and Planck-Scale Physics

Department of Mathematics, University of California

Riverside, California 92521, USA

* January 28, 1999 *

Published in *Physics Meets Philosophy at the Planck Scale*,

eds. Craig Callender and Nick Huggett, Cambridge U. Press, 2001,
pp. 172-195.

Also available in Postscript and PDF.

This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local degrees of freedom propagating causally'. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensional spacetime. These are background-free quantum theories lacking local degrees of freedom, so they only display some of the features we seek. However, they suggest a deep link between the concepts of `space' and `state', and similarly those of `spacetime' and `process', which we argue is to be expected in any background-free quantum theory. We sketch how higher-dimensional algebra provides the mathematical tools to make this link precise. Finally, we comment on attempts to formulate a theory of quantum gravity in 4-dimensional spacetime using `spin networks' and `spin foams'.

- Introduction
- The Planck Length
- Topological Quantum Field Theory
- 3-Dimensional Quantum Gravity
- Higher-Dimensional Algebra
- 4-Dimensional Quantum Gravity

This paper has a followup: Quantum Quandaries: a Category-Theoretic Perspective.

© 1999 John Baez

baez@math.removethis.ucr.andthis.edu