Black%20Hole%20Evaporation,%20Unitarity,%20and%20Final%20State%20Projection

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Black Hole Evaporation, Unitarity, and Final
State Projection

• Daniel Gottesman
• Perimeter Institute

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Black Hole Evaporation

• Black holes emit Hawking radiation at a
  temperature T 1/(8?M), where M black hole
  mass in Planck units
• Black holes have an entropy S A/4 associated
  with this temperature
• Outgoing Hawking radiation is entangled with
  some infalling Hawking radiation carrying
  negative energy, reducing black hole mass

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Information Loss Problem

• When a black hole evaporates, what happens to
  information about the matter that formed it or
  fell into it?
• Does quantum mechanics need to be modified to
  describe black hole evaporation?
• Is black hole evaporation unitary?

When you have eliminated the impossible,
whatever remains, however improbable, must be the
truth
Sherlock Holmes, The Sign of Four
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Solution 1 Information is Lost
When a black hole evaporates, the information is
really gone.
Advantages

• Agrees with semiclassical calculation

Disadvantages

• Trouble with energy conservation?
• Lose either time reversal invariance or
  predictability
• Implies quantum gravity includes non-unitary
  processes. Why dont we see them in atomic
  physics?

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Variant Solution Baby Universe
A baby universe is born at a black hole
singularity and the information goes there.
Advantages

• Overall unitarity is preserved

Disadvantages

• Doesnt explain why we dont see non-unitary
  effects in atomic physics

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Solution 2 Black Hole Remnants
Black hole evaporation leaves a remnant particle,
with mass comparable to the Planck mass,
containing all information.
Advantages

• No need to modify either quantum mechanics or
  semiclassical calculation

Disadvantages

• Very peculiar particles, with fixed mass, but
  unlimited entropy
• Why dont we see effects of virtual remnant
  production in particle physics?

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Solution 3 Information Escapes
The information escapes with the Hawking
radiation, subtly encoded in correlations between
particles.
Advantages

• Preserves unitarity
• Explains entropy as microstates of black hole
  horizon

Disadvantages

• Escaping information seems to require either
  quantum cloning or faster-than-light travel

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Penrose Diagram - Flat Space
Future timelike infinity
time
Future null infinity
Light moves along 45º lines
Spacelike infinity
Massive objects move slower than light, at less
than 45º from vertical
Past null infinity
Past timelike infinity
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Penrose Diagram - Black Hole
Future timelike infinity
Singularity
Spacelike infinity
Event horizon not even light can escape
An object which stays outside the black hole
An object which falls into the black hole
r0
Past timelike infinity
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Why quantum cloning?
For a large black hole, the horizon seems
(locally) like nothing special infalling object
should not be destroyed. (Copy 1)
But the escaping Hawking radiation also has a
copy of the information. (Copy 2)
There exist spacelike slices that include both
copies quantum mechanics is violated on them.
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Quantum Teleportation
time
1 quantum bit
???
Bell measurement produces 2 classical bits
Alice
???????????
(a,b)
Bob
XaZb
???
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Black Hole Final State
(Horowitz Maldacena, hep-th/0310281, JHEP 2004)
Black hole singularity projects onto some
maximally entangled final state of matter plus
infalling Hawking radiation.

• Acts like quantum teleportation, but with some
  specific measurement outcome
• Outgoing state rotated by some complicated
  unitary from original matter, so looks thermal,
  but is actually unitary
• Strangeness only required at singularity, which
  is strange anyway

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Black Hole Final State
Infalling matter
???
(I ? UT)(???????????) (Final state projection)
No communication needed
???????????
U???
Infalling Hawking radiation
Outgoing Hawking radiation
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Problem with Interactions
(DG, Preskill, hep-th/0311269, JHEP 2004)
Suppose the infalling matter interacts with the
infalling Hawking radiation before hitting the
singularity
???
(I ? UT)(???????????) (Final state projection)
???????????
U???
Similar to Bennett Schumacher, Simulated time
travel
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Problem with Interactions
We can absorb the interactions into the final
state. The resulting evolution need not be
unitary! For instance
???
???
(Final state projection)
???
???????????
?0?
Note Input state of ?1? not allowed.
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Faster-Than-Light Communication
(Yurtsever Hockney, hep-th/0402060)
Bob
?0?
???????????
Inside black hole
Alice
???
(Final state projection)
???
???????????
Hawking radiation
?0?
If Alice drops her qubit into the black hole, Bob
always sees ?0?. Otherwise, Bob sees a mixture
of ?0? and ?1?.
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Summary

• Is black hole information unitary or not? There
  is no consensus.
• Black hole final state proposal pushes new
  physics to the black hole singularity while
  allowing information to escape.
• However, under perturbation, non-unitarity
  reappears and can even leak outside the black
  hole.