Why is "super-determinism" a loophole to Bell's theorem?

[Lunct]

So I have often heard it argued that "super-determinism" is a loophole to Bell's theorem, that allows a local hidden variable theory. Bell himself alluded to it in a 1980s BBC interview.
But why is this the case? And how is super-determinism different to regular determinism. And the many-world's interpretation is deterministic, so does that fall under this loophole?

 

[Halc]

The way I understand it, superdeterminism is a sort of causation conspiracy, so if say a photon is a particle, you can only choose to measure it as a particle, and ditto with wave. The laws of nature are potentially completely different than the ones we glean, but is is determined that we will never perform an experiment that would show the true nature of those laws. One big example would be blatant information transfer faster than light, which occurs all the time but the lack of free will prevents us from choosing to perform a measurement to prove it.

MWI does not fall under this loophole. It is a local interpretation, and more importantly, one that denies the principle of counterfactual definiteness. Thus it satisfies Bell's theorem without need to leverage the superdeterminism loophole.

 

[Nugatory]

But why is this the case?

One of the assumptions going into the proof of Bell's inequaity is fair sampling. Loosely speaking, this means that our measurements are a fair sample of the total population of entangled pairs in our experiment: if at the end of the experiment we find that 40% of our pairs were spin up when measured at zero degrees on one side and spin down when measured at 60 degrees at the other side then it follows that overall, 40% of the pairs would have had that property if we had measured them all that way. It's the same logic that allows us to conclude that when we find 100 cases of a disease in a random sample of ten thousand people drawn from a much larger population, 1% of that larger population is infected.

Superdeterminism says that the fair sampling assumption is false; there is some unknwn physics at work that directs a disproportionate number of the up-on-0/down-on-60 pairs to our detectors when they're set in that position so the 40% is not representative of the larger population.

And how is super-determinism different to regular determinism.

Superdeterminism considers causal relationships far more extreme than we usually consider. I wrote up an explanation of that a while back: https://www.physicsforums.com/threads/superdeterminism-and-the-hidden-variable.994932/post-6405894

And the many-world's interpretation is deterministic, so does that fall under this loophole?

This is actually a bit of a red herring, for two reasons.
First, Bell's theorem applies to non-deterministic as well as deterministic hidden variable theories (the proof relies on integration across probability distributions). It's most often cited in discussions of deterministic hidden variable theories, but that's not because it's limited to these, it's because there is little interest in or discussion of any other kind.
Second, MWI is deterministic with regard to the time evolution of the wave function, but the non-determinism is still there when it comes to the observed results of our measurements - and Bell's theorem is a statement about measurement results. (There's an interesting digression about the difficulty of incorporating the Born rule into MWI, but there are already threads about this in the Quantum Interpretations subforum).

 

[Lunct]

one that denies the principle of counterfactual definiteness.

Can you please elaborate on this? I don't know what it means.

 

[Nugatory]

Can you please elaborate on this? I don't know what it means.

Counterfactual definiteness is the assertion that an observable has a definite value whether it's measured or not.

Consider the two statements: "If we measure the spin of this electron on the vertical axis there is a 100% probability that it will be spin-up"; and "This electron is spin-up on the vertical axis". The first only implies the second if you accept counterfactual definiteness - and indeed without counterfactual definiteness the second statement is meaningless. Although before the 20th century and the discovery of quantum mechanics no reasonable physicist seriously questioned counterfactual definiteness, QM just doesn't work that way.

 

[facenian]

Counterfactual definiteness is the assertion that an observable has a definite value whether it's measured or not.

Consider the two statements: "If we measure the spin of this electron on the vertical axis there is a 100% probability that it will be spin-up"; and "This electron is spin-up on the vertical axis". The first only implies the second if you accept counterfactual definiteness - and indeed without counterfactual definiteness the second statement is meaningless. Although before the 20th century and the discovery of quantum mechanics no reasonable physicist seriously questioned counterfactual definiteness, QM just doesn't work that way.

Unfortunately, this view is widespread and is not subject to mere opinion or interpretation but it is right down incorrect. I would like to start by pointing out that neither John Bell nor CHSH ever employed counterfactual reasoning in their derivations.

The first sentence is not an assumption when the inequality is correctly derived because the correct derivation only depends on the results of actually performed experiments and does not depend on metaphysical speculations.
The "two statements" example is also incorrect because it is not what CFD means when incorrectly used to derive the inequality. The example is only about determinism, is not related to a counterfactual prediction. The example given is just an indicative conditional that we can not afford with a non-deterministic theory. CFD on the other hand is about subjunctive conditionals and is physically meaningless because when you base your derivation on it the result turns out to be unfalsifiable and wouldn't make sense to perform an experiment to falsify it since they bear no relation with each other(prediction and experiment).
In my opinion, this paper nicely explains the problem of using CFD https://doi.org/10.1142/9789812810809_0002
Of course, the paper is wrong because Bell (and those who do it correctly) did not use CFD, but it nicely explains why the theorem does not make sense when derived through CFD.

 

[Demystifier]

Counterfactual definiteness is the assertion that an observable has a definite value whether it's measured or not.

If Alice measures observable A and Bob measures observable B, but nobody measures their product, is the assumption that the product has a definite value a counterfactual definiteness? (Alice and Bob are spatially separated, so A and B commute.)

 

[facenian]

If Alice measures observable A and Bob measures observable B, but nobody measures their product, is the assumption that the product has a definite value a counterfactual definiteness? (Alice and Bob are spatially separated, so A and B commute.)

No. I think that their product is an actual value once the factors were already measured. Counterfactuality means another thing. In the particular case of the Bell's theorem, it implies an expression with 8 numbers only 2 of which are supposed to be the results of an actual experiment and the 6 others are results of experiments that you can predict what they would have been if they were actually measured but in fact they were not.
Sure, it is a thought experiment but it is also devoid of any physical meaning because that imaginary experiment cannot be falsified with real experiments.
A Bell test experiment consists of a long series of measurements with 4 different settings randomly chosen. After the experiment, you have enough data to evaluate the mean for the 4 different settings.
Therefore the experiment can only falsify a prediction about those series of actual(realizable) experiments.

Surely the imaginary result predicted through CFD cannot be meaningfully compared with the real experiment simply because the real experiment is not what you predicted. It should be clear that the CFD inequality relies on 4 different experiments only one of which can actually be performed. By construction, the other 3 are actually impossible once you perform anyone of them. How on Earth a real experiment could falsify such a puzzling prediction? I guess poor John Bell should be scratching his head in his grave before all the absurdities uttered in his name.

The only conclusion of the CFD Bell inequality is what Asher Peres infered back in 1978 after deriving it: "unperformed experiments have ho results"
Of course, we do not need to perform any experiment to infer Peres's silly tautological conclusion, but he was right.

 

[Nugatory]

If Alice measures observable A and Bob measures observable B, but nobody measures their product, is the assumption that the product has a definite value a counterfactual definiteness? (Alice and Bob are spatially separated, so A and B commute.)

I wouldn’t consider that value counterfactual; the measurements of A and B are enough for factualness of the product AB.

 

[Demystifier]

I wouldn’t consider that value counterfactual; the measurements of A and B are enough for factualness of the product AB.

Good to know, because QBism denies that.

 

[*now*]

This paper linked elsewhere might be helpful here,
https://www.nature.com/articles/s41567-020-0990-x Nat. phys 2020

A strong no-go theorem on the Wigner’s friend paradox​

Abstract
Does quantum theory apply at all scales, including that of observers? A resurgence of interest in the long-standing Wigner's friend paradox has shed new light on this fundamental question. Here---building on a scenario with two separated but entangled "friends" introduced by Brukner---we rigorously prove that if quantum evolution is controllable on the scale of an observer, then one of the following three assumptions must be false: "No-Superdeterminism", "Locality", or "Absoluteness of Observed Events" (i.e. that every observed event exists absolutely, not relatively). We show that although the violation of Bell-type inequalities in such scenarios is not in general sufficient to demonstrate the contradiction between those assumptions, new inequalities can be derived, in a theory-independent manner, which are violated by quantum correlations. We demonstrate this in a proof-of-principle experiment where a photon's path is deemed an observer. We discuss how this new theorem places strictly stronger constraints on quantum reality than Bell's theorem.

 

[AndreiB]

So I have often heard it argued that "super-determinism" is a loophole to Bell's theorem"

This is correct.

But why is this the case?

Bell's derivation only works if the hidden variables are independent of the measurement settings. For example we know that if the measurements are performed on the same axis the spins are perfectly anticorrelated (for fermions). So, if particle a is UP on X, particle b will be DOWN on X. If a is DOWN on Z, b is UP on Z. And if a is UP on Y, b has to be DOWN on Y. This correlation is always true, regardless of the direction of the measurements, as long that direction is the same for both detectors.

In order to get to Bell's inequality you need to assume that the spins on, say, Z are anticorrelated even if the measurements happen on X. The measurement on Z (which always gives anticorrelated spins) is assumed to be representative for the experiment on X, Y or any other direction.

And how is super-determinism different to regular determinism.

You can have deterministic theories where the spins are independent of measurement settings. This is the case of Newtonian mechanics with contact forces only (billiard balls). Since no interaction takes place between the billiard balls and detectors, they can be treated as independent parameters.

A superdeterminstic theory needs to add supplementary constraints that force the hidden variables to only take some values for certain settings.

And the many-world's interpretation is deterministic, so does that fall under this loophole?

As far as I can tell the many worlds interpretation is unable to derive Born's rule so it is not clear how it works. One needs to understand how the correct probabilities arise in this theory in order to conclude that it is non-local or superdeterministic.

 

[AndreiB]

Good to know, because QBism denies that (the measurements of A and B are enough for factualness of the product AB).

Are you saying that QBists reject the validity of experimental records?

 

[Demystifier]

Are you saying that QBists reject the validity of experimental records?

If an experimental record is recorded by Alice but not recorded by Bob, QBists reject that the experimental record is valid for Bob. More generally, they reject that experimental records are objective, i.e. independent of the observer.

 

[AndreiB]

If an experimental record is recorded by Alice but not recorded by Bob, QBists reject that the experimental record is valid for Bob. More generally, they reject that experimental records are objective, i.e. independent of the observer.

OK, let's say that there is only one experimenter, Bob, and he controls, remotely, both labs. After the measurements take place, Bob gets the results on his computer. Would Bob accept both results as valid?

 

[morrobay]

In order to get to Bell's inequality you need to assume that the spins on, say, Z are anticorrelated even if the measurements happen on X. The measurement on Z (which always gives anticorrelated spins) is assumed to be representative for the experiment on X, Y or any other direction.

Well this is counterfactual definiteness. And then the inequality is based on counterfactuality. And from table ,the most basic inequality: N3+N4<=(N2+N4)+(N3+N7)

 

[Demystifier]

OK, let's say that there is only one experimenter, Bob, and he controls, remotely, both labs. After the measurements take place, Bob gets the results on his computer. Would Bob accept both results as valid?

Yes. But he would accept them valid only for time at which he gets the result on his computer. If his computer shows the result at time $t$, he would not accept that the result was valid before $t$. For instance, if he finds dinosaur bones today, he would not accept that as evidence that the dinosaur was living millions of years ago.

 

[AndreiB]

Well this is counterfactual definiteness. And then the inequality is based on counterfactuality

I think that one should be careful about how counterfactuality is to be applied.

Consider the situation of N interacting objects, say N massive objects interacting gravitationally as described by GR. The state of this system would be a solution to the N-body gravitational problem. Let's now say that I ask about the state of that system if one of those objects had twice the mass. I cannot simply take the previous solution and change the mass of the object. What I have to do is to solve again the N-body problem for the new system (with a mass changed). The new solution could be completely different from the previous one for all N objects, not only for the changed one.

If I define objects N1 and N2 to be "detectors" and the position of N3 the "hidden variable" it is not true that changing N1 or N2 leaves the hidden variable the same. So, GR does not satisfy Bell's independence assumption. But GR is counterfactual definite. I can calculate the state for any modified system without any problem.

If the N objects don't interact, their state consists of N solutions of 1-body problems. Changing one object has no influence upon the other objects. In this case, both counterfactuality and Bell's independence assumption are satisfied.

 

[AndreiB]

Yes. But he would accept them valid only for time at which he gets the result on his computer. If his computer shows the result at time $t$, he would not accept that the result was valid before $t$. For instance, if he finds dinosaur bones today, he would not accept that as evidence that the dinosaur was living millions of years ago.

So, if the measurements record the time when they were performed, the QBist would not accept such records? What would be his interpretation of the recorded times?

 

[Demystifier]

So, if the measurements record the time when they were performed, the QBist would not accept such records? What would be his interpretation of the recorded times?

Yes. He would say that, for him, the record did not exist before he seen it.

 

[AndreiB]

Yes. He would say that, for him, the record did not exist before he seen it.

If this is so, then QBists should reject pretty much all science, as most of it exists in the form of such records. I doubt however that any of them would make such a statement in front of the physics community. I've read quite a few QBist papers and had a debate with one (string theorist 4graviton) but I've never encountered the position you describe.

 

[Demystifier]

If this is so, then QBists should reject pretty much all science, as most of it exists in the form of such records. I doubt however that any of them would make such a statement in front of the physics community. I've read quite a few QBist papers and had a debate with one (string theorist 4graviton) but I've never encountered the position you describe

QBists are aware that their claims look preposterous to most people, so in normal conversations they don't insist on them in contexts other than quantum foundations. But yes, they reject pretty much all science. More precisely, they reject the common interpretation of science, according to which science reveals objective properties of the world. For them, science only serves to make predictions about future subjective observations.

 

[AndreiB]

QBists are aware that their claims look preposterous to most people, so in normal conversations they don't insist on them in contexts other than quantum foundations. But yes, they reject pretty much all science. More precisely, they reject the common interpretation of science, according to which science reveals objective properties of the world. For them, science only serves to make predictions about future subjective observations.

Even accepting their philosophy, QBism can be shown to be unsatisfactory. Without hidden variables the theory must be non-local, so it is conflicting with relativity. The rejection of an objective external world does not get them out of the hook because the contradiction simply moves from the objective world to their minds.

Both QM and relativity "make predictions about future subjective observations", yet, in the case of EPR, those predictions conflict. So, QBism must be supplemented either with hidden variables or with an absolute reference frame to accommodate non-local effects.

 

[vanhees71]

If an experimental record is recorded by Alice but not recorded by Bob, QBists reject that the experimental record is valid for Bob. More generally, they reject that experimental records are objective, i.e. independent of the observer.

But this doesn't make sense either. Take again our favorite experiment with two photons in the polarization-singlet state. As soon as Alice measures her photon to be H-polarized she knows that Bob must necessarily find his photon to be V-polarized (provided Bob also measures the polarization in the same direction has Alice). It doesn't matter whether Bob measures his photon before, after, or simultaneously with Alice.

The final outcome is observer independent given the setup of the experiment, and what Bob finds is always consistent with what Alice finds. There's no contradiction in the outcomes of measurements between Bob's and Alice's experience. Of course to reveal the correlations, Alice and Bob must exchange their measurement protocols.

If you take this overly emphasized subjective interpretation out of Fuchs's paper, it's in perfect agreement with the minimal interpretation.