I Understanding Bell's Statements on Freedom of Choice

[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.

 

[Lynch101]

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

I don't believe I am making assumptions on my own, though. I am drawing, or trying to draw, conclusions from the different sources I've referenced, as well as from your statements here. Those conclusions may not be accurate, but I'm not yet clear as to why they are, or even if they are.

With regard to what Bell says in his paper, the statement from Bell & Gao above suggests that there is an implicit assumption about screening off which is made explicit in his exchange with Shimony, Horne, and Clauser.

Thinking about the point I'm trying to get at, I'm tending toward greater clarity in my own thinking, which will hopefully translate here. I'll try and set out my thinking in numbered points. If there is an issue somewhere it might be easier to identify and home in on.

I hope my use of the terminology is correct here.

1. The preparation of the particles is a function of $\lambda$.
2. $\lambda$ itself is a function of everything in its past light cone.
3. Therefore, the preparation of the particles are a function of everything in their own past light cone (including the past light cone of $\lambda$).
4. The measurement settings are not a function of $\lambda$.
5. The measurement settings are a function of everything in their past light cone.
6. If we go far enough back into the past, the light cones of the measurement settings and the preparation process (including $\lambda$) intersect with a common cause.
7. This common cause would explain the observed correlations.
8. Therefore, either the measurement settings or the preparation process needs to be screened off from this common cause i.e. the chain of causality needs to be interrupted somehow.
9. Usually, this is simply assumed i.e. it is the assumption so pervasive that it is difficult to see how we could engage in experimental science without it.
10. Isolating the mechanism for choosing the measurement settings from the preparation process doesn't screen either off from the common cause in their past light cone - it means, perhaps, that the common cause event is located further in the past light cones.
11. Without some kind of "circuit breaker" event, to interrupt the chain of causality, the assumption of statistical independence appears to be unjustified.
12. The free will of the experimenters is invoked to justify the assumption, because "free will" is the only conceptual idea we have that necessitates non-correlation with events in the past light cone.

Hopefully this clarifies my thinking and makes it easier to identify where the breakdown is. I really hope my use of certain terminology is correct here.

 

[PeterDonis]

I don't believe I am making assumptions on my own, though.

When you say...

I'm assuming it means everything in the past light cone of the systems being measured

...you're assuming something on your own. The words "I'm assuming" are right there. Instead you should be reading Bell's paper to say what he says $\lambda$ means. Until you have done that I don't see the point of trying to critique what you are saying, since what you are saying is uninformed.

 

[Lynch101]

When you say...
...you're assuming something on your own. The words "I'm assuming" are right there. Instead you should be reading Bell's paper to say what he says $\lambda$ means. Until you have done that I don't see the point of trying to critique what you are saying, since what you are saying is uninformed.

Peter, I appreciate your patience in answering my posts, and I understand that patience is wearing thin, so I'll try to narrow down my questions. I'm not trying to assume these, I'm wondering if the understanding I have arrived at i.e. my deduction/conclusion is correct. I haven't arrived at this conclusion on my own, I've arrived at it from reading multiple sources, some of which I have referenced here, including Bell's own subsequent statements made to CHS (quoted above); as well as from discussions I've had here (including with yourself) and elsewhere. I've sought out these multiple sources precisely to inform myself. I have tried to lay out the conclusions I have arrived at in the hope that someone might be able to either confirm that they are correct, or - as is more often the case - point out where I have gone wrong.

In the original paper Bell says

The result A of measuring $\vec \sigma_1•\vec a$ is then determined by $\vec a$ and $\lambda$, and the result B of measuring $\vec \sigma_2•\vec b$ in the same instance is determined by $\vec b$ and $\lambda$.

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 $\vec b$.

Are the following deductions (not assumptions) accurate?

1. The preparation of the particles is a function of λ.
2. $\lambda$ is a function of everything in its past light cone.
3. The measurement settings are a function of everything in their past light cone.

If I am making a mistake, I think it is probably in one of the three of these (if not all three). I would genuinely appreciate your help in identifying where I am going wrong, or else confirming that I have understood the multiple sources I have encountered.

 

[PeterDonis]

In the original paper Bell says

Ok, good, now you're asking about what Bell actually said.

1. The preparation of the particles is a function of λ.
2. λ is a function of everything in its past light cone.
3. The measurement settings are a function of everything in their past light cone.

1: I wouldn't put it that way; I would put it that λ must include whatever information about the preparation of the particles is necessary to determine the results of the measurements.

2: λ isn't a function of anything. It's whatever information about the preparation of the particles is necessary to determine the results of the measurements. Bell makes no claim whatever about what, in the past light cone of the preparation, is necessary to produce that information.

That said, there is a much simpler observation that might help you here: the past light cone of the preparation event is not the same as the past light cone of either of the measurement events. Both measurement events have portions of their past light cones that are not in the past light cone of the preparation event. So λ cannot possibly include any information that is in the past light cones of either of the measurement events, but is not in the past light cone of the preparation event.

3. Bell does not claim this either. The only thing Bell assumes is that the measurement settings are statistically independent of λ. Given the observation just above about the light cones, there is nothing physically impossible about such statistical independence.

 

[Lynch101]

Ok, good, now you're asking about what Bell actually said.

Apologies, if I was straying away from that. Again, thanks for your patience; this reply has made things clearer for me.

Would Bell's paper, The Theory of Local Beables, be relevant to this question as well? I'm not quite sure how to catagorise the relationship of the two papers, but they're about the same general topic, aren't they?

1: I wouldn't put it that way; I would put it that λ must include whatever information about the preparation of the particles is necessary to determine the results of the measurements.

2: λ isn't a function of anything. It's whatever information about the preparation of the particles is necessary to determine the results of the measurements. Bell makes no claim whatever about what, in the past light cone of the preparation, is necessary to produce that information.

I'll try and take more baby steps this time. That way it might be easier to pinpoint where I'm lacking the key information.

I might have the wrong kind of picture in my head, but I'm thinking in terms of a chain of events, leading up to the preparation of the particles. For simplicity sake, I'm going to assume $\lambda$ is a single piece of information here.

I'm thinking that, at the preparation process, $\lambda$ itself would be the result of a causal chain, where everything in the past light cone of $\lambda$ would be necessary information to determine the results of the measurements.

In my mind, I'm making a distinction here between the past light cone of the measurement process and the past light cone of $\lambda$, where the past light cone of $\lambda$ would be a subset of the past light cone of the measurement process. Or are they one and the same thing?

Initially I was thinking that the past light cone of the preparation process and that of $\lambda$ would be the exact same, but I'm trying to focus in on $\lambda$, so I made the distinction, just in case. Is that possible?

That said, there is a much simpler observation that might help you here: the past light cone of the preparation event is not the same as the past light cone of either of the measurement events. Both measurement events have portions of their past light cones that are not in the past light cone of the preparation event. So λ cannot possibly include any information that is in the past light cones of either of the measurement events, but is not in the past light cone of the preparation event.

Would this be a graphical representation of that point, where $\lambda$ is represented by N?

3. Bell does not claim this either. The only thing Bell assumes is that the measurement settings are statistically independent of λ. Given the observation just above about the light cones, there is nothing physically impossible about such statistical independence.

This is my sticking point. That might be down to how I am thinking about it though.

As I mentioned above, I'm thinking of $\lambda$ in terms of a causal chain of events, where everything in the past light cone of $\lambda$ is information necessary to determine the measurement results. My interpretation of the different sources that I've read is that, if we look into the past light cone of $\lambda$ we will eventually arrive at a "common cause" event which would violate that statistical independence.

 

[PeterDonis]

Would Bell's paper, The Theory of Local Beables, be relevant to this question as well?

It's been a while since I read that paper, but as I remember it, it was more about the basic ontology of the theory and didn't really go into the freedom of choice aspect.

 

[PeterDonis]

I'm thinking in terms of a chain of events, leading up to the preparation of the particles.

There's no requirement to think of it that way. Bell's model is perfectly consistent with the preparation being just a single event. Adding a chain of events before it doesn't add anything significant to the model.

I'm making a distinction here between the past light cone of the measurement process and the past light cone of $\lambda$, where the past light cone of $\lambda$ would be a subset of the past light cone of the measurement process.

There are two measurement processes, not one: we are making spacelike separated measurements on two entangled particles.

For each of the measurement events, yes, the past light cone of the preparation event is a subset of the past light cone of the measurement event. That is true for any pair of events that are timelike or null separated: one of them will be in the causal past of the other, and the past light cone of the one in the past will be a subset of the past light cone of the one in the future.

Would this be a graphical representation of that point, where $\lambda$ is represented by N?

In that diagram, "information" is being assigned to regions of light cones, rather than to single events. The relationship between the three regions $\Lambda$, $M$, and $N$ is more or less the same as the relationship in the model we have been discussing up to now between the information at one measurement event, the other measurement event, and the preparation event.

My interpretation of the different sources that I've read is that, if we look into the past light cone of $\lambda$ we will eventually arrive at a "common cause" event which would violate that statistical independence.

No. As above, the past light cone of $\lambda$ is only a subset of the past light cones of the two measurement events. So it's perfectly possible for the settings of the measurements to be determined by data that is outside the past light cone of $\lambda$, but still within the past light cone of the appropriate measurement event. And if that is the case, you will have statistical independence.

In the diagram you showed, the measurement settings at $A$ would be determined by data that is in $\Lambda$ but not in $N$, and the measurement settings at $B$ would be determined by data that is in $M$ but not in $N$.

 

[Lynch101]

It's been a while since I read that paper, but as I remember it, it was more about the basic ontology of the theory and didn't really go into the freedom of choice aspect.

Ah yes, thanks. I wasn't sure how to categorise it.

Are you familiar with the exchange between Clauser, Horne, & Shimony Bell subsequent to The Theory of Local Beables? I they were published in Epistemological Letters.

I had a quick look for the CHS paper but I kept running into paywalls. The book I mentioned in the OP, John S. Bell on the Foundations of Quantum Mechanics (by Bell, Gottfried, and Veltman) includes The Theory of Local Beables paper and Bell's response to CHS. The statement I referenced previously is from that response.The following might give a bit more context to where my thinking is coming from.

My deduction, from reading of Bell's response, is that CHS "accuse" Bell of assuming the free will of the experimenter.

From section 8 of The Theory of Local Beables

It has been assumed that the settings of the instruments are in some sense free variables - say at the whim of the experimenters - or in any case not determined in the overlap of the backward light cones.

Am I correct in saying that the part I have emboldened is the same point you are making?

In the subsequent exchange with CHS from Epistemological Letters, Bell clarifies what he means by "at the whim of experimenters"

"... say at the whim of experimenters...>>
Here I would entertain the hypothesis that experimenters have free will. But, according to CHS, it would not be permissible for me to justify the assumption of free variables "by relying on a metaphysics which has not been proved and which may well be false". Disgrace indeed, to be caught in a metaphysical position! But it seems to me that, in this matter, I am just pursuing my profession of theoretical physics.

Bell is much more explicit here about the invocation of free will. The bit I have emboldened seems to echo the sentiment of [Mary] Bell & Gao, with regard to the pervasive assumption.As I mentioned, hopefully that gives a bit more context with regard to where my thinking is coming from.

 

[Lynch101]

No. As above, the past light cone of $\lambda$ is only a subset of the past light cones of the two measurement events. So it's perfectly possible for the settings of the measurements to be determined by data that is outside the past light cone of $\lambda$, but still within the past light cone of the appropriate measurement event. And if that is the case, you will have statistical independence.

In the diagram you showed, the measurement settings at $A$ would be determined by data that is in $\Lambda$ but not in $N$, and the measurement settings at $B$ would be determined by data that is in $M$ but not in $N$.

Thank you Peter! This has clarified a lot for me.

Am I right in saying that experiments which use distant starlight as the means of choosing the measurement settings, attempt to ensure that those settings are determined by data outside the past light cone of $\lambda$? Is this how we attempt to screen off common cause events, in the past light cones?

There's no requirement to think of it that way. Bell's model is perfectly consistent with the preparation being just a single event. Adding a chain of events before it doesn't add anything significant to the model.

My thinking is that every event is itself the result of a chain of events.

I'm thinking in terms of a pretty simplistic example, say potting a ball in pool/snooker. If we imagine the ball going into the pocket, this would have been caused by the cue ball striking the object ball and sending it in the direction of the pocket. The action of the cue ball was caused by the stick striking it. The connection of the stick with the cue ball is caused by the amount of chalk on the tip if the cue, together with the power and angle of the cuing action. There would be an uncountable number of events, back along the chain of causality, that lead to the pool ball going in the pocket, all of which would be information necessary to determine the measurement outcome - the pool ball going in the pocket, in this case.

 

[PeterDonis]

Are you familiar with the exchange between Clauser, Horne, & Shimony Bell subsequent to The Theory of Local Beables? I they were published in Epistemological Letters.

I haven't seen this exchange, no.

Am I correct in saying that the part I have emboldened is the same point you are making?

Yes.

Am I right in saying that experiments which use distant starlight as the means of choosing the measurement settings, attempt to ensure that those settings are determined by data outside the past light cone of $\lambda$?

This is one way of trying to do that, yes.

There would be an uncountable number of events, back along the chain of causality, that lead to the pool ball going in the pocket, all of which would be information necessary to determine the measurement outcome

No, you wouldn't have to know all of them. If you knew, for example, exactly how the cue ball hit the pool ball, the rest of the stuff before that wouldn't matter; knowing how the cue ball strikes the pool ball is sufficient to predict the pool ball's trajectory.

Strictly speaking, a physical theory could be deterministic without allowing this kind of thing: there could be a deterministic theory in which, for example, just knowing how the cue ball struck the pool ball wouldn't be enough to predict the pool ball's trajectory; where you would actually have to know every single event in the past light cone of the pool ball going into the pocket in order to predict that that would happen, instead of just a manageably small subset of those events (the cue ball striking the pool ball). But none of our actual physical theories seem to be like that; they all seem to allow us to make useful predictions about particular events while knowing only a miniscule fraction of everything that happened in the past light cone of those events.

 

[Lord Jestocost]

Bell is much more explicit here about the invocation of free will.

In „An Exchange on Local Beables“ by J. S. Bell, A. Shimony, M. A. Horne and J. F. Clauser (Dialectica Vol. 39, No. 2 (1985), pp. 85-110), Shimony, Horne and Clauser beat, to my mind, a little bit about the bush when writing;

“After all, the backward light cones of those two acts do eventually overlap, and one can imagine one region which controls the decision of the two experimenters who chose a and b. We cannot deny such a possibility. But we feel that it is wrong on methodological grounds to worry seriously about it if no specific causal linkage is proposed. 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 hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation.”

They merely try to avoid invoking the “free will” assumption as this would mean “relying upon a metaphysics“.

As Shimony puts it: „We will call the assumption that experimental settings may be regarded as “effectively free for the purpose at hand” and treated as statistically independent of the variable λ, the assumption of measurement independence.“
in https://plato.stanford.edu/entries/bell-theorem/

 

[PeterDonis]

They merely try to avoid invoking the “free will” assumption as this would mean “relying upon a metaphysics“.

I don't see them making that kind of argument in what you quoted. What I see is them making an obvious common sense argument that, if we can't assume that we can isolate an experiment sufficiently from unknown causal factors ("hidden conspiracies") to treat the measurement settings as statistically independent from the preparation of the system being measured, we can't do science.

The comment quoted earlier about "relying upon a metaphysics" was, I think, more about the specific term "free will" than about any dispute regarding what is said in the previous paragraph (which I think Bell would have agreed with).

 

[Lynch101]

This is one way of trying to do that, yes.

Are you familiar with some of the other ways?

No, you wouldn't have to know all of them. If you knew, for example, exactly how the cue ball hit the pool ball, the rest of the stuff before that wouldn't matter; knowing how the cue ball strikes the pool ball is sufficient to predict the pool ball's trajectory.

I'm thinking that it wouldn't be a case that we would have to know every single event in the chain of events that $\lambda$ encapsulates. Is that one of the characteristics of $\lambda$, that we don't necessarily know what that single event is, even?

My thinking is that $\lambda$ contains this information. So, while it would be sufficient for us to know only how the cue ball strikes the object ball, say direction, momentum, and spin. The direction, momentum, and spin would be a function(?) of the chain of events that preceded it. A chain of falling dominoes might give a more intuitive picture of how far the chain of causality can stretch.

My interpretation of what the likes of [Mary] Bell & Gao, CHS (as per @Lord Jestocost 's post), and others, is that the backward light cones of those two acts do eventually overlap and so there will inevitably be a common cause. The suggestion seems to be that this common cause would explain the correlations we observe in quantum experiments i.e. the violations of Bell's inequality.

 

[Lynch101]

In „An Exchange on Local Beables“ by J. S. Bell, A. Shimony, M. A. Horne and J. F. Clauser (Dialectica Vol. 39, No. 2 (1985), pp. 85-110), Shimony, Horne and Clauser beat, to my mind, a little bit about the bush when writing;

“After all, the backward light cones of those two acts do eventually overlap, and one can imagine one region which controls the decision of the two experimenters who chose a and b. We cannot deny such a possibility.
...
Unless we proceed under the assumption that hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation.

I may be misinterpreting this, but they appear to say "we cannot deny such a possibility...but we have to deny such a possibility"

But we feel that it is wrong on methodological grounds to worry seriously about it if no specific causal linkage is proposed.

Does every notion of cause & effect, be it deterministic or stochastic, not propose such a causal linkage?

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.

”

The thought that occurs to me reading this, and again I may be misinterpreting it, is that the very notion of cause & effect is what leads us to conjecture that some factor in the overlap of the backward light cones has controlled the presumably random choices.

Alternatively - again, this is my possibly naiive understanding - if we conjecture that there is not some factor in the backward light cones, which controlled the presumably random choices, then this has direct implications for the notion of cause and effect, where effects are not necessarily determined by their causes.

They merely try to avoid invoking the “free will” assumption as this would mean “relying upon a metaphysics“.

As Shimony puts it: „We will call the assumption that experimental settings may be regarded as “effectively free for the purpose at hand” and treated as statistically independent of the variable λ, the assumption of measurement independence.“
in https://plato.stanford.edu/entries/bell-theorem/

The different sources I've read, including Bell's own response to CHS, seems to suggest that free will is a necessary assumption. If we try to avoid invoking the metaphysics of "free will", would we not have to invoke a special type of event which has no prior cause?

 

[Lord Jestocost]

I don't see them making that kind of argument in what you quoted.

In „An Exchange on Local Beables“ by J. S. Bell, A. Shimony, M. A. Horne and J. F. Clauser (Dialectica Vol. 39, No. 2 (1985), pp. 85-110), Shimony, Horne and Clauser remark (page 99):

„It seems to us that (iii) could be made reasonable only if the settings of a and b are the results of some spontaneous events, such as acts of free will of the experimenters. (As Bell may have assumed tacitly in his derivation of (16) and explicitly in Sect. 8). This is a logical and metaphysical possibility, which we do not intend to exclude a priori. But since Bell’s argument is intended to be general, it would not be legitimate for him to justify the assertion (iii) by relying upon a metaphysics which has not been proved and which may well be false³.“

 

[Lord Jestocost]

I may be misinterpreting this, but they appear to say "we cannot deny such a possibility...but we have to deny such a possibility"

Take it as a FAPP statement.

 

[Lynch101]

Take it as a FAPP statement.

I'm not familiar with the acronym. Google is throwing up something about applied force, but I'm guessing it is something different. Fundamental Assumption...??

 

[Lord Jestocost]

I'm not familiar with the acronym. Google is throwing up something about applied force, but I'm guessing it is something different. Fundamental Assumption...??

For All Practical Purposes (FAPP)

 

[Lynch101]

For All Practical Purposes (FAPP)

Thank you. I just did a bit more searching and found it in a paper by Bell

If we do take it as a FAPP statement, we can still explore certain of its implications right?

Am I right in saying that, if we don't want to rely on the metaphysics of "free will" then we would need to invoke a special type of event that performs the same function as "free will"?

 

[Lord Jestocost]

Am I right in saying that, if we don't want to rely on the metaphysics of "free will" then we would need to invoke a special type of event that performs the same function as "free will"?

Whatever you are looking for, one cannot - to my mind - escape from Hans Primas' dictum (in „Hidden Determinism, Probability, and Time’s Arrow“ ):

"At present the problem of how free will relates to physics seems to be intractable since no known physical theory deals with consciousness or free will. Fortunately, the topic at issue here is a much simpler one. It is neither our experience of personal freedom, nor the question whether the idea of freedom could be an illusion, nor whether we are responsible for our actions. The topic here is that the framework of experimental science requires a freedom of action in the material world as a constitutive presupposition. In this way 'freedom' refers to actions in a material domain which are not governed by deterministic first principles of physics." [Italics in original, bold by LJ]