Essentially, in this paper it's a light wave were the spatial and temporal dimensions are not easily separable. What the authors seem to do here is essentially do a time dependent spatial correlation of a light pulse, which then exhibits "unintuitive" properties. The paper reads a little bit, like several similar papers in the field, where something relatively trivial is packed into a nice sounding story. That said I have not read the details yet and there might be something more profound.

Dunno why this comment was dead, I'd love to see a good ELI5 here

The quantum mechanical probability wave (which is a photon, or maybe there's a difference, but we don't know yet).