2. Gerard ’t Hooft Dublin November 13, 2007 Utrecht University on

3. CERN LHC Large Hadron Collider * *

4. 7 TeV + 7 TeV

5. The highway across the desert Today’s Limit … GUTs Planck length : Quantum Gravity LHC

6. The Universal Force Law: Gravitation: Distance Force Maxwell & YM:

7. General Relativity

8. Gravity becomes more important at extremely tiny distance scales ! However, mass is energy...

9. Planck Units

10. photon graviton The Photon Spin = 1 Spin = 2 P P P P P P P P P P P P P P P P Equal charges repel one another... Equal masses attract one another... The Graviton

11. Moon Earth Sun strength of force This is the wave function of a spin 2 particle Graviton Force and spin

12. The Black Hole Electromagnetism: like charges repel, opposite charges attract → charges tend to neutralize Gravity: like masses attract → masses tend to accumulate

13. horizon Where is the gravitational field strongest? The formation of a Black Hole even light cannot escape from within this region... Black Hole

14. The Schwarzschild Solution to Einstein’s equations Karl Schwarzschild 1916 “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”

15. The Schwarzschild Solution to Einstein’s equations Karl Schwarzschild 1916 “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”

16. Universe I Universe II “Time” stands still at the horizon So, one cannot travel from one universe to the other Black Hole

17. As seen by distant observer As experienced by astro- naut himself They experience time differently. Mathematics tells us that, consequently, they experience particles differently as well Time stands still at the horizon Continues his way through

19. Stephen Hawking’s great discovery: the radiating black hole

20. negative energy positive energy horizon Region I Region II

21. While emitting particles, the black hole looses energy, hence mass... they become smaller. Lighter (smaller) black holes emit more intense radiation than heavier (larger) ones The emission becomes more and more intense, and ends with...

22. 12 6 3 9 6 3 9 Black hole plus matter Heavier black hole compare Hawking’s particle emission process with the absorption process: → Heavier black hole In a black hole:

23. If the heavier black hole could exist in much more quantum states than the lighter one, the absorption process would be favored... If the heavier black hole could exist in much fewer quantum states than the lighter one, the emission process would be favored... Comparing the probabilities of these two processes, gives us the number of quantum states !

24. of the final states time reversal symmetry (PCT): forwards and backwards in time: the same

25. The black hole as an information processing machine The constant of integration: a few “bits” on the side...

26. Are black holes just “elementary particles”? Black hole “particle” Imploding matter Hawking particles Are elementary particles just “black holes”? Entropy = ln ( # states ) = ¼ (area of horizon)

27. Dogma: We should be able to derive all properties of these states simply by applying General Relativity to the black hole horizon... [ isn’t it ? ] That does NOT seem to be the case !! For starters: every initial state that forms a black hole generates the same thermal final state But should a pure quantum initial state not evolve into a pure final state? The calculation of the Hawking effect suggests that pure states evolve into mixed states !

28. Region I Region II Horizon The quantum states in regions I and II are coherent. This means that quantum interference experiments in region I cannot be carried out without considering the states in region II But this implies that the state in region I is not a “pure quantum state”; it is a probabilistic mixture of different possible states...

29. Alternative theories: 1.No scattering, but indeed loss of quantum coherence (problem: energy conservation) 2. After explosion by radiation: black hole remnant (problem: infinite degeneracy of the remnants) 3.Information is in the Hawking radiation

30. How do we reconcile these with LOCALITY? paradox Black Holes require new axioms for the quantization of gravity Unitarity, Causality,... paradox Black Hole Quantum Coherence is realized in String/Membrane Theories ! -- at the expense of locality? -- How does Nature process information ?

31. The physical description of the difficulty...

32. horizon Here, gravitational interactions become strong !! brick wall

33. interaction horizon

34. b By taking back reaction into account, one can obtain a unitary scattering matrix

35. Black Hole Formation & Evaporation by Closed Strings

36. BLACK HOLE WHITE HOLE A black hole is a quantum superposition of white holes and vice versa !! The Difference between

37. Particles and horizons, the hybrid picture