The Black Hole Information Paradox: aResolution on the Horizon?
Netta Engelhardt
MIT

Colloquium, Extreme Universe Project

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Black Hole Information Paradox

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Black Hole Information Paradox

1. What is it?

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Black Hole Information Paradox

1. What is it?

2. Why study it?

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Black Hole Information Paradox

1. What is it?

2. Why study it?

3. How to make progress on it?

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Information Paradox: the whatI“semiclassical gravity”: weakly coupled limit of quantum gravity

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Information Paradox: the whatI“semiclassical gravity”: weakly coupled limit of quantum gravity

I

Should be valid near event horizons of (large) black holes.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Information Paradox: the whatI“semiclassical gravity”: weakly coupled limit of quantum gravity

I

Should be valid near event horizons of (large) black holes.

I

The information paradox: semiclassical gravity prediction
contradicts QM. Fixing it requires large modifications tosemiclassical gravity at the event horizon of a black hole.

Image credit: Event Horizon Telescope

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Information Paradox: the what
Semiclassical gravity predicts that black holes evaporate

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Information Paradox: the what
Semiclassical gravity predicts that black holes evaporate... and along the way violate unitary evolution of closed quantum
systems.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Information Paradox: the what
Semiclassical gravity predicts that black holes evaporate... and along the way violate unitary evolution of closed quantum
systems. In direct violation of unitarity of quantum mechanics!

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: the why

I

Violations of unitarity of closed quantum systems (information loss)⇒ loss of determinism

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: the why

I

Violations of unitarity of closed quantum systems (information loss)⇒ loss of determinism

I

Black holes exist thanks, LIGO, EHT!, so nature has a definitive answer. And
furthermore, without an answer to this question, our description ofphysical phenomena in the universe is incomplete.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: the why

I

Violations of unitarity of closed quantum systems (information loss)⇒ loss of determinism

I

Black holes exist thanks, LIGO, EHT!, so nature has a definitive answer. And
furthermore, without an answer to this question, our description ofphysical phenomena in the universe is incomplete.

I

Ultimately, the information paradox has a lot to teach us about
quantum gravity!

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Information Paradox: Then and Now
Then:
I

Quantum gravity is necessary to see information conservation.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Information Paradox: Then and Now
Then:
I

Quantum gravity is necessary to see information conservation.

I

Basic idea: semiclassical gravity is inconsistent with unitaryevaporation.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then and Now
Then:
I

Quantum gravity is necessary to see information conservation.

I

Basic idea: semiclassical gravity is inconsistent with unitaryevaporation.

In 2019:I

A purely semiclassical analysis consistent with unitary evaporation.
Almheiri, Engelhardt, Marolf, Maxfield; Penington

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then and Now
Then:
I

Quantum gravity is necessary to see information conservation.

I

Basic idea: semiclassical gravity is inconsistent with unitaryevaporation.

In 2019:I

A purely semiclassical analysis consistent with unitary evaporation.
Almheiri, Engelhardt, Marolf, Maxfield; Penington I think it’s safe to say that many (most?) of
us thought this was impossible.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Overview

The Information Paradox: Then
The Black Hole Information Paradox: 2019
The Black Hole Information Paradox: Towards a Resolution
Conclusions

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

BH Entropy: Wheeler’s Gedankenexperiment“No Hair Theorem”: black holes in classical gravity have no microstates.

“Teacup Experiment”
No microstates ⇒ no entropy. Throw a hot teacup into the black hole –and decrease the entropy of the universe.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Second Law of Thermodynamics
If your theory is found to be against the second law of thermodynamics I can give
you no hope; there is nothing for it but to collapse in deepest humiliation.
– Sir Arthur Eddington

The Information Paradox: Then

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Conclusions

Black Hole Entropy

Bekenstein: Black holes are thermal: they have temperature and entropy
due to quantum gravity microstates:
SBH =Area[ event horizon ].
4G~

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Black Hole Entropy

Bekenstein: Black holes are thermal: they have temperature and entropy
due to quantum gravity microstates:
SBH =Area[ event horizon ].
4G~

Tjey also have a temperature T ∝ M−1 .

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Black Hole Entropy

Bekenstein: Black holes are thermal: they have temperature and entropy
due to quantum gravity microstates:
SBH =Area[ event horizon ].
4G~

Tjey also have a temperature T ∝ M−1 .
This is due to quantum corrections: black holes in classical gravity are
perfect absorbers.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes
Temperature ⇒ radiation. If
TBH > Tsurroundings
radiation ⇒ mass decreases
T ∝ M−1
BH evaporates until it “explodes”.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes
Temperature ⇒ radiation. If
TBH > Tsurroundings
radiation ⇒ mass decreases
T ∝ M−1
BH evaporates until it “explodes”.
Some numbers:
I

Sagittarius A∗ , T ∼ 10−14 K

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes
Temperature ⇒ radiation. If
TBH > Tsurroundings
radiation ⇒ mass decreases
T ∝ M−1
BH evaporates until it “explodes”.
Some numbers:
I

Sagittarius A∗ , T ∼ 10−14 K

I

Solar mass black hole, T ∼ 10−8 K

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes
Temperature ⇒ radiation. If
TBH > Tsurroundings
radiation ⇒ mass decreases
T ∝ M−1
BH evaporates until it “explodes”.
Some numbers:
I

Sagittarius A∗ , T ∼ 10−14 K

I

Solar mass black hole, T ∼ 10−8 K

I

Lunar mass black hole, T ∼ TCMB

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes
Temperature ⇒ radiation. If
TBH > Tsurroundings
radiation ⇒ mass decreases
T ∝ M−1
BH evaporates until it “explodes”.
Some numbers:
I

Sagittarius A∗ , T ∼ 10−14 K

I

Solar mass black hole, T ∼ 10−8 K

I

Lunar mass black hole, T ∼ TCMB

I

Coronavirus-sized black hole, T ∼ room temperature.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Collapsing Black Holestt=0Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Collapsing Black Holestt=0Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Collapsing Black Holestt=0Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Collapsing Black Holestt=0Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

Evaporating Black HolesThe Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

Evaporating Black HolesThe Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

Evaporating Black HolesThe Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

Evaporating Black HolesThe Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

Evaporating Black HolesThe Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Evaporating Black Holes

Semiclassical gravity ⇒ information loss during evaporation.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Hawking Radiation In a Nutshell
1. Some pure state collapses into a black hole.
Before the black hole forms:
SvN [ρoutside BH ] = SvN [ρuniverse ] = 0

N PARADOXINFORMATIOThe Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Hawking Radiation In a Nutshell
1. Some pure state collapses into a black hole.
Before the black hole forms:
SvN [ρoutside BH ] = SvN [ρuniverse ] = 0
2. At intermediate times:
SvN [ρoutside BH ] = SvN [ρrad ] > 0
N PARADOXINFORMATIOThe Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Hawking Radiation In a Nutshell
1. Some pure state collapses into a black hole.
Before the black hole forms:
SvN [ρoutside BH ] = SvN [ρuniverse ] = 0
2. At intermediate times:
SvN [ρoutside BH ] = SvN [ρrad ] > 0
N PARADOXINFORMATIO

3. After the BH evaporates, we must have
SvN [ρrad ] = SvN [ρuniverse ] = 0
if time evolution is unitary.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Hawking Radiation In a Nutshell
1. Some pure state collapses into a black hole.
Before the black hole forms:
SvN [ρoutside BH ] = SvN [ρuniverse ] = 0
2. At intermediate times:
SvN [ρoutside BH ] = SvN [ρrad ] > 0
N PARADOXINFORMATIO

3. After the BH evaporates, we must have
SvN [ρrad ] = SvN [ρuniverse ] = 0
if time evolution is unitary.
4. So we expect a non-monotonic curve for SvN [ρrad ].

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Page Curve

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

The Paradox
I

To compute SvN [ρrad ], we need a description of the physics at theblack hole event horizon.

I

Semiclassical gravity: the limit where large quantum gravity effects
are suppressed; should be valid at the horizon.

I

Semiclassical gravity
curve:

Hawking⇒−trρrad ln ρrad does not follow the Page

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Caricature of Information Loss

Quick argument for info loss:|ψi = |+i|−i + |−i|+i

After evaporation, Alice disappears from the universe – even though theuniverse is a closed system.
State after evaporation is just ρBob = 21 I.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Information Loss in Hawking Radiation

In toy model of the EPR pair, the initial state of the pair is pure:
Sinitial = 0.
After the black hole has finished evaporating,
Sfinal = SBob = log 2 6= 0
The entropy has increased: the system was not evolving unitarily.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Hawking’s Calculation

S

SHawkingtConclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Hawking’s Calculation
S

SHawkingtConclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Hawking’s Calculation
S

SHawkingtConclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Overview

The Information Paradox: Then
The Black Hole Information Paradox: 2019
The Black Hole Information Paradox: Towards a Resolution
Conclusions

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Progress: Computing the Entropy of Hawking RadiationI

It is hard to see where Hawking’s analysis goes wrong.

The Information Paradox: Then

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Conclusions

Progress: Computing the Entropy of Hawking RadiationI

It is hard to see where Hawking’s analysis goes wrong.

I

Are there large corrections from quantum gravity in a regime where
there shouldn’t be?

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Progress: Computing the Entropy of Hawking RadiationI

It is hard to see where Hawking’s analysis goes wrong.

I

Are there large corrections from quantum gravity in a regime where
there shouldn’t be?

I

3 years ago: a semiclassical calculation of the Page curve, but using
a different – holographic – formula for SvN .

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Progress: Computing the Entropy of Hawking RadiationI

It is hard to see where Hawking’s analysis goes wrong.

I

Are there large corrections from quantum gravity in a regime where
there shouldn’t be?

I

3 years ago: a semiclassical calculation of the Page curve, but using
a different – holographic – formula for SvN .

I

This formula is a bit of a black box: can be interpreted as indirect
input from quantum gravity

The Information Paradox: Then

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Conclusions

Holography
Holography
Quantum gravity “in a box” (with Anti-de Sitter boundary conditions) isdual to a lower-dimensional nongravitational QFT.

QF
The boundary: nongrav

T

Colloquially, we call the gravitational theory the bulk, and thenon-gravitational theory the boundary.

The Information Paradox: Then

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Conclusions

Holography: a Black Hole is just a Quantum System
This means that a black hole in AdS is just an ordinary, nongravitational
quantum system.

image credit: ESI Programme on AdS Holography and the Quark-Gluon Plasma... nongravitational (closed) quantum systems evolve unitarily.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Computing the Page Curve

We know that SvN [ρrad ] computed in the nongravitational “boundary”
theory follows the Page curve.

AdS/CFT is a dictionary: it relates quantities in the boundary theory to
the bulk theory.
What quantity in the bulk theory translates to SvN [ρrad ] as computed by
the boundary theory?

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Technical Aside: Auxiliary BathTechnically, AdS black holes don’t evaporate due to reflecting boundary
conditions at infinity (the radiation just bounces back into the black hole).
To force them to evaporate (and make them look more like flat space), we
introduce a nongravitating cold bath at infinity.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Technical Aside: Auxiliary BathTechnically, AdS black holes don’t evaporate due to reflecting boundary
conditions at infinity (the radiation just bounces back into the black hole).
To force them to evaporate (and make them look more like flat space), we
introduce a nongravitating cold bath at infinity. In the dual CFT can beviewed as coupling in an auxiliary CFT (the “bath”) at lower
temperature. The joint CFT+bath system evolves unitarily.

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Holographic von Neumann Entropy
SvN in AdS/CFT Ryu-Takayanagi, Hubeny-Rangamani-Takayanagi, Faulkner-Lewkowycz-Maldacena, Engelhardt-Wall
The von Neumann entropy of the radiation is given by:
SvN [ρrad ] =Area[χ]+ SvN [ρOut[χ] ]4where χ is a “quantum extremal surface”: if you slightly perturb χ, thesum Area4 [χ] + SvN [ρOut[χ] ] won’t change to leading order in theperturbation.

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Holographic von Neumann Entropy
SvN in AdS/CFT Ryu-Takayanagi, Hubeny-Rangamani-Takayanagi, Faulkner-Lewkowycz-Maldacena, Engelhardt-Wall
The von Neumann entropy of the radiation is given by:
SvN [ρrad ] =Area[χ]+ SvN [ρOut[χ] ]4where χ is a “quantum extremal surface”: if you slightly perturb χ, thesum Area4 [χ] + SvN [ρOut[χ] ] won’t change to leading order in theperturbation.
We get ρout[χ] from a bipartition of the system into interior of χ andexterior.

ρOut[]

Formula justified from euclidean gravity in evaporating black hole setup by Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini; Penington,
Shenker, Stanford, Yang

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Quantum Extremal Surfaces
Initially, the QES is the empty set.
SvN [ρbdy ] =Area[∅]+ SvN [ρall ] = SvN [ρall ]
4G~

ρall

With time SvN [ρall ] grows.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

QESs in Evaporating BHs

The Black Hole Information Paradox: Towards a Resolution

Almheiri, Engelhardt, Marolf, Maxfield; Penington

About halfway through evaporation, a new quantum extremal surface
appears:

ρOut[]ρOut[]As we evolve forward in time, Sgen [χ] decreases.

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

QESs in Evaporating BHs

The Black Hole Information Paradox: Towards a Resolution

Almheiri, Engelhardt, Marolf, Maxfield; Penington

About halfway through evaporation, a new quantum extremal surface
appears:

ρOut[]ρOut[]

As we evolve forward in time, Sgen [χ] decreases.
This alternative computation of SvN in gravity does yield a unitary Page
curve.

Conclusions

The Information Paradox: Then

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Conclusions

TakeawaysI

We’ve computed the unitary Page curve using semiclassical gravity!

I

What does this tell us?

I

For example, how do we see that information has escapes, and thatthe black hole interior is now encoded in the radiation?

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

The Entanglement Wedge

To answer this, we’ll take a detour by asking another question: what is
the significance of the region Out[χ]?

Reconstruction in AdS/CFT?
AdS/CFT is a quantum error correcting code see work beginning with Almheiri, Dong, Harlow.
How much of the bulk can we reconstruct from the state ρbdy of thenongravitational dual?

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

The Entanglement Wedge

To answer this, we’ll take a detour by asking another question: what is
the significance of the region Out[χ]?

Reconstruction in AdS/CFT?
AdS/CFT is a quantum error correcting code see work beginning with Almheiri, Dong, Harlow.
How much of the bulk can we reconstruct from the state ρbdy of thenongravitational dual?
Everything in Out[χ].∗Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

The Entanglement Wedge of the Radiation
After the Page time, this is most of the black hole interior: informationthat fell into the black hole is now available in the radiation.

dual

FT

to C

t
ia



n

io

ρOut[]

adR

dual toradiation

CFT

How do we use this to find a resolution of the black hole information
paradox?

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Overview

The Information Paradox: Then
The Black Hole Information Paradox: 2019
The Black Hole Information Paradox: Towards a Resolution
Conclusions

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

To recap:

Problem
The semiclassical approximation is:
1. Wrong: it is inconsistent with unitarity, i.e. we get the “Hawking”
entropy curve from it.
2. But not that wrong: we can still use the effective description tocompute, e.g. the unitary Page curve Page; Penington; Almheiri, NE, Marolf, Maxfield,
without resorting to nonperturbatively suppressed effects – but by
using the QES formula NE, Wall rather than the standard −trρ ln ρ.
So, just how seriously are we supposed to take semiclassical gravity?

Conclusions

The Information Paradox: Then

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Conclusions

Wrong and Right at the Same TimeI

The information paradox: an apparent breakdown of the effective
field theory where naively semiclassical gravity should be valid.

I

Possible conclusion: don’t take EFT seriously near the event
horizon...

I

The QES formula: take EFT seriously, but not too seriously.

I

Route towards resolution: understanding in what ways EFT is rightand in what ways it’s wrong in a black hole setting.

The Information Paradox: Then

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Accessibility of Information
I

If you throw a diary into the black hole, some time later its
information should be accessible in the radiation.

Conclusions

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Accessibility of Information
I

If you throw a diary into the black hole, some time later its
information should be accessible in the radiation.

I

Hayden-Preskill: Assume BH dynamics drawn from unitary
2-design. Take an old black hole B and its radiation E. Throw |ii into
it. The info is recoverable from the radiation in a time logarithmic in
SBH :VEL |ΨiB0 EL = |ii1 ⊗ |φiB0 ,2where E is the early radiation, L is the late radiation (after |ii isthrown in) and B0 is the black hole after L has radiated (and 1 and 2
are factors of HLE ). But:

The Information Paradox: Then

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The Black Hole Information Paradox: Towards a Resolution

Conclusions

Accessibility of Information
I

If you throw a diary into the black hole, some time later its
information should be accessible in the radiation.

I

Hayden-Preskill: Assume BH dynamics drawn from unitary
2-design. Take an old black hole B and its radiation E. Throw |ii into
it. The info is recoverable from the radiation in a time logarithmic in
SBH :VEL |ΨiB0 EL = |ii1 ⊗ |φiB0 ,2where E is the early radiation, L is the late radiation (after |ii isthrown in) and B0 is the black hole after L has radiated (and 1 and 2
are factors of HLE ). But:

I

Harlow-Hayden: decoding the radiation is exponentially complex in
the entropy of the black hole. Aaronson: decoding the radiation ispolynomially hard ⇒ there are no injective one-way functions.

The Information Paradox: Then

A Proposal

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Akers, NE, Harlow, Penington, Vardhan; see also earlier work starting with Harlow-Hayden

If you don’t have access to exponentially complex information, you’dconclude the information isn’t there!

Complexity as a Cutoff
Semiclassical gravity effective field theory accurately describes all the
low-curvature physics that can be measured by any observer whose
computational power is bounded to be subexponential in SBH .

Conclusions

The Information Paradox: Then

A Proposal

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Akers, NE, Harlow, Penington, Vardhan; see also earlier work starting with Harlow-Hayden

If you don’t have access to exponentially complex information, you’dconclude the information isn’t there!

Complexity as a Cutoff
Semiclassical gravity effective field theory accurately describes all the
low-curvature physics that can be measured by any observer whose
computational power is bounded to be subexponential in SBH . There are
violations of EFT for exponential observables.

The Information Paradox: Then

A Proposal

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Akers, NE, Harlow, Penington, Vardhan; see also earlier work starting with Harlow-Hayden

If you don’t have access to exponentially complex information, you’dconclude the information isn’t there!

Complexity as a Cutoff
Semiclassical gravity effective field theory accurately describes all the
low-curvature physics that can be measured by any observer whose
computational power is bounded to be subexponential in SBH . There are
violations of EFT for exponential observables. These violations are
critical for resolving the black hole information problem, but they cannot
be detected by any subexponential observer.

The Information Paradox: Then

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Conclusions

Does this work?

We want to show that it is possible to resolve the tension between thethree fundamental aspects of the black hole information paradox:
1. A unitary S-matrix;
2. A finite black hole entropy with a state-counting interpretation;
3. A black hole interior which is described to a good approximation by
gravitational effective field theory.
By modifying the last bulletpoint so it becomes...

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Does this work?

We want to show that it is possible to resolve the tension between thethree fundamental aspects of the black hole information paradox:
1. A unitary S-matrix;
2. A finite black hole entropy with a state-counting interpretation;
3. A black hole interior which is described to a good approximation by
gravitational effective field theory for subexponentially complex
measurements.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

Tension Can be Resolved in a Tensor Network Model
Model the map between semiclassical gravity and QG as a non-isometric
encoding from one Hilbert space to the next:
V : HEFT → HQG
Can accommodate all of the requisite elements: there are significant
violations of EFT at the event horizon of a black hole, but this iscompletely undetectable to a semiclassical observer.

In this model, the entropy of the radiation is computed by QESs.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions

The Non-Isometric Map

The map V annihilates a large number of “null states” that have no image
in HQG , resolving the tension between the spuriously large Hilbert spaceof EFT and the much smaller HQG .
Fortunately – and surprisingly – this can be done without being detectedby subexponential observers (due to measure concentration arguments).
Of course, even though the non-isometric nature of the map is hiddenfrom an observer in the EFT, the null states are absolutely critical for thismodel to provide a toy model for a resolution of the black hole
information paradox.

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Overview

The Information Paradox: Then
The Black Hole Information Paradox: 2019
The Black Hole Information Paradox: Towards a Resolution
Conclusions

Conclusions

The Information Paradox: Then

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

SummaryI

The black hole information problem is a longstanding paradox inmodern theoretical physics

I

In a little over three years, we’ve come to understand how to use
semiclassical gravity to make progress on it and propose a path
towards a resolution

I

We’ve found that QESs are an essential aspect of understanding
how and when semiclassical gravity is valid.

I... and we now have a proposal for resolving the paradox.

Conclusions

The Information Paradox: ThenThank you!

The Black Hole Information Paradox: 2019

The Black Hole Information Paradox: Towards a Resolution

Conclusions