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I'm trying to wrap my head around the recent 2022 nobel price and learned about the superdeterminism (https://en.wikipedia.org/wiki/Superdeterminism) loop hole in the now famous Aspect experiment (https://en.wikipedia.org/wiki/Aspect%27s_experiment).

The question is if this a good vivid example of a hypothetical super determinism to illustrate the concept?

Consider a particle with spin 1, up or down. Now assume that there is a time variation intrinsic to the particle so that the measurement of spin depends on when in the cycle the particle hit the sensor, then that phase $x$, can be perhaps be seen as a hidden variable to the measurement and the outcome of $P(X|x)$ is not equal to $P(X)$ where the $X$ is the conclusion of the measurement, and hence a super deterministic effect. To give a more vivid picture how spin can vary although it is conserved, note that the spin quantity is very much like a spinning earth but we have no clue how the particle physically spin, if it does, and consider it just as a property that is intrinsic. Anyway spinning 3D bodies in space like earth (can) wobble (precess) although having a conserved overall spin (angular momentum) and one could imagine that the particle exhibit a similar intrinsic wobble and that the measurement is sensitive to where in the phase it is when it is getting sensed.

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  • $\begingroup$ What you are really doing here is to create a classical mix of different particles. If you do this for a spin 1/2 case and you send it through a Stern Gerlach filter, then you end up with two mixes of one half of each. Apply two Stern Gerlachs turned by 90 degrees. Now you have four fractions. Rinse, repeat and soon you need an infinity of initial conditions. That's basically also the reason why MWI kind of setups are nonsense. You have to start with an infinite mix to explain even the most trivial physics. $\endgroup$
    – FlatterMann
    Commented Oct 20, 2022 at 20:53
  • $\begingroup$ Actually the question is not if the example is correct physically, just if one could give a correct example of what super determinism could mean in this experiment. But your comment is well noted. $\endgroup$
    – Stefan
    Commented Oct 20, 2022 at 20:57
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    $\begingroup$ How is this going to help you avoid violations of Bell's Theorem? $\endgroup$
    – WillO
    Commented Oct 20, 2022 at 22:21
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    $\begingroup$ @FlatterMann: Okay, you can have a chinese room that is not required to give the same responses to the same questions (though it might still give responses that are fully determined by the entire history of the questions it has been asked, and other environmental variables). But this is tangential to the point that for the system to be called superdeterministic, the actions of both the answerer and the asker should be deterministic in the same sort of ways. $\endgroup$
    – WillO
    Commented Oct 20, 2022 at 22:31
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    $\begingroup$ @Stefan Superdeterminism isn't really a loophole. It's a violation of the basic principles of science, which assume that nature is "honest" and that there is some level of freedom to ask it questions. $\endgroup$
    – FlatterMann
    Commented Oct 20, 2022 at 22:41

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What you have described would be a local hidden variable theory, but not super-determinism. It is therefore, without some further additions, in the class of theories ruled out by Bell's theorem.

To make the theory super-deterministic you would need $x$ to determine not only the value of $X$, but also which measurements we chose to make of it, that is in which direction we measured the spin. Since the measurement apparatus is typically some large complex system (to say nothing of a potential human experimenter) this is going to make the details of the theory much more complicated.

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  • $\begingroup$ Hmm, if we had super powers, we could choose which phase to measure and by doing so a hypothetical experiment would yield different answers no? Now reality is that we measure p(X) as we do not have super powers, e.g. x is hidden. $\endgroup$
    – Stefan
    Commented Oct 20, 2022 at 20:54
  • $\begingroup$ Note to illustrate more, if the measurement measure in a superhuman way the spin at a specific phase of a precession, then this can be interpreted in stead that we are measuring in a certain direction that is different from the conserved overall spin So for each phase, in principle it indeed looks like from your description that it is super deterministic. $\endgroup$
    – Stefan
    Commented Oct 20, 2022 at 21:27
  • $\begingroup$ I don't understand how the Aspect et al. (1982) papers (and other experiments) rule out local realist theories, despite everyone saying they do. What they show is that the correlation of the polarization of two entangled photons depends on the angles of the detectors relative to each other. If the two photons were locally real with their polarizations hidden until measurement, I'd expect the same results. In other words, the wavefunction is an incomplete description of the state of the photons. $\endgroup$
    – Paul
    Commented Feb 1 at 7:22

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