An electron-proton pair approaching each other will not necessarily form a hydrogen atom by emitting radiation. They could just scatter off each other, and if the impact parameter is large enough, this process could be modeled reasonably well by an analysis using classical relativity. Or, at high enough energy, other particles could be produced, which would require quantum field theory to model.
You can't just reject evidence like this though: electrons orbiting protons don't emit synchrotron radiation. So whatever else you want to the prize, you have to be able to reproduce this result.
And I have absolutely no idea what you think this explains. Which is the point of physics you know: to convey actionable concepts about the behavior of experiments. Not be cryptic and vague.
