Algebraic description of spacetime foam

TL;DR

This paper introduces an algebraic formalism to treat spacetime topology as a quantum observable, bridging classical general relativity and quantum concepts through limit constructions.

Contribution

It provides a novel algebraic framework for describing spacetime foam, integrating classical and quantum descriptions of spacetime topology.

Findings

Spacetime foam described algebraically.

Classical spacetime manifold expressed via limit constructions.

Framework bridges classical and quantum spacetime descriptions.

Abstract

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.