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GRAVITY AS AN EMERGENT FORCE Erik Verlinde University of Amsterdam

ICHEP conference, Paris , 22/07/10. GRAVITY AS AN EMERGENT FORCE Erik Verlinde University of Amsterdam. Emergence. Current Paradigm. FUNDAMENTAL FORCES: carried by elementary particles. Emergence of Particles and Forces. Gravity as an Emergent Force.

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GRAVITY AS AN EMERGENT FORCE Erik Verlinde University of Amsterdam

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  1. ICHEP conference, Paris , 22/07/10 GRAVITY AS AN EMERGENT FORCEErik VerlindeUniversity of Amsterdam

  2. Emergence

  3. CurrentParadigm FUNDAMENTAL FORCES: carriedbyelementaryparticles

  4. Emergence of Particles and Forces

  5. Gravity as anEmergentForce • At a microscopicscale Nature is describedbymanydegrees of freedom, most of which are invisible and at firstsight irrelevant for the observedmacroscopicphysics. • Gravityarisesdue to the factthat the amount of phasespace volume (“information”) occupiedby these microscopicdegrees of freedom is influencedby the observablemacroscopic variables, like the positions of materialobjects.

  6. Black Hole Horizon m • Black hole thoughtexperiments. • Consider a particlegradually • lowered in to a black hole. • Classically, the energy • associatedwith the particlegets • redshifted, and vanisheswhen • the particle is at the horizon. Penrose Christodoulou Bekenstein Hawking

  7. Black Hole Entropy=> HolographicPrinciple Maximalinformationassociatedwith a part of spacecanbeencoded in a # of bits equal to the area in Planck units

  8. ADS/CFT CORRESPONDENCE EQUIVALENCE BETWEEN FIELD THEORY ON THE “BOUNDARY” AND GRAVITY IN THE “BULK” ONE SPACE DIMENSION EMERGES CORRESPONDING TO THE “SCALE” OF THE BOUNDARY THEORY. RADIAL EVOLUTION IS LIKE RENORMALIZATION GROUP FLOW.

  9. Bulk description Black Hole In AdS space Particle gets lowered in to black hole Hot CFT • Boundary description: Thermal Heat Bath Delocalized state gets thermalized by heath bath

  10. Entropicforce (wikipedia) Anentropicforce is a macroscopicforcewhose properties are determinednotby the character of anunderlyingmicroscopicforce, butby the wholesystem'sstatistical tendency to increaseitsentropy.

  11. Heat Bath Entropic Force Polymer

  12. Thought experiment Black Hole Horizon • black hole m • “stretched • horizon”

  13. Consistencywith black • holethermodynamics • implies Black Hole Horizon m

  14. 001100011011101010 A HEURISTIC DERIVATION OF GRAVITY 010100101101001100 information is storedonholographicscreens moving a particle over oneComptonwavelength leads to one more bit of information

  15. 001100011011101010 To get a forceoneneeds a temperature. Bytakingthattemperature to be the Unruhtemperature onefindsNewton’slaw of inertia

  16. In order to getanentropicforce I need a temperature

  17. Holographicscreens at equipotential(= equal redshift) surfaces

  18. Whatabout General Relativity? Surface of constant redshift • Komarmass • => Einsteinequation

  19. Rindler Horizon m Suggestive link with QM: What is thisvelocityv?

  20. Cosmological Horizon DeSitter Space m

  21. Cosmological Horizon m

  22. Cosmological Horizon m

  23. Equipotential surface m v = escape velocity

  24. Born-Oppenheimer & Adiabatic theorem Schroedingereqnwith H dependingoninfinitely slow variable Instantaneouseigenstates AdiabaticReactionForce Semiclassically

  25. Born-Oppenheimer & Entropic Force The system stays in an energy eigenstate of the fast variables( adiabatic theorem). Microscopic Fast Variables Macroscopic Slow Variables

  26. Born-Oppenheimer & Entropic Force • Assuming eigenvalues don’t cross, the energy follows from Macroscopic Slow Variables

  27. What lives on the screens? According to stringtheory: open strings. Integrating out the UV open stringsproducesclosedstrings in the emergedspace.

  28. Open closedstringduality Open stringone loop diagram Masslesspole in dual channel x

  29. UV/IR correspondence Open stringwith UV cutoff Closedstring / gravitywith UV cutoff

  30. Matrix description of gravity.

  31. Matrix description of gravity.

  32. Gravity as anEmergentForce • At a microscopicscale Nature is describedbymanydegrees of freedom, most of which are invisible and at firstsight irrelevant for the observedmacroscopicphysics. • Gravityarisesdue to the factthat the amount of phasespace volume (“information”) occupiedby these microscopicdegrees of freedom is influencedby the observablemacroscopic variables, like the positions of materialobjects.

  33. Berry Phase and Crossing Eigenvalues Diracmonopool At the locus of coincidingeigenvalues onecan construct Non-abelian Berry

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