QUANTUM MECHANICS and DETERMINISM at the PLANCK SCALE*

9/11/00

* A different version of this talk, with the title "Quantum Mechanics and Information Loss", was presented at the Conference on "Decoherence", Spinoza Institute, Utrecht, June 10 - 14, 2000.


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Table of Contents

Title page

A new doctrine ...

Definition of states

"Beables" in an Atom in a Magnetic field

Changeables -- and simple models

Beables in the first quantized neutrino

A fundamental difficulty: positivity of the Hamiltonian

resolution: second quantization

Deterministic evolution of continuous degrees of freedom:

non-interacting Bosonic field:

(cont'd)

Decoupling Hamiltonians.

anharmonic forces

Compare (static) black hole

Dissipation (Information loss)

Equaivalence classes in black holes

Neutrinos are equivalence classes ...

Poincare cycles -- time as a gauge parameter

The equivalence classes are large

Predeterminism in quantum mechanics

Two weakly coupled degrees of freedom

dissipation -- lock in -- quantization

Strings are also harmonic oscillators !!

References

Author: Gerard 't Hooft, Utrecht University

Email: g.thooft@phys.uu.nl

Home Page: http://www.phys.uu.nl/~thooft