I'm not sure #598 describes nuclear decay exactly. I don't think that there are any micro-states that describe the time of decay. I think that the best one can do is get an expected decay time (or equivalently, a half-life.)
I was just checking. I don't know the math behind QM and am trusting the consensus on this one. I expect to get out on a limb occasionally and sawed off.
Ignore nuclei. Consider instead the following decay: Upsilon(4S) --> B0B0~ (i.e. a B meson and an anti-B meson, each with subsequently reconstructed flavor-tagged decays).
[Geek alert: "flavor tagged" means that each decays in such a way that you know whether it was a B meson or an anti-B meson. A B meson contains an anti-b quark, which weakly decays into an anti-c quark, which weakly decays to an anti-s quark, which is positively charged. So if you see a K+ meson, you know it was a B meson and not an anti-B meson.]
Consider: the B and anti-B are entangled. Until one of them decays--thereby "picking" a flavor--the other one doesn't know how it is supposed to decay. The "second" one to decay will subsequently oscillate back and forth between being a B and an anti-B meson: effectively, it has two decay rates, one in its role as a B and one in its role as an anti-B.
Here's the trick: those clocks got reset to zero when the "first" meson decayed, through the magic of EPR correlation. There's no hidden variable you can assign to the "longer-lived" meson that will describe its decay, because it didn't have enough information, back when it was born, about both how and when to decay. That information didn't exist. And you can't say that it was pre-informed about the decay fate of the "first" meson because that doesn't help: such a scheme will necessarily obey Bell's inequality, and the experimental fact--predicted by quantum mechanics--is that these decays do not obey.
It actually gets worse. Notice that I've been putting "first" and "second" in scare quotes. This is because by the time they decay, they have travelled some distance from each other. If they decay close enough in time, the decays have a space-like invariant interval between them. So "first" and "second", in that case, will be observer-dependent. But the correlation still works! This is predicted by quantum mechanics, but impossible to arrange with deterministic hidden variables. "Fate" is mathematically unable to perform this clock-reset trick.
Now, you say, fine for B mesons, but what about non-EPR correlated nuclear decays? Perhaps they're different. Perhaps B and K mesons are magic and causeless, but nuclear decays have a cause. Perhaps you'd be right. But there's no experimental reason to believe that the mechanisms governing B meson decays are any different from what governs nuclear decays. Occam's Razor leads us to conclude that all subatomic decays have a random, causeless element, somewhere.