Some questions about "superdeterminism" and Bell's Theorem

[penguin_surprise]

Hi. I'm not a physicist, but I’m intrigued by Bell's theorem and I've been stumbling with "superdeterminism." My understanding of the concept is that everything is not just predetermined, but the initial conditions of the universe are fine-tuned and "conspire" so choices of which versions of Bell test experiments to perform and which measurement settings to use are highly correlated with the variable being measured and can’t be made statistically independent in any way (guided by *any* process by which one might attempt to inject functional randomness -- consciousness, Brownian motion, any kind of PRNG, etc.), so that conscious beings performing Bell test experiments always get biased samples producing the wrong results, and a false picture of physics seeming to match QM even though reality is truly described by a local hidden variable theory. I'm trying to figure out if this is REALLY how bad it is, or is there any more to it?

Because this is, of course, completely at odds with what I originally read because half the sources I read equate it to determinism but then claim it somehow evades Bell. There’s a LOT of misinformation and this subject seems to really attract a lot of cranks, and because I've seen disputing claims on basically everything, I have a few questions.

1. Bell proves a local hidden variable theory would imply an inequality so that the correlations between two entangled spin measurements are essentially a linear function of the angle difference, and this inequality contradicts the one predicted by QM. Is it correct that since a "local hidden variable theory" is taken to be an *extension* of QM (in the original EPR context), and two different predictions are given for the correlations, this would mean such a "local hidden variable theory" wouldn’t just disagree with QM but be logically contradictory (unless Bell's inequalities don't hold)? (Or am I wrong, and that value for QM is only the one for "QM without hidden variables?")

2. Exactly how is superdeterminism supposed to be a “loophole?” Is it that a) We can't derive Bell’s inequality; the argument doesn't go through without assuming of statistical independence, so it IS possible for a superdeterministic local HVT to predict the same correlations as QM, or b) It's a loophole in Bell test experiments. Bell’s theorem still holds, but the highly robust observed violation of Bell's inequalities in our universe (and confirmation of QM) is illusory. For some angle between detectors, if the QM-predicted correlation is 25%, and the observed correlation is very close to 25%, but the correlation predicted by a local hidden variable theory is 33%, the correlation actually IS 33% in the universe. Local HVTs can only produce the QM predicted correlations by chance, and these would have to vanish with a sufficiently large unbiased, randomized sample; the universe just “conspires” to deceive us that QM is true. Even though “superdeterminism” is purported to allow, create, and explain away exceedingly unlikely statistical occurrences, systematic biases, and conspiracies already in things like spin correlations, those biases do have to be evened out in sufficiently large samples and couldn't be a universal thing. Superdeterminism couldn't actually make it so the actual correlation is 25% while preserving local realism; or c) both of those?

3. Does superdeterminism negate counterfactual definiteness? WP claims that since under superdeterminism it would be technically impossible to perform a different experiment, this negates CFD and that therefore the argument for Bell’s inequalities doesn’t go through. If that's correct, don't all deterministic theories negate CFD? This is very confusing to me because what I'm read elsewhere is invalidating CFD means invalidating realism (which it’s almost synonymous with) and determinism. And wouldn’t it invalidate superdeterminism too? How could getting rid of CFD recover realism; that seems backwards? Or is it just because of determinism? That seems to make no sense because regular determinism doesn't save local HVTs

4. Is the “conspiratorial” quality essential to superdeterminism? Instead of “superdeterminism” just being used to fine-tune selection of experimental settings for Bell tests to be performed by conscious experimenters, suppose it's predetermined that for all similar observations/ measurements in the universe, not just those directly observed by conscious experimenters, the correlations will mimic QM's predictions, and generally physical interactions would give the statistical appearance of QM even though reality is local realist; the universe always "pretends" to violate local realism even in all interactions not observed (even indirectly) by conscious experimenters. Could that be a possibility under a "superdeterministic" account? If even possible, it would be highly implausible and artificial, probably require new physics and every particle containing hidden variables with information about every particle in the universe, be horrible unfalsifiable, unscientific, violate occam's razor and 300 other heuristic principles, and just be downright terrible (and I feel silly for even proposing it) but at the very least avoid the most insane (to me at least) aspect of superdeterminism -- that the universe would arbitrarily, selectively only "fake" QM for measurements in experiments performed by conscious experimenters in order to systematically misrepresent the true result, and therefore would have to apparently "know" the difference between general physical interactions and ones that are part of experiments that conscious experimenters are going to reason from, and make some "cutoff" between measurements that are part of experiments and that aren't. I don't know if what I've said here made any sense, but my point is it's not clear to me (though there's probably a simple reason) why superdeterminism would NEED to be conspiratorial.

5. People espousing superdeterminism tend to either INSIST despite all evidence that superdeterminism = determinism, or, less often, recognize the difference but say their version of superdeterminism avoids a conspiracy, that "all I'm saying is that the measurement settings are correlated with the variable, somehow saving local realism" but fail to actually elaborate on the specifics of how that would work or be different, or to fully construct a workable theory based on this. t'Hooft seems to be the only mainstream physicist who's really worked on this. Do his proposals end up with a form of superdeterminism that avoids "conspiracy" in some way (I can't imagine him, or anyone, actually being a proponent of the crazy version)?

I think other than the low quality of resources on this subject, the main thing I'm lacking is an understanding of why even in the case of superdeterminism (which means we're entertaining the possibility of the universe being predetermined to cause exceedingly unlikely events) the universe must still on a large scale reproduce the correlations predicted by LHVTs (i have a feeling it's a really simple explanation though). I'm going off the derivation of Bell’s original inequality that is outlined on the Bell’s Theorem article on Wikipedia and I can mostly follow it but I also don't know whether Bell's inequality holds even without statistical independence.

Any help is much appreciated, and I have a couple follow-up questions if that's okay, and I apologize if this is too much or these kinds of questions don't belong; I lack a lot of knowledge of physics so there are probably really simple answers but I'm trying my best to understand. Thanks all, and thanks to anyone who read ^^

 

[PeroK]

You could try reading the other threads on here by searching for superdeterminism.

 

[penguin_surprise]

You could try reading the other threads on here by searching fir superdeterminism.

I did that before posting! the other threads on this site were largely helpful, they're where most of my actual understanding on it comes from, but I'm still confused about some things. I'll check again to see if there's answers to what I'm asking in the other threads, though

(and I'm sorry, btw, for bringing up again what I imagine is a really dead horse topic by this point)

 

[PeroK]

I did that before posting! the other threads on this site were largely helpful, they're where most of my actual understanding on it comes from, but I'm still confused about some things. I'll check again to see if there's answers to what I'm asking in the other threads, though

(and I'm sorry, btw, for bringing up again what I imagine is a really dead horse topic by this point)

It sounds more like flogging a dead unicorn to me.

At best it's an intellectual exercise and at worst unscientific crackpottery.

 

[penguin_surprise]

It sounds more like flogging a dead unicorn to me.

At best it's an intellectual exercise and at worst unscientific crackpottery.

To be clear: I don't believe it's a possibility. It's not a concept I believe should be seriously considered at all. I don't think it's desirable to find a "loophole" to Bell's theorem to "save" local realism. I don't think it's a promising research program. I'm just trying to figure out what the argument is even supposed to be and where this came from. It's not that I believe it, and I'm looking for a more coherent understanding of why to discount it than anything.

My questions 1) and 2) are about how Bell's inequality works (which most of this is couched in) -- do the derivation of Bell's inequalities depend on assuming statistical independence? -- and IMO, they're real questions. Honestly, a main motivation for researching the subject for me is that several expositions of Bell I've read have brought up this stupid "third possibility" and treated it as totally plausible and totally misled me for a long time about what it even meant and so I wanted to do research and find sources to edit some articles to be less misleading. It really shouldn't have ever been mentioned as a "possibility" in the first place, because it's essentially contentless, could apply as an absurd "loophole" to any scientific theory (in which case it would never be taken seriously), and basically exists only as a desperate attempt to preserve local realism. If it weren't for that, I wouldn't be interested in the subject. So I don't disagree, really, that it'd be better for the topic to just go away. (At the same time, reading about it on here and elsewhere rose genuine questions for me about Bell's theorem works and how I understand it, which I'm genuinely trying to understand.) I guess I just need to find better sources for learning physics.

 

[stevendaryl]

My questions 1) and 2) are about how Bell's inequality works (which most of this is couched in) -- do the derivation of Bell's inequalities depend on assuming statistical independence?

Yes, the assumption is that you have two experimenters, I always call them "Alice" and "Bob" each performing measurements, and that the choice of which measurement they will perform is chosen independently. If Alice's and Bob's choices were known ahead of time (or if Alice's choices had a known consistent relationship to Bob's choices), then it would be possible to reproduce the predictions of EPR using local means.

 

[ueit]

Hi. I'm not a physicist, but I’m intrigued by Bell's theorem and I've been stumbling with "superdeterminism." My understanding of the concept is that everything is not just predetermined, but the initial conditions of the universe are fine-tuned and "conspire" so choices of which versions of Bell test experiments to perform and which measurement settings to use are highly correlated with the variable being measured and can’t be made statistically independent in any way (guided by *any* process by which one might attempt to inject functional randomness -- consciousness, Brownian motion, any kind of PRNG, etc.), so that conscious beings performing Bell test experiments always get biased samples producing the wrong results, and a false picture of physics seeming to match QM even though reality is truly described by a local hidden variable theory. I'm trying to figure out if this is REALLY how bad it is, or is there any more to it?Any help is much appreciated, and I have a couple follow-up questions if that's okay, and I apologize if this is too much or these kinds of questions don't belong; I lack a lot of knowledge of physics so there are probably really simple answers but I'm trying my best to understand. Thanks all, and thanks to anyone who read ^^

Can you answer me the following questions:

1. According to classical electromagnetism do charged particles interact even if there is a large distance between them?
2. Are atoms composed of charged particles?
3. Are conscious beings and all devices used in a Bell test composed out of atoms?

If your answer to the above questions is "yes" then try to answer this one:

Does it make sense to claim that groups of charged particles (conscious or not) whose behavior is described by classical electromagnetism evolve independently?

I think it does not. This is what superdeterminism implies. No need of fine-tuning, conspiracies, there is no bias.

Regards,

Andrei

 

[stevendaryl]

Can you answer me the following questions:

1. According to classical electromagnetism do charged particles interact even if there is a large distance between them?
2. Are atoms composed of charged particles?
3. Are conscious beings and all devices used in a Bell test composed out of atoms?

If your answer to the above questions is "yes" then try to answer this one:

Does it make sense to claim that groups of charged particles (conscious or not) whose behavior is described by classical electromagnetism evolve independently?

I think it does not. This is what superdeterminism implies. No need of fine-tuning, conspiracies, there is no bias.

Regards,

Andrei

Andrei, yours is not a mainstream opinion, so I think you might be misleading the OP by not stating up front that almost no physicists agree with you.

Not about whether Alice and Bob are described by electromagnetism, but whether that in any way helps to explain Bell's inequalities without fine-tuning, conspiracies, etc. It's important to Physics Forums to distinguish between your own personal opinions/theories and generally accepted science, and we don't discuss personal opinions/theories here. It's not that accepted science is always right, but that this is an educational forum, and it's not the place to introduce ground-breaking work.

 

[Demystifier]

Can you answer me the following questions:

1. According to classical electromagnetism do charged particles interact even if there is a large distance between them?
2. Are atoms composed of charged particles?
3. Are conscious beings and all devices used in a Bell test composed out of atoms?

If your answer to the above questions is "yes" then try to answer this one:

Does it make sense to claim that groups of charged particles (conscious or not) whose behavior is described by classical electromagnetism evolve independently?

I think it does not. This is what superdeterminism implies. No need of fine-tuning, conspiracies, there is no bias.

I think you are mistaken. According to classical electromagnetism, charged particles do not interact if the separation between them is spatial. The interaction does not propagate faster than light. On the other hand, to explain the violation of Bell inequalities (for setups for which the causality loophole is closed) by non-fine-tuned determinism, one needs faster-than-light interaction.

 

[stevendaryl]

I think you are mistaken. According to classical electromagnetism, charged particles do not interact if the separation between them is spatial. The interaction does not propagate faster than light. On the other hand, to explain the violation of Bell inequalities (for setups for which the causality loophole is closed) by non-fine-tuned determinism, one needs faster-than-light interaction.

I think you misunderstood Andrei's point. As I pointed out, it's easy to come up with a local hidden-variables explanation for EPR if Alice's and Bob's measurement choices are predictable. He's saying that they actually may be predictable, in principle. That is a loophole in Bell's argument, but contrary to what Andrei says, there is no way to exploit this loophole to give a local explanation of EPR correlations without fine-tuning, conspiracies, etc.

 

[zonde]

To be clear: I don't believe it's a possibility.

It is a possibility, but there is no point in believing in this possibility, because as you say:

[It] could apply as an absurd "loophole" to any scientific theory

So this possibility should be discarded on philosophical grounds as inconsistent with scientific approach.

 

[zonde]

I will add reference for my previous statement https://arxiv.org/abs/1407.0363:
It is possible that all events in the universe share common causes, a philosophical view called superdeterminism (see e.g., Shimony, Horne, and Clauser, 1976; Bell, 1977; Brans, 1988). This constitutes a loophole, but if superdeterminism holds, there is no point in discussing what mathematical models could be used to model nature, be it local realist or quantum or any other model. We can never rule out this possibility using scientific methods, because (Shimony, Horne, and Clauser, 1976):
"In any scientific experiment in which two or more variables are supposed to be randomly selected, one can always conjecture that some factor in the overlap of the backward light cones has controlled the presumably random choices. But, we maintain, skepticism of this sort will essentially dismiss all results of scientific experimentation. Unless we proceed under the assumption that [superdeterminism does not hold,] we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation."
The loophole of superdeterminism cannot be closed by scientific methods; the assumption that the world is not superdeterministic is needed to do science in the first place.

 

[stevendaryl]

The difference between superdeterminism and just ordinary determinism is that ordinary determinism still has freedom of initial conditions, while in superdeterminism, the initial conditions themselves are constrained. And the peculiarity is that the constraints are easiest to formalize in terms of final states. So superdeterminism looks like a conspiracy. Whether there is a non-conspiratorial way to get the same results is complete speculation, and definitely is not mainstream. t'Hooft is a respected scientist, but his superdeterministic model of QM is really a toy--it is not a serious piece of research, as far as I know.

If we assume that

1. the universe is infinite (or at least is so large that light from the most distant regions have not yet reached us), and
2. the pattern of stars in the distant regions are unpredictable

then you can't have a superdeterministic theory of the type that would be needed to reproduce the predictions of QM for EPR without weird conspiracies.

For example, Alice and Bob can be far away from each other, looking through telescopes at the most distant regions of the universe, regions that have, up until this moment, been too far away for light to travel to us since the Big Bang. They can decide which measurement to perform based on the number of new stars they discover in the time between the creation of the twin pair and their detection.

For a deterministic hidden-variables theory to exploit superdeterminism to achieve the EPR statistics, it would have to be possible, in principle, to predict what choice Alice and Bob will make ahead of time. That would imply that it would be possible to predict the number of stars in regions of space that have never before been in causal contact with us. So the superdeterministic loophole really would require that everything about the future of an infinite universe be predictable now, based on a finite amount of observational data about a finite part of that universe.

So that's where the distinction between determinism and superdeterminism comes into play. Determinism would in principle allow you to predict future states of the universe from a complete description of the initial state of the universe. But that isn't good enough for superdeterminism, because we don't have any way of knowing the initial state of regions trillions of light years away. Superdeterminism would require the initial states of all the matter in an infinite universe to be carefully chosen so that Alice and Bob will end up making the right choices in an experiment here on little old Earth.

 

[penguin_surprise]

Yes, the assumption is that you have two experimenters, I always call them "Alice" and "Bob" each performing measurements, and that the choice of which measurement they will perform is chosen independently. If Alice's and Bob's choices were known ahead of time (or if Alice's choices had a known consistent relationship to Bob's choices), then it would be possible to reproduce the predictions of EPR using local means.

Thank you for answering!

I'm realizing what I was confused about above, I think, and I think I'm going to rephrase one of my questions into something coherent after I sleep. Probability can be confusing...

 

[penguin_surprise]

The difference between superdeterminism and just ordinary determinism is that ordinary determinism still has freedom of initial conditions, while in superdeterminism, the initial conditions themselves are constrained. And the peculiarity is that the constraints are easiest to formalize in terms of final states. So superdeterminism looks like a conspiracy. Whether there is a non-conspiratorial way to get the same results is complete speculation, and definitely is not mainstream. t'Hooft is a respected scientist, but his superdeterministic model of QM is really a toy--it is not a serious piece of research, as far as I know.

Ah, I didn't know of that way of distinguishing the two (and also a good explanation of what "conspiracy" means.) I thought if superdeterminism was actually "super" relative to determinism in any way it was that it negated even deterministic chaos / pseudorandomness in the context of Bell test experiments, but that's really interesting too. It seems like there are almost no examples of people who overtly espouse the crazy version of superdeterminism, or ever have -- even for crackpots it's too insane, so I suspected it might be a strawman. But I guess the "non-strawman version" of superdeterminism doesn't really exist in any fleshed out form (it only exists as wishful thinking)?

If we assume that

1. the universe is infinite (or at least is so large that light from the most distant regions have not yet reached us), and
2. the pattern of stars in the distant regions are unpredictable

then you can't have a superdeterministic theory of the type that would be needed to reproduce the predictions of QM for EPR without weird conspiracies.
...
So that's where the distinction between determinism and superdeterminism comes into play. Determinism would in principle allow you to predict future states of the universe from a complete description of the initial state of the universe. But that isn't good enough for superdeterminism, because we don't have any way of knowing the initial state of regions trillions of light years away. Superdeterminism would require the initial states of all the matter in an infinite universe to be carefully chosen so that Alice and Bob will end up making the right choices in an experiment here on little old Earth.

that's a good argument. It sounds like along with everything else SD also violates the Copernican principle.
I also find it surprising that with all the insane things SD would have to require, and all of the stringent constraints imposed on things, that it'd still be unfalsifiable and have no observable consequences...

 

[Zafa Pi]

Unless we proceed under the assumption that [superdeterminism does not hold,] we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation." {S.H.C.]

That's not true. One can know that they are watching a movie, but pretend what they are seeing is real in order to get a better experience. I personally believe in solipsism, but pretend that you and all the other pseudo-avatars I conjure up are real for the fun of it. The benifit is if I stop pretending I can fall asleep in a "crowded room".

The same applies to SD, denying its validity or merely ignoring it can reap rewards such as tenure and patents, but that doesn't prove it false. I love Bell's Theorem, and I find that measurements on entangled entities can refute the inequality mysterious and fascinating. On quiet evenings I often ponder how nature can pull off those amazing correlations at distant locations. But occasionally my mind will begin to cramp, then I can slide softly into the warm comforting arms of SD and know it was all ordained at the big bang.

And BTW, if you don't like this point of view, I want you to know it's not my fault, I had no choice.

 

[OCR]

I had no choice.

Nor do you now ! [COLOR=#black]..[/COLOR]

And BTW, if you don't like this point of view, I want you to know it's not my fault...

Nor mine...? [COLOR=#black]..[/COLOR]

 

[stevendaryl]

That's not true. One can know that they are watching a movie, but pretend what they are seeing is real in order to get a better experience. I personally believe in solipsism, but pretend that you and all the other pseudo-avatars I conjure up are real for the fun of it. The benifit is if I stop pretending I can fall asleep in a "crowded room".

The same applies to SD, denying its validity or merely ignoring it can reap rewards such as tenure and patents, but that doesn't prove it false. I love Bell's Theorem, and I find that measurements on entangled entities can refute the inequality mysterious and fascinating. On quiet evenings I often ponder how nature can pull off those amazing correlations at distant locations. But occasionally my mind will begin to cramp, then I can slide softly into the warm comforting arms of SD and know it was all ordained at the big bang.

And BTW, if you don't like this point of view, I want you to know it's not my fault, I had no choice.

Good points. Physicists insist that their theories have certain desirable properties, such as being objective, falsifiable, etc. They have good reasons for preferring such theories, because it's difficult or impossible to do good science unless the theories being investigated are amenable to the scientific method. However, logically speaking, nature is under no obligation to make science easy for us. So a "bad" theory (from the point of view of the scientific method) could actually be correct; it's just that we would have no good way to ever find that out. It's sort of like searching for your keys under a streetlight, because it's easier to see there.

 

[Zafa Pi]

Good points. Physicists insist that their theories have certain desirable properties, such as being objective, falsifiable, etc. They have good reasons for preferring such theories, because it's difficult or impossible to do good science unless the theories being investigated are amenable to the scientific method. However, logically speaking, nature is under no obligation to make science easy for us. So a "bad" theory (from the point of view of the scientific method) could actually be correct; it's just that we would have no good way to ever find that out. It's sort of like searching for your keys under a streetlight, because it's easier to see there.

Indeed, I concur with all that.

However, in my post I was attempting to go further. By lumping SD in with solipsism, I was saying (in my sardonic fashion) that SD is silly and irrelevant to science even if it uses sciency terminology. Another example: "Where does God fit into your theory?", with the apt response from Laplace, "I have no need of that hypothesis." I have found that this point of view has allowed me not to be frustrated while engaging with one that claims that all the scientists from NASA and IPCC are conspiring and lying and there is no global warming.

 

[ftr]

By lumping SD in with solipsism,

I think SD can be true if we take MUH to heart. For example, if the laws of physics "resembled" a triangle, then if the triangle is trillion light years long, and if we know the angle at one end then we can tell what the sum of other two angles are. With cause and effect being the relation.

Edit: to make it more like QM you can assume the triangle is also random, with the same results upon measurement.

 

[zonde]

The same applies to SD, denying its validity or merely ignoring it can reap rewards such as tenure and patents, but that doesn't prove it false.

Indeed, denying or ignoring SD doesn't prove it false. But this is not the argument.
The argument is that if you believe SD true you can newer find of out if it's false by doing some observations. You close the door to possibility that you might be wrong.

One can know that they are watching a movie, but pretend what they are seeing is real in order to get a better experience. I personally believe in solipsism, but pretend that you and all the other pseudo-avatars I conjure up are real for the fun of it.

What holds you back from adopting antisocial behavior? Nothing. It's dangerous belief not just for science but for society in general.

 

[Zafa Pi]

Indeed, denying or ignoring SD doesn't prove it false. But this is not the argument.
The argument is that if you believe SD true you can newer find of out if it's false by doing some observations. You close the door to possibility that you might be wrong.

How could one who believes in SD possibly be wrong? SD is not even wrong.

What holds you back from adopting antisocial behavior? Nothing. It's dangerous belief not just for science but for society in general.

I'm a kind and gentle solipsist, I have never hurt one of my fabrications. Some I've forgotten about so they are gone, but that's ok they never existed in the first place.
What holds you back?

 

[zonde]

What holds you back?

I chose to believe in physical reality as it won't hurt even if the reality is actually solipsistic.
So it makes sense to try to contribute to hypothetically real society in a constructive way.

 

[Zafa Pi]

I think SD can be true if we take MUH to heart. For example, if the laws of physics "resembled" a triangle, then if the triangle is trillion light years long, and if we know the angle at one end then we can tell what the sum of other two angles are. With cause and effect being the relation.

Edit: to make it more like QM you can assume the triangle is also random, with the same results upon measurement.

MUH and SD are peas in a pod.

The laws of physics most emphatically do not resemble a triangle. They resemble an Alexander horned sphere, with a random set of limit points to make it more like QM.

 

[Zafa Pi]

I chose to believe in physical reality as it won't hurt even if the reality is actually solipsistic.
So it makes sense to try to contribute to hypothetically real society in a constructive way.

Yeah, that's what Trump believes. I'm not taking any chances, I'm sticking with solipsism.
BTW, when you said, "I chose to believe ..." you forgot about SD. You're as delusional as me.

This is too much fun, the monitors must be on the way. Being a solipsist perhaps I'll report myself.

 

[forcefield]

Yes, the assumption is that you have two experimenters, I always call them "Alice" and "Bob" each performing measurements, and that the choice of which measurement they will perform is chosen independently. If Alice's and Bob's choices were known ahead of time (or if Alice's choices had a known consistent relationship to Bob's choices), then it would be possible to reproduce the predictions of EPR using local means.

Nick Herbert's "simple proof of Bell's Theorem" seems to be a counter-example. Hence superdeterminism seems to attack an assumption (statistical independence) that is not even necessary.

Unless by local you mean not FTL ?

 

[stevendaryl]

Nick Herbert's "simple proof of Bell's Theorem" seems to be a counter-example. Hence superdeterminism seems to attack an assumption (statistical independence) that is not even necessary.

The assumption that Alice's and Bob's measurement choices are unpredictable in principle is definitely necessary. If it is possible to predict their choices, then there is an easy hidden-variables theory that reproduce the predictions of quantum mechanics. If it is possible to know ahead of time that the angle between Alice's measurement direction and Bob's measurement direction is $\theta$, then the hidden variable $\lambda$ can be chosen with that in mind

Let $\lambda$ take on 4 values:
$\lambda_{++}$ with probability $\frac{1}{2} sin^2(\theta)$
$\lambda_{+-}$ with probability $\frac{1}{2} cos^2(\theta)$
$\lambda_{-+}$ with probability $\frac{1}{2} cos^2(\theta)$
$\lambda_{--}$ with probability $\frac{1}{2} sin^2(\theta)$

Assume that Alice's and Bob's results are completely determined by $\lambda$:

• If $\lambda = \lambda_{++}$, then Alice and Bob will both get result spin-up.
• If $\lambda = \lambda_{+-}$, then Alice will get result spin-up, and Bob will get result spin-down.
• etc.

 

[forcefield]

The assumption that Alice's and Bob's measurement choices are unpredictable in principle is definitely necessary. If it is possible to predict their choices, then there is an easy hidden-variables theory that reproduce the predictions of quantum mechanics. If it is possible to know ahead of time that the angle between Alice's measurement direction and Bob's measurement direction is $\theta$, then the hidden variable $\lambda$ can be chosen with that in mind

Let $\lambda$ take on 4 values:
$\lambda_{++}$ with probability $\frac{1}{2} sin^2(\theta)$
$\lambda_{+-}$ with probability $\frac{1}{2} cos^2(\theta)$
$\lambda_{-+}$ with probability $\frac{1}{2} cos^2(\theta)$
$\lambda_{--}$ with probability $\frac{1}{2} sin^2(\theta)$

Assume that Alice's and Bob's results are completely determined by $\lambda$:

• If $\lambda = \lambda_{++}$, then Alice and Bob will both get result spin-up.
• If $\lambda = \lambda_{+-}$, then Alice will get result spin-up, and Bob will get result spin-down.
• etc.

But your hidden variable is non-local...

 

[stevendaryl]

But your hidden variable is non-local...

Not if Alice's and Bob's measurement choices are predictable ahead of time.

For example, suppose Alice always measures along the z-axis, and Bob always measures along the x-axis. Then $\theta = 90^o$ always. I don't need nonlocal interactions to generate the values of $\lambda$ that would satisfy the probabilities predicted by quantum mechanics.

 

[forcefield]

Not if Alice's and Bob's measurement choices are predictable ahead of time.

So by local you mean not FTL (again) ?

 

[stevendaryl]

So by local you mean not FTL (again) ?

I mean something stronger--that the result of a measurement is completely determined by facts in the region near where the measurement takes place. What sense of "non-local" do you mean?

 

[forcefield]

I mean something stronger--that the result of a measurement is completely determined by facts in the region near where the measurement takes place.

But your hidden variable was in terms of measurement results from distant regions...

What sense of "non-local" do you mean?

I mean not "local realism" as in Nick Herbert's proof. Why is that not a counter-example ?

 

[stevendaryl]

But your hidden variable was in terms of measurement results from distant regions...

No, they were in terms of Alice's and Bob's measurement choices, not their measurement results. Surely, there is nothing nonlocal about Alice deciding to always measure spin along the z-axis?

I mean not "local realism" as in Nick Herbert's proof. Why is that not a counter-example ?

I don't know Herbert's proof, but what I described is certainly locally-realistic theory in Bell's sense.

 

[ftr]

do not resemble a triangle

I just meant a triangle as an example of a mathematical structure and not literally a triangle.

 

[forcefield]

Surely, there is nothing nonlocal about Alice deciding to always measure spin along the z-axis?

Yes but when you combine that with what Bob decides you have a non-local source for your hidden variable. Also, consider the possibility that someone tells Alice and Bob what to do.

I'm not getting what you are trying to say. Do you have a valid reference ?