This
Physicist Discovered an Escape From Hawking’s Black Hole Paradox
The five-decade-old paradox — long
thought key to linking quantum theory with Einstein’s theory of gravity
— is falling to a new generation of thinkers. Netta Engelhardt is leading the
way.
READ LATER
Netta Engelhardt puzzles over the fates of black holes in her
office at the Massachusetts Institute of Technology.
Tira Khan for Quanta Magazine
August 23, 2021
AdS-CFTblack hole information paradoxblack holesphysicsQ&Aquantum gravitytheoretical physicsAll topics
In
1974, Stephen Hawking calculated that
black holes’ secrets die with them. Random quantum jitter on the spherical outer boundary, or “event
horizon,” of a black hole will cause the hole to radiate particles and slowly
shrink to nothing. Any record of the star whose violent contraction formed
the black hole — and whatever else got swallowed up after — then seemed to be
permanently lost.
Hawking’s calculation posed a paradox — the infamous “black hole information paradox”
— that has motivated research in fundamental physics ever since. On the one
hand, quantum mechanics, the
rulebook for particles, says that information about particles’ past
states gets carried forward as they evolve — a bedrock principle called “unitarity.” But black holes take their
cues from general relativity, the
theory that space and time form a bendy fabric and gravity is the fabric’s
curves. Hawking had tried to
apply quantum mechanics to particles near a black hole’s periphery, and saw
unitarity break down.
So do evaporating black
holes really destroy information, meaning unitarity is not a true principle of
nature? Or does information escape as a black hole evaporates? Solving the
information paradox quickly came to be seen as a route to discovering the true, quantum theory of gravity,
which general relativity approximates well everywhere except black holes.
In the past two years, a
network of quantum gravity theorists, mostly millennials, has made enormous
progress on Hawking’s paradox. One of the leading researchers is Netta Engelhardt, a
32-year-old theoretical physicist at the Massachusetts Institute of Technology.
She and her colleagues have completed a new calculation that corrects Hawking’s
1974 formula; theirs indicates that information does, in fact, escape
black holes via their radiation. She and Aron Wall identified an invisible surface
that lies inside a black hole’s event horizon, called the “quantum extremal surface.” In 2019,
Engelhardt and others showed that this surface seems to encode the amount of
information that has radiated away from the black hole, evolving over the
hole’s lifetime exactly as expected if information escapes.
Engelhardt received a
2021 New Horizons in Physics Prize “for calculating the quantum information
content of a black hole and its radiation.” Ahmed Almheiri of
the Institute for Advanced Study, a frequent collaborator, noted her “deeply
rooted intuition for the intricate workings of gravity,” particularly in the
discovery of quantum extremal surfaces.
Engelhardt set her sights on quantum gravity when she was 9 years old.
She moved to Boston from Israel that
year with her family, and, not knowing any English, read every book in Hebrew
she could find in her house. The last was Hawking’s A
Brief History of Time. “What that book did for me was trigger a desire to understand
the fundamental building blocks of the universe,” she said. “From then on, I
was sort of finding my own way, watching different popular science videos and
asking questions of anybody who might have the answers, and narrowing down what
I wanted to work on.” She ultimately found her way to Hawking’s paradox.
When Quanta
Magazine caught
up with Engelhardt in a recent video call, she emphasized that the full
solution to the paradox — and the quantum theory of gravity — is a work in
progress. We discussed that progress, which centrally involves the concept of entropy, and the search for
a “reverse algorithm” that would allow someone to reconstruct a black
hole’s past. The conversation has been condensed and edited for clarity.
Would you say you and
your colleagues have solved the black hole information paradox?
Not yet. We’ve made a
lot of progress toward a resolution. That’s part of what makes the field so
exciting; we’re moving forward — and we’re not doing it so slowly, either — but
there’s still a lot that we have to uncover and understand.
Could you summarize what
you’ve figured out so far?
Certainly. Along the way
there have been a number of very important developments. One I will mention
is a 1993 paper by Don Page. Page said,
suppose that information is conserved. Then the entropy of everything outside
of a black hole starts out at some value, increases, then has to go back down
to the original value once the black hole has evaporated altogether. Whereas
Hawking’s calculation predicts that the entropy increases, and once the black
hole is evaporated completely, it just plateaus at some value and that’s it.
So the question became,
which entropy curve is right. Normally, entropy is the number of possible
indistinguishable configurations of a system. What’s the best way to understand
entropy in this black hole context?
You could think of this
entropy as ignorance of the state of affairs in the black hole interior. The
more possibilities there are for what could be going on in the black hole
interior, the more ignorant you will be about which configuration the system is
in. So this entropy measures ignorance.
Page’s discovery was
that if you assume that the evolution of the universe doesn’t lose information,
then, if you start out with zero ignorance about the universe before a black
hole forms, eventually you’re going to end up with zero ignorance once the
black hole is gone, since all the information that went in has come back out.
That’s in conflict with what Hawking derived, which was that eventually you end
up with ignorance.
You characterize Page’s
insight and all other work on the information paradox prior to 2019 as
“understanding the problem better.” What happened in 2019?
The activity that
started in 2019 is the steps towards actually resolving the problem. The two
papers that kicked this off were work by
myself, Ahmed Almheiri, Don Marolf and Henry Maxfield and,
in parallel, the second paper, which
came out at the same time, by Geoff
Penington. We submitted our papers on the same day and coordinated
because we knew we were both onto the same thing.
The idea was to
calculate the entropy in a different way. This is where Don Page’s calculation
was very important for us.
If we use Hawking’s method and his assumptions, we get a formula for the
entropy which is not consistent with unitarity. Now we want to
understand how we could possibly do a calculation that would give us the curve of the entropy that Page
proposed, which goes up then comes back down.
And for this we relied
on a proposal that Aron Wall and I gave in 2014: the quantum extremal surface
proposal, which essentially states that the so-called quantum-corrected area of a certain surface
inside the black hole is what computes the entropy. We said, maybe
that’s a way to do the quantum gravity calculation that gives us a unitary
result. And I will say: It was kind of a shot in the dark.
When did you realize
that it worked?
This entire time is a
bit of a daze in my mind, it was so exciting; I think I slept maybe two hours a
night for weeks. The calculation came together over a period of three weeks, I
want to say. I was at Princeton at the time. We just had a meeting on campus. I
have a very distinct memory of driving home, and I was thinking to myself, wow,
this could be it.
The crux of the matter
was, there’s more than one quantum extremal surface in the problem. There’s one
quantum extremal surface that gives you the wrong answer — the Hawking answer.
To correctly calculate the entropy, you have to pick the right one, and the
right one is always the one with the smallest quantum-corrected area. And so
what was really exciting — I think the moment we realized this might really
actually work out — is when we found that exactly at the time when the entropy
curve needs to “turn over” [go from increasing to decreasing], there’s a jump.
At that time, the quantum extremal surface with the smallest quantum-corrected
area goes from being the surface that would give you Hawking’s answer to a new
and unexpected one. And that one reproduces the Page curve.
What are these quantum extremal surfaces, exactly?
Let me try to intuit a
little bit what a classical, non-quantum extremal surface feels like. Let me
begin with just a sphere. Imagine that you place a light bulb inside of it, and
you follow the light rays as they move outward through the sphere. As the light
rays get farther and farther away from the light bulb, the area of the spheres
that they pass through will be getting larger and larger. We say that the
cross-sectional area of the light rays is getting larger.
That’s an intuition that
works really well in approximately flat space where we live. But when you
consider very curved space-time like you find inside a black hole, what can
happen is that even though you’re firing your light rays outwards from the
light bulb, and you’re looking at spheres that are progressively farther away
from the bulb, the cross-sectional area is actually shrinking. And this is
because space-time is very violently curved. It’s something that we call
focusing of light rays, and it’s a very fundamental concept in gravity and
general relativity.
The extremal surface
straddles this line between the very violent situation where the area is
decreasing, and a normal situation where the area increases. The area of the
surface is neither increasing nor decreasing, and so intuitively you can think
of an extremal surface as kind of lying right at the cusp of where you’d expect
strong curvature to start kicking in. A quantum extremal surface is the same
idea, but instead of area, now you’re looking at quantum-corrected area. This
is a sum of area and entropy, which is neither increasing nor decreasing.
What does the quantum
extremal surface mean? What’s the difference between things that are inside
versus outside?
Recall that when the
Page curve turns over, we expect that our ignorance of what the black hole
contains starts to decrease, as we have access to more and more of its
radiation. So the radiation emitted by the hole must start to “learn” about the
black hole interior.
It’s the quantum
extremal surface that divides the space-time in two: Everything inside the
surface, the radiation can already decode. Everything outside of it is what
remains hidden in the black hole system, what’s not contained in the
information of the radiation. As the black hole emits more radiation, the
quantum extremal surface moves outwards and encompasses an ever-larger volume
of the black hole interior. By the time that black hole evaporates altogether,
the radiation has to be able to decode everything that way.
Tira Khan for Quanta Magazine
Now that we have an
explicit calculation that gives us a unitary answer, that gives us so many
tools to start asking questions that we could never ask before, like where does
this formula come from, what does it mean about what type of theory quantum gravity
is? Also, what is the mechanism in quantum gravity that restores unitarity? It
has something to do with the quantum extremal surface formula.
Most of the
justification for the quantum extremal surface formula comes from studying
black holes in “Anti-de Sitter” (AdS) space — saddle-shaped space with an outer
boundary. Whereas our universe has approximately flat space, and no boundary.
Why should we think that these calculations apply to our universe?
First, we can’t really
get around the fact that our universe contains both quantum mechanics and
gravity. It contains black holes. So our understanding of the universe is going
to be incomplete until we have a description of what happens inside a black
hole. The information problem is such a difficult problem to solve that any
progress — whether it’s in a toy model or not — is making progress towards
understanding phenomena that happen in our universe.
Now at a more technical
level, quantum extremal surfaces can be computed in different kinds of
space-times, including flat space like in our universe. And in fact there
already have been papers written on the behavior of quantum extremal
surfaces within different kinds of space-times and what types of entropy curves
they would give rise to.
We have a very firm interpretation
of the quantum extremal surface in AdS space. We can extrapolate and say that
in flat space there exists some interpretation of the quantum extremal surface
which is analogous, and I think that’s probably true. It has many nice
properties; it looks like it’s the right thing. We get really interesting
behavior and we expect to get unitarity as well, and so, yes, we do expect that
this phenomenon does translate, although the interpretation is going to be
harder.
You said at the
beginning of our conversation that we don’t know the solution to the
information paradox yet. Can you explain what a solution looks like?
A full resolution of the
information paradox would have to tell us exactly how the black hole
information comes out. If I’m an observer that’s sitting outside of a black
hole and I have extremely sophisticated technology and all the time in the
world — a quantum computer taking incredibly sophisticated measurements, all
the radiation of that black hole — what does it take for me to actually decode
the radiation to reconstruct, for instance, the star that collapsed and formed
the black hole? What process do I need to put my quantum computer through? We
need to answer that question.
So you want to find the
reverse algorithm that unscrambles the information in the radiation. What’s the
connection between that algorithm and quantum gravity?
This algorithm that
decodes the Hawking radiation is coming from the process in which quantum
gravity encodes the radiation as it evaporates at the black hole horizon. The
emergence of the black hole interior from quantum gravity and the dynamics of
the black hole interior, the experience of an object that falls into the black
hole — all of that is encoded in this reverse algorithm that quantum gravity
has to spit out. All of those are tied up in the question of “how does the
information get encoded in the Hawking radiation?”
You’ve lately been
writing papers about something called a python’s lunch. What’s that?
It’s one thing to ask how
can you decode the Hawking
radiation; you also might ask, how complex is the task of
decoding the Hawking radiation. And, as it turns out, extremely complex. So maybe the difference
between Hawking’s calculation and the quantum extremal surface calculation that
gives unitarity is that Hawking’s calculation is just dropping the
high-complexity operations.
It’s important to
understand the complexity geometrically. And in 2019 there was a paper by some of my colleagues that
proposed that whenever you have more than one quantum extremal surface, the one
that would be wrong for the entropy can be used to calculate the complexity of
decoding the black hole radiation. The two quantum extremal surfaces can be
thought of as sort of constrictions in the space-time geometry, and those of us
who have read Le Petit Prince see an elephant
inside a python, and so it has become known as a python’s lunch.
We proposed that multiple quantum extremal
surfaces are the exclusive source of high complexity. And these two papers that
you’re referring to are essentially an argument for this “strong python’s
lunch” proposal. That is very insightful for us because it identifies the part
of the geometry that Hawking’s calculation knows about and part of the geometry
that Hawking’s calculation doesn’t know about. It’s working towards putting his
and our calculations in the same language so that we know why one is right, and
the other is wrong.
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Where would you say we
currently stand in our effort to understand the quantum nature of gravity?
I like to think of this
as a puzzle, where we have all the edge pieces and we’re missing the center. We
have many different insights about quantum gravity. There are many ways in
which people are trying to understand it. Some by constraining it: What are
things that it can’t do? Some by trying to construct aspects of it: things that
it must do. My personal preferred approach is more to do with the information
paradox, because it’s so pivotal; it’s such an acute problem. It’s clearly
telling us: Here’s where you messed up. And to me that says, here’s a place
where we can begin to fix our pillars, one of which must be wrong, of our
understanding of quantum gravity.
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