The only thing we know is happening for sure is interaction, which when studied using the so-called density matrices of the interacting subsystems gives insight

The only thing we know is happening for sure is interaction, which when studied using the so-called density matrices of the interacting subsystems gives insight into how any subsystem "sees" another one. You get all the "parallel universes" as separate terms this way, and see ways in which these terms evolve independently of each other and ways in which they can linearly interfere. This is all continuous evolution under the Schroedinger equation by the way. You unfortunately won't get any satisfactory answer to this but you can definitely scratch the itch if you take the time to study some QM and decoherence theory.