  We present a formalism to discern the effects of fluctuations of the
spacetime metric on electromagnetic radiation. The formalism works via the
measurement of electromagnetic field correlations, while allowing a clear
assessment of the assumptions involved. As an application of the formalism, we
present a model of spacetime fluctuations that appear as random fluctuations of
the refractive index of the vacuum in single, and two co-located Michelson
interferometers. We compare an interferometric signal predicted using this
model to experimental data from the Holometer and aLIGO. We show that if the
signal manifests at a frequency at which the interferometers are sensitive, the
strength and scale of possible spacetime fluctuations can be constrained. The
bounds, thus obtained, on the strength and scale of the spacetime fluctuations,
are also shown to be more stringent than the bounds obtained previously using
astronomical observation at optical frequencies. The formalism enables us to
evaluate proposed experiments such as QUEST for constraining quantum spacetime
fluctuations and to design new ones.
