Structure of random discrete spacetime.
Abstract
The usual picture of spacetime consists of a continuous manifold, together with a metric of Lorentzian signature which imposes a causal structure. The authors consider a model in which spacetime consists of a discrete set of points taken at random from a manifold, with only the causal structure remaining. Using only this structure, the authors show how to construct a metric, how to define the effective dimension, and how such quantities may depend on the scale of measurement.
 Publication:

Physical Review Letters
 Pub Date:
 January 1991
 DOI:
 10.1103/PhysRevLett.66.260
 Bibcode:
 1991PhRvL..66..260B
 Keywords:

 Discrete Functions;
 Manifolds (Mathematics);
 Metric Space;
 Probability Distribution Functions;
 SpaceTime Functions;
 Amount;
 Signatures;
 Physics (General);
 04.20.Cv;
 02.90.+p;
 04.60.+n;
 Fundamental problems and general formalism;
 Other topics in mathematical methods in physics