Understanding Bell's Statements on Freedom of Choice

[Lynch101]

I have no idea unless you give me a specific reference by a specific author that defines what in the math the author means by those terms. I have already said repeatedly that using ordinary language terms without saying precisely what in the math you are referring to by each of those terms is pointless. I have no interest in a pointless discussion.

I would have thought the idea that light propagates at a finite speed and therefore that causal influences cannot propagate at a speed faster than that, would be fairly well understood, regardless of which authority might state it.

If that is understood, then it is a simple question of whether or not that is encoded in the mathematics as one of the assumptions?

But you're not doing that. None of the terms you are throwing around refer to directly observable phenomena.

No, but the consequences do. That is the whole point of Bell's theorem. IF those unobservable phenomena were correct, as postulated by EPR, then Bell's inequality would be obeyed. However, experimental observations demonstrate that it isn't obeyed and therefore at least one of those unobservable phenomena must be incorrect.

Depends on who is saying it. Without a specific reference I cannot answer this question. As I have already said repeatedly, different sources give different meanings to these terms. So talking as if the terms have a single well-defined meaning is pointless. I have no interest in a pointless discussion.

I know you're not going to claim to be unfamiliar with the idea that light propagates at a finite speed, or the idea form relativity theory that causal influences cannot exceed that maximum speed.

Are you familiar with any interpretation of that, that is encoded in the mathematics?

You're not doing that. You're just throwing around terms as if they had a single well-defined meaning, when they don't. That's pointless.

Bell's inequality is violated in experiments. This refers to the observations made in experiments where measurements made on spatially separated entangled particles display higher than expected correlations. Here we are talking about observable phenomena i.e. the measurement outcomes on entangled particles.

Note, we say that the correlations are higher than expected. We can then ask what was the expected correlation? It was, of course, Bell's inequality. We can then ask, what does this violation mean?

In the literature, there are very clear statements about what the violations of Bell's inequality means. It means that one of the assumptions of the theorem must be given up.

What are those assumptions, we might ask.

One of them is the well understood idea that causal influences cannot propagate at a speed faster than light. I'm fairly certain you are familiar with this concept. Another is the idea that the settings on the measurement devices are free variables. Here, the term "measurement devices" refers to the physical piece of equipment used to measure the particle - it is an observable phenomena.

The term "free variable" according to Bell means a variable that it is only correlated with its effect. This is somewhat unusual because usually events would be correlated with their causes also - cause and effect being a observable phenomenon.

Bell appears to invoke the notion of human free will because human free will is a [supposedly] unique phenomenon where the variable of "the will" is only correlated with its effect because it can have no cause, otherwise it wouldn't be free. The actions of the experimenter and their choice of measurement settings are all observable phenomena.

You have suggested that what is being referred to was microscopic events which are only correlated with their effects, suggesting that you at least had some level of comprehension as to what I was talking about.

 

[PeterDonis]

I would have thought the idea that light propagates at a finite speed and therefore that causal influences cannot propagate at a speed faster than that, would be fairly well understood, regardless of which authority might state it.

The term "causal influence" is ambiguous, unless it just means "things that don't propagate faster than light", in which case the statement is a tautology.

Instead of continuing to wave your hands with generalities, why not find a specific reference and give it as a basis for further discussion?

Bell's inequality is violated in experiments.

Agreed.

This refers to the observations made in experiments where measurements made on spatially separated entangled particles display higher than expected correlations.

No, it doesn't. The correlations were not higher than "expected". Everybody expected the correlations to be those predicted by QM, which violate the Bell inequalities.

The correlations, since they violate the Bell inequalities, are higher than what could be produced by any model that satisfies Bell's assumptions. The usual term for such models is "local hidden variable" models. The assumptions involved are clearly stated in Bell's papers in mathematical terms, so that is where I recommend that you look if you want to understand them.

What are those assumptions, we might ask.

No, we might read Bell's papers and find out. Which is a much better idea than reading ordinary language descriptions in the literature without ever trying to match them up with the math.

I see no point in participating further in this discussion until you have done that.

 

[PeterDonis]

You have suggested that what is being referred to was microscopic events which are only correlated with their effects

That statement by Bell was in a different paper from any of the ones where he gives mathematical proofs of his theorem. IIRC Bell in that paper does not say what specific mathematical assumption that goes into his theorem corresponds to what he says he means by "the settings of instruments are in some sense free variables". The best way to make any further progress on such questions is to look at the actual math in Bell's papers where he derives his theorem.

 

[Lynch101]

The term "causal influence" is ambiguous, unless it just means "things that don't propagate faster than light", in which case the statement is a tautology.

Instead of continuing to wave your hands with generalities, why not find a specific reference and give it as a basis for further discussion?

Have you ever heard the term "causal influence" before, other than in the context of this discussion?

It's not difficult to understand and I can explain it in terms of specific observable phenomena, if necessary. Basically, even with a laypersons understanding of the notions of cause and effect and the finite speed at which objects move, including light, you can understand the concept.

No, it doesn't. The correlations were not higher than "expected". Everybody expected the correlations to be those predicted by QM, which violate the Bell inequalities.

Higher than expected under the EPR assumptions. I'll try to be more explicit in future. As long as the rest of it was right though, that's the important thing.

The correlations, since they violate the Bell inequalities, are higher than what could be produced by any model that satisfies Bell's assumptions. The usual term for such models is "local hidden variable" models.

Yes, I'm familiar with the idea of local hidden variables, even without knowing the mathematics because local hidden variables refers to [potentially] real world phenomena which can be understood in the context of other real world phenomena.

The assumptions involved are clearly stated in Bell's papers in mathematical terms, so that is where I recommend that you look if you want to understand them.

Those mathematical terms either describe or predict real world phenomena and so can be discussed in that context. For example, Bell's inequality predicts the expected correlations of the measurements of two spatially separated particles, under the EPR assumptions. The measurements are observable phenomena. Violations of the inequality are observed phenomena.

The violation of the inequality means that at least one of the underlying assumptions of the theorem need to be given up. While the theorem uses mathematics to predict the observable phenomenon, based on mathematically encoded assumptions, those mathematically encoded assumptions refer to [potentially] real world phenomena and so can be discussed on that basis.

One of those assumptions pertains to the finite speed of light and the finite speed at which a phenomenon can affect other phenomena in its locality. This can be understood, quite easily, in terms of real world phenomena.

No, we might read Bell's papers and find out. Which is a much better idea than reading ordinary language descriptions in the literature without ever trying to match them up with the math.

I see no point in participating further in this discussion until you have done that.

We still need to relate the mathematics back to the real world phenomena they describe.

I am attempting to learn the mathematics, but at a finite speed. That doesn't mean, however, that the phenomena to which the mathematics relates, cannot be discussed.

That statement by Bell was in a different paper from any of the ones where he gives mathematical proofs of his theorem. IIRC Bell in that paper does not say what specific mathematical assumption that goes into his theorem corresponds to what he says he means by "the settings of instruments are in some sense free variables". The best way to make any further progress on such questions is to look at the actual math in Bell's papers where he derives his theorem.

It is in a paper where it appears he is replying to a paper by Clauser Horne and Shimony. While he doesn't give a mathematical proof of his theorem and doesn't say what specific mathematical assumption the "free variables" assumption goes into, he does clearly state that it is in there.

If the assumptions are clearly there in the mathematics, should it not be easy to discern where this particular assumption is embedded? Unless the implication is that Bell is mistaken about what assumptions are in his own theorem?

 

[PeterDonis]

Have you ever heard the term "causal influence" before, other than in the context of this discussion?

Of course I have. You are seriously mistaken if you think the issue we are having with this discussion is that I am not sufficiently familiar with the terminology.

The issue we are having with this discussion is that it needs to be grounded in the actual math before it can usefully proceed further. If you are not presently familiar enough with the math to have that grounding, then the discussion needs to stop until you are.

That doesn't mean, however, that the phenomena to which the mathematics relates, cannot be discussed.

If we limit the discussion to just the phenomena, it will be a very short discussion: the Bell inequalities are violated, but special relativity is obeyed and Bell inequality violations cannot be used to send signals faster than light. Those are the phenomena. End of discussion.

What you actually want to discuss are various possible mathematical models that have been proposed, what predictions they make, and what properties they must have, or must not have, in order to predict and account for the observed phenomena. And that discussion needs to be grounded in the actual math in order to usefully proceed further. Trying to ground it in ordinary language terms without specific math to link them to is not working.

If the assumptions are clearly there in the mathematics, should it not be easy to discern where this particular assumption is embedded?

The way for you to answer this question is to read the papers, learn the math, and find out. If you need to take some time to do that, that's fine. I'll still be here whenever you are ready. There is no need to rush things.

 

[Lynch101]

The principle is fairly straight forward. IF the mathematics of quantum mechanics and/or Bell's theorem tell us anything about the observable universe, then we can talk about those observable real world phenomena. If the mathematics tells us anything about the universe that we may not necessarily be able to observe e.g. hidden variables, then we can discuss those in terms of their observable consequences and the real world properties they are assumed to have.

If, as is the case with the mathematics in Bell's theorem, the predicted observations do not match the actual observations then we can ask why this may be. There is an abundance of literature from physicists who certainly do understand the mathematics, which says that at least one of Bell's assumptions must be given up.

IF the mathematical codification of Bell's assumptions correspond to real world phenomena, then we can discuss them in terms of those real world phenomena.

You're statement here demonstrates that it is possible to have a discussion in the absence of the mathematics:

the Bell inequalities are violated, but special relativity is obeyed and Bell inequality violations cannot be used to send signals faster than light. Those are the phenomena. End of discussion.

Yes, the Bell inequalities are violated. What does this tell us about Bell's theorem? It tells us that at least one of the assumptions Bell used to calculate the inequality must be incorrect. What are those assumptions we might ask? Well, they are the EPR assumptions. What were the EPR assumptions we might ask.

One of those EPR assumptions was the idea that properties such as position and momentum can be ascribed to particles, even if they aren't measured. I believe this is referred to as counterfactual definiteness or sometimes as "realism". I might be incorrect about the specific terms, but the idea of particles having those properties prior to measurement, I'm pretty sure is one of the EPR assumptions and therefore one of Bell's. Is that accurate?

Now, you mention that special relativity is obeyed and that Bell inequalities cannot be used to send signals faster than light. We might wonder then about causality as opposed to signaling. Can causal influences propagate faster than light even if signals can't.

If there is any trouble in understanding what is meant here then it can be explained, quite simply, in terms of observable real world phenomena, such as that of throwing a baseball.

What you actually want to discuss are various possible mathematical models that have been proposed, what predictions they make, and what properties they must have, or must not have, in order to predict and account for the observed phenomena.

What I want to discuss in this particular thread are the statements made by Bell and others about the assumption of free will in Bell's theorem.

You initially seemed content to engage with this, correcting the idea that it was human free will that was meant - in spite of the fairly clear statements from Bell, Conway-Kochen, Wiseman (and others). The issue seemed to arise, ironically enough, when I asked a question about the math.

You made the statement:

I'm not sure that the proof of Bell's Theorem requires any assumptions about the statistical independence of the measurement settings and the properties of the particles to be measured. I think it only requires statistical independence of the probabilities of measurement results.

Note the language you use "I'm not sure", "I think". This despite stating that the assumptions of Bell's theorem are clear from his papers. What is clear from Bell's own statements is Bell's own interpretation of the mathematics. It is clear that he believes that he invoked the assumption of free variables i.e. events that are only correlated with their effects.

What is also clear from the statements of Bell, Wiseman and Conway-Kochen is that, in the absence of these free variables (they actually invoke human free will), then the assumption of statistical independence is violated and this would account for the observed violations of Bell's inequality.

You seem to disagree with the interpretation of Bell, Wiseman, Conway-Kochen (and others) and have your own interpretation. I was trying to explore that interpretation by asking about its implications. In particular your statement:

the statistical independence of the measurement settings and the properties of the particles

I was wondering how this idea (that I have only heard from your good self), would change the calculation of Bell's inequality or what it would actually mean. Clearly Bell's inequality is a prediction of measurement outcomes (under certain assumptions) i.e. the properties of particles. The violations of Bell's inequality is clearly due to the actual outcomes of experiments not matching the predictions of Bell's theorem. The other authors seem to suggest if the measurement settings and measurement outcomes are in fact correlated, then the violation of Bell's inequality are explained. This, they suggest, would seem to necessitate the dropping of the free variable assumption or, as Bell, Conway, and Wiseman seem to beleive, human free will.

You seem to have a different interpretation.

Of course I have. You are seriously mistaken if you think the issue we are having with this discussion is that I am not sufficiently familiar with the terminology.

The issue we are having with this discussion is that it needs to be grounded in the actual math before it can usefully proceed further. If you are not presently familiar enough with the math to have that grounding, then the discussion needs to stop until you are.

I had no doubt that you well understood the term "causal influence", the issue is that you were trying to maintain that it was unintelligible without recourse to mathematics, when it is easily explicable in terms of real world phenomena; such as that of throwing a baseball.

The discussion is grounded in the actual math. We are discussing the interpretation of that math. Interpreting the mathematics is seeing how the math applies to the world around us. It can be explained in terms of real world phenomena.

The way for you to answer this question is to read the papers, learn the math, and find out. If you need to take some time to do that, that's fine. I'll still be here whenever you are ready. There is no need to rush things.

I am doing that, and will continue to do so, but the mathematics still needs to be interpreted in relation to the world around us. It can, therefore, be discussed on the basis of real world phenomena.

I do appreciate your time and energy. I think perhaps we have somewhat of an ideological difference on this point. Until such point as I understand the mathematics however, I take at face value the different statements that I encounter as I cannot evaluate their veracity. That doesn't however mean that a meaningful discussion cannot be had. It could be the case that Bell, Wiseman, Conway-Kochen, yourself, all the other posters on here, and the posters elsewhere are all engaged in an elaborate conspiracy and that none of the statements are actually correct. That, however, doesn't prevent me from taking those statements at face value and drawing inferences and conclusions about them. This can all be done on the assumption that the statements are accurate representations.

 

[PeterDonis]

Note the language you use "I'm not sure", "I think". This despite stating that the assumptions of Bell's theorem are clear from his papers.

Yes, because I didn't have the papers in front of me and it's been a while since I read them, and, unlike you, I do not think it is a good idea to throw around ordinary language statements about these things without being sure what specific things in the actual math they refer to.

You seem to have a different interpretation.

No, I just, as I have said multiple times, believe that the discussion has reached a point where it cannot usefully proceed further without being grounded in the actual math instead of ordinary language descriptions. So I stopped proceeding until one of us took the time to go look up the actual math. I haven't had the time to do it, and you haven't done it either. So it hasn't been done, and I have not proceeded.

I had no doubt that you well understood the term "causal influence", the issue is that you were trying to maintain that it was unintelligible without recourse to mathematics, when it is easily explicable in terms of real world phenomena; such as that of throwing a baseball.

You are far too optimistic. David Hume, several centuries ago, already made the correct observation that "causality" is not something we directly observe; it's something we put into our models.

Until such point as I understand the mathematics however, I take at face value the different statements that I encounter as I cannot evaluate their veracity.

This is not a good approach. If you don't understand the mathematics, you don't know what the statements mean, since all of them refer to something in the mathematics; none of them refer only to directly observable phenomena that can be understood without knowing the mathematics.

 

[Lynch101]

Yes, because I didn't have the papers in front of me and it's been a while since I read them, and, unlike you, I do not think it is a good idea to throw around ordinary language statements about these things without being sure what specific things in the actual math they refer to.

No, I just, as I have said multiple times, believe that the discussion has reached a point where it cannot usefully proceed further without being grounded in the actual math instead of ordinary language descriptions. So I stopped proceeding until one of us took the time to go look up the actual math. I haven't had the time to do it, and you haven't done it either. So it hasn't been done, and I have not proceeded.

That's fair enough that you haven't you haven't read the papers recently and can't remember the math. Perhaps that means that you are not best placed to answer the questions being asked then? I do, genuinely appreciate your taking the time because you are always a good help in these discussions. There may, however, be other members here who are more familiar with the math to address the specific questions.

I will certainly continue my own attempt at studying the math but that will probably be a slow process. In the meantime, I was hoping to "stand on the shoulders of giants" and get the insight from those that are best placed to provide it.

On the point about "throwing around" ordinary language statements, I wouldn't quite say that I'm throwing around ordinary language statements. I'm referencing the statements of people who are obviously familiar with the mathematics.

And even the language itself is not so ordinary. Talking about variables being correlated only with their future light cones appears to be reasonably technical and specific. While this idea can be encoded in mathematics, it is equally an idea that can be discussed using ordinary language.

This is not a good approach. If you don't understand the mathematics, you don't know what the statements mean, since all of them refer to something in the mathematics; none of them refer only to directly observable phenomena that can be understood without knowing the mathematics.

The issue can also be discussed entirely hypothetically based on certain assumptions and "pending mathematical comparison". Those assumptions are:
1) Bell understands his own theorem well enough to make statements about it.
2) Wiseman, Conway-Kochen (and others) understand the mathematics sufficiently to make statements about it.
3) The statements made refer to real world phenomena.

In this manner, we wouldn't even need recourse to the mathematics because we would be discussing these statements about the theorem. This would allow us to draw certain conclusions that would have to be supported by the mathematics, if our reasoning is correct and if Bell et al do understand the theorem well enough to make the statements they have made.

It could even be discussed in the form of the Chinese Room argument, where the actual meaning of the terms doesn't even need to be understood. The terms themselves can simply be arranged in a given order to arrive at conclusion.

You are far too optimistic. David Hume, several centuries ago, already made the correct observation that "causality" is not something we directly observe; it's something we put into our models.

We don't need to be able to observe "causality" we can instead talk about "causality" as it is in relativity theory, or simply the idea that Mohammed Ali's famous quip about being so fast that when he turned out the light, he was in bed before the room was dark, is not possible. We can talk about how spatially separated events cannot have an instantaneous effect on each other.

We can also talk about the idea that effects are correlated with their causes. In fact, we don't need much else other than that for this particular discussion.

 

[PeterDonis]

Perhaps that means that you are not best placed to answer the questions being asked then?

If someone else wants to jump in based on the ordinary language terms without any grounding in the math, they're welcome to try. I don't think such a discussion would be productive at this point, but of course someone else's opinion might differ.

I'm referencing the statements of people who are obviously familiar with the mathematics.

Yes, I know, but if you yourself aren't familiar with the math, you don't know what those people are talking about, because you cannot match up the terms they're using with anything you personally understand.

You might think you can substitute intuitive concepts that you are familiar with for the actual math, but that strategy has a very poor track record, particularly in areas like this. Whatever intuitive concepts you have before you learn the math are simply not going to match up well with what's in the math. That's one of the things that makes QM so challenging to study.

1) Bell understands his own theorem well enough to make statements about it.
2) Wiseman, Conway-Kochen (and others) understand the mathematics sufficiently to make statements about it.
3) The statements made refer to real world phenomena.

1: yes. 2: yes. 3: no. The key ordinary language terms they are using do not refer to real world phenomena. They refer to particular mathematical things in particular theoretical models (or types of models). And different sources often use the same ordinary language term to refer to different mathematical things.

We don't need to be able to observe "causality" we can instead talk about "causality" as it is in relativity theory

Which means we're not talking about any "real world phenomenon", we're talking about a mathematical feature of a theoretical model. Which can't be described precisely in ordinary language.

We can talk about how spatially separated events cannot have an instantaneous effect on each other.

Which then pushes the problem back to what counts as an "effect". If that word had a single well-defined meaning, there would not be so much literature written about whether violations of the Bell inequalities count as an "instantaneous effect" or not.

We can also talk about the idea that effects are correlated with their causes.

Same problem, except now it's with the word "cause" as well as the word "effect". Do violations of the Bell inequalities count as "effects being correlated with their causes"? Depends on who you ask. We're not going to settle questions like that here.

 

[Lynch101]

If someone else wants to jump in based on the ordinary language terms without any grounding in the math, they're welcome to try. I don't think such a discussion would be productive at this point, but of course someone else's opinion might differ.

Again, why I do genuinely appreciate your taking the time to even discuss this far.

Yes, I know, but if you yourself aren't familiar with the math, you don't know what those people are talking about, because you cannot match up the terms they're using with anything you personally understand.

The issue of dispute appears to be whether the statements by Bell and other or the inferences I am drawing from the statements match up with the math. As you rightly point out, I am not in a position to evaluate whether they are or not. You seem to have ruled yourself out in that regard also.

That is OK, however, because we can make conditional statements about the issue, and at some later point, when I finally understand the math or when you re-read the papers, or someone more familiar with the mathematics responds, the correspondence of the statements to the mathematics can be checked.

Basically, we can still make statements like:
IF Bell meant abc, when he stated that in the theorem he assumes abc, then xyz must be the case.

You might think you can substitute intuitive concepts that you are familiar with for the actual math, but that strategy has a very poor track record, particularly in areas like this. Whatever intuitive concepts you have before you learn the math are simply not going to match up well with what's in the math. That's one of the things that makes QM so challenging to study.

The mathematics predicts the measurement outcomes of experiments. We can express this very crudely in ordinary language: this means they tell us how many dots to expect to hit a particular region of a screen over a given number of experiments.

The mathematics give us probabilistic predictions as opposed to deterministic predictions. This means they don't tell us the outcome of every individual experiment but rather the expected percentages over an ensemble.

We can talk about the propagation of light at a finite speed and we can talk about "cause and effect" in terms of throwing a baseball and breaking a window.

1: yes. 2: yes. 3: no. The key ordinary language terms they are using do not refer to real world phenomena. They refer to particular mathematical things in particular theoretical models (or types of models). And different sources often use the same ordinary language term to refer to different mathematical things.

Which means we're not talking about any "real world phenomenon", we're talking about a mathematical feature of a theoretical model. Which can't be described precisely in ordinary language.

The "mathematical things" themeselves refer to assumptions about the real world. They codify assumptions about the real world, in mathematic al terms. As such, they refer back to the real world and we can ask what are those mathematically encoded assumptions about the real world? What do they correspond to in the real world?

Which then pushes the problem back to what counts as an "effect". If that word had a single well-defined meaning, there would not be so much literature written about whether violations of the Bell inequalities count as an "instantaneous effect" or not.

We can talk about cause and effect in terms of observable phenomena. We can talk about throwing a baseball at a window and the window breaking. We can then talk about the length of time the baseball takes to travel from me to the window. We can talk about the speed of light and how it is finite.

We can also talk about cause and effect in terms of the observations we make in experiments i.e. that flash of light on the detector screen. We can drop the words "cause" and "effect" and instead talk about those particular phenomena.

Same problem, except now it's with the word "cause" as well as the word "effect". Do violations of the Bell inequalities count as "effects being correlated with their causes"? Depends on who you ask. We're not going to settle questions like that here.

We might be able to make certain deductions in relation to that question, if we talk in terms of the observable phenomena.

For example, if a particle registers on a detector in Alice's lab (A), is it possible for that event to interact with a particle in Bob's laboratory (B) located on another planet? Does this happen "instantaneously" or does it require time for any influence to travel between A and B - similar to how it takes time for the baseball to travel to the window?

We can talk about the experimental set-up similarly, and what observations we would expect to make given certain assumptions about how the world works. If the observations don't match the predictions, then we can deduce that one or more of our assumptions must be wrong.

 

[PeterDonis]

You seem to have ruled yourself out in that regard also.

Only for now since I don't have the time to go look up the papers again, and since you aren't doing it. I understand you have a lot of other things to learn besides those specific papers, but if you haven't, for example, read Bell's own papers about his theorem, aren't you at least curious what they say? They're not that long and fairly easy to read, and should be easily findable online.

we can still make statements like:
IF Bell meant abc, when he stated that in the theorem he assumes abc, then xyz must be the case.

Only if you can specify "abc" in terms of math, not ordinary language. Otherwise you're just trading one ambiguous ordinary language expression for another.

The rest of your post is just more examples of things you think "we can talk about" without math, that are really, again, just trading one ambiguous ordinary language expression for another.

 

[Lynch101]

Only for now since I don't have the time to go look up the papers again, and since you aren't doing it. I understand you have a lot of other things to learn besides those specific papers, but if you haven't, for example, read Bell's own papers about his theorem, aren't you at least curious what they say? They're not that long and fairly easy to read, and should be easily findable online.

I have read them but I tend to glaze over when it comes to the math, because I presume I won't understand it. I'll go back and have another read.

Only if you can specify "abc" in terms of math, not ordinary language. Otherwise you're just trading one ambiguous ordinary language expression for another.

The rest of your post is just more examples of things you think "we can talk about" without math, that are really, again, just trading one ambiguous ordinary language expression for another.

Interpretation of the mathematics necessarily means relating it to the real world i.e. interpreting what it says about the real world, including the assumptions. Without specifying what aspects of the real world the math is referring to, the math does not predict the outcomes of experiments.

 

[PeterDonis]

I have read them but I tend to glaze over when it comes to the math, because I presume I won't understand it.

Certainly there are physics papers that appear to be using math more as a bludgeon to beat the reader into submission than as an actual tool for modeling and exposition. However, I don't think that is at all the case for Bell's papers.

Interpretation of the mathematics necessarily means relating it to the real world

Sure, but that means you need both sides. You need to know what real world phenomena you are talking about, and you need to know the math. Otherwise how can you possibly understand how they relate to each other?

Do you think that the [finite] speed of light in a vacuum is an ambiguous concept?

As you've stated it, yes, because you haven't specified what you mean by "speed". Now go look for all the PF threads where exactly this ambiguity has caused confusion and misunderstanding (the cosmology forum is a good place to start). I can assure you there are a lot of them.

 

[Lynch101]

Certainly there are physics papers that appear to be using math more as a bludgeon to beat the reader into submission than as an actual tool for modeling and exposition. However, I don't think that is at all the case for Bell's papers.

Thanks, I'll go back over them and hopefully have a better time making sense of the math.

Sure, but that means you need both sides. You need to know what real world phenomena you are talking about, and you need to know the math. Otherwise how can you possibly understand how they relate to each other?

Ideally yes and if I did know both sides I wouldn't need to ask these questions.

In essence, I am asking anyone know knows the mathematics side of things to confirm, or deny, that the real world phenomena, which Bell and others have stated are encoded in the mathematics, are in fact encoded in the mathematics.

If someone confirms that they are, I will take it at face value. If someone says they are not, then I would be inclined to ask what assumptions are actually encoded in the mathematics - again, taking what they say at face value.

As you've stated it, yes, because you haven't specified what you mean by "speed". Now go look for all the PF threads where exactly this ambiguity has caused confusion and misunderstanding (the cosmology forum is a good place to start). I can assure you there are a lot of them.

But you probably have a decent idea of what I am referring to. Perhaps the velocity of light would be a more accurate term to use. Either way, the idea that everything in the Universe requires a non-zero amount of time to travel between two spatially separated laboratories is intelligible in terms of real world phenomena. Yes, it can be encoded in mathematics, but to interpret the mathematics, we need to interpret it in terms of real world phenomena.

 

[PeterDonis]

If someone confirms that they are, I will take it at face value. If someone says they are not, then I would be inclined to ask what assumptions are actually encoded in the mathematics - again, taking what they say at face value.

So you basically think that waiting around for someone else to do this for you--which could take days, or weeks, or months, or might never happen at all--is a better option than just looking up the papers for yourself and reading what they say? And you think that taking what other people say at face value about anything you don't understand yourself is a better option than trying to understand it yourself?

For the record, I think you are showing very bad judgment if that really is your preference.

 

[PeterDonis]

you probably have a decent idea of what I am referring to

Whether I do or not is irrelevant. You are the one who should be able to precisely describe what you mean. I should not have to guess or fill in blanks for you. Particularly about a concept that is so basic that anyone who wants to have an intelligible discussion about relativity should be able to precisely describe it.

At least, that's my preference. Yours is evidently different. Anyone else reading this thread is welcome to respond according to your preference if they wish.

 

[Lynch101]

So you basically think that waiting around for someone else to do this for you--which could take days, or weeks, or months, or might never happen at all--is a better option than just looking up the papers for yourself and reading what they say? And you think that taking what other people say at face value about anything you don't understand yourself is a better option than trying to understand it yourself?

For the record, I think you are showing very bad judgment if that really is your preference.

I do look up the papers for myself and read what they say. I just don't have the level of mathematics required to understand the math content. I have started to re-learn high school mathematics, but it may be a while before I'm at the level where I can answer questions like these for myself. That is why sites like this one can be a beneficial aid to the learning process because there are, or at least appear to be, members on here who do understand that side of things.

As I said, currently, I am in a position where I have to take at face value the statements people make, just as I have to take at face value plenty of other facts about the world around me, because it simply isn't practically possible to learn everything about everything. But, taking things at face value doesn't simply mean believing that they are an accurate representation. It involves cross-referencing them with other statements from other members and other sources, such as the authors of papers themselves.

If 99% of the sources one encounters all say effectively the same thing, then there is a higher likelihood that what they say is an accurate representation. It is possible that there is a giant conspiracy being perpetrated where all of these people are deliberately trying to mislead everyone else. So yes, taking things at face value is predicated on two assumptions:
1) Those making the statements are not engaged in a giant conspiracy
2) Those making the statements are knowledgeable enough to give an accurate representation of the topic under consideration.

Once you have these two assumptions you can then learn from other people's expertise.With regard to the mathematics in particular. As mentioned, the mathematics encodes assumptions and fact about the real world. A good example of this is Einstein's 1905 paper where he uses the example of a train pulling into a station to demonstrate the idea of "simultaneity", referring to a wrist watch. Or, as Leonard Susskind demonstrates in the the Theoretical Minimum, when he explains how to encode dynamical laws in equation form:

He takes a real world object i.e. a coin which can be in either of two states, H or T, and gives an example of a dynamical law. He then demonstrates how to write this in equation form. But, the equation always describes the real world scenario and to interpret the math, we must refer back to a real world scenario.

The same is true for the use of calculus to calculate rates of change or any other branch of mathematics, which purports to tell us things about the natural world. First, assumptions/facts about the natural world are encoded in mathematical form, then the mathematics can be manipulated (more precisely than ordinary language) to draw conclusions and make predictions about the natural world, but ultimately, the natural world is the arbiter of truth. If the observations made in the natural world don't match the predictions of the mathematics, then it is the mathematics that has to change. Similarly, to interpret the mathematics, is say what it tells us about the natural world.

Take the theory of relativity for example. The mathematics by itself doesn't tell us anything. It's just symbols. Only when it is related back to the natural world do the symbols have meaning. For the theory to make predictions about the natural world the mathematical symbols must be connected to phenomena in the natural world. This is how we determine if the mathematics is accurate.

There is also a conversation we had previously about the Block Universe. Some have argued that the Block Universe is the only way to interpret the mathematics of relativity, while you pointed out that this isn't necessarily true. You demonstrated that it can be interpreted in the context of presentism or in the manner outlined in your insight article. The mathematics doesn't tell us any of this because it is compatible with all of them. To develop a fuller picture of what the mathematics tells us about the natural world, we have to interpret it in terms of the natural world.Mathematics is one of the single most effective tools man has ever invented. It has allowed us to investigate ideas more efficiently than ordinary language. But, it does this by taking phenomena in the natural world, which can be described in ordinary language, albeit technical, and encoding it in the symbols of mathematics. By manipulating the math we can then analyse situations more effectively and efficiently. We can make predictions about future observations. But, those predictions are about observations in the natural world and can be described in ordinary language.

It is the first and last steps in that process that I have been enquiring about.

Whether I do or not is irrelevant. You are the one who should be able to precisely describe what you mean. I should not have to guess or fill in blanks for you. Particularly about a concept that is so basic that anyone who wants to have an intelligible discussion about relativity should be able to precisely describe it.

At least, that's my preference. Yours is evidently different. Anyone else reading this thread is welcome to respond according to your preference if they wish.

I'm not sure if you are familiar with the concept of a steelman? It's where you take the strongest possible interpretation of the other persons statement.

Either way, it serves to demonstrate the point I have been making when you say that anyone who wants to have an intelligible discussion about relativity should be able to precisely describe [the concept]. The concepts can be discussed using ordinary language, albeit technical.

I was trying to find out precisely what Bell meant and what assumptions about the natural world he had encoded in his theorem; I was inquiring about the precise statements made by Bell and others about those assumptions. Again, I was looking at the first and final steps in the process. Given the deficit in my mathematical ability, I am in a position where I have to take it at face value what those who are more familiar with the mathematics tell me.One conclusion that can be taken from this discussion is that it's not necessarily the case that Bell's statements about the assumption of free will or free variables in his own theorem, and the statements of the others, are inaccurate, it's that neither you nor I are not familiar enough with the mathematics to say whether they are or not.

We could always take Bell at face value and work on the assumption that he knows what he's talking about.

 

[PeterDonis]

I do look up the papers for myself and read what they say. I just don't have the level of mathematics required to understand the math content.

Then can you at least give specific references to specific statements Bell makes in the papers, or specific equations, that you're having trouble understanding? Or that you are trying to match up with statements by Bell from other papers that you referenced earlier in this discussion? At the very least, you should be able to pick out the places in Bell's papers where he appears to be making assumptions, so we can zero in on trying to clarify what those assumptions are. Doing that with the original papers directly seems to be a much better way of proceeding than trying to parse second-hand descriptions of what those papers say.

taking things at face value doesn't simply mean believing that they are an accurate representation

Hm, that clarifies how you were using the term, but it's very different from my understanding of the term "taking things at face value". To me, that term means you do simply believe that the statements are accurate without further checking; if you're doing further checking, you're not taking them at face value. My comments on doing that were based on that understanding of the term, so they don't apply if you are actually doing further checking.

However, there is still a potential issue with what further checking you do. See below.

If 99% of the sources one encounters all say effectively the same thing, then there is a higher likelihood that what they say is an accurate representation.

But if you have the primary source available, you don't need to rely on second-hand descriptions. You can just look at what the primary source says. And if you're asking someone else for help with your understanding, you can ask based on the primary source directly, instead of relying on second-hand descriptions. Particularly if it's not clear from the second-hand descriptions exactly which statements or equations in the primary source are being referred to.

Also, even if what the secondary sources say is an accurate representation for them, that doesn't mean it will necessarily be understandable by you, if you don't refer back to the primary source--since that's what the secondary sources were basing their statements on.

the mathematics encodes assumptions and fact about the real world.

I already know all this. You don't need to explain it to me. You are spending a lot of time on generalities that I already know, and no time at all, yet, pointing me at places in the primary sources (Bell's original papers) that are difficult for you to follow, which is what will move this discussion forward.

We could always take Bell at face value and work on the assumption that he knows what he's talking about.

That doesn't help at all if we don't know what he's talking about--what particular statements in his original papers he is referring to. So the obvious thing to do is to go back and look at the original papers and see what assumptions are being made there, so we have a good basis for further discussion.

 

[Lynch101]

Then can you at least give specific references to specific statements Bell makes in the papers, or specific equations, that you're having trouble understanding? Or that you are trying to match up with statements by Bell from other papers that you referenced earlier in this discussion? At the very least, you should be able to pick out the places in Bell's papers where he appears to be making assumptions, so we can zero in on trying to clarify what those assumptions are. Doing that with the original papers directly seems to be a much better way of proceeding than trying to parse second-hand descriptions of what those papers say.
Hm, that clarifies how you were using the term, but it's very different from my understanding of the term "taking things at face value". To me, that term means you do simply believe that the statements are accurate without further checking; if you're doing further checking, you're not taking them at face value. My comments on doing that were based on that understanding of the term, so they don't apply if you are actually doing further checking.

However, there is still a potential issue with what further checking you do. See below.
But if you have the primary source available, you don't need to rely on second-hand descriptions. You can just look at what the primary source says. And if you're asking someone else for help with your understanding, you can ask based on the primary source directly, instead of relying on second-hand descriptions. Particularly if it's not clear from the second-hand descriptions exactly which statements or equations in the primary source are being referred to.

Also, even if what the secondary sources say is an accurate representation for them, that doesn't mean it will necessarily be understandable by you, if you don't refer back to the primary source--since that's what the secondary sources were basing their statements on.
I already know all this. You don't need to explain it to me. You are spending a lot of time on generalities that I already know, and no time at all, yet, pointing me at places in the primary sources (Bell's original papers) that are difficult for you to follow, which is what will move this discussion forward.
That doesn't help at all if we don't know what he's talking about--what particular statements in his original papers he is referring to. So the obvious thing to do is to go back and look at the original papers and see what assumptions are being made there, so we have a good basis for further discussion.

I take your points Peter. I think I'm coming at it from a different angle. I was hoping that someone who was familiar with the mathematics could show me where the assumptions are, what those assumptions are, and whether Bell's statements about the assumptions are accurate.

If I were to go through the paper, I would effectively end up just posting each line of math, line-by-line. I was hoping that someone might be be able to post the relevant equations and show what the assumptions are.

 

[PeterDonis]

If I were to go through the paper, I would effectively end up just posting each line of math, line-by-line. I was hoping that someone might be be able to post the relevant equations and show what the assumptions are.

If you aren't going to even read the paper, IMO this would be a pointless exercise. If you are going to read the paper, then feel free to post here after you have done so. Bell's papers are not very long and are pretty easy to read.

In other words, if you're not willing to put in even the minimal effort of reading the paper before discussing it, why should you expect someone else to spoon feed you the equations and assumptions?

 

[Lynch101]

If you aren't going to even read the paper, IMO this would be a pointless exercise. If you are going to read the paper, then feel free to post here after you have done so. Bell's papers are not very long and are pretty easy to read.

In other words, if you're not willing to put in even the minimal effort of reading the paper before discussing it, why should you expect someone else to spoon feed you the equations and assumptions?

I have read the paper but I can't interpret the mathematics. Should I just post all the mathematics from the paper?

 

[PeterDonis]

I have read the paper but I can't interpret the mathematics. Should I just post all the mathematics from the paper?

What math can you not interpret? A link to the paper you have read and a reference to which equations (AFAIK all of the key equations are numbered) would be a good start.

 

[Lynch101]

What math can you not interpret? A link to the paper you have read and a reference to which equations (AFAIK all of the key equations are numbered) would be a good start.

This is the paper I read (aside from others relating to it). There are 22 equations in it, but equations 1-3 are under the heading of "formulation", so perhaps the assumptions of the theorem are contained in those?

In the paper Bell states

The vital assumption [2] is that the result B for particle 2 does not depend on the setting $\vec a$ , of the magnet for particle 1, nor A on $\vec b$

.
Is that referring to the assumption of statistical independence [as it pertains to the theorem]?

Are there other assumptions in the equations, do you know?

 

[PeterDonis]

This is the paper I read

Ok, that's Bell's original paper.

equations 1-3 are under the heading of "formulation", so perhaps the assumptions of the theorem are contained in those?

Some are, but not all.

Is that referring to the assumption of statistical independence

Yes. That is also the assumption of locality.

 

[Lynch101]

Some are, but not all.

Do you know which assumptions are in those equations, by any chance? Other material pertaining to Bell's theorem, that I have come across, suggest that Bell's theorem makes 4 key assumptions:
- Locality
- Realism
- Local Realism
- Free Will

Are any of those assumptions contained in the first three equations, do you know?

Yes. That is also the assumption of locality.

Thanks Peter.

Some of the statements I have referenced above, including that of Bell himself, appear to suggest that human free will is a necessary assumption for that assumption of statistical independence. Would you say that those statements are incorrect?

 

[Lord Jestocost]

Is that referring to the assumption of statistical independence [as it pertains to the theorem]?

In their paper “Experimenter’s freedom in Bell’s theorem and quantum cryptography”, J. Kofler, T. Paterek and C. Brukner define ‘the experimenter’s freedom of choosing between different possible measurement settings in Bell-type experiments’ in an elegant way:

“Following Gill et al. [1] this freedom will be defined as the independence of the experimenter’s choice of measurement settings from the local realistic mechanism that determines the actual measurement results.”

You can convert this definition into a statistical independence assumption.

[1] R. D. Gill, G. Weihs, A. Zeilinger, and M. Zukowski,“Comment on ‘Exclusion of time in the theorem of Bell’ by K. Hess and W. Philipp” https://arxiv.org/abs/quant-ph/0204169

 

[PeterDonis]

Other material pertaining to Bell's theorem, that I have come across, suggest that Bell's theorem makes 4 key assumptions

These aren't four separate assumptions. "Local Realism" is just "Locality" plus "Realism", so it isn't a separate assumption. "Free Will" basically means "statistical independence", which, as I have said, is basically the same as locality.

Some sources also give "Counterfactual Definiteness" as an assumption (basically, that it makes sense to talk about results that would have occurred if some other measurement were made besides the one that was actually made).

Are any of those assumptions contained in the first three equations

Equation (2) contains, as I have said, the locality assumption (aka statistical independence).

Some of the statements I have referenced above, including that of Bell himself, appear to suggest that human free will is a necessary assumption for that assumption of statistical independence.

Unless someone can give a mathematical definition of "free will" that logically implies the mathematical definition of statistical independence (which, AFAIK, no one has done), such a statement does not seem to me to add any actual content to the argument.

 

[Lynch101]

These aren't four separate assumptions. "Local Realism" is just "Locality" plus "Realism", so it isn't a separate assumption. "Free Will" basically means "statistical independence", which, as I have said, is basically the same as locality.

Can they be tested separately, or do different interpretations treat them separately? I was thinking that Bohmian Mechanics was realistic but non-local (in the sense of action-at-a-distance)

Some sources also give "Counterfactual Definiteness" as an assumption

Thanks Peter, I've heard this before alright.

Equation (2) contains, as I have said, the locality assumption (aka statistical independence).

Unless someone can give a mathematical definition of "free will" that logically implies the mathematical definition of statistical independence (which, AFAIK, no one has done), such a statement does not seem to me to add any actual content to the argument.

Is the following, from Quantum Nonlocality and Reality: 50 Years of Bell's Theorem [edited] by Mary Bell & Shan Gao (p.242/243), accurate? I may be misinterpreting it, but I'm interpreting it as echoing some of the statements I've referenced previously.

I'm including the following so as to reference the mathematics (hopefully the Latex codes are correct), but it's the commentary which follows this that I'm wondering about.

Now, consider a setup such as the one envisaged by Bell. Two systems are prepared at some source and sent to distant locations A, B, where there is a choice of experiments to be formed. Let λ be a specification of local initial conditions at the source relevant to the outcomes. We assume that, for any choice a, b, of experiments at A and B, respectively, and any specification of relevant initial conditions λ, there is a probability distribution Pa,b(x, y|λ) over outcomes of the experiments. We also assume that there is a probability distribution over the initial conditions λ given by ρa,b(λ), such that:

$$P_{a,b}(x, y) = \int dλ ρ_{a,b}(λ) P_{a,b}(x, y|λ). (14.3)$$

Given $P_{a,b}(x, y|λ)$, we define marginals

$$P^A_{a,b}(x|λ) = \sum_y P_{a,b}(x, y|λ)$$,

$$P^B_{ a,b}(y|λ) = \sum_x P_{a,b}(x, y|λ). (14.4)$$

This statement seems to echo the previously referenced statements.

We assume that it is possible to arrange things so that whatever device it is that switches between alternative experiments can be rendered effectively independent of the distribution $ρ_{a,b}(λ)$ of relevant initial conditions – an assumption implicit in Bell’s original exposition and made explicit following Bell’s exchange with Shimony, Horne, and Clauser [15, 16]. The preparation of the systems and the switching events will, of course, have events in their common past, but we assume that these can be effectively screened off. This assumption may be called the “free will” assumption, as long as one remembers that it is so called with tongue in cheek; metaphysical issues concerning the free will of the experimenters are not at stake, but only the more prosaic assumption that it is possible to set up things so that there is effective independence of state preparation and experiments subsequently performed, an assumption so pervasive that it is difficult to see how we could engage in experimental science without it.4

I might be misinterpreting this, but this is my reading of the statement I have emboldened above (together with the other sources of information I have encountered); to me it reads as though without effectively screening off the events in their common past i.e. a common cause in each of their past light cones, then statistical independence is violated.

Obviously they go on to say that metaphysical issues concerning the free will of the experimenters are not at stake, instead we rely on the more prosaic assumption that it is possible to set things up in such a way that statistical independence is preserved. But this seems like a pretty big assumption, if common cause events in the past light cones would, usually, violate statistical independence.

Would this suggest that we need a special kind of event that is unlike all other events in the Universe, an event which is not correlated with events in its own past light cone? I might be wrong in thinking that we would actually need two such events, in the each past light cone, because a singular event correlated with events in its future light cone would still violate statistical independence. We would therefore need two of these "circuit breaker" events.Does that make sense?

 

[PeterDonis]

Can they be tested separately

Depends on how you define them.

do different interpretations treat them separately?

Different interpretations might define them differently, so you can't really compare them.

I was thinking that Bohmian Mechanics was realistic but non-local (in the sense of action-at-a-distance)

The Bohmian interpretation is realistic in the sense that quantum objects always have definite positions. It is non-local in the sense that the wave function changes instantaneously based on changes in particle positions arbitrarily far away.

From Bell's standpoint, the definite positions in Bohmian mechanics would be hidden variables, but they violate Bell's locality assumption (equation 2 in the paper you linked to), which is how Bohmian mechanics can make the same predictions for experimental results as standard QM.

 

[PeterDonis]

to me it reads as though without effectively screening off the events in their common past i.e. a common cause in each of their past light cones, then statistical independence is violated.

Only if you interpret "screening off" very carefully.

Look at Bell's equation 2 again. That is the statistical independence assumption. Any common cause in the past light cones would be included in the hidden variables $\lambda$, and $\lambda$ isn't "screened off"; it's right there in the equation, and all three functions in the integrand on the RHS of the equation are allowed to depend on $\lambda$. Statistical independence means that $A$ in that equation is only a function of $\vec{a}$ and $\lambda$, not $\vec{b}$, and $B$ in that equation is only a function of $\vec{b}$ and $\lambda$, not $\vec{a}$.

What "screening off" means is that the settings $\vec{a}$ and $\vec{b}$ are not functions of $\lambda$. That is not explicitly stated by Bell, but it's implicit in the way the integral is written: $\lambda$ is integrated over to obtain a function of $\vec{a}$ and $\vec{b}$. That requires, mathematically, that $\vec{a}$ and $\vec{b}$ are not themselves functions of $\lambda$.

The way you would accomplish this in an actual experiment is simply to isolate whatever is determining the measurement settings from whatever is producing the thing to be measured. This is not something that is limited to quantum physics; experimenters in physics have been doing this for as long as there has been physics. It's an obvious precaution to take to ensure that you are measuring what you think you are measuring and not some extraneous influence.

Would this suggest that we need a special kind of event that is unlike all other events in the Universe, an event which is not correlated with events in its own past light cone?

Not at all. See above.

 

[Lynch101]

Depends on how you define them.

Different interpretations might define them differently, so you can't really compare them.

The Bohmian interpretation is realistic in the sense that quantum objects always have definite positions. It is non-local in the sense that the wave function changes instantaneously based on changes in particle positions arbitrarily far away.

From Bell's standpoint, the definite positions in Bohmian mechanics would be hidden variables, but they violate Bell's locality assumption (equation 2 in the paper you linked to), which is how Bohmian mechanics can make the same predictions for experimental results as standard QM.

Thanks for those explanations Peter.

 

[Lynch101]

Only if you interpret "screening off" very carefully.

Look at Bell's equation 2 again. That is the statistical independence assumption. Any common cause in the past light cones would be included in the hidden variables $\lambda$, and $\lambda$ isn't "screened off"; it's right there in the equation, and all three functions in the integrand on the RHS of the equation are allowed to depend on $\lambda$. Statistical independence means that $A$ in that equation is only a function of $\vec{a}$ and $\lambda$, not $\vec{b}$, and $B$ in that equation is only a function of $\vec{b}$ and $\lambda$, not $\vec{a}$.

[From the referenced sources] is the point not that the common cause isn't included in $\lambda$ because we assume that [common causes in the past light cone] can be effectively screened off ?

What "screening off" means is that the settings $\vec{a}$ and $\vec{b}$ are not functions of $\lambda$. That is not explicitly stated by Bell, but it's implicit in the way the integral is written: $\lambda$ is integrated over to obtain a function of $\vec{a}$ and $\vec{b}$. That requires, mathematically, that $\vec{a}$ and $\vec{b}$ are not themselves functions of $\lambda$.

Apologies, what do we mean here by the settings are not functions of $\lambda$? I've never been fully sure about what that phrasing means, when I've read it. Does it mean that the settings are not affected/determined by $\lambda$ i.e. the hidden variables?

The way you would accomplish this in an actual experiment is simply to isolate whatever is determining the measurement settings from whatever is producing the thing to be measured. This is not something that is limited to quantum physics; experimenters in physics have been doing this for as long as there has been physics. It's an obvious precaution to take to ensure that you are measuring what you think you are measuring and not some extraneous influence.

My reading of the statement from Bell & Gao above is, a common cause in the past light cone would explain the observed correlations. Isolating the two [relevant[ events doesn't "screen off" the common cause in the past light cone because - this is how it reads to me - we assume that common cause is screened off, somehow. This assumption so pervasive that it is difficult to see how we could engage in experimental science without it .

Isolating the two events wouldn't screen them off from the common cause in their past light cones, would it? Would it not just mean that the common cause is located further into the past light cone of each event?

The references by Bell et. al to "free will" would make sense in this context, because free will is possibly the only phenomenon we can conceptualise that isn't correlated with events in the past light cone. Invoking free will would therefore, "screen off" the common cause in the past light cones of the two relevant events.

If that makes sense?

 

[PeterDonis]

[From the referenced sources] is the point not that the common cause isn't included in $\lambda$ because we assume that [common causes in the past light cone] can be effectively screened off ?

Whatever common causes there are that apply to the systems being measured are included in $\lambda$. These would include things like the common preparation process that produced both of the entangled particles being measured. These can't possibly be "screened off" because that would mean not measuring the particles at all.

There should not be any common causes of the measurement settings. That's why those are independent of $\lambda$. The way you ensure that is to "screen off" whatever determines the measurement settings from whatever process produces the particles being measured (not to mention those particles themselves).

what do we mean here by the settings are not functions of $\lambda$? I've never been fully sure about what that phrasing means, when I've read it. Does it mean that the settings are not affected/determined by $\lambda$ i.e. the hidden variables?

Yes. See above.

 

[Lynch101]

Whatever common causes there are that apply to the systems being measured are included in $\lambda$. These would include things like the common preparation process that produced both of the entangled particles being measured. These can't possibly be "screened off" because that would mean not measuring the particles at all.

Sorry, I might be confusing the issue here by not being clear in my own mind about what $\lambda$ encapsulates. I'm assuming it means everything in the past light cone of the systems being measured, stretching back past the common preparation method, right through the formation of the planet, the galaxy, and so on back the line, unbroken.

There should not be any common causes of the measurement settings. That's why those are independent of $\lambda$. The way you ensure that is to "screen off" whatever determines the measurement settings from whatever process produces the particles being measured (not to mention those particles themselves).

I think this is the point I am trying to get at. I may have been causing confusion with my imprecise use of $\lambda$.

My interpretation of the referenced statements is that there is no real way to ensure that the two processes are truly screened; that is, there is no real way to ensure that the process' which determines the measurement settings. and the process that produces the particles, are both screened off from the inevitable common cause that lies in the intersection of the past light cones [of the two processes]. The referenced statements seem to suggest that this "screening off" is a pervasive assumption. The suggestion appears to be that this screening off is justified on the basis of invoking free will.

 

[PeterDonis]

I might be confusing the issue here by not being clear in my own mind about what $\lambda$ encapsulates.

What does Bell say it encapsulates in his paper? You should be reading that, not making assumptions on your own.