Transcript Black hole

Hyeong-Chan Kim* (Yonsei Univ. Korea)
Jae-Weon Lee (KIAS Korea),
Jungjai Lee (Daejin Univ. Korea),
KITPC “STrIng Theory and CoSmology”
2007, Oct. 10
Based on JCAP08(2007)005
and arXiv:0709.3573
Outlines

Landauer’s Principle of information erasure
(erasing information consumes energy)
 Classical information erasure process
 Black hole as a maximal entropy object
arXiv:0709.3573
 Rolf of Entanglement energy in Cosmology
JCAP 08(2007)005
(hep-th/0701199)
Information erasure
T
• Information is always
encoded in a physical
system.
• When information is
erased there is always an
energy cost larger than
k T log 2 per classical bit to
be paid.
Landauer, IBM Jl. Res.
Develop. 5, 183 (1961);
M. B. Plenio and V. Vitelli
quant-ph/0103108
Idealized information erasure process of one bit
Landauer’s principle
• Erasing information dS consumes energy dE=TdS
• Solves Maxwell’s demon problem: Bennett(1982)
T
M. B. Plenio and V. Vitelli
quant-ph/0103108
Maxwell’s demon problem by Landauer’s principle
Black hole in front of large Magellanic Cloud
From NASA
Today’s Image
Gravitational distortions caused by a black hole in front of
the Large Magellanic cloud
Black hole

Four law of black hole mechanics ~ thermodynamics:
For the Schwarzschild black
hole, the first law becomes,
 The variations of mass and area are related each other by surface gravity.
 Hawking found that the black hole really radiates! (Hawking,1975)
Bekenstein(1973)
Quantum nature of the temperature.
Speculations of the quantum gravity origin: Entropy bound, Holographic
principle, Holographic dark energy model, space-time non-commutativity
The black hole entropy has only indirect link with
the black hole mass through the geometric relation:
Information loss in black hole

What is the microscopic origin of the black hole entropy?




String theory,
Loop quantum gravity,
Brick wall,
Holographic principle etc.
 We ask “What happens if we lose information across horizon?” using
Landauer’s principle of information erasure.
The black hole mass is a direct consequence of
the fact that the black hole has maximal entropy.
• Here we do not need any help of geometric result
except for the black hole temperature.
 Quantum nature of the black hole  Information erasure
Merit: we don’t need to worry about the black hole’s internal structure since we
directly resort to our ignorance on the missing information.
Black Hole as an Information Eraser
Temperature = T
1 bit of information erased and
the system is absorbed into the
bath.
We postulate that the
black hole is an object
attaining maximal
information erasure.
T,
1 bit
 Temperature= Hawking temperature
The entropy of the thermal bath should
increase larger than k log 2.
The energy of the thermal bath should
increase larger than k T log 2.
 Mass = M
 Maximal information erasure implies
the Landauer’s bound.
First law,
Discrete.
Black Hole as an Eraser
 Zero temperature system has zero entropy.
 Assuming dS as an infinitesimal equation, we can integrate this
equation to get the relation between the entropy and mass:
(4)
Units:
The black hole mass is completely determined from its information contents.
All masses should be converted into missing information before they enter
the horizon.
How does this conversion happen? Future research topic!
Quantum black hole
 Black hole hides most of its information behind the horizon.
 Then, we may ask its quantum mechanical nature through the
informational erasure’s point of view.
Previous works on quantization of black hole:
Adiabatic invariance of the horizon area must be discrete on quantization!
Bekenstein (1974),
Hod (1998),
d A = 4 log 3.
Corichi et al.(2007). Loop quantum gravity
Quantum black hole and information
Consider a sequence of (N-1) bits of information erasing process bit by bit.
Start from Planck mass black hole, with one bit of information erased, S_1=log 2.
Mass M_1 is not a macroscopic quantity
• We do not require S=4 p M^2 in advance.
•Allow the possibility that quantum mechanical effect may alter
the relation.
The temperature of the black hole space-time is given by Hawking temperature.
•We discuss the possibility that the quantum gravity effect change
this temperature later in this talk.
Quantized black hole mass
Let the black hole absorb one bit of information. Then, the black hole mass
increases by
and the temperature of the black hole becomes
.
Recurrence formula:
Large N limit:
Approximate solution
For 0 <
or
Asymptotic solution
For intermediate values

is an exact solution which
maximize the black hole entropy.
we introduce a large value H
Black hole entropy and mass
Using
, we get
Mass spectrum of a spherical black hole:
Missing information?
Landauer’s principle explains the black hole mass from the contents of
missing information.
•Natural question is “how the missing information is represented in black hole
space-time?”
•A possible answer is the vacuum entanglement around the black hole.
Brustein(2006)
•The entanglement entropy is proportional to its area: Srednicki(1993).
•Entanglement entanglement entropy in adS/CFT: Fursaev(2006), Ryu
and Takayanagi(2006).
Fate of missing information?
•Horowitz, Maldacena conjecture on the final state of black hole
•Quantum information theory: The quantum information inside the black
hole can be transferred into the outside by quantum teleportation.Ahn(2006)
Quantum effect?
•Horizon area may fluctuate.
•Surface gravity and its temperature may also fluctuate.
•During the information absorption process, the temperature of the black hole
also changes. (Not an exact thermal bath).
The consumption of one bit of information
decreased the temperature of the black hole to:
Use effective temperature:
Deformed Recurrence relation:
Changes the subleading contribution of entropy:
Remarks
There is a minimum black hole mass:
Implies the existence of maximum
of the black hole temperature:
•Does this imply the existence of maximal temperature in physical system?
•If this is right, this may constrain the initial condition of our universe near the
Big Bang singularity.
Newscientist, Black hole Universe
http://space.newscientist.com/channel/astronomy/cosmolog
y/mg19626243.600-blackhole-universe-might-explain-darkenergy.html
Relativity, Informatics and Quantum physics
Particle physics
Classical
Physics
Gauge Theory
Special
relativity
General relativity
QFT
Gravity and cosmology
Entanglement
Quantum
Physics
Quantum information
Quantum Gravity
Informatics
String Physics
String theory
Two
mistakes? of Einstein
1) The universe is static
R
4 (   3 p)

+
R
3
“The biggest blunder of my life!”
Give birth to the modern cosmology
2) No correlation is faster than light
|z+>|z-> - |z->|z+>
“God does not play dice!”
Give a birth to quantum information
Is there Non-local quantum correlation (Spooky action at a distance)?
Two great puzzles of modern physics,
They seem to be related!
Entanglement for many fields
QKD
Quantum
complexity
Q. Computing
Entanglement
Cosmology
Black hole
Foundation of
Quantum physics
theory
Cf) There are already many attempts to relate entanglement (from '80s)
and Landauer's principle with Black hole physics
Energy budget of the universe

1
3
=0
R
Acceleration= Force
metric
Eq. of state
Candidates for dark energy
•Modified gravity
•Quintessence
•K-essence
•Quintom
•Chaplygin gas
•Phantom (w<-1)
•Braneworld
•Backreaction
•Cosmic string
•Vac. Energy, Casmir
•Quantum fluctuation
•Surface tension
•Holographic dark energy
•…. and more
Information loss in the universe
As the horizon of the universe increases
• More information disappears behind the horizon
• More dE= TdS consumed
• If this energy increases as scale factor increases, there
is negative pressure Dark Energy!
?
Rh
dE=TdS
If S is entanglement entropy, then this model is entanglement DE model
What is Entanglement?
Singlet state
|z+> A|z-> B - |z-> A|z+> B
B
| x +> A|x-> B - |x-> A|x+> B
A
Entanglement=Non-local quantum correlation
According to Copenhagen interpretation
•
Wave function instantaneously collapses when one party measure his particle.
•
If A get Z+, particle of B becomes Z- immediately regardless of distance of two parties
Violation of special relativity???
particles have no predetermined physical quantity before measurement
no physical reality?
•
Entanglement
= Spooky action at a distance?
QM is incomplete. We need something
more than wave-function.
There is Entanglement!
Singlet state
|z+> A|z-> B - |z-> A|z+> B
| x +> A|x-> B - |x-> A|x+> B
Bell inequality
Assumptions:
1) There is a hidden local variables
2) Locality: output of measurement B does not affect
output of A
| P(a, b)  P(a, b ')  P(a ', b ')  P(a ', b) | 2
Bell inequality
But Q.M. predicts 2 2 ,and it is experimentally verified
Einstein was wrong again,
There IS a non-local quantum correlation = entanglement
Entanglement entropy
,
SEnt  Tr (  A log  A )  Tr (  B log  B )
Ex)
For |z+>|z-> - |z->|z+>
The more entangled are A & B, the less information subsystem has.
A
A
B
If there is an event horizon, it is natural to divide the system by the horizon.
*Key point*
Entanglement dark energy
JCAP08(2007)005
Entanglement energy
Entanglement entropy
[Q]Find
Ent
Hawking temperature
Spin deg. Of freedom
(
for massless
scalar )
Entanglement energy
Holograhic Dark Energy and d is obtained
from quantum field theory!
Event horizon and particle horizon
,
WMAP team
Rh
RP
t

?
But who knows the end of the universe???
Where does negative pressure come from?
3d 2 M P2
 
Rh 2
d ( R3  )
p 
dR(3R 2 )
Freedman eq. & perfect fluid
If energy of perfect fluid increases as the universe expands, this matter
has a negative pressure
1  2  
   1 


3
d 
For Holographic
Dark Energy
Equation of state for DE
Concordance
,
observation
(Phantom) -1 <
?
SNIa
1) For SM
2) For MSSM
N dof  118
N dof  244
< -0.76
0
d
0
d
0.93
0.95
0.75
1.36
Movahed et al,PRD, 73 (2006) 083518
SNIa
SNIa+CMB
SM
MSSM
SNIa+CMB+SDSS
Zhang & Wu, astro-ph/0701405
Conclusions
Without
• Exotic particles or fields
• New Physics
• Modification of gravity
With
•
• SM fields and general relativity
• vacuum Entanglement & Q. information
We obtain a field theoretical model of Dark energy which
predicts observed equation of the state well.
• Need to find more exact input parameters
We suggest a new line of approach using quantum information science
to tackle dark energy and black hole problems
What we need for DE may be not a new physics or new material
but a new face of old quantum physics.
Thank you very much