Simple indicators for Lorentzian causets (v2)

Bolognesi T., Lamb A.

Causal sets  Lorentzian manifold  Quantum gravity  Discrete spacetime 

Several classes of DAGs (directed acyclic graphs), and associated growth dynamics, have been investigated over the last two decades, mainly in the context of the Causal Set Program, with the purpose of finding satisfactory discrete models of spacetime. We introduce some simple statistical indicators that can be used for comparing these graphs, and for assessing their closeness to the ideal Lorentzian causets -- those obtained by uniformly sprinkling points in a Lorenztian manifold. In particular, we introduce 'longest/shortest path plots' as a way to visually detect the extent to which a DAG matches the reversed triangular inequality of special relativity (and the twin paradox), and we use it for assessing causets both of stochastic and of deterministic, algorithmic origin. We identify a very simple deterministic algorithm that behaves optimally in this respect.

Source: ISTI Technical reports, 2014