March 6, 2020

*Answered by: Jonathan Gorard*

## How does wave-particle duality work in your models?

Much like Bell’s theorem, the phenomenon of wave-particle duality follows immediately from the basic combinatorial properties of the multiway causal graph.

A geodesic bundle propagating through an ordinary (i.e. purely relativistic) causal graph can be thought of as corresponding to the trajectory of a collection of test particles. On the other hand, a geodesic bundle propagating through a pure multiway evolution graph can be thought of as corresponding to the trajectory of a quantum wave packet (since each branch of the multiway evolution graph is analogous to the evolution history of a single quantum eigenstate, and therefore a collection of multiway branches corresponds to the evolution history of some linear superposition of those eigenstates).

Since the multiway causal graph reflects both the structure of the multiway evolution graph and the structure of all of its associated causal graphs, any valid foliation of the multiway causal graph will consist of a time-ordered sequence of hypersurfaces, each of which will contain pairs of updating events that can be either spacelike-separated, branchlike-separated, or some combination of the two, with the type of separation depending upon the particular choice of foliation. Therefore, an observer who is embedded within a particular multiway causal foliation will, in general, find it impossible to determine whether a geodesic bundle propagating through the multiway causal graph corresponds to the evolution of a collection of test particles, a wave packet, or both (since the geodesics themselves will either appear to be purely spacelike-separated, purely branchlike-separated, or a combination, depending on the observer). Thus, wave-particle duality is just one of many immediate consequences of the principle of multiway relativity—the preservation of timelike-orderings of updating events in the multiway causal graph, independent of the choice of foliation.