Quantum metric for null separated events and spacetime atoms

Understand

Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, related to their density, function of the point $P$ and vector $v^a$ at $P$.

• This has been done in the Euclideanized space one obtains through analytic continuation from Lorentzian sector at $P$.
• $\rho$ has been defined in terms of a peculiar `effective' metric $q_{ab}$, of quantum origin, introduced for spacelike/timelike separated events.
• This metric stems from requiring that $q_{ab}$ coincides with $g_{ab}$ at large (space/time) distances, but gives finite distance in the coincidence limit, and implements directly this way one single, very basic aspect associated to any quantum description of spacetime: length quantization.