Understanding Bell's Statements on Freedom of Choice

[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]

 

[Lynch101]

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

I will add this to my reading list, thank you.

"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]

I'm not sure if I'm interpreting this correctly. Is it saying that the framework of experimental science requires "free will" per se, or just some class of action/event that is not governed by a fundamental determinism?

 

[PeterDonis]

Are you familiar with some of the other ways?

Anything that isolates the measurement device from the preparation device. There are lots of ways of doing that.

I'm thinking...

I don't understand what's so hard to grasp about Bell's definition of $\lambda$. I think you're making this much, much harder than it needs to be.

the backward light cones of those two acts do eventually overlap

The backward light cones of any two events overlap if you go far enough back in time.

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.

No. That's the whole point of Bell's theorem; you can't violate the Bell inequalities with a model that tries to explain all of the correlations with a common cause contained in $\lambda$ if $\lambda$ is limited to the information in the overlap of the past light cones of both measurement events.

 

[Lynch101]

Anything that isolates the measurement device from the preparation device. There are lots of ways of doing that.

Ah cool. I was just wondering because I think I've only heard of the distant starlight example.

I don't understand what's so hard to grasp about Bell's definition of $\lambda$. I think you're making this much, much harder than it needs to be.

I probably am. I might be misinterpreting some of the statements I have read, because of an assumption I am making. It might be worth saying that I understand your explanation about the measurement settings being determined by information outside the overlap of the backward light cones, and how that would give us statistical independence.

My issue might be the references to free will that I have read, as per the statements made by Bell et al. I think I spotted something in the statement by CHS that Lord Jestocost posted that I wasn't fully processing previously. It is related to your next comments below.

The backward light cones of any two events overlap if you go far enough back in time.
...
No. That's the whole point of Bell's theorem; you can't violate the Bell inequalities with a model that tries to explain all of the correlations with a common cause contained in $\lambda$ if $\lambda$ is limited to the information in the overlap of the past light cones of both measurement events.

From the CHS comment:

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.

My reading of this is that it is possible that there is a region or event, in the overlap of the past light cones, which controls the decision of the two experimenters.

I had been interpreting this (and statements like it) to mean that the violations of Bell's inequality could be explained by such an event. But, I'm wondering now, is this where the assumption of free will comes in? Is free will needed in this case to maintain statistical independence?

Does using distant starlight, or the other means, seek to close the free will loophole, by choosing an event which has a much higher probability that the information comes from outside the overlap of the backwards light cones?

 

[PeterDonis]

My reading of this is that it is possible that there is a region or event, in the overlap of the past light cones, which controls the decision of the two experimenters.

If one insists on perfect certainty that no event in the overlap of the past light cones has somehow influenced the measurement settings, of course one can never have it: the overlap of the past light cones exists and we don't have perfect knowledge of all events. But one can easily set up conditions which make it so improbable that any such influence exists that it isn't worth worrying about. Experimental physicists do things like that all the time. Taking extra precautions like using distant starlight is just a way of lowering the probability of any such influence even further, to try to satisfy extreme skeptics who keep harping on the possibility to a point where, IMO, they are being unreasonable.

I had been interpreting this (and statements like it) to mean that the violations of Bell's inequality could be explained by such an event.

It's not enough just to have an event in the overlap of the past light cones "influencing" the measurement settings. Such an event would have to have precise control over the measurement settings and the properties of the particles being measured, precise enough to induce correlations that violated the Bell inequalities. This is what the term "superdeterminism" refers to.

In terms of Bell's theorem, superdeterminism violates his assumption of statistical independence between the measurement settings and the properties of the particles being measured. We have already discussed where that assumption appears in the math of his paper.

 

[Lynch101]

If one insists on perfect certainty that no event in the overlap of the past light cones has somehow influenced the measurement settings, of course one can never have it: the overlap of the past light cones exists and we don't have perfect knowledge of all events. But one can easily set up conditions which make it so improbable that any such influence exists that it isn't worth worrying about. Experimental physicists do things like that all the time. Taking extra precautions like using distant starlight is just a way of lowering the probability of any such influence even further, to try to satisfy extreme skeptics who keep harping on the possibility to a point where, IMO, they are being unreasonable.

Thanks PD, that is where I was misinterpreting the statements I had come across. I was reading them to mean that, if we go far enough back in the past light cones of the relevant event, there would eventually be a common cause event which does account for the observed correlations. It sounded to me like there was an inevitability about it, and free will had to be invoked to circumvent that.

My understanding of what you are saying now, however, is that experimenters take measures to negate the likelihood that the measurement settings are determined by an event in the overlap of the past light cones. The visual aid and your explanation were very helpful in that regard, so thank you again.

I still have a lingering question, but I suspect that is down to a preconceived idea of the phenomena in question. It's more directly related to your next point.

It's not enough just to have an event in the overlap of the past light cones "influencing" the measurement settings. Such an event would have to have precise control over the measurement settings and the properties of the particles being measured, precise enough to induce correlations that violated the Bell inequalities. This is what the term "superdeterminism" refers to.

Is there a reason why the big bang would not be such an event?

This is related to something I have mentioned before, about thinking that superdeterminsim is just determinism taken to its logical consequences. I suspect, however, that this question is partly based on my preconceived idea about the Big Bang itself and possibly also a preconceived notion of determinism.

It might be worth stating that I am not a proponent of superdeterminism and I have read some explanations of the conspiracies it would involve. I just haven't yet been able to make the distinction, in my own mind, between it and regular determinism.

My understanding of determinism is that effects are uniquely determined by their causes i.e. there is only one possible outcome from a given set of conditions. My reasoning is that, if we apply determinism to the Big Bang, then all subsequent events, including the measurement settings, were precisely controlled by the Big Bang, which would be that inescapable common cause event in the past light cones.

That may be my misinterpretation of either the Big Bang or determinism, or both.

 

[PeterDonis]

Is there a reason why the big bang would not be such an event?

The Big Bang was not a single event. The technical details are beyond the scope of this thread.

 

[Lynch101]

The Big Bang was not a single event. The technical details are beyond the scope of this thread.

That's cool. I was thinking that it was probably down to a preconception I had of it.

Thank you for your patience and considered responses. This is much clearer in my mind now.

 

[PeterDonis]

Thank you for your patience and considered responses.

You're welcome!