An argument against super-determinism

[MichPod]

TL;DR

Trying to disprove superdeterministic interpretation

I think I have something which can make an argument against superdeterministic interpretation of QM. Not that I am keen of disproving it, but I think that arguments even against some fringe ideas may have non-zero value and are anyway entertaining. I'll be glad to see feedbacks/review for whether this may be considered as a refutation of superdeterminism. I am sure this is not raised for the first time, i.e. my idea is not original, but I could not find it to be mentioned in available sources with either positive or negative attitude, nor with resolution.

Suppose that in the Bell Experiment (putting polarizers against two entrangled photons) we choose the angle of the photon polarizers on both directions based on the digits of decimal representation of two irrational numbers, let it be $\pi$ or $e$ or, say, $\sqrt 2$. So we make a choice (may be a super-determined choice, if we believe superdeterminism is an option) that on the one end we use the sequence of digits of $\pi$ and on the other end, say, of the $\sqrt 2$. Then, is it feasible that any super-deterministic local hidden variable theory could explain how the quantum statistics arises in such an experiment? Say, the digits of the irrational numbers are produced by 2 microcomputers staying each one near each polarizer correspondingly. But how the photons will know from any hidden variables of the environment, what are these digits on both sides? The information about the angles of both polarizers should be accessible per photons on the both sides of the experimental device via the hidden variables, either carried by them or found in the environment locally, but how could it ever be possible in such a case? I do understand this argument may lack rigor, i.e. by itself it is not a refutation. But how can it be satisfactory addressed by any possible superdeterministic interpretation?

 

[PeterDonis]

Suppose that in the Bell Experiment (putting polarizers against two entrangled photons) we choose the angle of the photon polarizers on both directions based on the digits of decimal representation of two irrational numbers

In a superdeterministic theory, you can't "suppose" this independently of the measurement results. A superdeterministic theory would say that if you set things up this way, it's because the carefully chosen initial conditions of the universe determined that you would set things up this way, and set things up so that, even though you set things up this way, you would still obtain measurement results that were consistent with the predictions of QM.

is it feasible that any super-deterministic local hidden variable theory could explain how the quantum statistics arises in such an experiment?

Note my strikethrough above. If you have specified that a theory is superdeterministic, you can't also specify that it's a local hidden variable theory. It might be, but you can't specify that, because it also might not be; you have no way of knowing unless you actually have a specific superdeterministic theory that you can look at.

With the strikethrough applied, my answer to this question is yes; see above.

 

[MichPod]

In a superdeterministic theory, you can't "suppose" this independently of the measurement results.

They are not independent and I do not suppose they are. Measurements of two entangled particles are correlated.

A superdeterministic theory would say that if you set things up this way, it's because the carefully chosen initial conditions of the universe determined that you would set things up this way, and set things up so that, even though you set things up this way, you would still obtain measurement results that were consistent with the predictions of QM.

Yes. So let's say that "carefully chosen initial conditions of the universe" caused that I'll put a $\pi$ digits generator on the one side and $\sqrt 2$ digits generator on the other side. Or vice versa. Or may be $e$ on one side and $\sqrt 10$ on the other. No problem with that.

Note my strikethrough above. If you have specified that a theory is superdeterministic, you can't also specify that it's a local hidden variable theory. It might be, but you can't specify that, because it also might not be; you have no way of knowing unless you actually have a specific superdeterministic theory that you can look at.

For my understanding, a superdeterministric theory is a kind of a "local hidden variable" theory by definition. I.e. superdeterministic theories are a subset in hidden variable theories. It's just a special sort of hidden variables which are "orchestrated" in a way to reproduce QM predictions. So each photon has its own hidden state + it might access the hidden state of the vacuum (whether it exists) along its trajectory + the hidden state of the polarizer, and in the end that should "help" the photon to decide whether it passes the polarizer or is absorbed on it.

 

[PeterDonis]

They are not independent

I'm not talking about the measurement results being independent of each other. I'm talking about the measurement results being independent of whatever process you say is determining the measurement settings. If superdeterminism is true, it is simply impossible to make the process that chooses the measurement settings independent of the measurement results, since superdeterminism by definition asserts that the initial conditions of the universe are carefully chosen so that those things are not independent.

let's say that "carefully chosen initial conditions of the universe" caused that I'll put a $\pi$ digits generator on the one side and $\sqrt{2}$ digits generator on the other side. Or vice versa. Or may be $e$ on one side and $\sqrt{10}$ on the other.

Yes.

For my understanding, a superdeterministric theory is a kind of a "local hidden variable" theory by definition.

No, it isn't. Superdeterminism simply says that however the carefully chosen initial conditions of the universe cause you to set up the measurement settings, those carefully chosen initial conditions of the universe also cause the measurement results to be consistent with QM. Superdeterminism says nothing specific at all about how all that causation comes about. It could be local hidden variables or it could be something else. Superdeterminism just asserts that, however it comes about, it ends up producing the results as described.

 

[MichPod]

No, it isn't. Superdeterminism simply says that however the carefully chosen initial conditions of the universe cause you to set up the measurement settings, those carefully chosen initial conditions of the universe also cause the measurement results to be consistent with QM. Superdeterminism says nothing specific at all about how all that causation comes about. It could be local hidden variables or it could be something else. Superdeterminism just asserts that, however it comes about, it ends up producing the results as described.

Well, if superdeteminism may be nonlocal, then why is it needed and what is its role? What problem should it resolve particularly if, say, we allow nonlocality?

 

[PeterDonis]

if superdeteminism may be nonlocal, then why is it needed and what is its role? What problem should it resolve particularly if, say, we allow nonlocality?

I have no idea, since I'm not an advocate of superdeterminism. You would have to ask someone who is.

 

[Demystifier]

I have no idea, since I'm not an advocate of superdeterminism. You would have to ask someone who is.

All advocates of superdeterminism assume that it is a local hidden variable theory. Otherwise it's pointless.

 

[Envirobridge98]

Yeah, it has to be a local hidden variable theory. Superdeterminism basically says that the entire universe is mechanistic and just proceeds mechanically from an initial state. This, by definition, requires local hidden variables so they can exert influences consistent with the speed of light being the universal speed limit. From what I can tell, such an experiment, if it was performed, would disprove the hidden variable theory, which would then leave the Copenhagen interpretation (the oldest and most plausible theory) as the only viable option! Of course, such an experiment would have to be performed, but once performed, it’s disproved. Fascinating stuff. Not to mention, the universe requires a starter to make a non-deterministic choice in order for time to start. (Von-Neumann paradox) So why would beings in the universe that followed have anything less than free will if we have the appearance of it? I hope someone does this experiment or one like it to finally put super-determinism (a dangerous theory which disallows Any justification of morality) to rest.

 

[Nugatory]

From what I can tell, such an experiment, if it was performed, would disprove the hidden variable theory, which would then leave the Copenhagen interpretation (the oldest and most plausible theory) as the only viable option!

What experiment are you talking about here? We have a half-century of Bell-type experiments that show that no realistic local hidden variable theory can be right, but that certainly does not limit us to Copenhagen - any non-realistic and/or non-local interpretation will work, and there are many of these.

Superdeterminism is the suggestion that these experiments are all flawed in one particular way: There are events common to the past light cones of state preparation and both choices of measurement. If these events are sufficient to determine the state preparation and measurement choices then all three can be related without requiring any non-local faster-than-light influence. It is impossible to construct an experiment that does not include such a shared past so there no way of experimentally disproving the superdeterministic explanation - the best we can do is to point to the unbounded absurdities that appear when we apply it to modern Bell tests.