Embedding Causal Sets into Minkowski Spacetime

Abstract

We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to construct matrices of inner products which are then factored using the singular value decomposition to give coordinates in Minkowski spacetime. Results are presented showing good quality embeddings into Minkowski spacetime for dimensions d=2,3,4. The method applies in any dimension and does not require spacelike distances to be used as an input. It offers a new way to define spatial orientation and spacelike distances in a causal set.

22 pages, 7 figures. Minor updates and corrections to match published version

References in corpus (2)

• Feynman Propagator for a Free Scalar Field on a Causal Set
• Spacelike distance from discrete causal order