Report

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’