Quantum Physics

1. Utrecht University BLACK HOLES and Quantum Physics Gerard ’t Hooft Spinoza Institute, Utrecht University

2. The 4 Force Laws: 1. Maxwell: Force 2. Weak: 3. Strong: 4. Gravitation: Distance

3. Gravity becomes more importantat extremely tiny distance scales ! However, mass is energy ...

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

5. Planck Units

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

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

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

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

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

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

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

14. 12 12 3 3 9 9 6 6 In a black hole: compare Hawking’s particle emission process with the absorption process: Black hole plus matter Heavier black hole

15. Probability = | Amplitude |2 × (Volume of Phase Space) of the final states time reversal symmetry (PCT): forwards and backwards in time: the same

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

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

18. 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 ! ❖

19. time space Horizon The quantum states in regions I and II are coherent. Region II Region I 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 ...

20. Alternative theories: • 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) • Information is in the Hawking radiation

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

22. The physical description of the horizon problem ...

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

24. interaction horizon

25. 2-d surface

26. Particles and horizons, the hybrid picture

27. Black hole complementarity principle An observer going into a black hole can detect all other material that went in, but not the Hawking radiation An observer outside the black hole can detect the Hawking particles, but not all objects that have passed the horizon. Yet both observers describe the same “reality”

28. Elaborating on this complementarity principle: An observer going into a black hole treats ingoing matter as a source of gravity, but Hawking radiation has no gravitational field. An observer outside the black detects the gravitational field due to the Hawking particles, but not the gravitational fields of the particles behind the horizon. Yet both observers describe the same “space-time”

29. Space-time as seen by ingoing observer Space-time as seen by late observer outside

30. This may be a conformal transformation of the interior region: Light-cones remain where they are, but distances and time intervals change! An exact local symmetry transformation, which does not leave the vacuum invariant, unless: (the conformal transformation)

31. This local scale invariance is a local U (1) symmetry: electromagnetism as originally viewed by H. Weyl. Fields may behave as a representation of this U (1) symmetry. ???????? Is this a way to unify EM with gravity? The cosmological constant (“Dark energy”) couples directly to scales Is this a way to handle the cosmological constant problem? ???????????????

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

33. Gravitational effect from ingoing objects in particles out

35. The non-commucativity between and lleads to a Horizon Algebra : Also for electro-magnetism:

36. The string world-sheet

37. Black Hole Formation & Evaporation by Closed Strings

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

39. y y x Black holes and extra dimensions 4-d world on “D -brane” Horizon of “Big Hole” “Little Hole”

40. These would have a thermal distribution with equal probabilities for all particle species, corresponding to Hawking’s temperature

41. THE END