Transcript Black Hole Evaporation, Unitarity, and Final State Projection

Black Hole Evaporation,
Unitarity, and Final State
Projection
Daniel Gottesman
Perimeter Institute
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
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
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 don’t we see them in atomic physics?
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:
• Doesn’t explain why we don’t see non-unitary
effects in atomic physics
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 don’t we see effects of virtual remnant
production in particle physics?
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
Penrose Diagram - Flat Space
Future timelike infinity
time
Future null
infinity
Light moves along 45º lines
Spacelike
infinity
Past null infinity
Past timelike infinity
Massive objects move
slower than light, at less
than 45º from vertical
Penrose Diagram - Black Hole
Singularity
Event horizon:
not even light
can escape
r=0
Future timelike infinity
Spacelike infinity
An object which stays
outside the black hole
An object which falls
into the black hole
Past timelike infinity
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.
Quantum Teleportation
time
Alice

1 quantum bit
Bell measurement:
produces 2 classical bits

Bob
(a,b)
XaZb

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
Black Hole Final State
Infalling matter


(I  UT)()
(Final state projection)
No communication
needed
U
Infalling Hawking
radiation
Outgoing Hawking radiation
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”
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.
Faster-Than-Light Communication
(Yurtsever & Hockney, hep-th/0402060)
Bob

Alice

0
Inside black hole


(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.
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.