A model-independent statistical framework is presented to interpret data from systems where the mean time derivative of positional cross correlation between world lines, a measure of spreading in a quantum geometrical wave function, is measured with a precision smaller than the Planck time. The framework provides a general way to constrain possible departures from perfect independence of classical world lines, associated with Planck scale bounds on positional information. A parameterized candidate set of possible correlation functions is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of information suggested by gravity. Frequency-domain power spectra are derived that can be compared with interferometer data. Simple projections of sensitivity for realistic experimental set-ups suggests that measurements will confirm or rule out a class of Planck scale departures from classical geometry.