Structure of random discrete spacetime

Details Structure of random discrete spacetime Structure of random discrete spacetime

Jan 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvl..66..260b&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 66, Jan. 21, 1991, p. 260-263. Research supported by DOE. Previously announced in

Mathematics

Probability

41

Discrete Functions, Manifolds (Mathematics), Metric Space, Probability Distribution Functions, Space-Time Functions, Amount, Signatures

Scientific paper

The usual picture of spacetime consists of a continuous manifold, together with a metric of Lorentzian signature which imposes a causal structure on the spacetime. A model, first suggested by Bombelli et al., is considered in which spacetime consists of a discrete set of points taken at random from a manifold, with only the causal structure on this set remaining. This structure constitutes a partially ordered set (or poset). Working from the poset alone, it is shown how to construct a metric on the space which closely approximates the metric on the original spacetime manifold, how to define the effective dimension of the spacetime, and how such quantities may depend on the scale of measurement. Possible desirable features of the model are discussed.

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