Is Bell's Logic Aimed at Decoupling Correlated Outcomes in Quantum Mechanics?

[Maaneli]

This is a very strange thing to say. First, no one is waiting for anything. There is nothing to wait for! Second, are you saying that someone has done an experiment that did NOT violate an expected Bell Inequality and then did not publish it? That is an outrageous suggestion, assuming you are in fact suggesting that - and I certainly hope you aren't.

Just a reminder, I am still waiting for you to read over Bell's La Nouvelle Cuisine and get back to me.

Regarding your proof about realism, I couldn't make sense of the logic, to be honest.

 

[ThomasT]

A single particle, Alice, has 3 elements of reality at angles 0, 120, 240 degrees. This is by assumption, the realistic assumption, and from the fact that these angles - individually - could be predicted with certainty.

It is obvious from the Bell program that there are NO datasets of Alice which match the QM expectation value. Ergo, the assumption is invalid. And you don't need to consider settings of Bob at all. You simply cannot construct the Alice dataset. QED.

The key difference is that the elements of reality are NOT referring to separate particles. They never were intended to! All the talk about Bob's setting affecting Alice's outcome only relates to Bell tests. But it should be clear that there is no realistic Alice who can match the QM expectation value.

What you seem to be saying is that an LHV model of Alice's individual setup is incompatible with qm. If this is what you're saying, then Bell has already proven you wrong. If this isn't what you're saying, then what are you saying?

First, I don't think that the realist assumption is saying what you say it's saying. To wit:

A single particle, Alice, has 3 elements of reality at angles 0, 120, 240 degrees. This is by assumption, the realistic assumption, and from the fact that these angles - individually - could be predicted with certainty.

The realist assumption is that Alice, the underlying polarization vector or optical vector, has a definite but unknown value wrt any given trial. The source is emitting randomly polarized optical disturbances. The average angular difference between the optical vector and the unit vector (the polarizer setting) is 45 degrees. So, the expectation value of individual results wrt Alice (and Bob) is cos^2(45 degrees). Which is what the qm prediction is, and what's observed.

Second, considering the foregoing, the following makes no sense at all:

It is obvious from the Bell program that there are NO datasets of Alice which match the QM expectation value. Ergo, the assumption is invalid. And you don't need to consider settings of Bob at all. You simply cannot construct the Alice dataset. QED.

The key difference is that the elements of reality are NOT referring to separate particles. They never were intended to! All the talk about Bob's setting affecting Alice's outcome only relates to Bell tests. But it should be clear that there is no realistic Alice who can match the QM expectation value.

So, at this point, I have to agree with Maaneli that I don't understand what you're trying to say.

 

[JesseM]

Finally, it is common sense to realize that, rather than wait for the perfect experiment which closes a loophole, say "detection efficiency loophole", it should be easier to derive new inequalities, which take into account what is really observed, ie the fact that not all photons emitted will be detected. Obviously, if an experiment violates these new inequalities, there would be no talk of any possible "detection efficiency".

Yes, like the inequality in the giant equation here which I already directed you to. $$\eta$$ in that equation refers to the probability both photons are detected in any case where a single photon is detected (i.e. if $$\eta < 1$$ you're dealing with a case of imperfect detector efficiency).

 

[JesseM]

First, I don't think that the realist assumption is saying what you say it's saying. To wit:
The realist assumption is that Alice, the underlying polarization vector or optical vector, has a definite but unknown value wrt any given trial. The source is emitting randomly polarized optical disturbances. The average angular difference between the optical vector and the unit vector (the polarizer setting) is 45 degrees. So, the expectation value of individual results wrt Alice (and Bob) is cos^2(45 degrees). Which is what the qm prediction is, and what's observed.

Can you express your "optical vector" picture in terms of probabilities in an individual experiment rather than expectation values? If the optical vector for a given photon is at 30 degrees and the polarizer setting is at 70 degrees, does that mean the probability of a particular spin result is going to be cos^2(70-30)=cos^2(40)? Or are you imagining the result is generated deterministically from the optical vector and the polarizer setting, and if so what would the result be for the angles above? Without these kinds of basic details you simply don't have a well-defined LHV model, so any claims about the expectation value under your model are basically meaningless.

 

[DrChinese]

Regarding your proof about realism, I couldn't make sense of the logic, to be honest.

Now come on, it's not that hard. 3 elements of reality? Really, just read the last couple of paragraphs of EPR and tell me you have no idea what this is about. I understand that you want locality to be part of the equation, and I am not debating the point since I know you won't agree, but certainly you can see that EPR is about elements of reality for ONE particle. And that does not require a locality assumption at all.

 

[ThomasT]

Can you express your "optical vector" picture in terms of probabilities in an individual experiment rather than expectation values? If the optical vector for a given photon is at 30 degrees and the polarizer setting is at 70 degrees, does that mean the probability of a particular spin result is going to be cos^2(70-30)=cos^2(40)?

No. The optical vector is random.

Or are you imagining the result is generated deterministically from the optical vector and the polarizer setting, and if so what would the result be for the angles above? Without these kinds of basic details you simply don't have a well-defined LHV model, so any claims about the expectation value under your model are basically meaningless.

The optical vector is known to be varying randomly. So it would be meaningless to associate any particular optical vector with any particular polarizer setting and detection attribute. In order to say anything about individual detection statistics, given the assumption that each detection results from the deterministic association between some definite but unknown and randomly varying emission-produced optical vector, and some polarizer setting, then don't you have to consider the average angular difference between the optical vectors and the polarizer settings, and calculate accordingly?

 

[DrChinese]

The optical vector is known to be varying randomly.

Oh really? If I have a photon polarized H>, please tell me what is varying randomly.

Or if it is of unknown polarization, please tell me of ONE experiment which demonstrates that it varies randomly with time.

Again, textbook references or similar would be nice.

 

[JesseM]

No. The optical vector is random.

I'm talking about the optical vector on each individual trial. Presumably each time you make a single measurement, the optical vector had a single well-defined angle on that one measurement, even if the angle varies randomly from one measurement to another?

 

[billschnieder]

Yes, like the inequality in the giant equation here which I already directed you to. $$\eta$$ in that equation refers to the probability both photons are detected in any case where a single photon is detected (i.e. if $$\eta < 1$$ you're dealing with a case of imperfect detector efficiency).

And how many of the numerous experiments performed so far violate this new inequality?

 

[JesseM]

And how many of the numerous experiments performed so far violate this new inequality?

Don't know about that precise inequality, but as I mentioned in an earlier post:

There have been experiments where the detection efficiency loophole was closed and some Bell inequality was still violated (see here for instance), it's just that the experiments in question didn't adequately ensure there was a spacelike separation between measurements, so there's the loophole that in principle one particle's detection could have sent a hidden "message" to the other particle telling it how to behave. Again, I think it would be an extremely contrived local realist theory that gave correct predictions about both these experiments and also the experiments where the locality loophole was closed (so there was a spacelike separation between measurements) but the detection efficiency loophole wasn't.

 

[billschnieder]

Don't know about that precise inequality, but as I mentioned in an earlier post:

DId I hear ONE with a but attached?

 

[JesseM]

DId I hear ONE with a but attached?

There have been others that closed the detection loophole since, see here for example. But no experiments have been done that have closed all loopholes, though as I said it would probably require a very contrived local realist model to exploit all the loopholes simultaneously and agree perfectly with QM predictions in all cases that have been tested so far. Why do you care anyway? You don't believe that local realism implies the Bell inequalities anyway, so even if a loophole-free experiment were performed you would just return to some of your old mathematically confused arguments about the proof itself or the idea that any experiment could test it without "controlling for" the hidden variables.

 

[Maaneli]

Now come on, it's not that hard. 3 elements of reality? Really, just read the last couple of paragraphs of EPR and tell me you have no idea what this is about. I understand that you want locality to be part of the equation, and I am not debating the point since I know you won't agree, but certainly you can see that EPR is about elements of reality for ONE particle. And that does not require a locality assumption at all.

Edit - I modified the below, thanks to the clarifications by JenniT and Hurkyl of what you (probably) intended to say in your argument.

<< A single particle, Alice, has 3 elements of reality at angles 0, 120, 240 degrees. This is by assumption, the realistic assumption, and from the fact that these angles - individually - could be predicted with certainty. >>

What, precisely, is the experimental set-up you're talking about, and what do these elements of reality correspond to in the experimental set-up? Measurement settings, perhaps? But then in what sense does the "single particle" "have" these elements of reality? Is the single particle just being measured by these elements of reality fixed at these angles? Are the measurements simultaneous? Or one at a time?

<< It is obvious from the Bell program that there are NO datasets of Alice which match the QM expectation value. Ergo, the assumption is invalid. And you don't need to consider settings of Bob at all. You simply cannot construct the Alice dataset. QED. >>

Nonsense. Bell's inequality is completely contingent on a comparison of statistical correlations between two space-like separated measurement outcomes on two separate particles. Without that, you simply have no dataset to compare to the QM-predicted correlations, in a way which implies a violation of Bell's inequality.

<< The key difference is that the elements of reality are NOT referring to separate particles. >>

Again, WHAT do they refer to? If they are just the measurement settings, then this already amounts to the assumption of local beables.

<< They never were intended to! All the talk about Bob's setting affecting Alice's outcome only relates to Bell tests. >>

The whole point of your argument was, allegedly, to show that the QM violation of Bell's inequality only relies on the assumption of realism, and not locality! And you have shown nothing in this respect.

<< But it should be clear that there is no realistic Alice who can match the QM expectation value. >>

No, I don't see how this follows from anything you've said.

And there was nothing I saw in the last couple of paragraphs in the EPR paper which helped to clarify your argument.

BTW, I am still waiting for your response after reading Bell's La Nouvelle Cuisine.

 

[Hurkyl]

I would have assumed the "element of reality at angle 120 degrees" is the physical quantity that determines which result Alice will get if she sets her measuring device at 120 degrees.

 

[billschnieder]

I would have assumed the "element of reality at angle 120 degrees" is the physical quantity that determines which result Alice will get if she sets her measuring device at 120 degrees.

If the assumption is that a single particle has three such elements of reality at three different angles, then the fact that no experiment has ever been performed in which a single particle was measured at three angles, let alone 2, should be a relevant omission, shouldn't it?

 

[Gordon Watson]

I would have assumed the "element of reality at angle 120 degrees" is the physical quantity that determines which result Alice will get if she sets her measuring device at 120 degrees.

Dear Hurkyl, I am drafting a reply to an excellent post by JesseM and I would like to use the correct physical term for Bell's lambda. I would have assumed that "element of reality TESTED at angle 120 degrees" has some meaning and that "the element of reality" would be a random variable = Bell's lambda?

Would it be acceptable to a physicist to say that Bell's lambda represent spin vectors unconstrained as to length or orientation? And to add ... but correlated by the conservation of angular momentum?

And to say that the measurement interactions reduce the random variables of infinite variability to a few discrete orientations equating to the test settings of the detectors?

I hope this is clear?

Thank you.

 

[Maaneli]

I would have assumed the "element of reality at angle 120 degrees" is the physical quantity that determines which result Alice will get if she sets her measuring device at 120 degrees.

In DrC's argument, Alice is not the experimentalist setting the measuring device at some angle. Alice is just a "particle".

 

[Gordon Watson]

In DrC's argument, Alice is not the experimentalist setting the measuring device at some angle. Alice is just a "particle".

Yes, agreed, that is what I have found. A bit confusing but I always thought DrC's "slips" could be "ignored" ... and that Alice was the experimenter with setting a and outcome A.

 

[Maaneli]

Yes, agreed, that is what I have found. A bit confusing but I always thought DrC's "slips" could be ignored.

I prefer not to do his thinking for him. Besides, that's not the only slip I found in his argument.

 

[Hurkyl]

In DrC's argument, Alice is not the experimentalist setting the measuring device at some angle. Alice is just a "particle".

Fine, it's the physical quantity that would determine the result if it happened to be measured by a measuring device set to 120 degrees.

 

[Gordon Watson]

Maaneli: OK - Touché!

 

[Maaneli]

Fine, it's the physical quantity that would determine the result if it happened to be measured by a measuring device set to 120 degrees.

Bravo. But his conclusion still doesn't follow.

 

[Hurkyl]

Bravo. But his conclusion still doesn't follow.

I haven't followed the discussion. I was just hoping to accelerate things by clearing up the use of the term, allowing you to formulate another response if appropriate.

 

[Gordon Watson]

I would have assumed the "element of reality at angle 120 degrees" is the physical quantity that determines which result Alice will get if she sets her measuring device at 120 degrees.

Fine, it's the physical quantity that would determine the result if it happened to be measured by a measuring device set to 120 degrees.

Dear Hurkyl, this seems to be confusing?

"Element of reality at angle 120 degrees" is probably NOW best allocated to the orientation a of Alice's test device.

"NOW" now being added because "the" physical quantity impacting on, and interacting with the device, is a random member of an infinite set.

So to say "it's the physical quantity" seems confusing to me.

I am hoping your answer to my query re spin-vectors will clarify it all for me.

Thank you.

 

[Maaneli]

I haven't followed the discussion. I was just hoping to accelerate things by clearing up the use of the term, allowing you to formulate another response if appropriate.

Thanks ...

 

[Maaneli]

If the assumption is that a single particle has three such elements of reality at three different angles, then the fact that no experiment has ever been performed in which a single particle was measured at three angles, let alone 2, should be a relevant omission, shouldn't it?

Yes, I agree (assuming that set-up is exactly what DrC has in mind).

 

[ThomasT]

Oh really? If I have a photon polarized H>, please tell me what is varying randomly.

I thought we were talking about photons incident on the polarizers. Are you talking about photons transmitted by the polarizers?

Or if it is of unknown polarization, please tell me of ONE experiment which demonstrates that it varies randomly with time.

This is getting very confusing. If the polarization of the photons is unknown, then this would indicate that you're talking about the photons incident on the polarizer. If the polarization of the photons incident on the polarizer isn't varying randomly, then how would you account for the observed photon flux for individual setups. Isn't it the same no matter what the polarizer setting is?

 

[DrChinese]

1. I thought we were talking about photons incident on the polarizers. Are you talking about photons transmitted by the polarizers?

2. This is getting very confusing. If the polarization of the photons is unknown, then this would indicate that you're talking about the photons incident on the polarizer. If the polarization of the photons incident on the polarizer isn't varying randomly, then how would you account for the observed photon flux for individual setups. Isn't it the same no matter what the polarizer setting is?

Grrr. Photons *incident* on a polarizer can be of known polarization (such as H>) or unknown polarization.

1. Photons of known polarization do not have a "randomly varying vector" or whatever you called it. They may oscillate, but their polarization remains fixed and does not vary. We know that experimentally.

2. Photons of unknown polarization do not have a "randomly varying vector" either - as far as anyone knows. There is no test that indicates this is as you describe it. However, they do provide random results when they are measured with a polarizer. Of course, if you have a pair of entangled photons, which of course are of unknown polarization, you would deduce that they definitely do not have a "varying" polarization. "Varying" meaning changing with time. They definitely do not change with time, otherwise you would not have perfect correlations (since those correlations are time invariant).

My point is that characterization of entangled photons in the manner you describe is not warranted.

 

[DrChinese]

If the assumption is that a single particle has three such elements of reality at three different angles, then the fact that no experiment has ever been performed in which a single particle was measured at three angles, let alone 2, should be a relevant omission, shouldn't it?

Bill, please read EPR. They specifically address this point, there is no omission. And that is the crux of my argument. They say "no reasonable definition of reality can be expected" to require that all individual elements of reality be predicted at the same time. So that means that if Alice (yes the particle) has elements of reality at 0, 120 and 240 degrees, these must be ASSUMED to be simultaneously existing.

a. Yes, that there are individual elements of reality is deduced from tests of different particles.
b. No, there is no test of one particle which demonstrates that there are more that one polarization element of reality at a time (per the EPR definition).

So I am simply accepting EPR at their word. And so did Bell. So it should be obvious now that there cannot be any group of photons that have simultaneous elements of reality for 0, 120 and 240 degrees which also satisfy the QM expectation relationship of cos^2 (cos for spin 1/2 particles). There is absolutely no locality involved in this deduction.

And Bell was quite aware of this. But he was also aware that an experimental test using entangled particles might suffer from the idea that detector a might influence an outcome B (and vice versa). Enter locality.

 

[DrChinese]

<< A single particle, Alice, has 3 elements of reality at angles 0, 120, 240 degrees. This is by assumption, the realistic assumption, and from the fact that these angles - individually - could be predicted with certainty. >>

What, precisely, is the experimental set-up you're talking about, and what do these elements of reality correspond to in the experimental set-up? Measurement settings, perhaps? But then in what sense does the "single particle" "have" these elements of reality? Is the single particle just being measured by these elements of reality fixed at these angles? Are the measurements simultaneous? Or one at a time?

<< It is obvious from the Bell program that there are NO datasets of Alice which match the QM expectation value. Ergo, the assumption is invalid. And you don't need to consider settings of Bob at all. You simply cannot construct the Alice dataset. QED. >>

Nonsense. Bell's inequality is completely contingent on a comparison of statistical correlations between two space-like separated measurement outcomes on two separate particles. Without that, you simply have no dataset to compare to the QM-predicted correlations, in a way which implies a violation of Bell's inequality.

Read EPR!

EPR is not talking about whether Alice and Bob have simultaneous elements of reality, they are talking about Alice only. Bob is used to prove there is an element of reality to Alice because, by their definition: if an Alice outcome can be predicted in advance with certainty. then it is real. They observe Bob to accomplish this, that is all Bob is for.

Now, it should be clear that I can choose to measure Bob any way I like, let's say 0, 120 or 240 degrees. So if I measure Alice the same way, I can demostrate an element of reality for those settings. The EPR conclusion was that it is unreasonable to require that all of those settings be predictable at once!

I don't happen to agree with that conclusion, but there it is. Realism is defined a la EPR. And if you don't think Bell used that exactly, read Bell again. I will be glad to supply the reference quotes (which can then be suitably ignored in favor of something else). But I am operating nearly verbatim at this point, both for EPR and Bell.

 

[DrChinese]

Dear Hurkyl, this seems to be confusing?

"Element of reality at angle 120 degrees" is probably NOW best allocated to the orientation a of Alice's test device.

"NOW" now being added because "the" physical quantity impacting on, and interacting with the device, is a random member of an infinite set.

So to say "it's the physical quantity" seems confusing to me.

I am hoping your answer to my query re spin-vectors will clarify it all for me.

Thank you.

JenniT, you should read EPR yourself. As I keep telling you, this is assumed by Bell.

The 2nd to last paragraph of EPR:

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simulataneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."

It takes a minute to parse that out, but it say that it is unreasonable to require the spin elements of reality at 0, 120 and 240 degrees (my angle settings not theirs) to be simultaneously proven.

That is for a single particle and you can call it anything you like. Alice, a, A, particle 1, or whatever. According to the EPR result (which is wrong because of Bell): QM is incomplete because there exist elements of reality which QM does not provide values for.

 

[DrChinese]

Bravo. But his conclusion still doesn't follow.

My conclusion being exactly: That both EPR's definition of reality AND the QM expectation values (cos^2) cannot both be accurate for a group of photons. This deduction is completely independent of any kind of experimental proof. In fact, this is simply the Bell result before you imagine trying to put together an experimental version. When you put together an experimental version, then locality comes into play.

So yes, it follows from EPR and Bell. In fact, this is what my_wan and several others are alluding to when they say that Malus implies violation of BIs.

 

[billschnieder]

It takes a minute to parse that out, but it say that it is unreasonable to require the spin elements of reality at 0, 120 and 240 degrees (my angle settings not theirs) to be simultaneously proven.

That is for a single particle and you can call it anything you like. Alice, a, A, particle 1, or whatever. According to the EPR result (which is wrong because of Bell): QM is incomplete because there exist elements of reality which QM does not provide values for.

DrC,
Your interpretation of EPR is not correct.

The paragraph before the one you quoted says:

"Previously we have proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that the two physical quantities with noncommuting operators can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2). We are forced thus to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

This is the main conclusion of the paper. The part you quoted is merely pre-empting how someone might object to their main conclusion. You are trying to parse that final paragraph in a way which contradicts their main conclusion.

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."

Note they are saying here that, if you assume that QM is complete, then as they have just proven above, according to QM, both the the local P and the remote Q are simultaneously real, but then such a reality in which measurement of local P automatically changes the reality of a remote Q, is unreasonable. Therefore it does not matter for their argument whether you choose to restrict the definition of "simultaneous reality" to "only when they can be simultaneously measured or predicted".

In short, they are saying either QM is not complete, or if you insist that QM is complete, you must adhere to an unreasonable reality in which FTL is possible.
Therefore your statement underlined above is not remotely similar to what EPR wrote.

 

[DrChinese]

DrC,
Your interpretation of EPR is not correct.

I can't make you read it my way. You'll have to do that on your own.

But they say it. True, one might object to their conclusion regarding the completeness of QM on the ground mentioned - elements of reality must be simultaneously predictable. And that would negate their conclusion, as you mention. But they still say that, in their opinion, their definition should stand - the less restrictive one. And their definition is (paraphrased):

"Two or more physical quantities can be regarded as simultaneous elements of reality when they can be predicted with certainty without disturbing the particle in any way - regardless of whether those elements can be simultaneously predicted."

I don't think that definition is hard to take away from EPR. Seriously, you do see that much, don't you? Well, assuming you can stop being craggly long enough to agree to something... that is the definition Bell uses. As I keep saying, you don't have to agree with the definition. You merely accept that is what Bell was working with. Along with most everyone after...

 

[billschnieder]

I can't make you read it my way. You'll have to do that on your own.

But they say it. True, one might object to their conclusion regarding the completeness of QM on the ground mentioned - elements of reality must be simultaneously predictable. And that would negate their conclusion, as you mention. But they still say that, in their opinion, their definition should stand - the less restrictive one. And their definition is (paraphrased):

"Two or more physical quantities can be regarded as simultaneous elements of reality when they can be predicted with certainty without disturbing the particle in any way - regardless of whether those elements can be simultaneously predicted."

I don't think that definition is hard to take away from EPR. Seriously, you do see that much, don't you? Well, assuming you can stop being craggly long enough to agree to something... that is the definition Bell uses. As I keep saying, you don't have to agree with the definition. You merely accept that is what Bell was working with. Along with most everyone after...

Again you are putting words in the "mouth" of EPR. They never provided a definition reality like the one you are suggesting. They said:

A comprehensive definition of reality is, however, unnecessary for our purpose. We shall be satisfied with the following criterion, which we regard as reasonable. If, without in any way disturbing a system, we can predict with certainty (i.e, with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way, whenever the conditions set down in it occur. Regarded not as a necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality.

Note that they do not say the physical quantity being predicted, is itself an element of reality, just that it corresponds to one.

Secondly, Bell is squarely focused on locality and causality as has been pointed out to you on this thread before. Specifically, in Bell's own words, he says:

The paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.

So this idea that there is something out-there such as the EPR definition of reality which Bell was supposedly working from is just not accurate. The words of the authors themselves confirm that to be the case.