A Pointless Model for the Continuum as the Foundation for Quantum Gravity

TL;DR

This paper proposes a novel approach to quantum gravity that eliminates the classical point set continuum, using handlebody decompositions and nondistributive lattices to describe spacetime states.

Contribution

It introduces two complementary models for quantum gravity that replace the classical continuum with topological and lattice-based structures.

Findings

Handlebody decomposition of loop space as a model

Nondistributive lattice for classical limit

Potential extension of state sum models to loop space

Abstract

In this paper, we outline a new approach to quantum gravity; describing states for a bounded region of spacetime as eigenstates for two classes of physically plausible gedanken experiments. We end up with two complementary descriptions in which the point set continuum disappears. The first replaces the continuum of events with a handlebody decomposition of loop space. We conjecture that techniques fron algebraic topology will allow us to extend state sum models on spacetime to loop space. The second picture replaces the continuum with a nondistributive lattice; the classical limit seems more tractible in this picture.