Gerard ’t Hooft Berlin November 1, 2007 Utrecht University of the

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 ?

The physical description of the difficulty...

horizon Here, gravitational interactions become strong !! brick wall

interaction horizon

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

Gravitational effect from ingoing objects particles out in

Strategy: infinitesimal modification of in-state

a string theory amplitude !!nearly Repeat procedure:

The string world-sheet

Black Hole Formation & Evaporation by Closed Strings

Horizon Algebra

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

very early very late in out S-matrix Ansatz: Qu. Gr. gives us a boundary condition here But, our algebra does not generate the area law. Can we be more precise? Transverse gravity? Now, let us look at the contributions from the Standard Model Scale

It all happens at the origin of Rindler Space

2-d surface

The Standard Model Contribution to the Horizon Algebra. I. The U (1) field

The role of the Standard Model’s scalar fields

Scalar field acts as quantum hair It generates a modification in the vector field equations:

are as their (Euclidean) quantum exp. values The average values of the scalar fields:

Questions: - What is the effect of Standard Model fermions ? - How do we handle non-Abelian vectors ? - What is the effect of the instanton angle  ? - What modifications of the algebra are generated by the transverse grav. force ? - Does this allow for a representation of the algebra with discrete states, as suggested by the entropy – area law?

A related question that we can answer: What is the effect of magnetic monopoles ? arg has a Dirac string - ambiguity 2  n N S

A non-Abelian gauge theory may now be treated in its Cartan subalgebra, where the diagonal components of electric and magnetic charges are well-defined.

Particles and horizons, the hybrid picture

We intend to obtain the complete algebra relating the in-operators to the out-operators from whatever Standard Model Lagrangian. Once the rules are clear, we should be able once again to add (transversal) gravity. The representation of our algebra should then respect the entropy / area law. The algebra should generate the details of quantum black hole dynamics. “The black Hole Horizon as a Dynamical System”, Int.J.Mod.Phys. D15 (2006) 1587 earlier version: gr-qc/