I have two questions about superdeterminism: Does superdeterminism allow for free will? Is superdeterminism a viable interpretation of quantum mechanics?
- Does superdeterminism allow for free will?
In this respect superdeterminism is identical with classical determinism as displayed by physical theories such as Newtonian mechanics, Newtonian gravity, Maxwell's electrodynamics, Einstein's general relativity. Everything that happens, including human actions, is determined by the initial conditions + physical laws. Superdeterminism does not add anything to that. If you are a compatibilist, you can accept superdeterminism, no problem.
2.Is superdeterminism a viable interpretation of quantum mechanics?
Superdeterminism is a class of theories which claim that, in a Bell test, the hidden variables and the settings of the detector are pre-correlated in some way. Some such theories could be successful in reproducing QM, some not, so it's not possible to give a general answer. There are some proposed superdeterministic models such as:
A. 't Hooft's cellular interpretation:
Explicit construction of Local Hidden Variables for any quantum theory up to any desired accuracy (not yet published)
Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics
Found Phys 51, 63 (2021)
B. Stochastic electrodynamics (not advertized as superdeterministic, but it is):
Stochastic electrodynamics and the interpretation of quantum theory
E.Santos: Realistic interpretation of quantum mechanics, Cambridge Scholars Publishing, 2022. Chapter 5
This theory was successful in reproducing many so-called "uniquely quantum" phenomena, like black-body radiation, specific heat of solids, and to a limited degree, the stability of atoms.
C. Invariant set theory:
Front. Phys. 8:139 (2020)
Bell's Conspiracy, Schrödinger's Black Cat and Global Invariant Sets
Phil. Trans. R. Soc. A, 373, 2015.
As far as I know there is not much debate around any of these models, none of them is accepted as "mainstream" but they are not proven wrong either. So It's hard to say how successful they really are. Time will tell.
The first question is more related to philosophy rather than physics, however the second one touches the matter of interpretations of quantum mechanics. For the first question, it varies from philosophical interpretation of will itself. However advocates for determinism also advocate for no free will. There is no free will in determinism. Super-deterministic interpretation of quantum mechanics had its supporters, notably Einstein with hidden variables postulation. However, this was quantum mechanics allows pure statistical randomness to occur. This test for whether Albert Einstein was correct about his hidden variables or no was done in the name of Bell test. According to Bell's speculation, if the universe actually functions in accord with any theory of hidden variables as Einstein postulated, then the results of a Bell test will be constrained in a quantifiable way, which it was not. Henceforth any real deterministic approach to quantum mechanics, other than some interpretations such as Bohemian mechanics and more, were essentially disregarded and the Copenhagen interpretation was the dominant consensus.
Superdeterminism allows for a reformulation of free will. The Creator can predetermine a universe that exhibits what the Creator already knows what your freely willed decisions would be. This theory of free will under superdeterminism is called cinematism. Superdeterminism is an underlying theory in itself which explains quantum mechanics. However, one can also posit a superdeterministic interpretation of quantum mechanics at least. You should be aware that there are two fundamentally different versions of superdeterminism. The first version is based on hidden variables. The second version simply says that the universe is a predetermined static block reality without continuous causation in physics, essentially poking a hole in a little known fourth assumption underlying Bell’s Inequalities. This second version has been proven by Dr. Johan Hansson at Physics Essays Vol. 33, No. 2 (2020).
Both superdeterminism and free will are nonsensical terms that philosophers like to amuse themselves with. "Superdeterminism" is basically just a variation on "god did it" after we strip off the supernatural aspect. Superdeterminism can explain absolutely everything, which means that in reality it explains absolutely nothing. Free will, on the other hand, is simply not a testable concept. Reduce it to the question "Chocolate or Vanilla?" and you will notice that the only time you can make a "free" decision in your life is before you have tasted either of these two flavors. The second time around you already know whether you like one or the other better and hence your decision is not free. Of course the first time around your decision is simply a random choice exactly because you don't know anything about your preferences, yet.
The far more interesting question concerns "interpretations of quantum mechanics". That is indeed a boondoggle that physicists have gotten themselves into. I would suggest to you to look at the structure of the "Copenhagen interpretation" very carefully if you are interested in this "problem". It didn't just happen by "random" reasoning and it is not easily replaceable with a somehow equivalent framework that uses different terms to arrive at exactly the same conclusions. Instead Copenhagen tries to teach a very important lesson about reality, which bisects into two different kinds of physical processes: reversible and irreversible ones. The free propagation of the quantum mechanical ensemble is a reversible process that happens in isolation from the environment. It can be described in many ways, the best known and most simple one to compute is the Schroedinger equation. And then there is a second kind of process in which quantum mechanical systems couple to their environment and which is dominated by the irreversible exchange of energy, momentum, angular momentum and charges. We call this the "preparation" and "measurement" processes and they are being described by the Born rule.
So if you want to take a piece of "ontological" advice: before you jump on the bandwagon of a non-Copenhagen interpretation, do a sanity check and ask the obvious question: "Does the new interpretation acknowledge the existence of reversible/irreversible interactions and their fundamental difference?". If it does not, then it is not an equivalent interpretation to begin with and in all likelihood it will fail to provide the correct physical analysis in at least some cases.