Transcript Gravity and dark energy from quantum information

Gravity and dark energy
from quantum information
Jae-Weon Lee* (Jungwon Univ.)
Jungjai Lee (Daejin Univ.)
Hyungchan Kim (Chungju Univ.)
Relativity and Quantum information
Quantum
Mechanics
Relativity
Information
Quantum information and special relativity have a fundamental relation.
But there is no obvious reason for this!
Two Great mistakes of Einstein
= 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!
Surprising relations!
Dark
energy
Gravity
Entanglement
energy
Holographic
principle
Thermody
Jacobson
namics
& Verlinde
& Padmanabhan
Quantum
Mechanics
Causal horizons
Landauer’s principle
Information
Landauer’s principle
• Erasing information dS consumes energy TdS
•dE=TdS
(Two level system)
M. B. Plenio and V. Vitelli
quant-ph/0103108
Quantum mechanics and Information

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
It from Bit!
Black hole entropy contains everything
relativity
thermodynamics
Bekenstein-Hawking entropy
S BH
Holographic principle
kc3 Area

4G
gravity
quantum
Entanglement and Horizon
,
SEnt  Tr (  A log  A )  Tr ( B log B )
A
A
0
Entanglement
entropy
information
B
AB
If there is a causal horizon (information barrier),
it is natural to divide the system by the horizon.
Conjecture
•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
Dark energy from information
LLK:JCAP08(2007)005
Landauer’s principle
Black hole-like universe
Hawking temperature
Entanglement entropy
Horizon energy
Holographic dark energy
Expanding
event horizon
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
More general Version
Entropic force
Holographic DE
For Bekenstein-Hawking entropy
Negative pressure
M. Li
3d 2 M P2
 
Rh 2
d ( R3  )
p 
dR(3R 2 )
1  2  
   1 


3
d 
Freedman eq. & perfect fluid
Effective
EOS
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
EOS
WMAP7
Gong et al
Zero Cosmological Constant
JWLee, 1003.1878
From QFT
But from dE=TdS
should be zero
 QFT should be modified for large scale!
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

Due to quantum
3) Why now?

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
Verlinde’s Idea 1: Newton’s equation
arXiv:1001.0785
E  F x  T S
F  E / x  T S / x
S  mx
T a
 F  ma !
Entropic
force
But strange assumption??
 S  m x
Holographic screen
Verlinde’s Idea 2: Newton’s gravity
# of bits
Ac3 R 2
N

 entropy
G
G
NkT R 2
2
E  Mc 
 T
2
G
GM
T  2
R
S  mx
GMm
 F  T S / x  2
R
,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
Einstein Equation
Information erasing
Generalizing
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”
QFT from information
constraint
Maximize

Energy conservation
Shannon entropy
Boltzmann distribution
Rindler shows
Quantum partition function
Conclusions
1. Landauer’s principle, dE=TdS
 Information is thermal Energy
2
E

mc
2.
 Energy is Mass (matter)
3. Einstein Equation G=M
Matter generates Gravity
4. Unruh effect  Quantum is thermal
1+2= Matter is information,
1+2+3= Gravity is information!
1+4= Quantum is information
Conclusions
Landauer’s principle  1st 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
Merits of our theory
•simple
•links information to gravity
•calculable
•explain dark energy, black hole mass
& BH information paradox (hopefully)
•gives some hints on the holographic principle
Schrödinger’s cat
정보가 새어나감
Environment
|Dead>+|Alive> pure state
entanglement
실제
Decoherence
State=|Dead>|Env0>+|Alive>|Env1>
 Tracing Env
 Dear or Alive, density matrix=|Dead><Dead|+|Alive><Alive|
 Classical world
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.
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
Entanglement
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!
Black hole and Entanglement
|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
• entropy
Eigenvalues
 Area
Calculable!
Li’s idea
H
Let's use
instead of
R
L=
L=
L=
t
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?
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
• Naive expectation
Zero point Energy
But • Observed
Sum of all oscillators
Where does negative pressure come from?
perfect fluid
d ( R3  )
p 
dR(3R 2 )
1st-law
If energy increases as the universe expands, this matter has a
negative pressure
3d 2 M P2
 
Rh 2
1
d 1


HR 2
dR HR
H2 
8 G  
3
is an increasing function of t
P<0
Quantum mechanics and Information

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
It from Bit!
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
1) Why it is so small?
2) Why it is not zero?
problem
3) Why now?
Holographic principle
( QFT over-counts modes!)
Entanglement energy
( There is always quantum fluctuation!)
Cosmic coincidence problem
(We need an inflation!)
Holography and Entanglement
Entanglement 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!