Hyeong-Chan Kim* (Yonsei Univ. Korea)

1. Informational approach to Black hole and Dark Energy 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

2. Outlines • Landauer’s Principle of information erasure • Classical information erasure process • Black hole as a maximal entropy object • arXiv:0709.3573 • Rolf of Entanglement energy in Cosmology (erasing information consumes energy) JCAP 08(2007)005   (hep-th/0701199)

3. Information erasure • Information is always encoded in a physical system. • When information is erased there is always an energy cost larger than • k T log 2per classical bit to be paid. T Landauer, IBM Jl. Res. Develop. 5, 183 (1961); M. B. Plenio and V. Vitelli quant-ph/0103108 Idealized information erasure process of one bit

4. Information is Physical! 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

5. 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

6. Black 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, Bekenstein(1973) Quantum nature of the temperature. The black hole entropy has only indirect link with the black hole mass through the geometric relation:

7. 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.

8. Black Hole as an Information Eraser We postulate that the black hole is an object attaining maximal information erasure. Temperature = T 1 bit of information erased and the system is absorbed into the bath. T, 1 bit • Temperature= Hawking temperature • Mass = M • Maximal information erasure implies the Landauer’s bound. 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. First law, Discrete.

9. 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) The black hole mass is completely determined from its information contents. All masses should be converted into missing information before they enter the horizon. Units: How does this conversion happen? Future research topic!

10. 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

11. 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=4pM^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.

12. 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:

13. Approximate solution For 0 < or

14. Asymptotic solution For intermediate values we introduce a large value H  is an exact solution which maximize the black hole entropy.

15. Black hole entropy and mass Using , we get Mass spectrum of a spherical black hole:

16. 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)

17. 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:

18. 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.

19. Newscientist, Black hole Universe http://space.newscientist.com/channel/astronomy/cosmology/mg19626243.600-blackhole-universe-might-explain-dark-energy.html

20. Relativity, Informatics and Quantum physics Classical Physics Particle physics Gauge Theory Special relativity General relativity QFT Gravity and cosmology Entanglement Quantum Physics Quantum Gravity Quantum information Informatics String Physics String theory

21. Twomistakes? of Einstein great 1) The universe is static “The biggest blunder of my life!”  Give birth to the modern cosmology 2) No correlation is faster than light “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!

22. Entanglement for many fields QKD Q. Computing Entanglement Quantum complexity Black hole Cosmology Foundation of Quantum physics theory Cf) There are already many attempts to relate entanglement (from '80s) and Landauer's principle with Black hole physics

23. Energy budget of the universe R Eq. of state Acceleration= Force metric

24. 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 Entanglement DE

25. 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! Information loss in the universe Rh ? dE=TdS If S is entanglement entropy, then this model is entanglement DE model

26. What is Entanglement? Singlet state 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.

27. There is Entanglement! Singlet state Bell inequality • Assumptions: • There is a hidden local variables • Locality: output of measurement B does not affect • output of A Bell inequality But Q.M. predicts ,and it is experimentally verified  Einstein was wrong again,  There IS a non-local quantum correlation = entanglement

28. , Entanglement entropy Ex) For The more entangled are A & B, the less information subsystem has. A B If there is an event horizon, it is natural to divide the system by the horizon.

29. *Key point* Entanglement dark energy JCAP08(2007)005 Entanglement energy Entanglement entropy [Q]Find Hawking temperature Spin deg. Of freedom (for massless scalar ) Entanglement energy Holograhic Dark Energy and d is obtained from quantum field theory!

30. Event horizon and particle horizon , WMAP team t ? But who knows the end of the universe???

31. Where does negative pressure come from? Freedman eq. & perfect fluid If energy of perfect fluid increases as the universe expands, this matter has a negative pressure For Holographic Dark Energy

32. Equation of state for DE , Concordance observation (Phantom) -1 < < -0.76 SNIa ? 1) For SM 2) For MSSM

33. Movahed et al,PRD, 73 (2006) 083518 SNIa SNIa+CMB SM MSSM SNIa+CMB+SDSS

34. Zhang & Wu, astro-ph/0701405

35. 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