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Entropic Gravity. SISSA, Statistical Physics JC Friday 28, 2011. E. Verlinde , arXiv : 1003.4464v2 [ hep-th ]. F. Entropy. Outlook. Background: Holographic Principle (Black Hole Thermodynamics , Entropy Bound ) Verlinde argument for an entropic gravity - PowerPoint PPT Presentation
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Entropic Gravity
SISSA, Statistical Physics JCFriday 28, 2011
E. Verlinde, arXiv: 1003.4464v2 [hep-th]
F
๐ฅ1 ๐ฅ2
๐ฅ3
๐ฅ4
๐ฅ5
Entropy
๐ฅ5 โฒ
โ ๐ฅ ๐ญ โ๐บ
Outlook
โข Background: Holographic Principle (Black Hole Thermodynamics, Entropy Bound)
โข Verlinde argument for an entropic gravity (II principle of dynamics, Newtonโs law of gravity)
โข โฆ editorial discussion
Hawking (1971)
Bekenstein (1972)
Hawking (1973)
Black body radiation
๐๐๐๐๐ก๐ก+๐๐๐ต๐ปโฅ0
๐๐๐๐ก๐กโ 0 =
๐๐ต๐ป ๐ด
R Bekenstein (1981)
E
A
๐ธ<๐๐ต๐ป
๐บ๐๐=๐บ๐๐๐๐+๐บ๐๐๐๐๐
Susskind (1995)
โค๐บ๐๐๐=๐บ๐ฉ๐ฏ=๐จ๐๐๐ต๐ปโ๐ธ
Toward the holographic principleโฆ
๐ =๐ฅ๐ง๐ต=๐๐๐ ๐๐ (๐ฏ )
Ex 1 ๐=100 ๐๐2 100 bits of information
Ex 2 !
Number of degrees of freedom
Ex 3 Quantum field theory
๐ช๐๐๐ ๐๐๐๐ ๐ท๐๐๐๐๐ ๐ณ๐๐๐๐๐ ๐ ๐=๐บ๐๐2h ฮฝ=๐๐2
๐๐=โโ๐บ๐3 =1.6ร10โ33๐๐
๐ธ๐๐๐๐๐ฆ ๐ ๐๐๐๐ก๐๐ข๐๐๐๐ข๐๐๐๐๐๐ฆ h๐ก ๐ ๐๐๐๐๐๐๐๐๐ ๐
๐๐=โโ๐๐บ =1.3ร1019๐บ๐๐V oscillators and n states per oscillator
๐=๐๐ ๐=๐ ๐๐๐
How many different states can be in a region to describe all the physics inside of it?
๐๐บ ๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
What is the entropy of the ยซfundamental systemยป?
๐โค ๐ด4
๐๐๐๐๐๐ ๐๐ ๐๐๐๐=๐ =๐จ
๐ ๐จ๐ท
๐=๐๐ด4
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
โข Background: Holographic Principle (Black Hole Thermodynamics, Entropy Bound)
โข Verlinde argument for an entropic gravity (II principle of dynamics, Newtonโs law of gravity)
โข โฆ editorial discussion
SPACE as a storage of information
Holographic screen
โฆ nothing yetโฆ
Emerged space
110011110010001111101001
We further assume the theory has a notion of time and that its dynamics is traslational invariant
EnergyStat. Phys.
Temperature
Holographic screen
โ ๐
โ๐บ=2๐ ๐๐๐โ โ ๐ ๐น โ๐ฅ=๐ โ๐
๐๐ป=๐๐๐
โ๐๐
โ๐บ
๐ป
Unruh Effect
๐ญ=๐๐
Force and Inertia
Newtonโs law of gravity
๐=๐ด๐3๐บโ
๐ธ=12๐๐๐ ๐ธ=๐๐2
โ๐บ=2๐ ๐๐๐โ โ ๐ ๐น โ๐ฅ=๐ โ๐
Holographic principle
T
๐ญ=๐ฎ๐ด๐๐น๐
(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
๐พ๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐ ? ๐ ,โ ,๐ฎ
(iii) There is a change of entropy in the emergent direction
๐๐2=12๐๐๐ Bekenstein + Unruh
โ๐บ๐ต =๐ ๐โ ๐
๐๐๐ ๐=โ๐ต๐ โ๐บ๐ต =โ๐ โ๐
๐๐๐
โ๐บ=2๐ ๐๐๐โ โ ๐ ๐๐ป=๐๐๐
โ๐๐
ษธ is a coarse-graining variableโ๐บ๐ต =โ๐ โ๐
๐๐๐
๐<โ ๐๐๐๐<๐
Coarse- Graining
Space is emerging!
Amount of coarse graining
Dark Energy
radius of the observable universe
holographic principle
๐๐2=12 ๐๐๐=12 ๐ด๐๐
๐=1.4 1060๐๐๐ ๐ ๐๐ h๐ก ๐๐๐๐ ๐๐๐ฃ๐๐๐๐๐ข๐๐๐ฃ๐๐๐ ๐
๐๐=๐๐2๐ด 10โ 64
h๐ก ๐๐๐๐ก๐๐๐๐๐ ๐๐๐๐๐๐น=๐๐ ๐ป๐=๐๐๐๐๐๐ (๐ ๐ 2 )=2๐๐๐๐
1๐ ๐2๐ ๐๐ก2
=๐น๐๐ =2๐ ๐๐๐ 1.310โ123
๐๐ป=๐๐๐
โ๐๐Unruh Effect
It works for dimensional consistency!
Referencesโข E. Verlinde โOn the origin of Gravity and the Newton
lawsโโข S.Gao Comment on "On the Origin of Gravity and the
Laws of Newton" โข A. Chivukula โGravity as an entropic phenomenonโโข T. Jacobson, โThermodynamics of Spacetimeโ Phys. Rev.
Lett. (1995)
โข R. Bousso โThe holographic principleโโข R. Ruffini and H. Ohanian โGravitation and spacetimeโ
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