Distance Measurement and Wave Dispersion in a Liouville-String Approach   to Quantum Gravity
  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. 
G. Amelino-Camelia, J. Ellis, N.E. Mavromatos, and D.V. Nanopoulos