Galileo Galilei Colloquium, Pisa, March 3, 2006 Gerard ’t Hooft Utrecht University

BANG !!

curved space and time heavy planet Gravity = free fall in curved space-time

A Black Hole

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

The part of the universe that we know contains about particles Only a small fraction of them are of the kind that build up the world that is familiar to us

The Universe of the sub-atomic particles

Quantum Mechanics

? 10 Unification x SU (3) x SU (2) x U (1) Super Symmetry SU (5) Unification ?

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

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

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

Planck Units

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

When gravity becomes strong: - space-time fluctuations run out of control: infinities - the definition of time becomes ambiguous: one cannot talk of “the state of the universe at a given time”. - the universe might close into itself, in which case the use of quantum mechanics becomes ambiguous. - notions such as “distance” and “locality” become ambiguous super string theory? Wheeler – DeWitt equ’n? Statistics of universes ? Non-local theories ?  bad understanding of UV region  bad understanding of probability and causality  the real universe isn’t closed...  and what about reduction ?

microscopic black holes Where does the gravitational field become as strong as it ever can get ?

negative energy positive energy horizon Region I Region II

The black hole as an information processing machine

Are black holes just “elementary particles”? Black hole “particle” Imploding matter Hawking particles Are elementary particles just “black holes”?

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...

Three competing 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

interaction horizon One must take interactions into account:

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

Particles and horizons, the hybrid picture

SuperSymmetry and SuperGravity -1 -½ 0 ½ N = 1 N = 2 N = 4 N = 1 N = 2 N = 4 N = 8 SUSY SUGRA ½ 1½ 2 Spin along z-axis

“Loop quantum gravity”

The SuperString Theory

y Could the Planck length be much larger? Do “extra dimensions” exist ? x y 4-d world on “D -brane” Horizon of “Big Hole” “Little Hole”

Type IIA Closed Superstring Super Gravity in 11 dimensions Type I Open Superstring Type IIB Closed Superstring Heterotic String SO(32) Heterotic String E8 x E8 M - theory

The Landscape x Our Universe ?

How do we reconcile this with LOCALITY? paradox All degrees of freedom of some section of the universe reside on its BOUNDARY Unitarity, Causality,... paradox Thie paradoxical behaviour is indeed reproduced in string / membrane theories ! -- at the expense of locality? -- How does Nature process information ?

Quantum Mechanics is usually seen as a blessing Quantum Mechanics solves the problem of the UV divergence in thermal radiation (Planck, 1900) But Quantum Mechanics generates new infinity problems of its own at the Planck scale... Could Quantum Mechanics not be replaced by something better there ?

The Cosmological Constant Problem stretchability very small stiffness very large

Super Nova Luminosity against Red Shift

The cellular automaton

How does God produce random numbers ? Could these random numbers be actually created by “ordinary” physical processes at the Planck scale? Determinism at the Planck length ( cm) Why not ? Simple-minded, “direct” approaches are doomed to fail. Problem that keeps coming up: why is energy always positive ?

Energy is related to time. If two systems are compared, both energies must be positive (but both being negative could also be allowed) Modest discovery : such a constraint might come about if the two clocks are allowed to be non- synchronous (due to grav. fields), while we have the following restriction: if time goes forward in one system, it must also go forward in the other (and vice versa):

What is the true nature of space and time ?