1. 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 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. Vitelli quant-ph/0103108 T

4. Landauer’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. Vitelli quant-ph/0103108 T

5. 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

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

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= 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 = T 1 bit of information erased and the system is absorbed into the bath. T, 1 bit

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: 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)

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=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.

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 valueswe 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). 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:

18. Remarks 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:

19. Newscientist, Black hole Universe http://space.newscientist.com/channel/astronomy/cosmology/mg1 9626243.600-blackhole-universe-might-explain-dark-energy.html

20. Informatics Relativity, 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

21. Two mistakes? 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, They seem to be related! 1) The universe is static 2) No correlation is faster than light “God does not play dice!”  Give birth to the modern cosmology  Give a birth to quantum information

22. Entanglement QKD Entanglement for many fields Q. Computing Black hole Quantum complexity 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 Acceleration= Force Eq. of state metric R

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

25. Information 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!

26. What is Entanglement? Singlet state 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

27. There is Entanglement! But Q.M. predicts,and it is experimentally verified  Einstein was wrong again,  There IS a non-local quantum correlation = entanglement Singlet state Bell inequalityAssumptions: 1)There is a hidden local variables 2)Locality: output of measurement B does not affect output of A Bell inequality

28. Entanglement 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), For

29. Entanglement 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 JCAP08(2007)005 *Key point*

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

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 1) For SM 2) For MSSM (Phantom) -1 < < -0.76 SNIa observation Concordance, ?

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

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 Thank you very much 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.