Understanding Bell's Statements on Freedom of Choice

[Lynch101]

TL;DR

I'm looking to get a better understanding of some statements made by John Bell on the freedom of choice of experimenters.

I recently saw this video by Sabine Hossenfelder on free will, which prompted me to re-watch and re-read a few different resources. One of those resources is a book called John S. Bell on the Foundations of Quantum Mechanics (by Bell, Gottfried, and Veltman).

An Exchange on Local Beables - J.S. Bell - Free Variables and Local Causality (p.103)

Roughly speaking it is supposed that an experimenter is quite free to choose among the various possibilities offered by his equipment. But it might be that this apparent freedom is illusory. Perhaps experimental parameters and experimental results are both consequences, or partially so, of some common hidden mechanism. Then the apparent non-locality could be simulated.

Is he referring here to what some people refer to as "superdeterminism"? Is that what is meant by "the apparent non-locality could be simulated?

"It has ben assumed that the settings of instruments are in some sense free variables..."
For me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about, what has gone before.

Does this mean that the experimenters choice is only free when that choice is correlated to events in its (the choices) causal future and not its causal past; meaning, no information from the experimenter's own past light cone and accessible to the experimenter at the moment the choice is made, can be assumed to have a causal influence on the choice in question?

 

[PeterDonis]

Is he referring here to what some people refer to as "superdeterminism"?

Yes.

Is that what is meant by "the apparent non-locality could be simulated?

Yes.

no information from the experimenter's own past light cone and accessible to the experimenter at the moment the choice is made, can be assumed to have a causal influence on the choice in question?

No; that condition is obviously too strong. Taken literally, it would mean that, for example, the experimenter's choice of instrument settings must not convey any information about what the experimenter told his lab assistant about how he was going to set up the measurement settings, five minutes before he set them up. Which is obviously not going to be the case in any experiment that involves more than one person.

The actual requirement, if we assume that we want to eliminate superdeterminism as a possibility, is only that the measurement settings and the preparations of the objects to be measured, before measurement, are independent of each other. If we want to make extra sure of that, we set things up so that the preparations of the objects to be measured, and the selection of the measurement settings, occur at spacelike separated events, as, for example, in the Aspect experiments. And if we want to double check afterwards, we simply do statistical analysis of the distribution of measurement settings vs. the distribution of preparations, to ensure that they are independent.

(Technically, the above doesn't logically eliminate superdeterminism as a possibility; it's impossible to eliminate it logically since one can always hypothesize some particular superdeterministic model with some carefully chosen set of initial conditions that would produce the same results. But it makes superdeterminism seem a lot more implausible.)

 

[Lynch101]

Thanks @PeterDonis.

...the measurement settings and the preparations of the objects to be measured, before measurement, are independent of each other.

Ah, this is what is meant by "statistical independence", is it?

"It has ben assumed that the settings of instruments are in some sense free variables..."
For me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about, what has gone before.

Just on the emboldened part. This isn't true for all events is it, that they are in no sense a record of, nor give information about, what has gone before?

 

[PeterDonis]

this is what is meant by "statistical independence", is it?

In this particular context, yes.

Just on the emboldened part. This isn't true for all events is it

It's not really true of any events, taken literally. Every event gives some information about something that has gone before.

I think that, in context, Bell meant something more limited, along the lines I suggested in my previous post. But of course I can't know for sure, and unfortunately Bell is no longer around to be asked for clarification.

 

[Lynch101]

It's not really true of any events, taken literally. Every event gives some information about something that has gone before.

OK, cool. That's what I was thinking. I was wondering how it would be possible to have the device settings be free variables in that sense.

I think that, in context, Bell meant something more limited, along the lines I suggested in my previous post.

The actual requirement ... is only that the measurement settings and the preparations of the objects to be measured, before measurement, are independent of each other. If we want to make extra sure of that, we set things up so that the preparations of the objects to be measured, and the selection of the measurement settings, occur at spacelike separated events, as, for example, in the Aspect experiments.

I tend to go off track around this particular point because I'm not sure how to make the link between the statistical independence [of the measurements settings and the preparations of objects] and the freedom of choice of the experimenter. Would you have any thooughts on how the two are connected?

I've read a few articles on experiments that propose to close the "free will loophole" where light from distant stars is used to set the angle of the polarisers. I thought the purpose of this was to attempt to remove the experimenters free will from the experimental set-up entirely, but I've also heard that this isn't the case because the experimenters free choice is still being exercised with regard to choosing the source that ultimately sets the measurement settings. Would that mean that the "free will loophole" hasn't been closed?

 

[PeterDonis]

I'm not sure how to make the link between the statistical independence [of the measurements settings and the preparations of objects] and the freedom of choice of the experimenter. Would you have any thooughts on how the two are connected?

Suppose you are an experimenter and you are worried that what seems to you like "free choice" of experimental settings might not be (for example, you might be worried that something like superdeterminism is true and that what seem to you like "free choices" are actually determined by carefully chosen initial conditions). How would you test that?

The only real test you have is whether your choices of measurement settings are statistically independent of the preparations of the objects you are measuring.

I've read a few articles on experiments that propose to close the "free will loophole" where light from distant stars is used to set the angle of the polarisers. I thought the purpose of this was to attempt to remove the experimenters free will from the experimental set-up entirely, but I've also heard that this isn't the case because the experimenters free choice is still being exercised with regard to choosing the source that ultimately sets the measurement settings.

To me the people who raise objections like that to closing the "free will loophole" are quibbling. Since humans are the ones who think up the experiments in the first place (because we are the ones who care about the results), obviously you're always going to be able to say that "human free will" was involved somewhere in the process. So it's obviously absurd to insist on completely eliminating "human free will" from the entire process as a condition of accepting that the "free will loophole" is closed.

I also think the term "free will" in this connection is actually irrelevant. If we're testing what kinds of theories are not ruled out by experiment, it doesn't matter how the measurement settings are chosen--whether by human free will, by computerized random number generators, by watching decays of radioactive atoms, or by watching light from distant stars--as long as the measurement settings are statistically independent of the preparations of the objects being measured. Going through all these elaborate procedures for how the measurement settings are determined is, in my view, just taking extra precautions because we know our tests for statistical independence only have finite accuracy (since any real test does), so we want to have other indirect ways of increasing our confidence that the independence we want to be true is actually true.

 

[Lynch101]

The only real test you have is whether your choices of measurement settings are statistically independent of the preparations of the objects you are measuring.

I also think the term "free will" in this connection is actually irrelevant. If we're testing what kinds of theories are not ruled out by experiment, it doesn't matter how the measurement settings are chosen--whether by human free will, by computerized random number generators, by watching decays of radioactive atoms, or by watching light from distant stars--as long as the measurement settings are statistically independent of the preparations of the objects being measured.

If none of these methods for choosing measurement settings violate statistical independence, does that not tell us that the computerized random number generator's choice of measurement settings, or that of the light from distant star, is as free as the experimenters choice of measurement settings?

EDIT: or should we take it that these experiments simply tell us nothing about the free will of the experimenter?

 

[PeterDonis]

should we take it that these experiments simply tell us nothing about the free will of the experimenter?

This is what I would say, since we are comparing a method involving humans "making a choice" with methods that do not involve humans at all.

 

[Lynch101]

This is what I would say, since we are comparing a method involving humans "making a choice" with methods that do not involve humans at all.

Ah OK. Thank you.

 

[Lynch101]

I came across the following in an article by Howard Wiseman in Nature and I'm wondering if this is an accurate summation of the issue in question?

The issue is whether the settings in one laboratory are uncorrelated with variables (hidden or otherwise) in the other. If they are correlated, then the experiment violates the assumptions of Bell’s theorem, opening the free-choice loophole, so called because of how it can be closed: the only things correlated with free choices are their effects, so (by Einstein’s principle) settings that are freely chosen late enough would be uncorrelated with the other variables, as desired.

Physics: Bell’s theorem still reverberates

If it is, then it will probably come as no surprise that I have been looking at the question all wrong.

 

[PeterDonis]

I came across the following in an article by Howard Wiseman in Nature and I'm wondering if this is an accurate summation of the issue in question?

He's equating "free choice" with "a human makes a free choice". To me that's a red herring, but he might be insisting on this meaning of "free choice" because he is concerned with the "collapse loophole": if a human doesn't consciously register the result, one could always argue (though such arguments quickly become highly contrived) that the measurement wasn't actually completed. By analogy, if a human doesn't consciously choose a measurement setting, one could always argue that it wasn't really "freely chosen". This all seems contrived to me--to me, using, say, the unpredictable decay of radioactive atoms as the source of "free choices" about measurement settings is quite good enough--but people's opinions differ.

 

[Morbert]

"It has ben assumed that the settings of instruments are in some sense free variables..."
For me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about, what has gone before.

This is very similar to free will as stipulated by Kochen[1] (of the Bell-Kochen-Specker theorem fame). I.e. If an experiment is freely chosen, it means the choice of experiment is not a function of information accessible to the experimenter.

As mentioned previously in the thread, an experiment cannot be wholly free. And also, this definition is very much stipulative. Its purpose is not to address questions about the nature of our will and whether it is free.

[1] https://arxiv.org/abs/quant-ph/0604079

 

[Lynch101]

Can I try and outline my reading of a number of statements with regard to Bell's theorem and free will? It might be easier that way, to identify incorrect assumptions and gaps in the reasoning.

Assumptions
One of the key assumptions of Bell's theorem is that of statistical independence. The absence (or violation) of statistical independence necessarily leaves us with superdeterminism.

In order for statistical independence to be preserved Bell says (as above):

it has been assumed that the settings of instruments are in some sense free variables.

He goes on to say (as above):

for me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about, what has gone before.

@PeterDonis you mentioned that, taken literally, it's not really true of any events that they are in no sense a record of the past. "Every event gives some information about something that has gone before." I'm reading this to mean that, in general, effects are correlated with their causes.Correlation
In an offline conversation with a mathematician friend*, he told me that the chain of correlation can be extended back through the chain of causality. For example, if A causes B and B causes C, then A and C can be correlated. This would seem to be an issue for the idea of statistical independence because the values of these variables wouldn't be correlated with only their future light cones, but also their past light cones.

To me, superdeterminism sounds as though it is this basic idea taken to its necessary conclusion, that the chain of correlation stretches back through the chain of causality until we reach a common cause.Human Free Will
If we consider this statement then:

The issue is whether the settings in one laboratory are uncorrelated with variables (hidden or otherwise) in the other. If they are correlated, then the experiment violates the assumptions of Bell’s theorem, opening the free-choice loophole, so called because of how it can be closed: the only things correlated with free choices are their effects, so (by Einstein’s principle) settings that are freely chosen late enough would be uncorrelated with the other variables, as desired.

Here Wiseman says, "if they [the settings] are correlated, then the experiment violates the assumptions of Bell’s theorem". We might ask how they might possibly be correlated? The default answer might seem to be superdeterminism; that is, they are correlated because an effect is correlated not only with its cause, but with the causes of its cause, and so on back through the chain of causality.

Wiseman says, this opens the "free-choice loophole, so called because of how it can be closed". This seems to suggest that human free will is a necessity to establish statistical independence. The reason being that human free will (if such exists) is a pretty unique phenomenon in the Universe because it is, by way of necessity, only correlated with its effects.@Morbert The following from the Conway-Kochen Free Will paper seems to be saying something similar:

replacing the human choice by a pseudo–random number generator does not allow us to dispense with the Free Will assumption since free will is used in choosing this generator! The necessity for the Free Will assumption is evident, since a determined determinist could maintain that the experimenters were forced to choose the computer programs they did because these were predetermined at the dawn of time.

*I'm not stating this as an appeal to authority, I'm just saying that I can't reference it here. Well, I could post the voice note if necessary. His answer was in response to a general question also, so it's possible that I didn't give him all the necessary details.

 

[PeterDonis]

"Every event gives some information about something that has gone before." I'm reading this to mean that, in general, effects are correlated with their causes.

I didn't mean anything that specific. I was simply trying to caution against an overly literal reading of Conway's statement.

For example, suppose we measure the spin of a spin-1/2 particle. The Free Will Theorem basically says that if we are free to choose the orientation of the spin measuring device, the particle is free to choose which result is obtained. A literal reading of the way Conway defines "free" would mean that the orientation of the spin measuring device gives no information about anything in the past light cone of the measurement. But that is obviously not literally true. Setting the orientation of the device is not an instantaneous process that happens at a single point. It is a continuous process that covers a significant region of spacetime. Conway's definition of "free" implies that there must be some event during that continuous process that gives no information about what is in the past light cone of that particular event; but it in no way implies that the entire process, the whole region of spacetime occupied by it, gives no information about what is in the past light cone of that whole region of spacetime.

To me, superdeterminism sounds as though it is this basic idea taken to its necessary conclusion, that the chain of correlation stretches back through the chain of causality until we reach a common cause.

No, that's just determinism. Superdeterminism (at least as applied to QM) means, not just that every event in spacetime is included in some chain of causation, but that the initial conditions are carefully chosen so that measurement results are consistent with QM even though the underlying physics is not QM at all. In other words, superdeterminism claims that the initial conditions of a deterministic universe are carefully chosen to mislead us about what the actual underlying physics of the universe is.

It is true, however, that Conway's definition of "free" excludes determinism, not just superdeterminism. Conway's definition of "free" requires that there are some events that are only part of a chain of causation to their future, not their past. That is inconsistent with determinism, which requires that every event is part of a chain of causation to both its future and its past.

Wiseman says, this opens the "free-choice loophole, so called because of how it can be closed". This seems to suggest that human free will is a necessity to establish statistical independence.

If that is what Wiseman is suggesting, I think he's wrong, at least if by "human free will" he means "free" by Conway's definition, since, as above, Conway's definition is inconsistent with determinism (not just superdeterminism, but determinism period). It is perfectly possible for different events to be statistically independent in a deterministic universe, so "free will" in Conway's sense is not required.

 

[Lynch101]

Conway's definition of "free" implies that there must be some event during that continuous process that gives no information about what is in the past light cone of that particular event; but it in no way implies that the entire process, the whole region of spacetime occupied by it, gives no information about what is in the past light cone of that whole region of spacetime.
...
Conway's definition of "free" requires that there are some events that are only part of a chain of causation to their future, not their past. That is inconsistent with determinism, which requires that every event is part of a chain of causation to both its future and its past.

Apologies that I need spoon feeding on this one Peter, but is there a difference between what you say here (or your interpretation of what Conway says) and what Bell says here?

For me this means that the values of such variables have implications only in their future light cones. They are in no sense a record of, and do not give information about, what has gone before.

 

[PeterDonis]

is there a difference between what you say here (or your interpretation of what Conway says) and what Bell says here?

Bell appears to be using Conway's definition of "free", more or less, yes. But the "variables" he speaks of might just be individual microscopic events that are only part of a chain of causation to their future, not their past.

 

[Lynch101]

Bell appears to be using Conway's definition of "free", more or less, yes. But the "variables" he speaks of might just be individual microscopic events that are only part of a chain of causation to their future, not their past.

Am I correct in saying that both appear to be saying that, in the absence of these "free variables", these individual microscopic events, we are left with superdeterminism?

 

[PeterDonis]

Am I correct in saying that both appear to be saying that, in the absence of these "free variables", these individual microscopic events, we are left with superdeterminism?

I'm not sure. If they are saying that, I would disagree; I don't think determinism, which is all that would be implied by the absence of the "freedom" they appear to be describing, is the same thing as superdeterminism. It's perfectly possible to have a deterministic universe whose initial conditions are not carefully set up to make measurement results mislead us about what the underlying physics is.

 

[Lynch101]

I'm not sure. If they are saying that, I would disagree; I don't think determinism, which is all that would be implied by the absence of the "freedom" they appear to be describing, is the same thing as superdeterminism. It's perfectly possible to have a deterministic universe whose initial conditions are not carefully set up to make measurement results mislead us about what the underlying physics is.

Ah OK. Am I at least correct in saying that in the absence of these individual events/free variables statistical independence is violated?

If so, would that then mean that, in the absence of these free variables, simple determinism can account for the observed correlations i.e. the violations of Bell's Inequality?

 

[PeterDonis]

Am I at least correct in saying that in the absence of these individual events/free variables statistical independence is violated?

No. It's perfectly possible to have a completely deterministic underlying physics but still have particular measurement settings and results be statistically independent.

in the absence of these free variables, simple determinism can account for the observed correlations i.e. the violations of Bell's Inequality?

No. For example, Bohmian mechanics is a perfectly deterministic theory that accounts for Bell inequality violations just fine. It's just a nonlocal deterministic theory; it violates Bell's locality assumption.

 

[Lynch101]

Just when I thought I was getting a grasp on it

Thank you for your patience btw!

I'm not sure if you've ever heard of the Irish TV show called Father Ted, but I'm reminded of this scene:

 

[Lynch101]

No. It's perfectly possible to have a completely deterministic underlying physics but still have particular measurement settings and results be statistically independent.

Is Bohmian Mechanics an example of that?

No. For example, Bohmian mechanics is a perfectly deterministic theory that accounts for Bell inequality violations just fine. It's just a nonlocal deterministic theory; it violates Bell's locality assumption.

Is it possible to maintain locality but drop the assumption of statistical independence?

 

[PeterDonis]

Is Bohmian Mechanics an example of that?

With the usual assumption about initial conditions (that they satisfy the particular constraints that are required for the Born Rule to work), I believe so, yes.

Is it possible to maintain locality but drop the assumption of statistical independence?

I don't know what that would mean, specifically, or whether there is any interpretation that does this.

 

[Lynch101]

With the usual assumption about initial conditions (that they satisfy the particular constraints that are required for the Born Rule to work), I believe so, yes.

Is that assumption about initial conditions required by every interpretation of quantum mechanics, for the Born Rule to work, or is it just Bohmian Mechanics that requires it?

I don't know what that would mean, specifically, or whether there is any interpretation that does this.

Am I correct in thinking that the following two statements (from yourself and Wiseman) are statements about statistical independence?

The actual requirement ... is only that the measurement settings and the preparations of the objects to be measured, before measurement, are independent of each other.

The issue is whether the settings in one laboratory are uncorrelated with variables (hidden or otherwise) in the other. If they are correlated, then the experiment violates the assumptions of Bell’s theorem.

 

[PeterDonis]

Is that assumption about initial conditions required by every interpretation of quantum mechanics, for the Born Rule to work, or is it just Bohmian Mechanics that requires it?

Just Bohmian mechanics.

Am I correct in thinking that the following two statements (from yourself and Wiseman) are statements about statistical independence?

Mine is. I'm not sure about Wiseman's, because 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 (the joint probability has to be factorizable).

 

[Lynch101]

Just Bohmian mechanics.

Are there variations of BM which don't incorporate the assumption about initial conditions? As in, do you know if the version of BM that @Demystifier advocates includes it?

Mine is. I'm not sure about Wiseman's, because 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 (the joint probability has to be factorizable).

Ah, OK, cool that's an interesting take on it. I haven't come across that idea before, thanks. Could you recommend some literature that discusses that?

Does that assumption, that only the probabilities of measurement results be statistically independent, also require the presence of individual microscopic events that are only part of a chain of causation to their future?

EDIT: Aren't the experimental violations of Bell's inequality (as it is traditionally represented) based on the actual outcomes of experiments, as opposed to the probabilistic predictions of those outcomes?

 

[PeterDonis]

Are there variations of BM which don't incorporate the assumption about initial conditions?

No. BM has to have them in order to match the predictions of standard QM.

Does that assumption, that only the probabilities of measurement results be statistically independent, also require the presence of individual microscopic events that are only part of a chain of causation to their future?

I don't think there is a definite answer. Statistical assumptions generally leave open multiple possibilities for the underlying microscopic physics.

 

[Lynch101]

No. BM has to have them in order to match the predictions of standard QM.

Ah, OK! Thank you, that's very interesting.

I don't think there is a definite answer. Statistical assumptions generally leave open multiple possibilities for the underlying microscopic physics.

Could you recommend some literature on that particular interpretation of Bell's theorem? I haven't come across it before.

Would that assumption change the calculation of the inequality? To my mind it sounds like it should, because the traditional rendering of Bell's theorem appears to be based on the actual experimental outcomes, as opposed to the probabilities of the outcomes.

What would a violation of that rendering of the theorem tell us? From the literature I've read, Bell's formulation of the theorem was predicated on 4 basic assumptions:
1. Relativistic locality
2. Realism
3. Relativistic local realism
4. Free will - or the microscopic events mentioned previously.

Violation of the inequality then meant that one of those 4 assumptions would have to be abandoned. Would the rendering you have suggested here mean that of the assumptions 1-3 would have to be violated, while remaining silent on #4?

 

[PeterDonis]

Could you recommend some literature on that particular interpretation of Bell's theorem?

What interpretation? I was stating my understanding of what Bell is assuming in his papers that derive the theorem.

From the literature I've read, Bell's formulation of the theorem was predicated on 4 basic assumptions

You really need to look at the actual math in Bell's papers. Ordinary language is not a good tool here since different people put different, incompatible intepretations on the words you are using. The mathematical assumptions underlying Bell's theorem are clear from his papers, and those are a much better starting point for understanding.

 

[Demystifier]

Are there variations of BM which don't incorporate the assumption about initial conditions? As in, do you know if the version of BM that @Demystifier advocates includes it?

In Bohmian mechanics, even if the initial conditions are not consistent with the Born rule, a sufficiently complex system typically evolves towards an equilibrium which corresponds to the Born rule. That's analogous to similar behavior in classical statistical physics, where most initial conditions imply evolution towards a thermal equilibrium. That's briefly discussed in my paper, with references to further details.