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

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

2008-03-31

arxiv.org/abs/0804.0030v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

latex document. Submitted to GRF

Scientific paper

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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