Fuzzy spacetime from a null-surface version of general relativity

The null-surface formulation of general relativity-recently introduced-provides novel tools for describing the gravitational held. as well as a fresh physical way of viewing it. The new formulation provides 'local' observables corresponding to the coordinates of points-which constitute the spacetime manifold-in a geometrically defined chart, as well as nonlocal observables corresponding to lightcone cuts and lightcones. In the quantum theory, the spacetime point observables become operators and the spacetime manifold itself becomes 'quantized', or 'fuzzy'. This novel view may shed light on some of the interpretational problems of a quantum theory of gravity. Indeed. as we discuss briefly, the null-surface formulation of general relativity provides (local) geometrical quantities-the spacetime point observables-which are candidates for the long-sought physical operators of the quantum theory.