Scholarpedia article on Bell's Theorem

[harrylin]

But why should there be any influence?

Bell's conclusion - which according to ttn has been perfectly proven - is that the predicted correlations cannot be explained without such an influence (a "spooky action at a distance", as Einstein called it).

 

[martinbn]

Bell's conclusion - which according to ttn has been perfectly proven - is that the predicted correlations cannot be explained without such an influence (a "spooky action at a distance", as Einstein called it).

I thought that the conclusion is that if you want to explain it with and influence it cannot be local. But why should there be an influence?

 

[martinbn]

Uh, the proof of Bell's theorem. I agree that "there is no QM involved", if I understand correctly what you mean. The point is just that, in deriving the inequality from the assumption of locality, one doesn't have to assume that the state of the particle pair can be broken up as "the state of the first particle" and then, separately, "the state of the second particle". It is perfectly compatible with the derivation for the state to be somehow "holistic" (i.e., not "separable") as is basically the case in ordinary QM.

Yes, of course. So?

 

[ttn]

Yes, of course. So?

So, that answers the question you asked in 298.

 

[harrylin]

I thought that the conclusion is that if you want to explain it with and influence it cannot be local. But why should there be an influence?

No, nothing like that! Again, what is meant with "an influence" or "spooky action at a distance": Bell concluded that the measurement at one place - however remote - instantly affects what is measured at another place; according to him the predicted correlations cannot be explained without such an influence.

See also my citations in post #294.
martinbn, perhaps ttn's summary statement in his article is not clear enough and he should retain more of Bell's words? You are as an apparently "fresh" reader of this topic the best positioned to answer that question.

 

[lugita15]

ttn, would it be possible for you (or anyone else) to scan "La Nouvelle Cuisine" for those of us who don't have Bell's book handy?

 

[DrChinese]

Bell concluded that the measurement at one place - however remote - instantly affects what is measured at another place; according to him the predicted correlations cannot be explained without such an influence.

... perhaps ttn's summary statement in his article is not clear enough and he should retain more of Bell's words?

If you want to retain more of Bell's words, you would want to add this important phrase to your first sentence: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements". I.e. a theory "supplemented by additional variables". A hidden variable theory.

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

 

[lugita15]

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

DrChinese, I still don't understand why you don't agree with this. You said that EPR argument is only that "simultaneous perfect correlations" implies hidden variables, but it seems to me that perfect correlations implies simultaneous perfect correlations, assuming the no-conspiracy condition.

I claim that the following two statements together imply hidden variables:
1. There is perfect correlation at identical polarizer settings.
2. When you don't set the polarizers to identical angles, it is still true (and meaningful) that you WOULD have gotten perfect correlations if you HAD set the polarizers to identical angles.

Do you disagree with this?

 

[harrylin]

If you want to retain more of Bell's words, you would want to add this important phrase to your first sentence: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements". I.e. a theory "supplemented by additional variables". A hidden variable theory.

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

I had not elaborated on this as my comment there was directed at ttn and martinbn, and I suppose that ttn understands this well.

An important difference in the two papers that I cited is that the second paper clearly does not suggest that his conclusion would only be valid for the addition of variables. And his conclusion as expressed in his first paper evidently also applies to a null-variable. Therefore I hold that citing that other phrase without explaining the history (he was obviously simply referring to EPR) or without also citing his reformulation in a later paper (as I did in my post #294) can put people on a wrong track. My summary in post #305 for martinbn points to what I believe to be the essence of Bell's theorem.

 

[mattt]

After a second thought, I changed my mind. I think that the way Bell defines "local causality" for a fundamental theory to respect the causal structure of Relativity Theory, is correct for a deterministic fundamental theory, but I would not use that definition for a stochastic fundamental theory. I'll expand on this in the following days...

 

[DrChinese]

DrChinese, I still don't understand why you don't agree with this. You said that EPR argument is only that "simultaneous perfect correlations" implies hidden variables, but it seems to me that perfect correlations implies simultaneous perfect correlations, assuming the no-conspiracy condition.

I claim that the following two statements together imply hidden variables:
1. There is perfect correlation at identical polarizer settings.
2. When you don't set the polarizers to identical angles, it is still true (and meaningful) that you WOULD have gotten perfect correlations if you HAD set the polarizers to identical angles.

Do you disagree with this?

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

For Bell: That assumption (also along with locality, explicitly assumed) is necessary to arrive at the contradiction - see after Bell's (14) where we now have the 3 angles a, b and c in one equation simultaneously. (There were only 2 in the EPR program.) As with EPR, if either locality or realism are bad assumptions, then there is no contradiction. Because Bell extended the idea of realism from 2 (in EPR) to 3 simultaneous values, he was able to latch on to a tiebreaker in the debate.

 

[lugita15]

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

For Bell: That assumption (also along with locality, explicitly assumed) is necessary to arrive at the contradiction - see after Bell's (14) where we now have the 3 angles a, b and c in one equation simultaneously. (There were only 2 in the EPR program.) As with EPR, if either locality or realism are bad assumptions, then there is no contradiction. Because Bell extended the idea of realism from 2 (in EPR) to 3 simultaneous values, he was able to latch on to a tiebreaker in the debate.

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

 

[ttn]

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

http://www.scholarpedia.org/article/Bell%27s_theorem#Some_controversy_regarding_the_EPR_argument

 

[ttn]

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

No, it doesn't. The confusion giving rise to the impression that it does is called positivism -- i.e., the insistence that everything we're ever talking about has to be entirely reducible to directly measureable things.

But in fact the whole argument is about *candidate theories* and what predictions they make in various situations. There is nothing at all like "counter-factual definiteness" assumed in saying, e.g.: consider candidate theory A; in situation 1 it predicts such-and-such; in situation 2 it predicts thus-and-so; and so on. That is the structure of the argument. It's about what a theory predicts when various different things are measured. The question of whether some outcome of some experiment "really exists" even when that experiment isn't actually performed, is a completely and total philosophical red herring. Strictly speaking, this all means that, at the end of the day, the conclusions is that *no local theory can explain the quantum predictions*. So maybe there is some wiggle room if, for example, you think that you can explain the quantum predictions in a local way without using a theory, or some such thing. Good luck with that.

 

[ttn]

ttn, would it be possible for you (or anyone else) to scan "La Nouvelle Cuisine" for those of us who don't have Bell's book handy?

Sorry, no, I'm not comfortable doing that. This paper of mine quotes *extensively* from "la nouvelle cuisine", though, so maybe you could look at this if for some reason you really can't get a copy of Bell's book (2nd edition).

http://arxiv.org/abs/0707.0401

 

[lugita15]

http://www.scholarpedia.org/article/Bell%27s_theorem#Some_controversy_regarding_the_EPR_argument

ttn, you make an interesting argument there that I can't seem to immediately refute:

"Here is the formulation of the "several axes" version of the EPR argument that does not involve counterfactuals: in order to explain (without violation of locality) the fact that the outcomes will be perfectly anti-correlated if the experimenters both measure spin along the z-axis, one has to assume that these outcomes are pre-determined. The same goes for measurements of spin along the x-axis. Even though, in each run of the experiment, either the z-axis or the x-axis is chosen along which to perform the measurements, the elements of physical reality that exist before the measurements cannot depend on choices that will be made later by the experimenters! This, indeed, doesn't follow from the assumption of locality itself but it does follow from the so-called "no conspiracy" assumption which states, roughly speaking, that the pair of particles prepared by the source does not "know" in advance what experiments are going to be performed on them later." (italics in original)

 

[DrChinese]

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

I think it is safe to say that ttn is comfortable with his position as is. On the other hand, ttn is unlikely to sway (with his argument) those who follow MWI or one of the other non-realistic (or non-deterministic) interpretations (since the vast majority of physicists are not Bohmian).

So my point to ttn remains: why make an argument that depends on wording ("simultaneous") that is soundly rejected? In other words: I reject his starting point that perfect correlations implies hidden variables*, a position I am quite comfortable with and involves no controversy. With my position, I can peacefully coexist with other interpretations, and await additional evidence to clarify matters. A position shared by most, and for which ttn has no lever to move any of us (since his assertion that he is right and we are wrong doesn't even make sense unless we all start from the same point).

Other than perhaps badgering, but I get than from the other side (local realists) just as well.

*In a time symmetric interpretation, there are no hidden variables but there are perfect correlations. Ditto for MWI. Ditto for the Copenhagen interpretation, because there is no possible greater specification of the system, and we live in a non-deterministic world. All of these interpretations reject realism. And all of these interpretations reject the idea that the current position of ALL distant particles in a system directly determines the outcomes of measurements here and now.

 

[harrylin]

http://www.scholarpedia.org/article/Bell%27s_theorem#Some_controversy_regarding_the_EPR_argument

I have read that argumentation and it looks sound to me - not that I'm sure that it gets rid of "counterfactuals", but simply that there is no need for the introduction of such additional complex new concepts.

 

[harrylin]

[..] All of these interpretations reject realism. And all of these interpretations reject the idea that the current position of ALL distant particles in a system directly determines the outcomes of measurements here and now.

OK, you're right of course that Bell's argument assumes realism, and in the Bertlman's socks paper he mentions that point - I guess that without realism (like in the movie Matrix) about anything is possible because nothing really happens.

 

[DrChinese]

ttn, you make an interesting argument there that I can't seem to immediately refute...

I have read that argumentation and it looks sound to me - not that I'm sure that it gets rid of "counterfactuals",...

The fact that the Bohmian view is contextual should be an immediate tipoff that there is something wrong with his argument. Contextual essentially being code for "non-realistic". So of course in the end, there are no simultaneous definite values for a, b and c which is my assertion. If there are no counterfactuals, there is no realism. Of course, the Bohmian view is that there is determinism. So again we are back to the meaning of words. The Bohmian view is non-local deterministic, i.e. there are non-local hidden variables. But it is not any more realistic than other interpretations.

To ttn, of course, this distinction is meaningless: he argues "against realism". But to you, you must decide if you accept the idea that at the time entanglement begins, the outcomes have been predetermined in the context of the inevitable future measurement settings and NO OTHERS (since Bohmian theories don't address the DrChinese challenge either). If that doesn't blatantly violate ttn's premise ("cannot depend on choices that will be made later by the experimenters") to you, then I would say his argument can be accepted. I see a contradiction, but hey, that's why my conclusion is different.

So the answer is: your viewpoint subtly colors your definitions. A slight change will make a difference. I, for example, would be likely to answer ttn's "Against Realism" with an argument we can call "Against Locality". By a suitable shift in definitions, we would be left concluding that locality is irrelevant to the matter; i.e. realism is not tenable by any theory agreeing with the predictions of QM. And you know what: Bohmian types would fall inside, not outside, my definition. For the reasons stated in the first paragraph.

 

[ttn]

ttn, you make an interesting argument there that I can't seem to immediately refute:

At least try to pretend that you're not surprised!

 

[ttn]

I think it is safe to say that ttn is comfortable with his position as is. On the other hand, ttn is unlikely to sway (with his argument) those who follow MWI or one of the other non-realistic (or non-deterministic) interpretations (since the vast majority of physicists are not Bohmian).

None of this has anything to do with being Bohmian. One of the biggest supporters of Bell's view of all this (which view I of course share) is GianCarlo Ghirardi, the principle proponent of the non-deterministic GRW version of QM. Also, I don't understand why you call MWI "non-realistic (or non-deterministic)". I would call it both realistic and deterministic -- if what you mean by "realistic" is just that it gives some definite account of micro-physical reality. (Of course, if you mean by "realistic" something about non-contextual hidden variables, then, OK, MWI isn't "realistic" in that sense... but maybe the point here is that you and others should stop using the word "realistic" without saying *exactly* what you mean.)

So my point to ttn remains: why make an argument that depends on wording ("simultaneous") that is soundly rejected? In other words: I reject his starting point that perfect correlations implies hidden variables*, a position I am quite comfortable with and involves no controversy. With my position, I can peacefully coexist with other interpretations, and await additional evidence to clarify matters. A position shared by most, and for which ttn has no lever to move any of us (since his assertion that he is right and we are wrong doesn't even make sense unless we all start from the same point).

After all these years, I don't hold out any hope of changing your position, that's true. But it is factually wrong to suggest that my attempts to change your mind are based on the mere "assertion that [I am] right". They have instead all along been based on trying to explain the *argument*, which you systematically fail to grasp. Once more for the record, it's not an argument "that perfect correlations implies hidden variables" -- it's rather an argument that perfect correlations *plus locality* implies hidden variables. That is, the only way to explain the perfect correlations locally is for each particle to carry pre-determined answers to all possible questions that can be asked of it.

I honestly have no clue what you have in mind with this word "simultaneous". I think you mean to be referring back to the actual EPR paper, where they talk about simultaneous values for non-commuting operators. But that's just an awkward way of saying that there are more real definite properties than QM can consistently attribute values to, i.e., that QM doesn't provide a complete description of the physical state. But who cares about QM. It plays no role whatever in the argument for the conclusion I wrote in the last sentence of the previous paragraph. Also, you remember that the EPR paper was written by Podolsky, and Einstein thought he botched it, right? So please don't think of its precise wording as somehow perfectly capturing the argument. Einstein didn't think it did, and neither do I.

*In a time symmetric interpretation, there are no hidden variables but there are perfect correlations.

As I explained back in the beginning of this thread, a time symmetric interpretation isn't local. It involves causal influences coming from outside the past light cone.

Ditto for MWI.

It's hardly that simple. Normally the phrase "perfect correlations" denotes the following: the single actual outcome on the right perfectly matches the single actual outcome on the left, for each particle pair. MWI denies that there *is* such a thing as "the single actual outcome on the right", and same on the left. So saying that "there are perfect correlations in MWI" involves, at least, changing the meaning of the terms involved. Probably the right thing to say is that, in an MWI-ish world, the inhabitants will be fooled into thinking that "perfect correlations" occur. That's not quite the same as saying that perfect correlations do actually occur.

Ditto for the Copenhagen interpretation, because there is no possible greater specification of the system, and we live in a non-deterministic world.

Copenhagen is also not a local theory.

All of these interpretations reject realism.

What do you mean by "realism"? Hidden variables? If that, then I would put the conclusion differently: there are a bunch of ("regular type") theories, some "realistic" and some not, and they're all nonlocal. (Oh and then there's this one very irregular type theory, MWI, where nothing is as it seems and it's not really clear what the heck to say.) So the upshot is clear: you can have "realism" or not, but what you can't do is explain the correlations in a local way (at least, not without playing MWI games).

And all of these interpretations reject the idea that the current position of ALL distant particles in a system directly determines the outcomes of measurements here and now.

Actually, as worded, Bohmian mechanics also rejects this idea. See, you really need to be more careful/precise/clear with what you mean by "realism".

 

[lugita15]

OK, you're right of course that Bell's argument assumes realism, and in the Bertlman's socks paper he mentions that point - I guess that without realism (like in the movie Matrix) about anything is possible because nothing really happens.

Denying realism, in this context, may not necessarily mean you believe the world is an illusion and nothing is real. Realism here just means that measurable attributes have well-defined values no matter what, even if they're not measured.

 

[lugita15]

I honestly have no clue what you have in mind with this word "simultaneous".

He means that e.g. three polarization attributes for a given photon pair are assumed to have simultaneously well-defined values, even though we only measure at most two of those polarization attributes in the experiment.

 

[lugita15]

To ttn, of course, this distinction is meaningless: he argues "against realism". But to you, you must decide if you accept the idea that at the time entanglement begins, the outcomes have been predetermined in the context of the inevitable future measurement settings and NO OTHERS (since Bohmian theories don't address the DrChinese challenge either).

Isn't what you're describing superdeterminism, i.e. a violation of the no-conspiracy condition? Are you saying that Bohmian mechanics is superdeterministic?

 

[harrylin]

Denying realism, in this context, may not necessarily mean you believe the world is an illusion and nothing is real. Realism here just means that measurable attributes have well-defined values no matter what, even when they're not measured.

Then it may be that "realism" isn't sufficiently well defined... for example we can measure an orange by pushing on it so that it bursts and we detect the range of drops on the floor. The drop pattern on the floor isn't "well-defined no matter what, even when it's not measured"; from which I would conclude that some attributes of an orange are "non-realistic". I don't see what such a concept has to do with Bell's analysis.

 

[lugita15]

Can anyone think of a refutation of the argument by ttn I quoted in post #316, which says that if the question of which elements of reality exist before measurement is determined by the measurement decisions of the experimenter, then this constitutes a violation of the no-conspiracy condition?

 

[lugita15]

Then it may be that "realism" isn't sufficiently well defined... for example we can measure an orange by pushing on it so that it bursts and we detect the range of drops on the floor. The drop pattern on the floor isn't "well-defined no matter what, even when it's not measured"; from which I would conclude that some attributes of an orange are "non-realistic". I don't see what such a concept has to do with Bell's analysis.

Would you not say that the question of what pattern of drops it produces if we pushed on it is a measurable attribute of the orange, and that this question has a well-defined answer even if we do NOT push on it?

 

[ttn]

The fact that the Bohmian view is contextual should be an immediate tipoff that there is something wrong with his argument. Contextual essentially being code for "non-realistic". So of course in the end, there are no simultaneous definite values for a, b and c which is my assertion.

First off, for the millionth time, a, b, and c are angles. They are axes along which one might contemplate measuring the spin/polarization of a particle. They aren't properties. So it doesn't even make any sense to talk about whether "there are simultaneous definite values for a, b, and c" or not. Presumably what you mean is whether there are simultaneous definite values for spin-along-a, spin-along-b, and spin-along-c. OK. You're right that, for Bohmian mechanics, spin is contextual. That means, basically, that Bohmian mechanics does not claim that spin-along-a, spin-along-b, and spin-along-c all exist with simultaneous definite values.

But what in the world do you think this has to do with Bell's argument? In the two-step version (as opposed to going directly from locality to CHSH) the argument runs like this:

step 1: locality + perfect correlations --> X

where X is "spin-along-a, spin-along-b, and spin-along-c all exist with simultaneous definite values that are simply revealed by whichever measurement actually gets made"

step 2: X --> Bell's inequality

overall conclusion (i.e., what you get by combining step 1 and step 2):

locality + perfect correlations --> Bell's inequality

We know from experiment that "perfect correlations" is true and "Bell's inequality" is false. It follows that "locality" is false.

Now you want to come along and say "Aha, but there's this one candidate theory, Bohmian Mechanics, which denies X -- so the argument falls apart." But what in the world are you thinking? Nothing falls apart. Theories can say X or deny X or dip X in chocolate and eat it, and none of it has any implications whatsoever for the argument just presented. You are just saying something that is a complete and total non-sequitur.

If there are no counterfactuals, there is no realism.

OK, so Bohm's theory isn't "realistic". So what? You think that somehow refutes Bell's argument?

Of course, the Bohmian view is that there is determinism. So again we are back to the meaning of words. The Bohmian view is non-local deterministic, i.e. there are non-local hidden variables. But it is not any more realistic than other interpretations.

OK, fine, yes, great, let's use the words that way. I agree, Bohm's theory is no more realistic than other interpretations. So what? You think that somehow refutes Bell's argument??

To ttn, of course, this distinction is meaningless: he argues "against realism". But to you, you must decide if you accept the idea that at the time entanglement begins, the outcomes have been predetermined in the context of the inevitable future measurement settings and NO OTHERS (since Bohmian theories don't address the DrChinese challenge either).

Hogwash. Maybe you have to decide that if you are trying to decide which theory to believe. But you simply do not have to decide that, or even confront the question at all, if you are just trying to follow Bell's proof that you can't explain the empirical data without nonlocality. Dr Chinese continues to fall back to this totally false idea that X (which stands for "realism" or "non-contextual hidden variables" or "simultaneous elements of reality" or whatever) is an *assumption* of the argument. But it's simply not. There is no such assumption. To quote Bell: to the limited extent to which it plays any role at all, it is *inferred* rather than *assumed*. And note clearly that if there is even the slightest bit of confusion or uncertainty about this, all you have to do is go and look at the "Bell's theorem without perfect correlations" section of our article (or any of several of Bell's papers) where the empirically refuted inequality is derived *straight* from locality, without the need even to ever *mention* any suspicious-sounding X.

So the answer is: your viewpoint subtly colors your definitions.

That's probably true. But more relevant here is the idea that missing an argument entirely, blatantly dumps buckets of paint on your definitions such that what you are talking about is entirely and fatally obscured.

By a suitable shift in definitions, we would be left concluding that locality is irrelevant to the matter; i.e. realism is not tenable by any theory agreeing with the predictions of QM.

Actually I agree. If you redefine "realism" to mean "causal influences on an event come exclusively from its past light cone" -- and redefine "locality" to mean whatever the heck anybody wants -- then indeed, Bell's theorem would refute realism and have nothing to do with locality. Is that a "suitable shift"?

And you know what: Bohmian types would fall inside, not outside, my definition. For the reasons stated in the first paragraph.

OK, so let me drop the sarcasm and ask you straight: how precisely do you propose to redefine words? I *think* your point in the first paragraph was supposed to be that, actually, Bohmian mechanics is not realistic (because it is contextual). OK, fine, I'm cool with that. But that's not going to show *anything* about locality. Bohmian mechanics will still be nonlocal, no matter how you define "realistic". So... how do you propose to redefine "local" such that Bohmian mechanics becomes a local theory?

And a more important question (since Bell's argument has nothing to do with Bohmian mechanics): are you suggesting that you can still derive a Bell inequality from (your) "locality"?

But the most important question of all: what the heck does any of this have to do with Bell's argument? Even supposing you could redefine "locality" (in some way such that Bohm's theory comes out as local) and still derive a Bell inequality from this redefined "locality", who cares? We're all busy being shocked by *Bell's argument*, which proves that his regular kind of locality is false! Do you think that somehow you playing this game (defining things a new way and trying to construct your own argument) refutes Bell's argument? At best, you could only hope to *distract* people from Bell's argument with this game. But if Bell's argument is sound -- and I don't exactly hear you pointing out a flaw in it -- then it's sound, end of discussion.

 

[ttn]

He means that e.g. three polarization attributes for a given photon pair are assumed to have simultaneously well-defined values, even though we only measure at most two of those polarization attributes in the experiment.

Actually we only measure at most *one* of them (on any single particle).

But, whatever. The point is, whatever exactly he means, he's *wrong* if he's saying it's an *assumption* in Bell's argument -- i.e., something that you could deny in order to escape the conclusion that nonlocality is required.