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I don't have a background in physics, but I have an amateur interest in quantum mechanics, and I recently found out about the notion of superdeterminism. From what I understand, superdeterminism justifies the observed results of Bell tests by presupposing the existence of a hidden variable $\lambda$ that is not only correlated with the state of the particles being measured, but also with the measurement choices (thus violating the assumption in Bell's theorem that the measurement choices are independent). In fact, in a deterministic universe such a hidden variable must exist, because the entire present state of the universe follows directly from the initial state at the time of the Big Bang and the evolution of this state according to the (deterministic) laws of physics.

But it's not enough for this hidden variable to exist, it also must have the right value to produce the results that we observe when conducting a Bell test. Intuitively, this seems to be very unlikely if we consider an arbitrary choice for the initial conditions of the universe. So I can think of a few explanations (with different degrees of plausibility and parsimony) that someone might give for this fortuitous choice of the value of $\lambda$:

  • Intelligent design: Some conscious entity has purposely picked the initial conditions of the universe to give the results that we observe (this seems to be how critics of superdeterminism most commonly interpret it; for instance, this answer compares it to Descartes' demon).
  • Anthropic principle: For whatever reason, this choice of variables is necessary to produce intelligent life, so any other configuration is impossible to be observed (maybe this is trivially disproved by the existence of classical models of physics, but my knowledge is not deep enough to be able to tell).
  • Newcomb's paradox: The future choice of measurement can be predicted by some physical mechanism, and this mechanism then sets the state of the particles appropriately.
  • Luck: The choice truly was arbitrary, and it happened to be the right one to give these results (unsatisfying).

So my question is: which explanations (either the ones I listed here or others) have been used by proponents of superdeterminism to justify the seemingly improbable choice of value for the hidden variables that violates the Bell inequality?

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  • $\begingroup$ I think out of the four options, the third option (Newcomb's paradox) is the most serious one. My (imperfect) understanding is that people advocating for SD want to propose a new theory (as opposed to a re-interpretation of existing QM) that makes its own novel testable/falsifiable predictions. I'm not an advocate for SD, but it is easily strawmanned. $\endgroup$ Commented Aug 14, 2023 at 22:45
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    $\begingroup$ There are some interesting responses to the standard objections here - Sabine Hossenfelder is a big proponent of not ruling out superdeterminism $\endgroup$ Commented Aug 14, 2023 at 23:05
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    $\begingroup$ You could also read up some recent proposals by 't Hooft (doi.org/10.1007/s10701-021-00464-7, doi.org/10.1007/978-3-030-99642-0_13), or his old question here $\endgroup$ Commented Aug 14, 2023 at 23:07
  • $\begingroup$ the assumption that any particular values for hidden variables are "improbable" is questionable. $\endgroup$ Commented Aug 15, 2023 at 9:09

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Advocates of superdeterminism such as Sabine Hossenfelder don't have any explanation of the specific way in which the correlations between particle states and measurement settings arise (Section 10):

The two biggest problem with superdeterminism at the moment are (a) the lack of a generally applicable fundamental theory and (b) the lack of experiment.

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The simplest physical mechanism by which the hidden variables (say the particles' spins) get correlated with the settings of the distant detectors is the long-range interaction between the particle source and detectors (electromagnetic and gravitational interaction).

Once you have this sort of interactions, the combined system (source + detectors) cannot be described in terms of independent subsystems. This is analogous with a binary star system. You cannot describe it in terms of the objects moving independently (which would predict straight trajectories). You need to treat it as a whole, and this system would only be found in a state that is a solution of the 2-body problem (an ellipse).

In the case of a Bell test, the state of the system at the time of measurement must be a solution to the N-body problem (where N is the number of particles involved). The superdeterministic explanation for the observed correlations would be that they are a generic property of those solutions. So, the particles' spins are correlated with the settings of the detectors for the same reason the trajectories of the two orbiting stars must be in the same plane.

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The way you defined "superdeterminism" actually includes retrocausation, also sometimes known as "future input dependence". This is really the only set of accounts in the literature with an explanation of how the past hidden variables $\lambda$ might be correlated with the future settings in the appropriate way to explain Bell-inequality violations. In a retrocausal model the future settings directly cause the past hidden values of $\lambda$ via some sort of future-boundary-condition or all-at-once global constraint. This violates our conventional expectation of causal order, but at least the settings are in the future light cone of $\lambda$, so such models don't have to violate Lorentz Covariance. Some examples of such "future-input dependent" models can be found in this Rev. Mod. Phys. paper.

Now, I suspect that what you mean by "superdeterminism" sets aside retrocausal explanations; you didn't list it in your options. Certainly, I think the terms should be kept distinct. If that's true, you should redefine superdeterminism to be the case where a past common cause is the explanation of the correlations between the settings and $\lambda$. But you won't be able to find any plausible explanation of this scenario in the literature, despite occasional claims to the contrary.

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