Is Quantum Spacetime Foam Unstable?

TL;DR

This paper models a simple wormhole in quantum spacetime foam, showing it is quantum-mechanically unstable with no bound states, implying potential constraints on the stability and existence of spacetime foam.

Contribution

It introduces a quantum mechanical model of a wormhole in spacetime foam and demonstrates its instability through WKB analysis.

Findings

Wormhole has no bound states, indicating quantum instability.

Wave functions leak to large radii, suggesting instability.

Stability considerations may constrain spacetime foam theories.

Abstract

A very simple wormhole geometry is considered as a model of a mode of topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of the hole reduces to quantum mechanics of one variable, throat radius, and admits a WKB analysis. The hole is quantum-mechanically unstable: It has no bound states. Wormhole wave functions must eventually leak to large radii. This suggests that stability considerations along these lines may place strong constraints on the nature and even the existence of spacetime foam.