Fuzzy spacetime from a null-surface version of GR

摘要

The null-surface formulation of general relativity -- recently introduced --provides novel tools for describing the gravitational field, as well as a freshphysical way of viewing it. The new formulation provides ``local'' observablescorresponding to the coordinates of points --- which constitute the spacetimemanifold --- in a {\em geometrically defined chart\/}, as well as non-localobservables corresponding to lightcone cuts and lightcones. In the quantumtheory, the spacetime point observables become operators and the spacetimemanifold itself becomes ``quantized'', or ``fuzzy''. This novel view may shedlight on some of the interpretational problems of a quantum theory of gravity.Indeed, as we discuss briefly, the null-surface formulation of generalrelativity provides (local) geometrical quantities --- the spacetime pointobservables --- which are candidates for the long-sought physical operators ofthe quantum theory.