Gravitons and light cone fluctuations. II. Correlation functions

A model of a fluctuating light cone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating light cone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.