Distance Measurement and Wave Dispersion in a Liouville-String Approach to Quantum Gravity

TL;DR

This paper investigates how space-time foam effects in a Liouville-string quantum gravity framework induce frequency-dependent wave dispersion, potentially impacting low-energy particle measurements and aligning with some heuristic quantum-gravity estimates.

Contribution

It introduces a model for space-time foam effects causing wave dispersion in a Liouville-string quantum gravity context, linking theoretical predictions with measurement errors.

Findings

Space-time foam induces frequency-dependent dispersion in wave propagation.

Measurement errors from foam effects are comparable to recent quantum-gravity estimates.

Astrophysical measurement precision could detect or constrain these foam effects.

Abstract

Within a Liouville approach to non-critical string theory, we discuss space-time foam effects on the propagation of low-energy particles. We find an induced frequency-dependent dispersion in the propagation of a wave packet, and observe that this would affect the outcome of measurements involving low-energy particles as probes. In particular, the maximum possible order of magnitude of the space-time foam effects would give rise to an error in the measurement of distance comparable to that independently obtained in some recent heuristic quantum-gravity analyses. We also briefly compare these error estimates with the precision of astrophysical measurements.