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Entropic Gravity
SISSA, Statistical Physics JC
Friday 28, 2011
E. Verlinde, arXiv: 1003.4464v2 [hep-th]
F
3
1
2
5
4
E
n
t
r
o
p
y
=
∆



~∆
5 ′
Outlook
• Background: Holographic Principle
(Black Hole Thermodynamics, Entropy Bound)
• Verlinde argument for an entropic gravity
(II principle of dynamics, Newton’s law of gravity)
• … editorial discussion
 ≥  Hawking (1971)
 =


 +  ≥ 0
Bekenstein (1972)
Black body radiation
=
ℏ

Hawking (1973)
 ≠ 0
 = 0
 ~
R
 <  Bekenstein (1981)
E
 < 
 − 

=  +  ≤
A
 ≤



= 

=

Susskind (1995)
Toward the holographic principle…
 =   =  ()
Ex 1    = 2100 
Ex 2
 
Ex 3
Quantum field theory
Number of degrees of freedom
 = 100 2
  ~ 
100 bits of information
 = ∞!
ℎν =  2
 =

 = 2

ℏ
= 1.6 × 10−33 
3

    ℎ  
V oscillators and n states per oscillator
 = 
 =   
 =
ℏ
= 1.3 × 1019 

How many different states can be in a region to describe all the physics inside of it?
 ~  
What is the entropy of the «fundamental system»?

≤
4
=

4

   =  =

A region with boundary of area A is fully described by no more than A/4
degrees of freedom, or about 1 bit of information per Planck area
Outlook
• Background: Holographic Principle
(Black Hole Thermodynamics, Entropy Bound)
• Verlinde argument for an entropic gravity
(II principle of dynamics, Newton’s law of gravity)
• … editorial discussion
SPACE as a storage of information
… nothing yet…
110
011
110
010
001
111
101
001
Emerged space
Holographic screen
We further assume the theory has a notion of time and that its dynamics is traslational invariant
Energy
Temperature
Stat. Phys.
Force and Inertia
∆

∆
Holographic screen

∆ = 2
∆
ℏ
 =
∆ = ∆
 ℏ
 
Unruh Effect
 = 
Newton’s law of gravity
Holographic principle
 3
=
ℏ

∆ = 2
∆
ℏ
=
1

2
 =  2
∆ = ∆

=

T
(i) The number of degrees of freedom is proportional to the area
of the screen (Holographic principle)
(ii) The energy is evenly distributed over these degrees of freedom
    ? , ℏ, 
(iii) There is a change of entropy in the emergent direction
 2
1
= 
2
Bekenstein + Unruh
∆ = 2
∆
∆
= 


 = −

∆
ℏ
 =
 ℏ
 
∆
∆
= − 


ɸ is a coarse-graining variable
∆
∆
= − 



<− <

Amount of coarse graining
Coarse- Graining
Space is emerging!
Dark Energy
~2.7 1061 radius of the observable universe
 =  = 2 holographic principle
1
1
 2 =  = 
2
2
 = 1.4 1060   ℎ  
 2
 =
~10−64

ℎ    =  =  2 = 2
1 2 


−123
=
=
2
~1.3
10
  2 

Unruh Effect
 ℏ
 =
 
It works for dimensional consistency!
References
• E. Verlinde ‘On the origin of Gravity and the Newton
laws’
• S.Gao Comment on "On the Origin of Gravity and the
Laws of Newton"
• A. Chivukula ‘Gravity as an entropic phenomenon’
• T. Jacobson, ‘Thermodynamics of Spacetime’ Phys. Rev.
Lett. (1995)
• R. Bousso ‘The holographic principle’
• R. Ruffini and H. Ohanian ‘Gravitation and spacetime’

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