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

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.

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.

### Reference:

Xavier Calmet et. al, Quantum gravitational corrections to particle
creation by black holes, Physics Letters B, DOI: 10.1016/j.physletb.2023.137820

Tags:
Space & Astrophysics