I was also thinking about the uncertainty principle in regards with energy & time. The question of something like:
Alpha tunneling out of the nucleus is where this can be invoked, but having an uncertainty in energy does not imply that energy is not conserved - it just means that energy got borrowed from somewhere and then can be returned such that the product of uncertainties remains above the minimum and it looks like a fluctuation. So I got to wondering where the energy is borrowed from and the only thing I can really come up with right now is that it gets borrowed from another field that it interacts with. Perhaps because of Coulomb repulsion in the nucleus, whose interaction field would extend far outside the nucleus, there is a temporary drop in the Coulomb field energy? That was my guess, because I don't consider borrowing from other matter fields very realistic, since several would all have to contribute something, rather than just one. Anyways, just thinking "out loud" here.