Download horizons

Collaboration with JJLEE & HCKIM
Jae-Weon Lee
(Jungwon univ.)
Outline
• Dark energy from information loss
• Quantum mechanics from information
loss at causal horizons
• Entropic gravity from information loss
Dark energy problem
Sum of all oscillators
• Zero point Energy
10121 discrepancy
• Observed
for
1) Why it is so small?

2) Why it is not zero?
  0
3) Why now?
  H 02 M P2
M P2
4) Why the cosmological constant is zero or tiny
0
QFT can not solve these problems naturally
We need more ingredients
 Holography?
What matters is information
than perturbation
Physics students are still taught this measurementdisturbance version of the uncertainty principle in
introductory classes, but it turns out that it's not
always true. Aephraim Steinberg of the University of
Toronto in Canada and his team have performed
measurements on photons (particles of light) and
showed that the act of measuring can introduce less
uncertainty than is required by Heisenberg’s principle.
The total uncertainty of what can be known about the
photon's properties, however, remains above
Heisenberg's limit.
-Scientific American
Gravity , QM & information
• In Q. information science, QM is deeply
linked with information
• In BH physics, gravity is linked with
Thermodynamics
• But we know thermodynamics is
involved with information (entropy)
•  Gravity & QM have a common
ingredient, INFORMATION!
What is information?
The information embodied by a thing
= 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
or Von Neumann Entropy)
•For a given wave function or density matrix, we can
calculate information entropy
Why entropy?
BH horizon
?
an outside observer
Shannon entropy
Entropy is
1)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
Roadmap
Gauge
theory
BH
physics
Dark
energy
Entanglement
Holographic DE
Lee11
KK?
Gravity
Bekenstein
-Hawking
Unruh
Q. Informational DE
LLK 2007
Holographic
principle
Thermody
namics
Jacobson
Verlinde
Padmanabhan
LLK
Lee11
dE=TdS
Quantum
Mechanics
Information
No-signaling
Lee10
loss
Verlinde
Newton
Mechanics
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)
Mach & Einstein gravity
Einstein ' s Conjecture
G  T ; Geometry=Matter why????
It is thermal, TdS=dE
Jacobson
Jacobson’s idea
•We can always choose a LIF
•Einstein eq. Is related to
•local Rindler observers!
Jacobson’s idea
where
using Raychaudhuri eq.

using Bianchi identity
Einstein eq. Is related to local Rindler observers!
Li’s derivation
1207.0661
Entanglement entropy
,
Entanglement
entropy
SEnt  Tr (  A log  A )  Tr (  B log  B )
A
A
0
~ Area
information
B
AB
If there is a causal horizon (information barrier),
it is natural to divide the system by the horizon
and consider entanglement entropy.
Dark energy from entanglement
LLK:JCAP08(2007)005
Landauer’s principle
A black hole-like universe
Hawking temperature
Entanglement entropy
Or Bekenstein-Hawking
entropy
Horizon energy
Expanding
event horizon
Information
Holographic dark energy
One can also say it is cosmic Hawking radiation!
loss
Li’s derivation for Verlinde
1207.0661
+ Stokes’s
Verlinde’s Idea 1: Newton’s 2nd law
JHEP04(2011)029 arXiv:1001.0785,
E  T S  F x
E
T S
F 

x
x
S  mx
Unruh T  TU  a
Entropic
force
 F  ma !
Newton’s 2nd law
Holographic screen??
Verlinde’s Idea 2: Newton’s gravity
Ac3 R 2
# of bits N  G  G  entropy
2
NkT
R
Equipartition E  Mc 2 
 T
2
G
GM
T 2
R
S  mx
T S GMm
F
 2
x
R
Newton’s gravity!
Inverse square law explained?
DE seems to be a quantum effect of curved space time

We need a DE model that explains both of
• Origin of Gravity
• Accelerating expansion of the universe
• Cosmic horizon is an inside-out version of BH horizon
Double horizon model
Li & Yang 1001.446
Two horizons
In the universe there can be two horizons,
local Rindler AND Cosmic horizons.
We need to consider thermodynamics
of the 2 horizons simultaneously.
dE  TR dS R  Th dSh
 Einstein Eq + HDE
QFT from information
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!
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
Rindler horizon
NkTU
Mc  Eh 
 2kTU S BH
2
TU  Mc 2 / 2kS BH
2
GM
TU  2
R
S  mx
TU S GMm
F
 2
x
R
Entropic gravity
Gravity from Information loss
Lee FOP arXiv:1003.4464
Rindler horizon
Mc 2  Eh  2kTU S BH
TU  Mc 2 / 2kS BH
GM
R2
S  mx
TU 
TU S GMm
F
 2
x
R
Information loss
Entropic gravity
S  mx
Big questions
•What is the origin of
Gravity, QM, Q. Entanglement? &
holography?
A motivation) There are strong similarities between holography
and Q. entanglement;
Area proportional, related to information loss,
observer dependency….
 Information can be the key to the solution
Cf) Bekenstein, Wheeler, ‘t Hooft …
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? 
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
For a fixed outside observer
 entropy S increases
(Thermodynamics)
?
M
Coordinate trans.
Horizon
2
dE=Mc =TdS
For an free falling observer
(QM)
Physical laws should be such that the
both observers are satisfied
QFT from information loss
???
f?
f: field,
some function of spacetime
Maximize
Shannon entropy
Constraint
Energy conservation
Boltzmann distribution
Thermal with temperature 1/
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.
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
1)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?
S phasespace
Volume
 O(
)
3
lP
Sint ernal  O(10)
S phasespace
S  S phasespace  Sint ernal  S phasespace
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
 1/   T, some fundamental temperature
associated with one bit of information
1bit.E 
dE=k TdS=k* * red shift
Derivation of 1st law dE=TdS
Free E
F  E  TS  
1

ln Z R
dF  0  dE  TdS
 dE  TdS
Maximum entropy  minimum F  extremizing action  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
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
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
Lagrange multiplier 
 Boundary op
Bulk
Witten’s prescription
Boundary
Quantum Entanglement from holography
R
Proof by contradition
1) Assume there is no entanglement in the bulk
2) All possible states are product states B1 B2
Bj
3) # of boundary bits O(R 2 )
# of bulk bits O(R 3 )
4) One can not fully describe the bulk physics using only boundary DOF
5) contradictory to the holographic principle
QED
0
1
00
01
10
11
Entaglement
~ horizon radius
Then exactly how entanglement arises?
1) There is redundancy in the bulk bits Bi
2) Bi  Bi ({b })
3) There always should be correlated bits which have smaller information than bit size
ex) Assume combination of two bits B1and B2 which is decribed by b0 such that
both of (B1 , B2 )  (1, 0) and (B1 , B2 )  (0,1) corresponds to b0  1
Outside observer can not distinguish two cases. Thus statistical prob. should be added.
 P=P((1, 0))  P((0,1))
For inside observer this corresponds to an entangled state  ~ 1 0  0 1
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
10121 discrepancy
for
Sum of all oscillators
• Zero point Energy
1) Why it is so small?

2) Why it is not zero?
  0
3) Why now?
  H 02 M P2
M P4
QFT can’t solve this
4) Why the cosmological constant is zero or tiny
0
Zhang & Wu, astro-ph/0701405
Our solution to dark energy problem
1) Why it is so small?
Holographic principle
(QFT overcounts ind. DOF; QFT is emergent not fundamental)
2) Why it is not zero?
3) Why now?
Due to quantum vacuum fluctuation
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,
1)gauge theory and Q. gravity
2)BH information paradox
3)Fermions
4)Cosmology including dark energy
5)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 (reverting Unruh’s theory)
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

R
1
3
Scale
factor
=0
DE+DM
DE w<0, negative pressure  antigravity
Acceleration
= Force
Eq. of state
metric
Holography and Entanglement
Entanglement has
1.Area Law (in general)
2.Nonlocality
3.Related to causality
4.Fundamental
5.Observer dependent
It reminds us of the Holographic principle!
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
1) 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
3d 2 M P2
 
Rh 2
d ( R3  )
p 
dR(3R 2 )
1  2  
   1 


3
d 
Friedmann eq. & perfect fluid
EOS
Friedmann equations from entropic force
Cai et al
T
M
Friedmann equation
QM from information loss
Lee , FOP
f?
f: matter filed inside the horizon
Maximize
Shannon entropy
Constraint
Energy conservation
Boltzmann distribution
This Z is equivalent to QM partition function. (Unruh effect)
 QM is emergent!
S  mx
Comparison with Verlinde’s theory
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
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
•Mainly thermodynamic
•Assume degrees of freedom on screen
Concerns about Verlinde’s Idea
1. strange entropy-distance relation
????
2. 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
arXiv:0709.0047, 1003.1878
without QFT
~ Horizon area
For Event horizon
r=Rh
~ Rh
Holographic
dark energy
~1/Area
The simplest case, S= Bekenstein-Hawking entropy
M P2
magnitude 
M P2 H 2 for r O(1/H).
2
r
For event horizon we need an inflation with N ~ 60
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
Holographic dark energy
Only modes with Schwarzschild radius
E~
a
survives (Cohen et al)
Relation between a and L
UV
IR
saturating
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.
3d 2 M P2
 
Rh2
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?
Basic Logic of my theory
Outside observer
:Thermodynamics
inside observer: QM
?E, S
Coordinate
transformation
dE=TdS
Double Slit Experiment
Lee arXiv:1005.2739, FOP
How to calculate Entanglement
entropy
Srednicki,PRL71,666
• Hamiltonian
,
• Vacuum=ground state of oscillarots
• Reduced density matrix
R
• entropy
Eigenvalues
 Area
Calculable!
Holographic dark energy
Only modes with
survives (Cohen et al)
E~
a
Relation between a and L
UV
IR
saturating
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.
3d 2 M P2
 
Rh2
But what is its physical origin?
Hawking radiation as dark energy
Without regularization in flat spacetime
After renormalization in de Sitter spacetime
Too small
T  g  H 4  p   
But With UV cut-off Mp
~ M P2 H 2
since k
2
( H )2
~
(2k ) 2
HDE
LLK, Mod.Phys.Lett.A25:257
Black hole mass
Landauer
Hawking
Mass increase
T decrease
KLL 0709.3573
Black hole thermodynamics
Bekenstein &
Hawking
1) The First Law
2) 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
thermodynamics
Bekenstein-Hawking
entropy
S BH
relativity
Holographic principle
k B c3 Area

4G
gravity
quantum
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.
S within R  S BH
Area

 R 2  S Ent
4 Plank area
R
Scientific American August 2003
Planck’s constant
Relativity, Quantum & Information
Q. Gravity
Quantum
Physics
Relativity
Information
• Information links quantum mechanics with relativity
Superluminal signaling using entanglement?
  Alive
cat
0
Al i en
- Dead
cat
1 Al i en
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
Single
Thermal
Bath with T
M. B. Plenio and V. Vitelli
quant-ph/0103108
C. Bennett
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