The most popular theory is that it's transferring momentum via virtual particles. That has some startling implications, but it's less physics shaking than violating conservation of momentum. I'm not sure anyone has come up with any solid testable hypotheses yet, but it seems to be something that is likely to be testable in principle.
You'd have to work out the math, but I'd be cautious being too aggressive with relativistic reasoning. Conservation of energy and momentum in special relativity are a bit tricky to start with, and don't hold when you start jumping between reference frames.