Zooming in on discrete space

Although we lack complete understanding of quantum aspects of gravitation, it is usually agreed, using general arguments, that a final quantum gravity theory will endow space and time with some (fundamental or effective) notion of discreteness. This granular character is supposed to lie on space and time scales of $l_P \sim 10^{-33}$ cm and $\tau_P\sim 10^{-42}$ s, respectively -- the Planck scale -- , far beyond any hope of direct assessment. Here, by modeling displacements of particles on a discrete underlying space as Poisson processes, we speculate on the possibility of amplifying the effects of space discreteness (if existent) by several orders of magnitude, using the statistical variance of correlated displacements of particles/systems with very different masses. Although still out of reach by current technology, the analysis presented here suggests that it may be possible to see hints of space(time) discreteness at larger scales than one would usually expect.
Comment: 6 pages, 4 figures