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

OutlinesOutlines

Landauer’s Principle of information erasure

Classical information erasure process

Black hole as a maximal entropy object arXiv:0709.3573Rolf of Entanglement energy in Cosmology

(erasing information consumes energy)

JCAP 08(2007)005   (hep-th/0701199)

Information erasureInformation erasure

• 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.

Idealized information erasure process of one bit

Landauer, IBM Jl. Res. Develop. 5, 183 (1961);M. B. Plenio and V. Vitelliquant-ph/0103108

T

Landauer’s principleLandauer’s principle

• Erasing information dS consumes energy dE=TdS• Solves Maxwell’s demon problem: Bennett(1982)

Maxwell’s demon problem by Landauer’s principle

M. B. Plenio and V. Vitelliquant-ph/0103108

T

Gravitational distortions caused by a black hole in front of the Large Magellanic cloud

Black hole in front of large Magellanic Cloud From NASA Today’s Image

Black holeBlack hole Four law of black hole mechanics ~ thermodynamics:

The variations of mass and area are related each other by surface gravity. Hawking found that the black hole really radiates! (Hawking,1975)

Speculations of the quantum gravity origin: Entropy bound, Holographic principle, Holographic dark energy model, space-time non-commutativity

For the Schwarzschild black hole, the first law becomes,

Quantum nature of the temperature.

The black hole entropy has only indirect link with the black hole mass through the geometric relation:

Bekenstein(1973)

Information loss in black holeInformation 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?” usingLandauer’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 EraserBlack Hole as an Information Eraser

We postulate that the black hole is an object attaining maximal information erasure.

Temperature= Hawking temperature

Mass = M Maximal information erasure implies the Landauer’s bound.

First law,Discrete.

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.

Temperature = T1 bit of information erased and the system is absorbed into the bath.

T,1 bit

Black Hole as an EraserBlack 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:

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!

(4)

Quantum black holeQuantum 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), A = 4 log 3.Corichi et al.(2007). Loop quantum gravity

Quantum black hole and informationQuantum 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 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 massQuantized black hole massLet 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 solutionApproximate solution

For 0 < or

Asymptotic solutionAsymptotic solutionFor intermediate values

we introduce a large value H

is an exact solution which maximize the black hole entropy.

Black hole entropy and massBlack hole entropy and massUsing , we get

Mass spectrum of a spherical black hole:

Missing information?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?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).

Use effective temperature:

The consumption of one bit of information decreased the temperature of the black hole to:

Deformed Recurrence relation:

Changes the subleading contribution of entropy:

RemarksRemarks

•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.

There is a minimum black hole mass:

Implies the existence of maximum of the black hole temperature:

Newscientist, Black hole Universe

http://space.newscientist.com/channel/astronomy/cosmology/mg19626243.600-blackhole-universe-might-explain-dark-energy.html

Informatics

Relativity, Informatics and Quantum physicsRelativity, Informatics and Quantum physics

Special relativity

General relativity

Quantum Gravity

Quantum Physics

Entanglement

String theory

QFT

Gauge Theory

Particle physics

Quantum information

Gravity and cosmology

String Physics

Classical Physics

TwoTwo mistakes? of Einsteinmistakes? of Einstein

“The biggest blunder of my life!”

Is there Non-local quantum correlation (Spooky action at a distance)?

Two great puzzles of modern physics,Two great puzzles of modern physics,

They seem to be related!

1) The universe is static

R 4 ( 3 )

R 3

p

2) No correlation is faster than light

“God does not play dice!”

|z+>|z-> - |z->|z+>

Give birth to the modern cosmology

Give a birth to quantum information

+

Entanglement

QKD

Entanglement for many fieldsEntanglement for many fields

Q. Computing

Black holeQuantum complexity

CosmologyFoundation of

Quantum physicstheory

Cf) There are already many attempts to relate entanglement (from '80s) and Landauer's principle with Black hole physics

Energy budget of the universeEnergy budget of the universe

Acceleration= ForceEq. of state

=0

1

3

metric

R

Candidates for dark energyCandidates 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 universeInformation loss in the universe

Rh

?

dE=TdS

If S is entanglement entropy, then this model is entanglement DE model

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!

What is Entanglement?What is Entanglement?

Singlet state

B|z+> |z-> - |z-> |z+>

| +> |x-> - |x-> |x+>xA B A

A B A B

• 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=Non-local quantum correlation

= Spooky action at a distance?QM is incomplete. We need something more than wave-function.

Entanglement

According to Copenhagen interpretation

A

B

There There isis Entanglement! Entanglement!

But Q.M. predicts ,and it is experimentally verified Einstein was wrong again, There IS a non-local quantum correlation = entanglement

Singlet state |z+> |z-> - |z-> |z+>

| +> |x-> - |x-> |x+>xA B A B

A B A B

Bell inequality Assumptions:1) There is a hidden local variables2) Locality: output of measurement B does not affect output of A

| ( , ) ( , ') ( ', ') ( ', ) | 2P a b P a b P a b P a b

2 2

Bell inequality

Entanglement entropyEntanglement entropy

A B

If there is an event horizon, it is natural to divide the system by the horizon.

The more entangled are A & B, the less information subsystem has.

Ex)

A

( log ) ( log )Ent A A B BS Tr Tr

,

|z+>|z-> - |z->|z+>For

Entanglement dark energyEntanglement dark energy

( for massless scalar )

Spin deg. Of freedom

Entanglement energy

Entanglement entropy

Hawking temperature

Holograhic Dark Energy and d is obtained from quantum field theory!

[Q]Find

Entanglement energy

Ent

JCAP08(2007)005*Key point*

t

hRPR

Event horizon and particle horizonEvent horizon and particle horizon

But who knows the end of the universe???

WMAP team

?

,

Where does negative pressure come from?Where does negative pressure come from?

3

2

( )

( 3 )

d Rp

dR R

2 2

2

3 P

h

d M

R

211

3 d

Freedman eq. & perfect fluid

If energy of perfect fluid increases as the universe expands, this matter has a negative pressure

For Holographic Dark Energy

Equation of state for DEEquation of state for DE

1) For SM

2) For MSSM

(Phantom) -1 < < -0.76 SNIaobservation

Concordance,

?

118dofN

244dofN

0 0.93

0.95d

0 0.75

1.36d

SNIa

SNIa+CMB

SNIa+CMB+SDSS

Movahed et al,PRD, 73 (2006) 083518

SM

MSSM

Zhang & Wu, astro-ph/0701405

ConclusionsConclusionsWithout

• 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

Thank you very much

We suggest a new line of approach using quantum information scienceto tackle dark energy and black hole problemsWhat we need for DE may be not a new physics or new material but a new face of old quantum physics.