Wolfram Physics Q&A

Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory.

The twistor correspondence, at least in Penrose’s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. twistor space) and massless Yang–Mills fields on Minkowski space. Mathematically speaking, the twistor space is the Grassmannian of lines in complexified Minkowski space, and the massless Yang–Mills fields correspond to the Grassmannian of planes in the same space. The correspondence space is therefore the Grassmannian of lines in planes in complexified Minkowski space, and it somehow encodes both the quantum mechanical structure of the Yang–Mills fields, and the geometrical structure of the underlying spacetime. This is directly analogous to the definition of the multiway causal graph, whose causal edges between branchlike-separated updating events encode the quantum mechanical structure of the multiway evolution graph, and whose causal edges between spacelike-separated updating events encode the relativistic structure of a pure (spacetime) causal graph.