For QM it can be shown that there are no hidden variables, at least no local ones [1]. Quantum randomness really cannot be modeled by a TM. You need a random oracle.
> For QM it can be shown that there are no hidden variables, at least no local ones
If we assume that the experimenter has free will in choosing the measurement settings, so that the hidden variables are not correlated with the measurement settings, then it can be shown.
That's true, but "less strict" is understating the case pretty seriously. It's not enough for experimental physicists to lack free will. To rescue local hidden variables, nothing in the universe can have free will, not even God. That's a bridge too far for most people. (It's a bridge too far for me, and I'm an atheist! :-)
Note also that superdeterminism is unfalsifiable. Since we are finite beings living in a finite universe, we can only ever have access to a finite amount of data and so we can never experimentally rule out the possibility that all experimental results are being computed by some Cosmic Turing Machine churning out digits of pi (assuming pi is normal). But we also can't rule out the possibility that the moon landings were faked or that the 2020 election was stolen by Joe Biden. You gotta draw a line somewhere.
> Note also that superdeterminism is unfalsifiable.
I think the many worlds interpretation of quantum mechanics is also unfalsifiable. The annoying thing about quantum mechanics is that any one of the interpretations of quantum mechanics has deep philosophical problems. But you can't choose a better one because all of them have deep problems.
That is indeed what I was referring to. To clarify, plenty of classical physical models work only with distributions too. You don't need a random oracle because your model doesn't predict a single microstate. It wouldn't be possible or useful to do so. You can model the flow of heat without an oracle to tell you which atoms are vibrating.
Yes, all this is true, but I think you're still missing the point I'm trying to make. Classical mechanics succumbs to statistics without any compromises in terms of being able to make reliable predictions using a TM. But quantum mechanics is fundamentally different in that it produces macroscopic phenomena -- the results of quantum measurements -- that a TM cannot reproduce. At the most fundamental level, you can always make a copy of the state of a TM, and so you can always predict what a given TM is going to do by making such a copy and running that instead of the original TM. You can't make a copy of a quantum state, and so it is fundamentally impossible to predict the outcome of a quantum measurement. So a TM cannot generate a random outcome, but a quantum measurement can.
[1] https://en.wikipedia.org/wiki/Bell%27s_theorem