Slides - Sissa.it

```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)
=
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’
```