137820

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