Causal Sets

My published work deals with causal set theory, a proposal for the quantization of space-time. It can be shown that you can reconstruct important features of a space-time manifold from the causal connections of randomly distributed points on it. However almost all random distributions of causal links, instead of looking like a manifold, form some small number of moments of time (typically three, in an arrangement known as a Kleitman-Rothschild order).

This distribution of causal sets presents a problem, as the natural way to work with quantum gravity on these sets is a path integral across all possible arrangements. In Path Integral Suppression of Badly Behaved Causal Sets, my collaborators and I show that Kleitman-Rothschild sets, while common, have a negligible impact on the path integral, as the weight given by each due to its action drops as \(2^{-n^2}\). A followup work, The Einstein–Hilbert action for entropically dominant causal sets, extends this result to other such layered sets.

The main body of the work, and my primary contribution to it, consists of combinatorics. The formula used for the action involves counting the number of points in 2 layers that are connected through exactly some small number of intermediate points. As it is highly unlikely that there are no other intermediate points, the number of such arrangements in any given set falls extremely quickly with the set’s size.