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I see superdeterminism come up as one way that local realism and all that other good stuff can be preserved, but it also seems like it's a minority view. I've been trying to understand why, and really, what I need is just a clarification on what superdeterminism implies. Does it

a) only state that the universe is deterministic, with everything set in stone from the Big Bang onward, or

b) state that it's deterministic in what appears to be a very unlikely way, considering the results of Bell's Theorem experiments. Like, it'd have to be the equivalent of every time you reach into a scrabble bag, you happen to pull out "QUANTUM".

I don't understand the Bell's Theorem experiments well enough to ascertain whether this is what is claimed about superdeterminism. If it implies that things are pre-correlated in what seems to be a wildly unlikely manner, that's very different than if it just implies that things are pre-correlated, and I would understand the prevailing skepticism. Otherwise, not so much.

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    $\begingroup$ Superdeterminism is like saying the moon continuously and deterministically blinks out of existence, but the initial conditions of the universe have been set up so that this only happens exactly at the moments you're not looking at it. $\endgroup$
    – knzhou
    Commented Jul 13, 2021 at 15:57
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    $\begingroup$ That is, superdeterminism is a much much much stronger assumption than mere determinism (though some disingenuous popularizers try to elide the difference), and stronger in a way that feels weird to almost all physicists. $\endgroup$
    – knzhou
    Commented Jul 13, 2021 at 15:57
  • $\begingroup$ physics.stackexchange.com/questions/106725/… $\endgroup$
    – alanf
    Commented Jul 13, 2021 at 17:30
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    $\begingroup$ How strongly correlated are Alice's choices of measurement orientations and Bob's actual measurements? Are these correlations microscopically small, detectable only with an incredibly large sample size, or are the correlations uncannily large, larger than one would expect for causally distant yet nevertheless connected events? If superdeterminism is a thing, shouldn't we be able to detect the same sort of correlations in causally distant non-quantum events. Have these correlations been detected in non-quantum experiments? If not, how would we explain this? $\endgroup$
    – Geoffrey Johnson
    Commented Nov 2, 2022 at 16:19

2 Answers 2

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The gist of nonlocality à la Bell is that there are conditional probability distributions $p(ab|xy)$, where $a,b$ and $x,y$ denote possible measurement outcomes and possible choice of measurements, respectively, which do not admit a "local realistic explanation", that is, a decomposition of the form $$p(ab|xy) = \sum_\lambda p(\lambda) p_\lambda(a|x)p_\lambda(b|y).\tag 1$$ Some quantum systems produce probability distributions which behave like this (i.e. cannot be decomposed like (1)), hence quantum mechanics not being local realistic etc.

One major assumption in (1) is that you still assume that the choices of measurement bases, $x,y$, are not correlated. This means that you assume that Alice and Bob "choose freely" how to interact and observe the systems they are given. "Superdeterminism" is what you get lifting this assumption. If you assume that Alice and Bob's choices of measurements were also determined beforehand (e.g. maybe they organised before moving apart and decided on what they'll measure), then the problem becomes trivial: any possible observation can be explained deterministically.

Let me stress that this is not even really about quantum mechanics. I'm saying that any possible observation (in the two-party scenario we consider here), quantum mechanical or not, can be explained deterministically with a "superdeterministic hidden variable".

The trivial "proof" of this is that, if you consider the measurement choices $x,y$ as also determined beforehand, you effectively remove the locality aspect from the equation. If the measurement choices are also correlated/chosen beforehand, then the fact that Alice and Bob are spatially separated is effectively vacuus. You just have a joint probability distribution $p(abxy)$, which you can always describe using some deterministic "classical" theory.

Of course, the downside of such a "superdeterministic explanation" is that it involves some sort of "cosmic conspiracy theory". Sure, it might just so happen that the weird correlations observed by Alice and Bob are actually due to the way they chose to measure their apparatuses being determined a priori together with some corresponding deterministic outcome, but how would that actually happen? If you were to devise a theory explaining that, it would be yes fully classical, but also likely quite weird and convoluted.

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    $\begingroup$ well in deterministic universe Alice and Bob cannot freely choose anything, so there is nothing weird that in deterministic theory there is "cosmic conspiracy theory", because there is. We usually assume that due to the massive amount of unknown variables that goes into Bob's and Alice choice, their choices are well modeled by randomness. But is it? $\endgroup$
    – Umaxo
    Commented Aug 2, 2022 at 3:32
  • $\begingroup$ @Umaxo That's how I see it too. It seems that determinism is synonymous with superdeterminism which is synonymous with predestination? It seems like to have things be otherwise would be like wanting to cherry pick what is deterministic and what is not: the matter and energy which I study is deterministic but but the matter and energy which I made of is not? Might have something to do with quantum mechanics itself being probabilistic but not deterministic? But things on a larger scale seem to be deterministic. $\endgroup$
    – DKNguyen
    Commented Aug 2, 2022 at 3:45
  • $\begingroup$ @DKNguyen you do not need to assume that Alice and Bob are not deterministic, only that they are not correlated (or at least that they are very weakly correlated). This can be true even in deterministic theory. In fact, I would even say that it is, intuitively, quite a reasonable assumption, which is probably why superdeterminism seems to many people as unlikely. Case in point might be throwing two independent coins. In fact, the tendency for randomizations seems to be backed up by countless experiences with many games people like to play in their free time. $\endgroup$
    – Umaxo
    Commented Aug 2, 2022 at 4:25
  • $\begingroup$ @DKNguyen in this light determinism and superdeterminism is different. Superdeterminism has one more assumption that determinism does not, which is that the randomization of experimentators choices will not happen and they will remain correlated. In only deterministic theory, it might or may not happen and we intuitively tend to think (backed up by our experiences with statistical samples from deterministic processes) they should be uncorrelated, unless the theory is somehow "weird and convoluted" as glS put it. $\endgroup$
    – Umaxo
    Commented Aug 2, 2022 at 4:35
  • $\begingroup$ @Umaxo I fail to see where this correlation coming from because it's not like Bob observes a spin of -1 which is also why I do not understand why knzhou's example of the moon blinking out of existence is relevant. $\endgroup$
    – DKNguyen
    Commented Aug 2, 2022 at 13:20
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Dr. Johan Hansson proved that the universe is superdeterministic. Read his publication at Physics Essays Vol. 33, No. 2 (2020).

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  • $\begingroup$ It's unlikely that one person has fully resolved this long-standing philosophical debate on their own in a single publication. But, outside of that, your answer would be a stronger contribution if you summarized the content of the paper and explain why it argues in favor of superdeterminism, rather than simply stating it and pointing to a reference. $\endgroup$
    – Andrew
    Commented Sep 2, 2022 at 17:36
  • $\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Sep 2, 2022 at 17:40
  • $\begingroup$ That journal is, well, speculative at best. $\endgroup$
    – Jon Custer
    Commented Sep 2, 2022 at 17:52
  • $\begingroup$ Proofs require assumptions. What assumptions did Hansson make? $\endgroup$
    – Galen
    Commented Sep 2, 2022 at 18:50
  • $\begingroup$ Read Dr. Hansson’s proof. Here it is: diva-portal.org/smash/get/diva2:1432225/… $\endgroup$
    – John J. Bannan
    Commented Mar 15, 2023 at 18:04

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