Utrecht University on Gerard t Hooft Dublin November

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

CERN LHC Large Hadron Collider **

7 Te. V + 7 Te. V

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

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

General Relativity

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

Planck Units

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

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

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

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

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

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

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

Stephen Hawking’s great discovery: the radiating black hole

horizon Region II negative energy positive energy

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. . .

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

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 !

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

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

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 !

Horizon Region II Region I 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. . .

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

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