Fuzzy spacetime from a null-surface version of GR

TL;DR

This paper explores a null-surface formulation of general relativity that introduces geometrically defined local and non-local observables, leading to a 'fuzzy' quantum spacetime that could clarify quantum gravity issues.

Contribution

It presents a novel null-surface approach to GR that defines local spacetime observables and suggests a way to quantize spacetime points, offering new insights into quantum gravity.

Findings

Spacetime points become operators in the quantum theory.

The spacetime manifold is 'fuzzed' or quantized.

Provides geometrically defined observables for quantum gravity.

Abstract

The null-surface formulation of general relativity -- recently introduced -- provides novel tools for describing the gravitational field, 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 {\em geometrically defined chart\/}, as well as non-local 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.