Embeddings of Causal Sets

A key postulate of the causal set program is that this discrete partial order offers a sufficiently rich structure to make it a viable model of spacetime for quantum gravity. If the deep structure of spacetime is that of a causal set, then the correspondence principle (with the spacetimes of general relativity) must be obeyed. Therefore, one of the requirements of this program is to establish that the causal set structure is in fact, not just in principle, fully consistent with our macroscopic notion of spacetime as a Lorentzian manifold. An important component of any such “manifold test” is the ability to find embeddings of causal sets into Lorentzian manifolds.