Decay is fairly well understood. You can model the components of the nucleus as being trapped in a well then find the rate at which the probability current leaks out.
A realist QM interpretation would then say that the wave really does leak out. Of course the wave is in configuration space so it isn't a wave like an electromagnetic wave.
A specific realistic QM interpretation such as dBB would say that whether you see interactions with the decay products at a particular time is determined by whether the portion of the probability current that guides the "true" configuration of the particles has guided them out of the confining well configuration yet.
So whatever your interpretation or lack thereof, decay is not any less or more mysterious than any other quantum dynamics.
As for Bell, it's really about ruling out some joint assumptions, such as regarding repeated measurements where your hidden variables somehow can't affect you choice of an axis even though the hidden variables can determine how every other interaction in the universe turns out. Sure it rules out certain theories, but every other theory is still on the table to be used on not used. I thought you had to go back over 60 years to find anyone that liked any of the theories that Bell rules out. But obviously I don't actually know what other people think.
Basically if you were on the fence about whether you wanted a hidden variable and the only kinds of hidden variables you liked were the kind that Bell ruled out then Bell is helpful. To everyone that doesn't care for hidden variables or likes different ones, then it means almost nothing.
And I think almost everyone is in that latter group, they either already didn't care for hidden variables or else they wanted hidden variables that actually agree with quantum mechanical observations and so use different hidden variables than the ones Bell considered.
edit to try to be more clear
If you can make detectors, then the probability current onto a detector is measurable as the rate it fires. So it is a real thing that any theory must predict, and they do. And if you look at the probability current for a particle in a well you can get the rate at which it decays which is entirely determined by the probability current out on the well.
If you have position as a hidden variable that is passively revealed as itself (not all hidden variables have to do that) then current plus that hidden variable tells you when it decays (and in which direction the decay products go).
So the indeterminism of the decay is resolved by accepting that the decay is determined by knowing when particle detectors go off. So it is determined by anything that determines position, and for instance dBB does that.
If you want to see decay as quantum mechanical, the quantum zeno effect can delay a decay and it does so by adjusting the probability current.
[...] I agree that the decay itself is "real" but I was just wondering if the underlying principle behind it is so well-understood that the seeming indeterminism is necessarily quantum. And is not due to just high complexity in the particle interactions in the nucleus [...]?
Take the weather - it is very hard to predict but I think most people would agree that is not due to the potential indeterminism of the quantum but due to "hidden variables" and the chaotic nature of the system. And I don't think people would say Bell's theorem precludes such hidden variables. So my question is, could nuclear decay be the same thing... i.e. deterministic at the core?
We might be talking past each other, since the decay can be deterministic at its core and be entirely quantum. The Schrödinger equation is entirely deterministic. You can watch the so called probability current track the motion of the wave. You'll see streamlines everywhere tangent to the probability current and you'll see that it is the wave of the wave closest to the barrier of the well that leak out first, and that then new parts will be closer and then the closest of those get out.
And sure it can be quite chaotic of there are multiple nucleons in there bouncing around but it will always be the last closest to the barrier that leaks out. And none of this has any probability going on. The wave is chaotically and deterministically leaking out of the well.
Probability is related to the rate that detectors go off outside the nucleus which depends on the current out there.
And when a detector goes off, that means its parts evolves differently, so since the current is for the configuration of all particles the current actually evolves where the detector is too. And it evolves in a way to make the current of the decay product entangled with the state of the detector and the things the detector interacts with.
You can do this all at the level of the Schrödinger equation, all deterministic, no probability, just bits of waves here and there. Evolving according to the Schrödinger equation.
Probability comes up when you compare the relative frequency of different results in a repeated setup. If you want to do that (which you don't need to) you can consider also modeling the thing that keeps track of the relative frequency as well as modelling the individual detectors and modelling the individual nucleons.
That is truly where probability comes up experimentally and so if you use he tested theory of the Schrödinger equation on the actual experimental setup then you can model the evolution of the subsystem that tracks the relative frequency.
Like any system designed to track something else it is designed to have a gross robust response that is sensitive to what it tracks and insensitive to random other things happening in the universe. Which means it develops a state whose gross characteristics are the same regardless of how it got that total because that regardless is supposed to include its insensitivity to noisy influence by other stuff.
So things that interact with the gross state of the detector just get that relative frequency.
That's where the probability comes from. And if you are too lazy to bother analyzing the actual devices and aggregators and the whole ensemble of nucleons then sure there are shortcuts (called the Born rule) to describe the results of the whole process without actually doing it all.
But the first step is the wave evolves in a deterministic way, in particular it deterministically evolves its way out of the nucleus before it interacts with any detectors so that part happens before the Born rules starts to simplify your mathematical modelling (if you choose to use it).
