Regardless of their spatial energy-momentum. But if I'm not mistaken, all these properties are associated with particles that have mass?

So, I mean equivalent in the sense that they could be packets of temporal kinetic energy (in the form of their mass), in the way that photons are packets of spatial kinetic energy. It's quite possible that because their kinetic energy is temporal rather than spatial, they should have different and complementary properties compared to photons.

Or maybe the hypothetical Axions are a better candidate.

Edit: Or for that matter, the Higgs Boson.