Molecules of Discrete Spacetime

Causal set theory replaces the spacetime continuum with locally finite posets, a.k.a. causal sets. Given causal sets, we can utilize abundances of certain combinatorial structures to restore the geometry. For example, one can utilize chains to recover the Ricci scalar. We have calculated in Riemann normal coordinates the expected number of 2-pixies* in a causal set that is drawn from randomly picking points in an Alexandrov set. I will first quickly go through the calculation, and then present tests of this abundance in conformally flat spacetimes. I will also talk about how we can reconstruct more quantities beyond the scalar curvature with 2-pixies.

* The structure specified by a root spacetime element to the causal past of a spacelike pair of elements is called the upward 2-pixie; and the downward 2-pixie is time reversal of the upward one.