Jae-Weon Lee (Jungwon univ.) Collaboration with JJLEE & HCKIM

Outline Dark energy from information loss Quantum mechanics from information loss at causal horizons Entropic gravity from information loss

1) Why it is so small? 2) Why it is not zero? 3) Why now? 4) Why the cosmological constant is zero or tiny Dark energy problem Observed for Zero point Energy Sum of all oscillators QFT can not solve these problems naturally  We need more ingredients  Holography?

What matters is information than perturbation Physics students are still taught this measurement- disturbance version of the uncertainty principle in introductory classes, but it turns out that it's not always true. Aephraim Steinberg of the University of Toronto in Canada and his team have performed measurements on photons (particles of light) and showed that the act of measuring can introduce less uncertainty than is required by Heisenberg’s principle. The total uncertainty of what can be known about the photon's properties, however, remains above Heisenberg's limit.principle -Scientific American

Gravity, QM & information In Q. information science, QM is deeply linked with information In BH physics, gravity is linked with Thermodynamics But we know thermodynamics is involved with information (entropy)  Gravity & QM have a common ingredient, INFORMATION!

What is information? The information embodied by a thing = a complete description of the thing, divorced from any particular language. (Wikipedia) = minimum BITS required to describe a thing completely For a thing with random variables  Information (Shannon or Von Neumann Entropy) For a given wave function or density matrix, we can calculate information entropy

Why entropy? an outside observer Entropy is 1)a measure of the uncertainty associated with a random variable 2) a measure of the average information content one is missing when one does not know the value of the random variable. BH horizon wikipedia Shannon entropy ?

Thermody namics dE=TdS Gravity Quantum Mechanics Lee10 Q. Informational DE LLK 2007 Roadmap Information loss Dark energy Jacobson Verlinde Padmanabhan LLK Holographic principle Newton Mechanics Verlinde Bekenstein -Hawking Unruh Lee11 Holographic DE Gauge theory KK? Entanglement No-signaling BH physics Lee11

History BH thermodynamics (Bekenstein & Hawking ) dE=TdS (Gravity +QM  BH Thermodynamics) Holographic principle (t’Hooft & Susskind) Entropy ~ Area Gravity from thermodynamics Thermodynamics  Gravity (Jacobson, Padmanabhan) Dark energy from information (Information  Gravity) JWLee, JJLee, HCKim (LLK) Entropic gravity (Verlinde) (Entropy  Gravity) QM and Entropic gravity from information loss (Lee11)

Mach & Einstein gravity It is thermal, TdS=dE Jacobson

Jacobson’s idea We can always choose a LIF Einstein eq. Is related to local Rindler observers!

where Jacobson’s idea Einstein eq. Is related to local Rindler observers! using Raychaudhuri eq. using Bianchi identity

Li’s derivation

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

Hawking temperature Horizon energy Entanglement entropy Or Bekenstein-Hawking entropy LLK:JCAP08(2007)005 Landauer’s principle Dark energy from entanglement Holographic dark energy  Information loss A black hole-like universe Expanding event horizon One can also say it is cosmic Hawking radiation!

Li’s derivation for Verlinde Stokes’s

Verlinde’s Idea 1: Newton’s 2nd law JHEP04(2011)029 JHEP04(2011)029 arXiv: , Entropic force Holographic screen?? Newton’s 2 nd law

Verlinde’s Idea 2: Newton’s gravity Equipartition # of bits Newton’s gravity! Inverse square law explained?

DE seems to be a quantum effect of curved space time  We need a DE model that explains both of Origin of Gravity Accelerating expansion of the universe Cosmic horizon is an inside-out version of BH horizon

Double horizon model Li & Yang

Two horizons In the universe there can be two horizons, local Rindler AND Cosmic horizons.  We need to consider thermodynamics of the 2 horizons simultaneously.

Shannon entropy Boltzmann distribution For Rindler observer (continuous version + coord. Transf. ) QFT from information Maximize Unruh showed that this is equivalent to Quantum partition function! (Unruh Eff.) Origin of QM and path integral!

Verlinde’s entropic force from information loss J.Lee FOP arXiv: Verlinde’s entropy formula Verlinde’s holographic screen is just Rindler horizon. Verlinde’s formalism is successfully reproduced ? ???

Gravity from Information loss Entropic gravity Rindler horizon

Gravity from Information loss Information loss  Entropic gravity Rindler horizon Lee FOP arXiv:

Big questions What is the origin of Gravity, QM, Q. Entanglement ? & holography? A motivation) There are strong similarities between holography and Q. entanglement; Area proportional, related to information loss, observer dependency….  Information can be the key to the solution Cf) Bekenstein, Wheeler, ‘t Hooft …

New postulates (not QM) 1)Information has finite density and velocity  Nosignaling  causal horizons 2) General Equivalence principle  All observers (coordinates) are equivalent in formulating physical laws; No observer has a privilege 3) Information is fundamental  Physical laws should respect observer’s information about a system 4) Metric nature of spacetime (not Einstein Eq.) 5) information theory From these we can derive QM and Einstein Gravity!  QM & Gravity are emergent

conjecture Major Physical Laws simply describe thermodynamics regarding phase space information loss at local causal (Rindler) horizons Information loss at horizons  Path integral & Thermodynamics  QM & Einstein (entropic) gravity  holographic principle  Q. Entanglement Too ambitious?

Unruh Effect QFT + curved spacetime  Thermal New theory Information loss + curved spacetime  Themal  QFT Inverting the logic of Unruh

Why random? For a fixed outside observer (Thermodynamics) Horizon dE=Mc 2 =TdS Phase space information loss  entropy S increases For an free falling observer (QM) M Coordinate trans. ? Physical laws should be such that the both observers are satisfied

QFT from information loss  ? ??? Energy conservation Shannon entropy Boltzmann distribution Maximize Constraint field, some function of spacetime

Quantum Mechanics from information Lee FOP arXiv: , Rindler observer will have no more information about fields crossing the horizon  What the observer can do is just to estimate the probability of the field configuration inside. accelerating observer rest observer

QM from phase space information loss Conventional QM is a single particle limit of QFT  QM can be easily reproduced in our theory. Quantum fluctuation is from ignorance of Rindler observer about the particle phase space information beyond a horizon

QM from information loss Quantum fluctuation for a free falling observer is a thermal fluctuation for a fixed observer QM for the FF observer is a statistical physics regarding information loss for the fixed observer  QM is not fundamental but emergent! Horizon entropy represents uncertainty about field configurations or phase space information Horizon Energy is just the total energy inside the horizon  BH laws of thermodynamics  Unruh effect and Hawking rad. are from information loss

1)Entanglement does not allow superluminal communication because QM itself is from the no-signaling condition. 2) Wave function collapse is just the realization of a uncertain information for some observers 3) Apparent non-locality is due to redundancy from the holography (shown later) 4) Thermal and path integral nature Explaining some Mysteries of QM

Microscopic DOF? Phase space entropy is dominant and internal structure is irrelevant upto Planck scale for gravity and QM (if there is no other force)  We can not know the true microscopic DOF with low energy gravity or QM experiments  Gravity and QM are universal

Planck’s constant

Derivation of 1 st law dE=TdS Maximum entropy  minimum F  extremizing action  Classical path  Newton’s mechanics  Verlinde theory Free E Maximum entropy condition is just quantization condition This seems to be the origin of the 1 st law of thermodynamics

Next order This also explains why Verlinde’s derivation involves Planck’s constant which is absent in the final F = ma formula. There is a log correction term

How our model avoids the problems of Verlinde’s model Entropy-distance relation naturally arises Unruh temperature is natural for Rindler horizon Horizon and Entropy are observer dependent  no worry about time reversal symmetry breaking.  Explains the identity of the DOF and entropy neutron interference experiments  Information loss depends on coordinates Canonical distr.  Equipartition law

A derivation of holographic principle 1) According to the postulate 2 (nosignaling), we restrict ourselves to local field theory 2) For a local field, any influence from the outside of the horizon should pass the horizon. 3) According to postulate 3, all the physics in the bulk is fully described by the DOF on the boundary  holographic principle! Lee

A derivation of holographic principle information loss at a horizon allows the outside observer to describe the physics in the bulk using only the DOF on the boundary. The general equivalence principle demands that this description is sufficient for understanding the physics in the bulk, which is the holographic principle. Theorem (holographic principle). For local field theory, physics inside 1-way causal horizon can be described completely by physics on the horizon. Lee

A derivation of Witten’s prescription Bulk Boundary Witten’s prescription

Quantum Entanglement from holography R

Entaglement ~ horizon radius

Gravity as Quantum Entanglement Force. Jae-Weon Lee, Hyeong-Chan Kim, Jungjai Lee arXiv: Arrow of time Entanglement force Total entanglement of the universe

Dark energy problem Observed for Zero point Energy Sum of all oscillators 1) Why it is so small? 2) Why it is not zero? 3) Why now? 4) Why the cosmological constant is zero or tiny QFT can’t solve this

Zhang & Wu, astro-ph/

Our solution to dark energy problem 1)Why it is so small? Holographic principle (QFT overcounts ind. DOF; QFT is emergent not fundamental) 2) Why it is not zero? Due to quantum vacuum fluctuation 3) Why now? Inflation with N~60 or r~ O(1/H) 4) Zero cosmological constant Holographic principle & dE=TdS Without fine tuning one can explain magnitude and equation of state of dark energy!

Open subjects Explain, in this context, 1)gauge theory and Q. gravity 2)BH information paradox 3)Fermions 4)Cosmology including dark energy 5)AdS/CFT correspondence etc

Conclusion: Physics from phase space information loss No-signaling  information loss at the horizons  1)General relativity (through Jacobson’s idea ) & dark energy (applied at a cosmic horizon) 2) Verlinde’s theory (F=ma)  Classical Mechanics 3) Quantum Mechanics (reverting Unruh’s theory) Physical laws seem to simply express the information loss at local Rindler horizons. Thank you very much! Albeit heuristic, this approach seems provide a new way to explain many puzzles in a self-consistent manner

Merits of our theory Our new quantum theory i is simple & calculable explain origin of entropic gravity and path integral Connect Jacobson’s model with Verlinde’s model

Energy budget of the universe Acceleration = Force Eq. of state metric R DE+DMDE Scale factor w<0, negative pressure  antigravity

Entanglement has 1. Area Law (in general) 2. Nonlocality 3. Related to causality 4. Fundamental 5. Observer dependent It reminds us of the Holographic principle! Holography and Entanglement

1)Dark energy from vacuum entanglement. JCAP 0708:005,2007.  dark energy from information 2) Does information rule the quantum black hole? arXiv: (MPLA)  Black hole mass from information 3) Is dark energy from cosmic Hawking radiation? Mod.Phys.Lett.A25: ,2010  Dark energy is cosmic Hawking radiation Verlinde’s paper: Gravity and mechanics from entropic force arXiv: )Gravity from Quantum Information [hep-th]  gravity is related to quantum entanglement or information loss 2) Gravity as Quantum Entanglement Force. arXiv: [hep-th] 3) Zero Cosmological Constant and Nonzero Dark Energy from Holographic Principle. arXiv: (Lee) 4) On the Origin of Entropic Gravity and Inertia. arXiv: [hep-th] (Lee) Verlinde’s theory from quantum information model 5) Quantum mechanics emerges from information theory applied to causal horizons arXiv: (Lee) Our works so far

Negative pressure Friedmann eq. & perfect fluid EOS M. Li

Friedmann equations from entropic force Cai et al Friedmann equation

QM from information loss Energy conservation Shannon entropy Boltzmann distribution Maximize Constraint matter filed inside the horizon This Z is equivalent to QM partition function. (Unruh effect)  QM is emergent! Lee, FOP ?? ???

Comparison with Verlinde’s theory Verlinde’s theory # of bits N Holographic principle on screen dS~ dx Equipartition energy E~NkT Spacetime is emergent? Thermal horizon energy? Differential geometry Unruh T in general Information coarse graining Our theory Holographic entropy S Landauer’s principle, dE=TdS Causal (Rindler) horizon Jacobson’s formulation Spacetime is given Differential geometry Information erasing (loss) Mainly thermodynamic Assume degrees of freedom on screen Mainly informational

1. strange entropy-distance relation 2. Using holographic principle and Unruh T for arbitrary surfaces? 3. Time reversal symmetry breaking? 4. Origin of the entropy and boundary DOF? 5. Why can we use equipartition law? 6. neutron interference experiments Concerns about Verlinde’s Idea ???? Our information theoretic interpretation resolves these problems

Gong et alWMAP7 EOS

Our idea2:Quantum Informational dark energy without QFT For Event horizon r=Rh The simplest case, S= Bekenstein-Hawking entropy ~ Horizon area ~ Rh ~1/Area Holographic dark energy arXiv: ,

Zero Cosmological Constant Jae-Weon Lee, But according to our theory (holographic principle + dE=TdS) should be zero Cf) Curved spacetime effect  QFT should be modified at cosmological scale Action in QFT Too large vacuum energy

Holographic dark energy La If L~1/H, a~1/Mp Problem: no acceleration! Only modes with Schwarzschild radius survives (Cohen et al) Relation between a and L This energy behaves like matter rather than dark energy UV IR E~ saturating M. Li suggested that if we use future event horizon Rh we can obtain an accelerating universe. But what is the physical origin?

Black hole and Entanglement Quantum vacuum fluctuation (Hawking Radiation) allows entanglement between inside and outside of the horizon due to the uncertainty problem. |Env> |Dead>|Env0>+|Alive>|Env1> possible? ’t Hooft G, (1985), Bombelli L, Koul R K, Lee J and Sorkin (1986) Black hole entropy is geometric entropy ( Entanglement entropy) Entanglement of what?

Basic Logic of my theory ?E, S Outside observer :Thermodynamics inside observer: QM Coordinate transformation dE=TdS

Double Slit Experiment Lee arXiv: , FOP

How to calculate Entanglement entropy, Srednicki,PRL71,666 R Hamiltonian Vacuum=ground state of oscillarots Reduced density matrix entropy Eigenvalues Calculable!

Holographic dark energy La If L~1/H, a~1/Mp Problem: no acceleration! Only modes with survives (Cohen et al) Relation between a and L This energy with H behaves like matter rather than dark energy UV IR E~ saturating M. Li suggested that if we use future event horizon Rh we can obtain an accelerating universe. But what is its physical origin?

Hawking radiation as dark energy But With UV cut-off Mp LLK, Mod.Phys.Lett.A25:257 Too small Without regularization in flat spacetime After renormalization in de Sitter spacetime HDE

Landauer Hawking Mass increase T decrease Black hole mass KLL

Black hole thermodynamics 1)The First Law 2)The Second Law dE=T H dS Bekenstein & Hawking BH area always increases =entropy always increases Nobody knows the physical origin of these laws!

Black hole entropy contains fundamental constants thermodynamics gravity quantum Holographic principle Bekenstein-Hawking entropy relativity Entropy is proportional to Area not to volume  Holographic principle Hawking radiation

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 not volume. R Scientific American August 2003

Planck’s constant

Relativity, Quantum & Information Relativity Quantum Physics Information links quantum mechanics with relativity Information Q. Gravity

Superluminal signaling using entanglement? Quantum mechanics somehow prohibits superluminal communications even with q. entanglement NO! 1) No-signaling could be one of the fundamental principles 2) QM and Gravity cooperate mysteriously 3) Information may be physical

It from Bit I think of my lifetime in physics as divided into three periods. In the first period, extending from the beginning of my career until the early 1950's, I was in the grip of the idea that Everything Is Particles…. I call my second period Everything Is Fields. From the time I fell in love with general relativity and gravitation in 1952 until late in my career, I pursued the vision of a world made of fields,… "Now I am in the grip of a new vision, that Everything Is Information. The more I have pondered the mystery of the quantum and our strange ability to comprehend this world in which we live, the more I see possible fundamental roles for logic and information as the bedrock of physical theory. J. Wheeler.

Why does physics involve with information? Landauer’s principle Erasing information dS consumes energy >=TdS M. B. Plenio and V. Vitelli quant-ph/ Single Thermal Bath with T Solving Maxwell’s demon problem C. Bennett

Experimental Demonstration Toyabe et al, Nature Physics We can extract energy from information

Quantum mechanics and bit 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 quant-ph/ Cf) Simon, Buˇzek, Gisin: nosignaling as an axiom for QM

t’ Hooft’s quantum determinism “ Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. “ quant-ph/ Equivalence class =information loss