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Jae-Weon Lee* (Jungwon Univ.) Jungjai Lee (Daejin Univ.) Hyungchan Kim (Chungju Univ.)

Gravity and dark energy from quantum information. Jae-Weon Lee* (Jungwon Univ.) Jungjai Lee (Daejin Univ.) Hyungchan Kim (Chungju Univ.). Relativity and Quantum information. Modern Physics. Quantum Mechanics. Relativity. Information.

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Jae-Weon Lee* (Jungwon Univ.) Jungjai Lee (Daejin Univ.) Hyungchan Kim (Chungju Univ.)

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  1. Gravity and dark energy from quantum information Jae-Weon Lee* (Jungwon Univ.) Jungjai Lee (Daejin Univ.) Hyungchan Kim (Chungju Univ.)

  2. Relativity and Quantum information Modern Physics Quantum Mechanics Relativity Information Quantum information and special relativity have a fundamental relation. But there is no obvious reason for this!

  3. Two Great mistakes of Einstein = The biggest blunder of my life!  Dark energy Entanglement = Spooky action at a distance?  Quantum information science Two great puzzles of modern physics Surprisingly, they are related!

  4. Surprising relations! Dark energy Entanglement energy Quantum Mechanics Gravity Holographic principle Thermody namics Jacobson & Verlinde & Padmanabhan Causal horizons Landauer’s principle Information

  5. Information is Physical! Landauer’s principle • Erasing information dS consumes energy TdS • dE=TdS (Two level system) M. B. Plenio and V. Vitelli quant-ph/0103108

  6. Quantum mechanics and Information The most elementary quantum system represents the truth value of one proposition only (bit?). This principle is then the reason for the irreducible randomness of an individual quantum event and for quantum entanglement Cˇ . Brukner, A. Zeilinger It from Bit!

  7. Black hole entropy contains everything relativity thermodynamics Holographic principle Bekenstein-Hawking entropy gravity quantum BH

  8. Entanglement and Horizon , Entanglement entropy information A B If there is a causal horizon (information barrier), it is natural to divide the system by the horizon.

  9. Conjecture • Information is fundamental • Holographic principle and Landauer’s principle • as basic principles • Causal (Rindler) horizons are involved with • information erasing Physical Laws describe information loss at causal horizons! Horizon information barrier (erasing, entanglement)  dE =TdS

  10. Dark energy from information LLK:JCAP08(2007)005 Black hole-like universe Landauer’s principle Hawking temperature Entanglement entropy Horizon energy Expanding event horizon Holographic dark energy Information erasing One can also think this DE as cosmic Hawking radiation! In short, T~1/r, S~ r^2  density M_P^2 /r^2 ~ M_P^2 H^2 as observed

  11. More general Version Entropic force Holographic DE For Bekenstein-Hawking entropy

  12. Negative pressure M. Li Freedman eq. & perfect fluid Effective EOS

  13. Newscientist Prokopec "They've come up with an interesting physical mechanism for how [virtual particles] could lead to dark energy, They have chosen a very reasonable value for this, but if it turns out that this value is slightly wrong, it could throw off all their predictions " Seth Lloyd "I think they could really be onto something,"

  14. Zhang & Wu, astro-ph/0701405

  15. EOS WMAP7 Gong et al

  16. From QFT But from dE=TdS should be zero Zero Cosmological Constant JWLee, 1003.1878  QFT should be modified for large scale! Cf) Curved spacetime effect Dark energy is cosmic Hawking radiation (it has an appropriate EOS!)

  17. Our solution to dark energy problem • 1) Why it is so small?  Holographic principle • 2) Why it is not zero?  Due to quantum fluctuation • 3) Why now?  Inflation or r~ O(1/H) • 4) Zero cosmological constant •  Holographic principle & dE=TdS without fine tuning

  18. Our works so far • Dark energy from vacuum entanglement.JCAP 0708:005,2007.  dark energy from information • 2) Does information rule the quantum black hole? • arXiv:0709.3573 (MPLA)  Black hole mass from information • 3) Is dark energy from cosmic Hawking radiation?Mod.Phys.Lett.A25:257-267,2010 Dark energy is cosmic Hawking radiation • <Verlinde’s paper> Gravity and mechanics from entropic forcearXiv:1001.0785 • Cai, Cao, Ohta. Friedmann eq. • Easson, Frampton, Smoot entropic dark energy & inflation • Gravity from Quantum Information.1001.5445 [hep-th] (suggested in 2009) • Gravity as Quantum Entanglement Force. arXiv:1002.4568 [hep-th] • Zero Cosmological Constant and Nonzero Dark Energy from Holographic Principle.arXiv:1003.1878 • On the Origin of Entropic Gravity and Inertia.arXiv:1003.4464 [hep-th] • Deriving Verlinde’s theory from quantum information model • 5) Quantum mechanics emerges from information theory applied to causal horizons  arXiv: today

  19. Verlinde’s Idea 1: Newton’s equation arXiv:1001.0785 Entropic force But strange assumption?? Holographic screen

  20. Verlinde’s Idea 2: Newton’s gravity # of bits ,Holographic , Equipartition , Newton’s gravity Verlinde’s holographic energy is very similar to our entanglement energy!

  21. Gravity from Quantum Information.JW Lee, HC Kim, JJ Lee, 1001.5445 Rindler horizon

  22. Einstein Equation Information erasing Generalizing a la Jacobson where using Raychaudhuri eq. using Bianchi identity Einstein eq. represents information erasing for Rindler observers!

  23. Verlinde’s entropic force from information theory J.Lee arXiv:1003.4464 Verlinde’s entropy! Verlinde’s theory is recovered from information theory.

  24. QFT from information JWLee hep-th today Rindler observer has no information about field or paths in the F wedge  Quantum Randomness  No “objective physical reality”

  25. QFT from information Energy conservation constraint Maximize Shannon entropy Boltzmann distribution  Rindler shows Quantum partition function

  26. Conclusions • 1. Landauer’s principle, dE=TdS •  Information is thermal Energy • 2. Energy is Mass (matter) • 3. Einstein Equation G=M • Matter generates Gravity • 4. Unruh effect  Quantum is thermal 1+2= Matter is information, 1+2+3= Gravity is information! 1+4= Quantum is information

  27. Conclusions • Landauer’s principle  1st law of thermodynamics •  Jacobson’s idea (Gravity=Thermodynamics) • General relativity • dark energy • + some hints on arrow of time and • origin of quantum mechanics?

  28. Gravity as Quantum Entanglement Force.Jae-Weon Lee, Hyeong-Chan Kim, Jungjai Lee arXiv:1002.4568 Arrow of time Entanglement force

  29. Merits of our theory • simple • links information to gravity • calculable • explain dark energy, black hole mass • & BH information paradox (hopefully) • gives some hints on the holographic principle

  30. Schrödinger’s cat Environment 정보가 새어나감 |Dead>+|Alive> pure state entanglement Decoherence 실제 State=|Dead>|Env0>+|Alive>|Env1>  Tracing Env  Dear or Alive, density matrix=|Dead><Dead|+|Alive><Alive|  Classical world

  31. Holographic principle • All of information in a volume can be described by physics • on its boundary. • The maximum entropy within the volume is proportional to • its Area. R QFT over-counts independent d.o.f. inside a boundary! Whole new physics! vanrenesse-consulting. Scientific American August 2003

  32. Entanglement Nonlocal quantum correlation |Dead>|Env0>+|Alive>|Env1> Subluminal signaling Superluminal signaling? Measurement |Env0> or |Env1> Quantum mechanics somehow protects superluminal communications even though it has a NONLOCAL correlation!

  33. Black hole and Entanglement |Env> |Dead>|Env0>+|Alive>|Env1> possible? Quantum vacuum fluctuation allows entanglement between inside and outside of the horizon due to the uncertainty problem. Hawking radiation

  34. Information of matter: Padmanabhan matter vacuum

  35. R How to calculate Entanglement entropy • Hamiltonian Srednicki,PRL71,666 , • Vacuum • Reduced density matrix Eigenvalues • entropy Calculable!

  36. L= L= L= L= Li’s idea H Let's use instead of R t time ~ is consistent with SNIa,CMB,SDSS,BAO. • Ok. It seems to work now, But • Why this form? • Why instead of ? • Why d ~1? Our work answers to these questions

  37. Sum of all oscillators Zero point Energy The Cosmological constant problem in detail = Huge sum of harmonic oscillators Quantum field= UV cutoff a ~1/Mp L IR cutoff • Naive expectation • Observed But

  38. Where does negative pressure come from? perfect fluid 1st-law If energy increases as the universe expands, this matter has a negative pressure is an increasing function of t P < 0

  39. Quantum mechanics and Information The most elementary quantum system represents the truth value of one proposition only (bit?). This principle is then the reason for the irreducible randomness of an individual quantum event and for quantum entanglement Cˇ . Brukner, A. Zeilinger It from Bit!

  40. The Cosmic coincidence problem • Observed for If we think this is an accidental coincidence Cosmic coincidence problem If we believe there is a hidden law behind this Holographic dark energy models • 1) Why it is so small? Holographic principle • 2) Why it is not zero? Entanglement energy • 3) Why now? Cosmic coincidence problem ( QFT over-counts modes!) ( There is always quantum fluctuation!) problem (We need an inflation!)

  41. Holography and Entanglement • Entanglement is • Area Law (in general) • Nonlocal • Related to Horizons • Fundamental • Observer dependent • Very fast decoherence • Information erasing! It reminds us of the Holographic principle!

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