  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 parametrized 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
specific experimental set-ups suggests that measurements will directly yield
constraints on a universal time derivative of the correlation function, and
thereby confirm or rule out a class of Planck scale departures from classical
geometry.
