Approaches to Numerical Simulations of Causal Sets

Abstract

This project found mixed results for the class of so-called Feynman posets, partially ordered sets with a maximum vertex degeneracy of three. Sets that admit "Y" shaped vertices (so-called "no holes" posets) pass several conditions for manifoldlikeness and are likely to be embeddable in 2D flat spacetime, and also possibly 2D curved spacetime. The manifoldlikeness of sets that admit both "Y" shaped vertices and "fork" shaped vertices (so-called "holes" posets) is inconclusive. The latter posets feature a large diversity of potential topologies ranging between 4 and 7 spacetime dimensions and do not meet manifoldlikeness conditions. The conditions for manifoldlikeness explored in this project include d-rigidity analysis and dimension estimator agreement tests.

I also propose improvements to the model used in this project and outline a few next steps for investigating fundamental event properties. In particular, I suggest some measures that may be taken to improve the study of the "holes" posets and to definitively test both posets for manifoldlikeness.

Finally, I offer some comments on the possible physical interpretation of the event types explored in this project. I maintain that "no holes" posets serve as promising candidates for use in exploring the fundamental properties of 2D spacetime.