Quantum mechanics, entropic gravity, & dark energy from phase space information loss Jae-Weon Lee (Jungwon univ.)

Outline Quantum mechanics from information loss at causal horizons Entropic gravity from information loss A derivation of Holographic principle Origin of quantum entanglement Dark energy from information loss

Problems of Newton’s gravity Instant action at a distance? (nonlocal) Origin of the Inverse square law??

Mach & Einstein gravity Einstein gravity dispelled the “action at a distance”; Spacetime distortion mediates gravity with light velocity. It is thermal, TdS=dE Jacobson

Action at a distance revived QM has “Spooky action at a distance”! = Nonlocal quantum correlation (entanglement) But even with entanglement we can not send information faster than light (No-Signaling) Why????

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

What is information? The information embodied by a thing = the identity of the particular thing itself, that is, all of its properties, all that makes it distinct from other things. = 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) entropy

Why entropy? ? BH horizon Entropy is an outside observer Shannon entropy Entropy is 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. wikipedia

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? 

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

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

? Why random? Phase space information loss  entropy S increases For a fixed outside observer (Thermodynamics) M ? Coordinate trans. Horizon dE=Mc2=TdS For an free falling observer (QM) Physical laws should be such that the both observers are satisfied

f? QFT from information loss ??? f: field, some function of spacetime Maximize Shannon entropy (Entanglement entropy) Energy conservation Constraint Boltzmann distribution

Quantum Mechanics from information Lee FOP arXiv: 1005.2739,  rest observer accelerating observer 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.

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

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

Explaining some Mysteries of QM 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

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

Next order Saddle point approx. 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

Verlinde’s entropic force from information loss J.Lee FOP arXiv:1003.4464 ? ??? Verlinde’s entropy formula Verlinde’s holographic screen is just Rindler horizon. Verlinde’s formalism is successfully reproduced

Gravity from Information loss Lee FOP arXiv:1003.4464 Rindler horizon Information loss Entropic gravity

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

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 Lee 1107.3448  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!

A derivation of holographic principle Lee 1107.3448  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.

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

Quantum Entanglement from holography

boundary bits b Bulk bits B 00 01 10 11 1 Entaglement ~ horizon radius

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

Dark energy problem Observed Sum of all oscillators Zero point Energy for Sum of all oscillators Zero point Energy 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

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

Zhang & Wu, astro-ph/0701405

Our solution to dark energy problem 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, gauge theory and Q. gravity BH information paradox Fermions Cosmology including dark energy 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 (by reverting Unruh’s logic) Physical laws seem to simply express the information loss at local Rindler horizons. Albeit heuristic, this approach seems provide a new way to explain many puzzles in a self-consistent manner Thank you very much!

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 Scale factor w<0, negative pressure  antigravity DE+DM DE Acceleration = Force Eq. of state metric

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

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

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 force arXiv:1001.0785 Gravity from Quantum Information. 1001.5445 [hep-th]  gravity is related to quantum entanglement or information loss 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  (Lee) 4) On the Origin of Entropic Gravity and Inertia. arXiv:1003.4464 [hep-th] (Lee) Verlinde’s theory from quantum information model 5) Quantum mechanics emerges from information theory applied to causal horizons  arXiv:0041329 (Lee)

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

Friedmann equations from entropic force Cai et al Friedmann equation

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

Comparison with 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 informational Mainly thermodynamic Assume degrees of freedom on screen

Verlinde’s Idea 1: Newton’s 2nd law JHEP04(2011)029 arXiv:1001.0785, Entropic force Newton’s 2nd law Holographic screen??

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

Concerns about Verlinde’s Idea strange entropy-distance relation 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 ???? Our information theoretic interpretation resolves these problems

EOS WMAP7 Gong et al

Our idea2:Quantum Informational dark energy without QFT arXiv:0709.0047, 1003.1878 For Event horizon r=Rh ~ Horizon area ~ Rh Holographic dark energy ~1/Area The simplest case, S= Bekenstein-Hawking entropy

Zero Cosmological Constant Jae-Weon Lee, 1003.1878 Action in QFT Too large vacuum energy But according to our theory (holographic principle + dE=TdS) should be zero  QFT should be modified at cosmological scale Cf) Curved spacetime effect

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

Holographic dark energy Only modes with Schwarzschild radius survives (Cohen et al) E~ Relation between a and L UV IR saturating a L If L~1/H, a~1/Mp Problem: no acceleration! This energy behaves like matter rather than dark energy 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 |Dead>|Env0>+|Alive>|Env1> possible? Quantum vacuum fluctuation (Hawking Radiation) allows entanglement between inside and outside of the horizon due to the uncertainty problem. |Env> ’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?

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

Double Slit Experiment Lee arXiv:1005.2739, FOP  

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

Holographic dark energy Only modes with survives (Cohen et al) E~ Relation between a and L UV IR saturating a L If L~1/H, a~1/Mp Problem: no acceleration! This energy with H behaves like matter rather than dark energy 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 Without regularization in flat spacetime After renormalization in de Sitter spacetime Too small But With UV cut-off Mp HDE LLK, Mod.Phys.Lett.A25:257

Black hole mass Landauer Hawking Mass increase T decrease KLL 0709.3573 Landauer Hawking Mass increase T decrease

Black hole thermodynamics Bekenstein & Hawking The First Law The Second Law dE=THdS BH area always increases =entropy always increases Nobody knows the physical origin of these laws!

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

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

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

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)

Superluminal signaling using entanglement? NO! Quantum mechanics somehow prohibits superluminal communications even with q. entanglement 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 Solving Maxwell’s demon problem C. Bennett Single Thermal Bath with T M. B. Plenio and V. Vitelli quant-ph/0103108 Information is Physical!

Experimental Demonstration Toyabe et al, Nature Physics 6 2010 We can extract energy from information

Quantum mechanics and bit Cˇ . Brukner, A. Zeilinger quant-ph/0005084 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. Cf) Simon, Buˇzek, Gisin: nosignaling as an axiom for QM

t’ Hooft’s quantum determinism quant-ph/0212095 “Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. “ Equivalence class =information loss