in that I could take a hydrogen atom in an excited state, which at some point transitions to the ground state. In standard Quantum Mechanics this transition is uncaused.
Of course, if you *model* the situation in the usual way with QM. But you are setting up an oversimplification of the what is actually occurring. I'm not claiming that QM is deterministic, but we are looking at higher level processes.
similarly with the tunneling of an alpha particle out of a nucleus, reagrdless of how complicated the interactions are, they are still only a complicated development of a wavefunction which only gives a probability.
Yes, but this *single* wavefunction is a coarse-graining of what is going on within the nucleus. To simply describe the emission of the alpha particle as uncaused suggests some random-number-generator associated with a solid-ball nucleus, rather than the nucleus as a complex composite quantum entity, and the alpha emission as a complex quantum process. As you well know, the half-life isn't some god-inspired parameter casually associated with a particular nucleus.
In the current scientific theory of the strong interactions (QCD), I think Nonukes' statement is correct. Alpha emission is uncaused.
As far as I am aware we only have an excessively idealised and over-simplified QCD description of alpha emission, so this is not exactly surprising.
My concern with this kind of language, attributing the acausal behaviour to high-level QM phenomena (H-atom transition, alpha-emission), is it suggests that there is no further underlying mechanism to investigate (E-W and QCD)
But more to the point, while the probabilistic nature of QM may very well have something to do with the "trivial" idea of our Universe coming into being from some pre-existing state, it has nothing to do with the theists' (and KB's) ideas of "creation" of existence itself - "something from nothing" - and talking about uncaused quantum events within our Universe is decidedly unhelpful, not to mention a great example of the fallacy of composition.