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Gravity and dark energy from quantum information Jae-Weon Lee* (Jungwon Univ.) Jungjai Lee (Daejin Univ.) Hyungchan Kim (Chungju Univ.) Relativity and Quantum information Quantum Mechanics Relativity Information Quantum information and special relativity have a fundamental relation. But there is no obvious reason for this! 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! Surprising relations! Dark energy Gravity Entanglement energy Holographic principle Thermody Jacobson namics & Verlinde & Padmanabhan Quantum Mechanics Causal horizons Landauer’s principle Information Landauer’s principle • Erasing information dS consumes energy TdS •dE=TdS (Two level system) M. B. Plenio and V. Vitelli quant-ph/0103108 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! Black hole entropy contains everything relativity thermodynamics Bekenstein-Hawking entropy S BH Holographic principle kc3 Area 4G gravity quantum Entanglement and Horizon , SEnt Tr ( A log A ) Tr ( B log B ) A A 0 Entanglement entropy information B AB If there is a causal horizon (information barrier), it is natural to divide the system by the horizon. 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 Dark energy from information LLK:JCAP08(2007)005 Landauer’s principle Black hole-like universe Hawking temperature Entanglement entropy Horizon energy Holographic dark energy Expanding event horizon 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 More general Version Entropic force Holographic DE For Bekenstein-Hawking entropy Negative pressure M. Li 3d 2 M P2 Rh 2 d ( R3 ) p dR(3R 2 ) 1 2 1 3 d Freedman eq. & perfect fluid Effective EOS 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," Zhang & Wu, astro-ph/0701405 EOS WMAP7 Gong et al Zero Cosmological Constant JWLee, 1003.1878 From QFT But from dE=TdS should be zero QFT should be modified for large scale! Cf) Curved spacetime effect Dark energy is cosmic Hawking radiation (it has an appropriate EOS!) Our solution to dark energy problem 1) Why it is so small? Holographic principle 2) Why it is not zero? fluctuation Due to quantum 3) Why now? Inflation or r~ O(1/H) 4) Zero cosmological constant Holographic principle & dE=TdS without fine tuning Our works so far 1) 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 force arXiv:1001.0785 Cai, Cao, Ohta. Friedmann eq. Easson, Frampton, Smoot entropic dark energy & inflation 1) Gravity from Quantum Information. 1001.5445 [hep-th] (suggested in 2009) 2) Gravity as Quantum Entanglement Force. arXiv:1002.4568 [hep-th] 3) Zero Cosmological Constant and Nonzero Dark Energy from Holographic Principle. arXiv:1003.1878 4) 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 Verlinde’s Idea 1: Newton’s equation arXiv:1001.0785 E F x T S F E / x T S / x S mx T a F ma ! Entropic force But strange assumption?? S mx Holographic screen Verlinde’s Idea 2: Newton’s gravity # of bits Ac3 R 2 N entropy G G NkT R 2 2 E Mc T 2 G GM T 2 R S mx GMm F T S / x 2 R ,Holographic , Equipartition , Newton’s gravity Verlinde’s holographic energy is very similar to our entanglement energy! Gravity from Quantum Information. JW Lee, HC Kim, JJ Lee, 1001.5445 Rindler horizon Einstein Equation Information erasing Generalizing a la Jacobson where using Raychaudhuri eq. using Bianchi identity Einstein eq. represents information erasing for Rindler observers! Verlinde’s entropic force from information theory J.Lee arXiv:1003.4464 Verlinde’s entropy! Verlinde’s theory is recovered from information theory. 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” QFT from information constraint Maximize Energy conservation Shannon entropy Boltzmann distribution Rindler shows Quantum partition function Conclusions 1. Landauer’s principle, dE=TdS Information is thermal Energy 2 E mc 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 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? Gravity as Quantum Entanglement Force. Jae-Weon Lee, Hyeong-Chan Kim, Jungjai Lee arXiv:1002.4568 Arrow of time Entanglement force 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 Schrödinger’s cat 정보가 새어나감 Environment |Dead>+|Alive> pure state entanglement 실제 Decoherence State=|Dead>|Env0>+|Alive>|Env1> Tracing Env Dear or Alive, density matrix=|Dead><Dead|+|Alive><Alive| Classical world 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. S within R S BH Area R 2 S Ent 4 R vanrenesse-consulting. QFT over-counts independent d.o.f. inside a boundary! Whole new physics! Scientific American August 2003 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! 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 Information of matter: Padmanabhan matter vacuum How to calculate Entanglement entropy • Hamiltonian Srednicki,PRL71,666 , • Vacuum • Reduced density matrix R • entropy Eigenvalues Area Calculable! Li’s idea H Let's use instead of R L= L= L= t time ~ L= 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 The Cosmological constant problem in detail Quantum field= UV cutoff a ~1/Mp = Huge sum of harmonic oscillators L IR cutoff • Naive expectation Zero point Energy But • Observed Sum of all oscillators Where does negative pressure come from? perfect fluid d ( R3 ) p dR(3R 2 ) 1st-law If energy increases as the universe expands, this matter has a negative pressure 3d 2 M P2 Rh 2 1 d 1 HR 2 dR HR H2 8 G 3 is an increasing function of t P<0 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! 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? 2) Why it is not zero? problem 3) Why now? Holographic principle ( QFT over-counts modes!) Entanglement energy ( There is always quantum fluctuation!) Cosmic coincidence problem (We need an inflation!) Holography and Entanglement Entanglement is 1.Area Law (in general) 2.Nonlocal 3.Related to Horizons 4.Fundamental 5.Observer dependent 6.Very fast decoherence 7. Information erasing! It reminds us of the Holographic principle!