The Small Scale Structure of Spacetime

TL;DR

The paper reviews evidence that quantum gravity may exhibit two-dimensional behavior at small scales and proposes an argument from the Wheeler-DeWitt equation's strong-coupling limit, linking quantum spacetime to cosmological singularities.

Contribution

It introduces a new argument for spontaneous dimensional reduction in quantum gravity based on the Wheeler-DeWitt equation's strong-coupling limit.

Findings

Evidence for effective two-dimensionality at small scales

Proposed connection between quantum spacetime and cosmological singularities

New argument from Wheeler-DeWitt equation analysis

Abstract

Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the strong-coupling limit of the Wheeler-DeWitt equation. If this description proves to be correct, it suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity.