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Dimensional reduction in quantum gravity

Gerard 't Hooft
(
- Utrecht U.
)

Oct 25, 1993

15 pages

Published in:

Conf.Proc.C 930308 (1993) 284-296

Contribution to:

Conference on Highlights of Particle and Condensed Matter Physics (SALAMFEST)

e-Print:

gr-qc/9310026 [gr-qc]

Report number:

THU-93-26

View in:

ADS Abstract Service

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Abstract: (arXiv)

The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. Essay dedicated to Abdus Salam.

Note:

Essay dedicated to Abdus Salam

talk
quantum gravity
operator: algebra
algebra: Boole
dimension: >4
dimensional reduction
temperature
black hole
constraint
phase space: Hilbert space

References(19)

Figures(0)

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