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

2. 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

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

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

5. 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????

6. 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 …

7. 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

8. 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

9. 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

10. 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? 

11. 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

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

13. ? 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

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

15. 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.

16. 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!

17. 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

18. 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

19. 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

20. 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

21. Planck’s constant

22. 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

23. 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

24. 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

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

26. 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!

27. 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

28. A derivation of holographic principle
Lee  
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!

29. A derivation of holographic principle
Lee  
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.

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

31. Quantum Entanglement from holography

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

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

34. 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

35. 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!

36. Zhang & Wu, astro-ph/

37. 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!

38. Open subjects Explain, in this context, gauge theory and Q. gravity
BH information paradox
Fermions
Cosmology including dark energy
AdS/CFT correspondence
etc

39. 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!

41. 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

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

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

46. 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.

48. 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)

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

50. Friedmann equations from entropic force
Cai et al
Friedmann equation

51. 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!

52. 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

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

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

55. 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

56. EOS
WMAP7
Gong et al

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

58. 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

59. 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

60. 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?

61. 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?

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

63. Double Slit Experiment
Lee arXiv: , FOP  

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

65. 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?

66. 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

67. Black hole mass Landauer Hawking Mass increase T decrease
KLL
Landauer
Hawking
Mass increase
T decrease

68. 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!

69. 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

70. 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

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

72. 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)

73. 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

74. 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.

75. 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/
Information is Physical!

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

77. Quantum mechanics and bit
Cˇ . Brukner, A. Zeilinger
quant-ph/
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

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