1. Gravity from
quantum entanglement
Jae-Weon Lee (Jungwon univ.)

2. Outline Gravity is emergent
Thermodynamics  Gravity (Jacobson, Padmanabhan)
Entropy  gravity (Verlinde, 2010)
Entanglement  Gravity (Lee, Lee, Kim, 2010)
Spacetime is emergent
Entanglement  Time (Page & Wooters)
Entanglement  Spacetime (Raamsdonk)
QM is emergent
Information loss  QM (Lee, 2011)

3. The most beautiful physics formula (at leat for me)
relativity
thermodynamics
Holographic principle
Bekenstein-Hawking
entropy
quantum
gravity BH
Hawking radiation
Entropy is proportional to area not to volume
 Holographic principle

4. Black Hole Entropy mysteries
Origin  Area law?  Entanglement Entropy?
The information paradox  via Hawking Rad.?
The infall problem  Firewall?

5. History BH thermodynamics (Bekenstein & Hawking 1972) dE=TdS
Entanglement  Time (Page & Wooters 1983)
Entanglement  BH entropy (Bombelli et al 1986)
BH war (Hawking vs Susskind)
Entanglement  Arrow of time (Llyod,1988)
Holographic principle (t’Hooft & Susskind)
Thermodynamics  Gravity (Jacobson, Padmanabhan)
Entanglement  Dark energy (Lee, Lee, Kim, 2007)
Entropy  Gravity (Verlinde, 2010)
Entanglement  Gravity (Lee, Lee, Kim, 2010)
Entanglement  Spacetime (Raamsdonk 2010)
Holography  Entanglement (Takayhanagi, 2012)
BH Firewall paradox
Entanglement=Wormhole (ER=EPR, Maldacena)
Experimental realization of PaW (Moreva et al, 2013)
Entanglement  Gravity in AdS/CFT (Raamsdonk 2014)
Entanglement  Gravity (Jacobson 2015)

6. Entanglement (nonlocal quantum correlation) entropy,
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 across the horizon.

7. Holography and Entanglement
Entanglement has
Area Law (in general)
Nonlocality
Relation to causality
Something fundamental
Observer dependency
It reminds us of the Holographic principle!
* Entanglement is faster than light! ( v > O(103)c )
 Entanglement is more fundamental than anything with v <= c

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

9. Entanglement entropy? Divergent Species problem Physics dependent
l = UV cutoff
Divergent
Species problem
Physics dependent

10. Dark energy from entanglement
LLK:JCAP08, 005
Entanglement 1st law
A black hole-like universe
Hawking temperature
Entanglement entropy
Or Bekenstein-Hawking
entropy
Horizon Entanglement energy
Expanding
event horizonn
d ~1
Holographic dark energy

11. Observation
Zhang & Wu, astro-ph/
The Hubble constant H0 predicted by the base ΛCDM model according to the Planck CMB data: ± 0.66 km/s/Mpc
But, H0 locally determined:73.02±1.79 km/s/Mpc,
 One solution can be the dynamical DE
arXiv:
DE is not the Cosmological constant?

12. Jacobson’s Great idea
Padmanabhan R x
where
Raychaudhuri equation
using Bianchi identity
Einstein equation is related to local Rindler observers!

13. Gravity from entanglement
Lee, Lee, Kim, dE
A derivation of Entanglement 1st law

14. Thermofield doubled state
Pure state (entangled)
Thermal state
Not directly related to gravity

15. Bisognano Wichmann theorem
Density matrix is thermal (KMS state) with respect to the Hamiltonian generating time translation leaving the wedge invariant.
KMS-condition describes precisely the thermal equilibrium
states

16. Modern interpretationL R t x a

17. Perturbative QG Einstein Eq. + low energy QG  EE is SBH
Bianchi
Einstein Eq. + low energy QG  EE is SBH
Perturbative quantum gravity
EOM

18. t AH
Matter+gravity A0 L R
thermal x
Raychaudhuri equation

19. Verlinde’s entropic gravity
# of bits
Equipartition
Newton’s gravity!
But has problems such as neutron interference exp.

20. Gravity from Information loss
Lee FOP arXiv:
Rindler horizon
Information loss
 Change of entanglement entropy
 Entropic gravity

22. Return of the Jacobson M Confirmal mapping to Rindler wedge
T. Jacobson
Causal diamond M
Space-like slice
Killing vector
Confirmal mapping to Rindler wedge

23. continued C.C. T. Jacobson 1505.04753
The area variation at constant V for a maximally symmetric spacetime
C.C.

24. Gravity from AdS/CFT
area of the bulk extremal surface

25. Eternal BH

26. Thermofield doubled state
Pure state (entangled)
Thermal state
Maldacena’s proposal: the eternal
black hole is dual to |TFD> of CFT

27. Holographic entanglement entropy
Takayanagi
Strange connection btw Entanglement & holography

28. Spacetime from entanglement
Israel: The two sides of the eternal
BH are the entangled copies of a thermal system.
Maldacena: The dual to the eternal BH is two entangled copies of a CFT
(thermofield double formalism)
Raamsdonk: Entangled sum of CFT state as an entangled sum of spacetime

29. Spacetime from entanglement
Raamsdonk
Entanglement glue
quantum superposition of disconnected spacetime
= (connected) eternal AdS black hole spacetime

30. The Time problem Wave function of WDE is static.
In QM time labels the dynamics but does not participate as a degree of freedom.
In GR, time is just an arbitrary label-
the theory is invariant under time reparameterizations.
Wave function of WDE is static.
 There is no time in canonical Q. Gravity

31. Page-Wooters Mechanism
Stationary
& entangled
Clock and rest
Conditional probability

32. where

33. Gravity as Quantum Entanglement Force. Lee Kim Lee arXiv:1002.4568
Total entanglement of the universe
Arrow of time (Lyod)
Entanglement force

34. EPR=ER Entanglement ~ worm hole 1 No Superluminal Signals
Maldacena & Susskind
1 No Superluminal Signals
2 No Creation By LOCC
3 Restoring the thermo field state
Entanglement ~ worm hole

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

36. Quantum Mechanics from information
Lee FOP arXiv: , 
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.

37. QFT from information
J.Lee FOP 2011
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! & Entropic gravity

38. Conclusion: Emergent universe?
Gravity is emergent
Thermodynamics  Gravity (Jacobson, Padmanabhan)
Entropy  gravity (Verlinde, 2011)
Entanglement  Gravity (Lee, Lee, Kim, 2011)
Spacetime is emergent
Entanglement  Time (Page & Wooters)
Entanglement  Spacetime (Raamsdonk)
QM is emergent
Information loss  QM (Lee, 2011)
Universe is emergent! from what???
Information! Information of what???

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

42. Lovelock Theorem
in a 3+1D differentiable manifold, the Einstein tensor
is the only tensorial and divergence-free function of the
and at most their first and second partial derivatives.

43. Our works so far
Dark energy from vacuum entanglement. JCAP 0708:005,  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)

44. 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!

45. 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