Quantum Space-Time as a Quantum Causal Set

Details Quantum Space-Time as a Quantum Causal Set Quantum Space-Time as a Quantum Causal Set

2002-01-02

arxiv.org/abs/gr-qc/0201004v8

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, ReV-TeX, substantially revised, expanded and updated version

Scientific paper

A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically interpreted as a locally finite, causal and quantal version of the kinematical structure of general relativity: the 4-dimensional Lorentzian space-time manifold and its continuous local orthochronous Lorentz symmetries. We discuss various possible dynamical scenarios for quantum causal sets mainly by using sheaf-theoretic ideas, and we entertain the possibility of constructing an inherently finite and genuinely smooth space-time background free quantum theory of gravity. At the end, based on the quantum causal set paradigm, we anticipate and roughly sketch out a potential future development of a noncommutative topology, sheaf and topos theory suitable for quantum space-time structure and its dynamics.

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