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I have two questions about superdeterminism: Does superdeterminism allow for free will? Is superdeterminism a viable interpretation of quantum mechanics?

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  1. 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)

https://arxiv.org/abs/2103.04335

Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

https://arxiv.org/abs/2010.02019

Found Phys 51, 63 (2021)

B. Stochastic electrodynamics (not advertized as superdeterministic, but it is):

Stochastic electrodynamics and the interpretation of quantum theory

https://arxiv.org/abs/1205.0916

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:

Rethinking Superdeterminism

https://arxiv.org/abs/1912.06462

Front. Phys. 8:139 (2020)

Bell's Conspiracy, Schrödinger's Black Cat and Global Invariant Sets

https://arxiv.org/abs/1502.06972

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.

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  • $\begingroup$ All stochastic models are trivially wrong because of the fluctuation-dissipation theorem. $\endgroup$
    – FlatterMann
    Commented Oct 19, 2022 at 11:20
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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.

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    $\begingroup$ Superdeterminism is actually a loophole in the Bell test. It allows for local hidden variable theories which violate the Bell constraint $\endgroup$
    – Ryder Rude
    Commented Oct 17, 2022 at 3:45
  • $\begingroup$ What JS Bell showed was that Einstein's "local realism" was untenable, and that only non-local realist theories could explain QM. The DeBroglie-Bohm interpretation is an example of the space that remains. $\endgroup$
    – Steve
    Commented Oct 17, 2022 at 9:20
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    $\begingroup$ @RyderRude, I can't claim to fully understand "superdeterminism" or how it differs from ordinary determinism, but whilst it preserves a space for "local realism", it does so only by undermining other assumptions which local realists (and all others) would have been loath to relinquish. That assumption is broadly that there are so many variables involved in the setting of the experimental apparatus, that to believe it can be traced back only to the same cause as the local variables which the experiment is measuring, is inconsistent with how we understand multi-variable causation to work. $\endgroup$
    – Steve
    Commented Oct 17, 2022 at 9:52
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    $\begingroup$ @RyderRude, indeed thinking more on this, this "superdeterminism" is probably most preferred by anti-scientific forces, since it avoids denying determinism in principle, but it does invite us to hold that it must be an unknown, and perhaps even unknowable, mechanism by which the world is determined and such seemingly bizarre correlations occur. Accepting this invitation helps to rescue their preferred theory - whether it be the controlling deity or the soul of the religious, or the individuality and free will of the liberal - from the jaws of science and rational enquiry as we know it today. $\endgroup$
    – Steve
    Commented Oct 17, 2022 at 10:48
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    $\begingroup$ @Steve Agreed. And there is no reason we should be hating non local realism and determinism in the first place, if it can be made consistent with relativity. The price of saving locality using superdeterminism is too huge. Plus superdeterminism has no mathematical basis. It's only a claim that some model might be able to do it. That model will have to explicitly involve the postulate "Humans must be fooled". It's the worst interpretation of quantum mechanics. $\endgroup$
    – Ryder Rude
    Commented Oct 17, 2022 at 11:07
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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).

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  • $\begingroup$ One can "explain" quantum mechanics fairly easily with relativity. It doesn't require any effort along the lines mentioned here. There are no hidden variable theories. Nobody has ever proposed one, let alone one that makes any relevant physical predictions. I general most of these things spring from the desire to somehow "save" classical mechanics. We have known since the 19th century that classical mechanics is not even compatible with the existence of stable matter. It's simple not a good theory. No need to waste any further effort on it. $\endgroup$
    – FlatterMann
    Commented Mar 26, 2023 at 19:57
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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.

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    $\begingroup$ "Superdeterminism is basically just a variation on 'god did it'" - I don't think that is an accurate representation of any writing I have seen on "superdeterminism". The "super" in superdeterminism was supposedly to emphasise the degree of determinism, not to imply that the supernatural was involved. $\endgroup$
    – Steve
    Commented Oct 17, 2022 at 9:14
  • $\begingroup$ @Steve Superdeterminism is the vague philosophical concept that it doesn't matter what we are measuring because all measurements are biased in such a way that we will get a specific (deceptive) result anyway. It is the physics equivalent of the anti-evolution response "the devil put them bones in them hills". It is not even a scientifically testable hypothesis by any standard. You could call it the intellectually empty last stand of classical physics. It is also not needed. Classical physics is a limiting case of quantum mechanics. We can reproduce it just fine. Just not the other way around. $\endgroup$
    – FlatterMann
    Commented Oct 17, 2022 at 18:52
  • $\begingroup$ You have no idea what you are speaking about. Superdeterminism is just the denial of the statistical independence assumption in Bell's theorem. It means that the hidden variable and the detector settings are not independent parameters. This can be the result of any type of physical interaction (electromagnetic, gravitational). It has nothing to do with "god did it" which is more representative for Bohr-Copenhagen philosophy. $\endgroup$
    – Andrei
    Commented Oct 18, 2022 at 10:48
  • $\begingroup$ @Andrei Copenhagen represents the trivial reality of quantum systems. Now, I admit that most textbooks that contain the von Neumann formalism don't tell you the "why it is so", but that is a problem of the textbooks, it's not a problem of Copenhagen. Happy to discuss in the chat if you are actually interested. Superdeterminism is simply not a testable scientific hypothesis. It basically tells you that your experiment has to say "green" because some magical initial setting before the big bang says so. That's religion, not physics. $\endgroup$
    – FlatterMann
    Commented Oct 18, 2022 at 14:24
  • $\begingroup$ FlatterMann, I'd like to discuss in the chat but I don't know how. My problem with Copenhagen is its non-locality, not it's inability to answer "Why" questions. Superdeterminism is as testable as any other physical theory. In fact, classical electromagnetism, as it is, is a superdeterministic theory. It imposes some constraints (Maxwell's equations need to be satisfied) that are disregarded by Bell's independence assumption. The so-called "classical prediction" (inequality not violated) is incorrectly assessed due to the failure of satisfying those constraints. $\endgroup$
    – Andrei
    Commented Oct 19, 2022 at 7:46

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