Jae-Weon Lee* (Jungwon Univ.)
Jungjai Lee (Daejin Univ.)
Hyungchan Kim (Chungju Univ.)

Quantum
Mechanics
Relativity
Quantum information and special relativity have a fundamental relation.
But there is no obvious reason for this!

= 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!

Gravity
Dark energy
Holographic principle
Entanglement energy
Quantum
Mechanics
Jacobson
& Verlinde
& Padmanabhan
Thermody namics
Causal horizons
Landauer’s principle
Information

• Erasing information dS consumes energy TdS
•dE=TdS
(Two level system)
M. B. Plenio and V. Vitelli quant-ph/0103108


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

relativity thermodynamics
Bekenstein-Hawking entropy
S
BH

4 G
Holographic principle gravity quantum

,
S
Ent
 
Tr (

A log

A
)
 
Tr (

B log

B
) information

A
A
B
Entanglement entropy
0
AB
If there is a causal horizon (information barrier) , it is natural to divide the system by the horizon.

• 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

Landauer’s principle
LLK:JCAP08(2007)005
Black hole-like universe
Hawking temperature
Entanglement entropy
Horizon energy
Expanding event horizon
Holographic dark energy
 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

Entropic force
Holographic DE
For Bekenstein-Hawking entropy

M. Li



3 d M
2
P
R h
2 p


(
3


) dR ( 3 R
2
)


 
1
1

3


2 d




Freedman eq. & perfect fluid

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

WMAP7 Gong et al

Zero Cosmological Constant JWLee, 1003.1878
From QFT
But from dE=TdS
 QFT should be modified for large scale!
should be zero
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
3) Why now?

Due to quantum
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

arXiv:1001.0785
E F x T S
F

E / x T S /
 x
S m x
T
 a

F
 ma !
But strange assumption??
Entropic force
S m x
Holographic screen

# of bits
N
3
Ac R
2
  
G G entropy
E

Mc
2 
NkT

R
2 G
2
T
GM
R
2
S m x
GMm
R
2
,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

Generalizing
Information erasing 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”

constraint
Maximize

Rindler shows
QFT from information
Energy conservation
Shannon entropy
Boltzmann distribution
Quantum partition function

1. Landauer’s principle, dE=TdS
 Information is thermal Energy
2.  Energy is Mass (matter)
3. Einstein Equation G=M
 Matter generates Gravity
4. Unruh effect  Quantum is thermal

Landauer’s principle  1 st 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

•simple
•links information to gravity
•calculable
•explain dark energy, black hole mass
& BH information paradox (hopefully)
•gives some hints on the holographic principle

정보가 새어나감
Environment
실제
|Dead>+|Alive> pure state entanglement Decoherence
State=|Dead>|Env0>+|Alive>|Env1>
 Tracing Env
 Dear or Alive, density matrix=|Dead><Dead|+|Alive><Alive|
 Classical world

• 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

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!

|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
Eigenvalues
• entropy
Calculable!

Area

Let's use instead of
H
R
L=
L= 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?
L= t
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
Sum of all oscillators • Naive expectation
Zero point Energy
But
• Observed

perfect fluid p


(
3


) dR

R
2
( 3 )
1 st -law
If energy increases as the universe expands, this matter has a negative pressure



3
2 2 d M
P
R h
2
1
HR
2
  d 1 dR HR
H
2 
8
 

3 is an increasing function of t
P < 0


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

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 problem
1) Why it is so small? Holographic principle
( QFT over-counts modes!)
2) Why it is not zero? Entanglement energy
( There is always quantum fluctuation!)
3) Why now? Cosmic coincidence problem
(We need an inflation!)

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 !