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

2008/03/31 by Louis Crane, Crane, Louis
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc

paper · pdf · doi:10.48550/arxiv.0804.0030

latex document. Submitted to GRF

arxiv created 2008/03/31 · openalex publication_date 2008/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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