What I mean is (and I'm a layperson on the subject), can there exist a field that pervades the universe - like the Higgs field - that interacts with particles to give them "distance" or "space" between one another, in a similar way that the Higgs field give particles their mass? And could an exc...

The energy momentum equation in special relativity is: $$E^2=(pc)^2+(mc^2)^2.$$ and it holds for a moving but not accelerating object. One special case is the massless photon: $$E=pc.$$ And another one is a resting object: $$E=mc^2.$$ The first term in the energy momentum equation seems to be kin...