The paper refers to a "null path." What is that? Is it something moving in a pure "second time" direction? Would it be similar to, say, how the shadow from a body moving vertically in 3D, wouldn't necessarily move or change much in 2D?
In the 5D theory, dynamics of the higher (5th) dimension vacuum manifest matter/energy in the 4 dimension block we perceive from inside it.
Personally, I like to consider the consortium's 5D theory in conjunction with Max Tegmark's Level IV Parallel Universe. Tegmark's cosmology is the only closed multiverse - all the others propagate to prior universes, multi-worlds (the cat is both alive and dead) and prior geometry (brane theory).
Tegmark's theory is that everything in four dimensional space/time is a mathematical structure "beyond" space/time. Or conversely, mathematical structures in 5D manifest all of 4D (geometry, matter/energy etc.)
I think the concepts are similar. It is not 4D type particles moving about in a 5th dimension but a vacuum. IMHO, what one sees as mathematical structures (which are non-corporeal, non-spatial, non-temporal), the other sees as dynamics of a vacuum (the geometry). To me, they are equivalent because I see mathematical structures as rooted in geometry.
Any hoot, something to think about...