English

The Causal Poset is Directed but not Lattice Ordered

General Relativity and Quantum Cosmology 2013-10-01 v2 Quantum Physics

Abstract

In the causal set approach to discrete quantum gravity the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a discretely growing chain of causets. The collection of causets forms a partially ordered set (poset) in a natural way. We first show that this poset is directed. We then give a counterexample which shows it is not lattice ordered.

Cite

@article{arxiv.1208.3796,
  title  = {The Causal Poset is Directed but not Lattice Ordered},
  author = {Stanley P Gudder},
  journal= {arXiv preprint arXiv:1208.3796},
  year   = {2013}
}

Comments

The counterexample is incorrect. Thanks to Rafael Sorkin and David Rideout for pointing this out

R2 v1 2026-06-21T21:52:34.104Z