Boole vs. Bell - the latest paper of De Raedt et al

[harrylin]

Interesting further input from another thread:

That's not a counter-example.

What they claim to violate is Bell's original 1964 inequality. Bell's original inequality is something of an odd duckling in the zoology of Bell inequalities in that it relies on an extra (but entirely observable) assumption. Specifically, in their notation, and putting the locations back on (Lille = 1, Lyon = 2), the Bell inequality uses the assumption that A^{1}_{\mathbf{b}}(w) = A^{2}_{\mathbf{b}}(w). This is observable, since it implies that \langle A^{1}_{\mathbf{b}}(w) A^{2}_{\mathbf{b}}(w) \rangle = 1, and it just means that the correct way to state Bell's inequality should really be something like
\langle A^{1}_{\mathbf{a}}(w) A^{2}_{\mathbf{b}}(w) \rangle + \langle A^{1}_{\mathbf{a}}(w) A^{2}_{\mathbf{c}}(w) \rangle + \langle A^{1}_{\mathbf{b}}(w) A^{2}_{\mathbf{c}}(w) \rangle \geq -1 \quad \text{given that} \quad \langle A^{1}_{\mathbf{b}}(w) A^{2}_{\mathbf{b}}(w) \rangle = 1 \,.
Their counter-example isn't a counter-example because it has \langle A^{1}_{\mathbf{b}}(w) A^{2}_{\mathbf{b}}(w) \rangle = -1. Incidentally, if you try to read the inequality above in the same way as other Bell inequalities (i.e. without imposing a condition like A^{1}_{\mathbf{b}}(w) = A^{2}_{\mathbf{b}}(w)), then it's easy to see that its local bound is actually -3 (the same as the algebraic bound) instead of -1. [..]

Bell relied on the fact that deterministically A^{1}_{\mathbf{b}}(w) = A^{2}_{\mathbf{b}}(w); and while it is generally held that the sign isn't important, De Raedt reproduced similar observables in his illustration. However:

[..] Bell derived some inequalities for the case where \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = -1. You can alternatively derive some similar but not identical inequalities for the case where \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = +1. The particular inequality that de Raedt et. al. considered is derived assuming \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = +1, and there is simply no reason to expect it should be satisfied if \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = -1.

Specifically, if you assume \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = -1, you can derive the following four inequalities:
<br /> \begin{eqnarray}<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle + \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\geq&amp; -1 \,, \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle + \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\geq&amp; -1 \,, \qquad (*) \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle + \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle + \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; +1 \,, \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; +1 \,. \qquad (*)<br /> \end{eqnarray}<br />
The second and fourth of these inequalities, which I've marked (*), are the ones Bell derived in 1964. Specifically, they're equivalent to Eq. (15) of Bell's 1964 paper [1]. The other two can easily be derived in an analogous manner (or, alternatively, just by flipping the sign of A^{2}_{\mathbf{c}}).

If you instead set \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{b}} \rangle = +1, you get four slightly different inequalities, which you can basically all derive by flipping the sign on A^{1}_{\mathbf{b}}:
<br /> \begin{eqnarray}<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle + \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle + \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\geq&amp; -1 \,, \qquad (\#) \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\geq&amp; -1 \,, \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle + \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; +1 \,, \\<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle + \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; +1 \,.<br /> \end{eqnarray}<br />
The first of these, (#), is the one that de Raedt et. al. tested.
[..][1] J. S. Bell, Physics 1 3 195--200 (1964).

I had overlooked that the inequality that De Raedt gave as example is one of Boole - and not exactly one of Bell. Thanks for pointing that out!

So, he merely wanted to illustrate how that kind of inequalites (Boole/Bell) can be broken with local realism, if applied in the peculiar manner of Bell. And it appears to me that Boole did not assume a certain outcome result; according to the presentation, the Boole inequality of eq.113 in De Raedt's paper must be valid for all proper pair combinations, no matter what the products are. But instead of lingering on that point, for this discussion it will be interesting to test Bell's inequality (his equation no.15) on De Raedt's illustration.

Now, it looks to me that your representation here above of Bell's original inequality is still not quite right: an absolute sign is lacking. According to my copy, Bell's eq.15 for locations 1 and 2 is (rearranged):

<br /> \begin{eqnarray}<br /> |\langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle| - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; +1 \,. \qquad<br /> \end{eqnarray}<br />

And the same for location pairs (1,3) and (2,3).

Here are the fictive measurement results once more, for locations 1-3 on even and odd days:

... Even ...|.. Odd
L ...1...2...3.|..1...2...3
A_a +1 +1 +1.| -1. -1. -1
A_b +1. -1 +1.| -1 +1. -1
A_c. -1. -1. -1.|+1 +1 +1

Computing from the results for location pair (1,2), I obtain as outcomes: +1, -1.
That location pair does not break Bell's inequality, the average is 0.

For location pair (2,3), I obtain as outcomes: +1, +1. Average +1.
Also no breaking of Bell's inequality.

For location pair (1,3), I obtain as outcomes: +3, +3. Average +3.
If I'm not mistaken, this pair very strongly breaks Bell's inequality!

Thus it's easy to modifiy De Raedt's illustration for Bell's original inequality: just take Lille=1, Lyon=3.

Now, it's a bit of a weak point that this effect is not homegeneous; but while unrealistic for Lille and Lyon, we can imagine a random fluctuation of such funny properties between all locations. Let's see what that gives for the average result of all locations:

(0 + 1 + 3) / 3 = 4/3

Thus, Bell's inequality applied on that refined illustration, gives according to me (I may have made an error of course):

4/3 <= 1
Obviously that inequality is broken.

In conclusion, it still looks to me that De Raedt's modified illustration with patients does show how inequalites like those of Bell can be broken with local realism.

 

[DrChinese]

In conclusion, it still looks to me that De Raedt's modified illustration with patients does show how inequalites like those of Bell can be broken with local realism.

This is a bit of sleight of hand. We are talking about quantum particles, not patients and doctors. The DrChinese challenge, as applied to this scenario is, becomes:

a) Give me any local realistic sample you care to invent.
b) I get to pick what to measure in any particular trial. I will do this "randomly" as long as the sample is not overly cherry picked. Obviously since I get to see the data before I pick, I can always cheat but I agree not to unless your success depends on me selecting a particular set of measurement to make.
c) It must satisfy the perfect correlations condition so as to imply the existence of hidden variables. IE When I pick the same attribute to observe at both spots, I get the same answer.
d) And as Delta Kilo has pointed out, there must be at least 3 choices of things for me to measure (per b).

De Raedt's modified illustration may look one way to you, but that view won't be shared by most.

 

[harrylin]

This is a bit of sleight of hand. We are talking about quantum particles, not patients and doctors. The DrChinese challenge, as applied to this scenario is, becomes:

a) Give me any local realistic sample you care to invent.
b) I get to pick what to measure in any particular trial. I will do this "randomly" as long as the sample is not overly cherry picked. Obviously since I get to see the data before I pick, I can always cheat but I agree not to unless your success depends on me selecting a particular set of measurement to make.
c) It must satisfy the perfect correlations condition so as to imply the existence of hidden variables. IE When I pick the same attribute to observe at both spots, I get the same answer.
d) And as Delta Kilo has pointed out, there must be at least 3 choices of things for me to measure (per b).

De Raedt's modified illustration may look one way to you, but that view won't be shared by most.

That illustration comes close doing that - but obviously it was not intended to address the "DrChinese challenge".

 

[harrylin]

[concerning the quote "From our work above it is then an immediate corollary that Bell’s inequalities cannot be violated; not even by influences at a distance.":]

[..] Bell's inequalities are most certainly violated by influences at a distance. [...]

What they meant was not clear to me until now; it may be that they explained it, but it wasn't clear to me. However, they also refer to papers by Accardi.and just now morrobay put our attention to a pre-print by him, in which that point is explained clearer IMHO.

Accardi finds that with Bell's assumptions about probability distributions the Bell inequality must even hold for non-local processes. - p.8 of http://arxiv.org/pdf/quant-ph/0007005v2.pdf
I suppose that that is also what De Raedt means.

PS: I also found an interesting monograph by Gill contra Accardi: http://www.jstor.org/stable/4356235

 

[stevendaryl]

[concerning the quote "From our work above it is then an immediate corollary that Bell’s inequalities cannot be violated; not even by influences at a distance.":]What they meant was not clear to me until now; it may be that they explained it, but it wasn't clear to me. However, they also refer to papers by Accardi.and just now morrobay put our attention to a pre-print by him, in which that point is explained clearer IMHO.

Accardi finds that with Bell's assumptions about probability distributions the Bell inequality must even hold for non-local processes. - p.8 of http://arxiv.org/pdf/quant-ph/0007005v2.pdf
I suppose that that is also what De Raedt means.

I'm getting several different threads about Bell's inequalities mixed up. I thought I had given an example to the contrary.

Bell's inequality is proved under the assumption that joint probabilities can be written in this form:

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P(A | \lambda \wedge \alpha) P(B | \lambda \wedge \beta)

where A, B are the results at the two detectors, \alpha, \beta are the settings of the two detectors, and \lambda is the hidden variable. Note that the conditional probability for A depends only on \lambda and \alpha, but not \beta. The conditional probability for B does not depend on \alpha.

If you allow nonlocal interactions, then a more general expression is possible, that is still a "realistic hidden-variables" theory:

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P(A | \lambda \wedge \alpha \wedge \beta) P(B | \lambda \wedge \alpha \wedge \beta)

You can certainly violate Bell's inequalities with a realistic model of this form. To give a simple example:

Let P(\lambda) = 1 for 0 \leq \lambda \leq 1
Let P(A | \lambda \wedge \alpha \wedge \beta) = 1 for \lambda \leq \frac{1}{2} and 0 otherwise.
Let P(B | \lambda \wedge \alpha \wedge \beta) = 1 for \frac{1}{2} sin^2(\frac{1}{2}(\beta - \alpha)) \leq \lambda \leq \frac{1}{2} (1 + sin^2(\frac{1}{2}(\beta - \alpha))) and 0 otherwise.

This model reproduces exactly the predictions of QM for the spin-1/2 twin-pair EPR experiment, and violates Bell's inequality.

 

[harrylin]

[..] I thought I had given an example to the contrary.

Bell's inequality is proved under the assumption that joint probabilities can be written in this form:

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P(A | \lambda \wedge \alpha) P(B | \lambda \wedge \beta)

where A, B are the results at the two detectors, \alpha, \beta are the settings of the two detectors, and \lambda is the hidden variable. Note that the conditional probability for A depends only on \lambda and \alpha, but not \beta. The conditional probability for B does not depend on \alpha.

If you allow nonlocal interactions, then a more general expression is possible, that is still a "realistic hidden-variables" theory:

P(A \wedge B | \alpha \wedge \beta) = \sum_\lambda P(\lambda) P(A | \lambda \wedge \alpha \wedge \beta) P(B | \lambda \wedge \alpha \wedge \beta)

You can certainly violate Bell's inequalities with a realistic model of this form. [..]

At first sight, I see no disagreement between these statements of yours (incl. your example) and theirs.

What De Raedt seems to argue (and probably what he and others have shown), is that in order to break such an inequality one must have a joint probability that differs from the one that Bell assumed for deriving that inequality. That is not only true if the model is local (an option that Bell found hard to imagine) but even if the model is non-local. Do you disagree with that?

 

[DrChinese]

Accardi finds that with Bell's assumptions about probability distributions the Bell inequality must even hold for non-local processes. - p.8 of http://arxiv.org/pdf/quant-ph/0007005v2.pdf
I suppose that that is also what De Raedt means.

That doesn't even make sense (that they must apply to non-local theories as they do local ones). And that is acknowledged in EPR.

The point of a non-local realistic theory is that there is a relationship between distant objects and a mechanism whereby there is mutual instantaneous influence. No counterfactual measurement of the pair is possible due to the importance of the mutual influence. There is no product state by definition.

 

[harrylin]

That doesn't even make sense (that they must apply to non-local theories as they do local ones). And that is acknowledged in EPR.

The point of a non-local realistic theory is that there is a relationship between distant objects and a mechanism whereby there is mutual instantaneous influence. No counterfactual measurement of the pair is possible due to the importance of the mutual influence. There is no product state by definition.

I take it that you are saying that what De Raedt et all apparently mean (according to me) makes no sense according to you.

It looks to me that EPR's opinions are not taken as authority by De Raedt or Accardi (or Bell). Are you saying that it is impossible to create a non-local model (thus with influence at a distance) that adheres to Bell's assumptions for local models so that it can't break Bell's inequality? I guess not, for then you'd likely have stated that what they claim is wrong. Maybe you simply don't see the point that they made?

 

[stevendaryl]

At first sight, I see no disagreement between these statements of yours (incl. your example) and theirs.

What De Raedt seems to argue (and probably what he and others have shown), is that in order to break such an inequality one must have a joint probability that differs from the one that Bell assumed for deriving that inequality. That is not only true if the model is local (an option that Bell found hard to imagine) but even if the model is non-local. Do you disagree with that?

I'm not sure exactly what you're saying. As I said, the point of locality is that it allows you to assume that the conditional probability for Alice's result depends only on Alice's settings (and the shared hidden variable) while the conditional probability for Bob's result depends only on Bob's settings (and the shared hidden variable). If Alice's result depends on Bob's setting, or Bob's result depends on Alice's setting, then you can't derive Bell's inequality. So it seems to me that locality is pretty important.

There is an assumption made by Bell, which he expounds on his "theory of local be-ables", that in a realistic setting, the probability for an event should only depend on facts about the causal past of that event (where "causal past" means "past lightcone", if there are no faster-than-light influences). In other words, if I have complete information about the state of the universe in the causal past of an experiment, then I have the most information possible about the possible results of the experiment. Facts about regions of the universe that are not in the causal past of the experiment are only relevant in that they reveal facts about the causal past.

For instance, if I put a $1 bill and a $10 bill into two identical white envelopes, and give one to Alice and another to Bob, and they separate and open their envelopes, the knowledge that Bob found a $1 bill in his envelope tells me something about what Alice will find in her envelope. But the complete description of the causal past of Alice's envelope includes a specification of what bill was put into it. So if you had complete information about the causal past of Alice's envelope, knowledge about Bob's envelope would tell you nothing new.

In other words, Bell's assumption is basically that all state information about the universe is localized. There are no "nonlocal" facts that can't be factored into a collection of local facts.

 

[harrylin]

I'm not sure exactly what you're saying. As I said, the point of locality is that it allows you to assume that the conditional probability for Alice's result depends only on Alice's settings (and the shared hidden variable) while the conditional probability for Bob's result depends only on Bob's settings (and the shared hidden variable). If Alice's result depends on Bob's setting, or Bob's result depends on Alice's setting, then you can't derive Bell's inequality. So it seems to me that locality is pretty important.

Certainly, for Bell "locality" (as well as what he understood with "realism") was important to motify the separation of variables. Now, as the title of his paper suggests, De Raedt considers there such inequalities in the broader mathematical framework of Boole. That framework does not depend on such concepts as locality; what really matters are the conditional probabilities themselves.

There is an assumption made by Bell, which he expounds on his "theory of local be-ables", that in a realistic setting, the probability for an event should only depend on facts about the causal past of that event (where "causal past" means "past lightcone", if there are no faster-than-light influences). In other words, if I have complete information about the state of the universe in the causal past of an experiment, then I have the most information possible about the possible results of the experiment. Facts about regions of the universe that are not in the causal past of the experiment are only relevant in that they reveal facts about the causal past.

For instance, if I put a $1 bill and a $10 bill into two identical white envelopes, and give one to Alice and another to Bob, and they separate and open their envelopes, the knowledge that Bob found a $1 bill in his envelope tells me something about what Alice will find in her envelope. But the complete description of the causal past of Alice's envelope includes a specification of what bill was put into it. So if you had complete information about the causal past of Alice's envelope, knowledge about Bob's envelope would tell you nothing new.

In other words, Bell's assumption is basically that all state information about the universe is localized. There are no "nonlocal" facts that can't be factored into a collection of local facts.

That looks good to me - and I guess also to De Raedt. What he apparently tried to do is to make people think "outside of the box"; in this case, the "box" is the particular EPR setting and subsequent reasoning of Bell. Sometimes that helps to get a fresh look at puzzles like these.

 

[DrChinese]

I take it that you are saying that what De Raedt et all apparently mean (according to me) makes no sense according to you.

It looks to me that EPR's opinions are not taken as authority by De Raedt or Accardi (or Bell). Are you saying that it is impossible to create a non-local model (thus with influence at a distance) that adheres to Bell's assumptions for local models so that it can't break Bell's inequality? I guess not, for then you'd likely have stated that what they claim is wrong. Maybe you simply don't see the point that they made?

Not so much taking issue with you as the idea that non-local theories must adhere to the same requirements as local ones. Non-local theories can break a Bell Inequality because it violates the assumption of measurement/device independence. Ie a measurement choice here does affect an outcome there.

Obviously de Raedt et al are making a point that I don't think stands, sure it is possible I don't really understand it. I am not a poster boy for non-local theories anyway.

Accardi makes a lot of points I think are either wrong or irrelevant too. Example being his chameleon analogy, which like the Doctor/Patients analogy does not come close to addressing Bell. (Although perhaps Boole...) Sadly, many writers fail to play devil's advocate against their own position and end up far down the creek without a paddle.

 

[audioloop]

Two years ago an intriguing paper of De Raedt's team concerning Bell's Theorem appeared in Europhysics Letters (http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0767v2.pdf).

Now (officially next month), an elaboration on those ideas has been published:

Hans De Raedt et al: "Extended Boole-Bell inequalities applicable to quantum theory"
J. Comp. Theor. Nanosci. 8, 6(June 2011), 1011
http://www.ingentaconnect.com/content/asp/jctn/2011/00000008/00000006/art00013

Full text also in http://arxiv.org/abs/0901.2546

De Raedt et al do not pretend to be the first to discuss these issues, and they refer to quite a number of earlier papers by other authors that bring up similar points.

Below I present a little summary of their very elaborated explanations.

It all looks very plausible to me since I tend regard Bell's Theorem as a magician's trick - we tend to interpret a miracle as a trick, even if nobody can explain how the trick is done. Now, this paper appears to explain "how it's done" and I like to hear if there are valid objections.

Before we discuss their criticism about Bell's "element of reality", it may be good to discuss Boole's example of patients and illnesses, which De Raedt et all reproduce in this paper. They show that by failing to account for unknown causes for the observations, similar inequalities can be drawn up as those of Bell, without a valid reason to infer a spooky action at a distance - although it appears that way.

Does anyone challenge the correctness of that claim?

Regards,
Harald

--------------------------------------------------------
Abstract:
We address the basic meaning of apparent contradictions of quantum theory and probability frameworks as expressed by Bell's inequalities. We show that these contradictions have their origin in the incomplete considerations of the premises of the derivation of the inequalities. A careful consideration of past work, including that of Boole and Vorob'ev, has lead us to the formulation of extended Boole-Bell inequalities that are binding for both classical and quantum models. The Einstein-Podolsky-Rosen-Bohm gedanken experiment and a macroscopic quantum coherence experiment proposed by Leggett and Garg are both shown to obey the extended Boole-Bell inequalities. These examples as well as additional discussions also provide reasons for apparent violations of these inequalities.

The above summary is IMHO a rather "soft" reflection of its contents: the way I read it, basically this paper asserts to show that Bell's theorem is wrong! It does this in an elaborate way, here are some fragments of the text (the below is copied from the ArXiv version):

"the Achilles heel of Bell's interpretations: [..] all of Bell's derivations assume from the start that ordering the data into triples as well as into pairs must be appropriate and commensurate with the physics. [..] From our work above it is then an immediate corollary that Bell's inequalities cannot be violated; not even by influences at a distance."

The paper next discusses such things as "Filtering-type measurements on the spin of one spin-1/2 particle", "Application to quantum flux tunneling", "Application to Einstein-Podolsky-Rosen-Bohm (EPRB) experiments" (in particular Stern-Gerlach).

To top it off, illustrations of apparent Bell violations are given, even of a similar inequality with "a simple, realistic every-day experiment involving doctors who perform allergy tests on patients". [..] "Together these examples represent an infinitude of possibilities to explain apparent violations of Boole-Bell inequalities in an Einstein local way." Special attention is given to "EPR-Bohm experiments and measurement time synchronization".

"It is often claimed that a violation of such inequalities implies that either realism or Einstein locality should be abandoned. As we saw in our counterexample which is both Einstein local and realistic in the common sense of the word, it is the one to one correspondence of the variables to the logical elements of Boole that matters when
we determine a possible experience, but not necessarily the choice between realism and Einstein locality."
[..]
"The mistake here is that Bell and followers insist from the start that the same element of reality occurs for the three different experiments with three different setting pairs."

The -IMHO- most important conclusion of the paper is that "A violation of the Extended Boole-Bell inequalities cannot be attributed to influences at a distance"; they argue that a violation only can arise from a grouping in pairs.

interesting paper:

The irrelevance of Bell inequalities in Physics.
"Comments on the Extended Boole-Bell Inequalities Applicable to Quantum Theory"
http://hal.archives-ouvertes.fr/docs/00/82/41/24/PDF/RHM-hans.pdf

"the violation of the celebrated Bell inequalities in quantum mechanics is due only to a rather elementary, even if somewhat subtle error made in the way the statistical data are handled"



.

 

[stevendaryl]

interesting paper:

The irrelevance of Bell inequalities in Physics.
"Comments on the Extended Boole-Bell Inequalities Applicable to Quantum Theory"
http://hal.archives-ouvertes.fr/docs/00/82/41/24/PDF/RHM-hans.pdf

"the violation of the celebrated Bell inequalities in quantum mechanics is due only to a rather elementary, even if somewhat subtle error made in the way the statistical data are handled"



.

So there are papers saying that Bell is wrong, because it's easy for a local hidden variables theory to violate the inequalities. Then there are other papers saying that Bell is wrong because nothing can violate the inequalities, not even quantum mechanics.

 

[harrylin]

interesting paper:

The irrelevance of Bell inequalities in Physics.
"Comments on the Extended Boole-Bell Inequalities Applicable to Quantum Theory"
http://hal.archives-ouvertes.fr/docs/00/82/41/24/PDF/RHM-hans.pdf

"the violation of the celebrated Bell inequalities in quantum mechanics is due only to a rather elementary, even if somewhat subtle error made in the way the statistical data are handled"
.

OK I see that it's a commentary on De Raedt's paper, and it addresses the same rather obscure conclusion that I discussed in post #154. Thanks!

So there are papers saying that Bell is wrong, because it's easy for a local hidden variables theory to violate the inequalities. Then there are other papers saying that Bell is wrong because nothing can violate the inequalities, not even quantum mechanics.

Hmm yes at first sight it looks to me that that commentary exaggerates quite a bit! However, the point that De Raedt made is also here: such inequalities are purely mathematical, so that in order to break them one has to break one of the mathematical conditions on which they are based.
Of course, Bell never pretended otherwise; it's just a thing not to forget.

 

[stevendaryl]

OK I see that it's a commentary on De Raedt's paper, and it addresses the same rather obscure conclusion that I discussed in post #154. Thanks!

Hmm yes at first sight it looks to me that that commentary exaggerates quite a bit! However, the point that De Raedt made is also here: such inequalities are purely mathematical, so that in order to break them one has to break one of the mathematical conditions on which they are based.
Of course, Bell never pretended otherwise; it's just a thing not to forget.

The condition that must be broken to violate the inequality is locality. If the probability distribution for Alice's result depends on Bob's detector settings, then there is no reason for the inequality to hold.

 

[harrylin]

The condition that must be broken to violate the inequality is locality. [..]

If so, then De Raedt's illustration that I just discussed in post #151 is "non-local"?!

 

[DrChinese]

The irrelevance of Bell inequalities in Physics.
"Comments on the Extended Boole-Bell Inequalities Applicable to Quantum Theory"
http://hal.archives-ouvertes.fr/docs/00/82/41/24/PDF/RHM-hans.pdf

"the violation of the celebrated Bell inequalities in quantum mechanics is due only to a rather elementary, even if somewhat subtle error made in the way the statistical data are handled"

Hmmm, takes 20 pages and 64 formulae to correct an "elementary" error.

I will definitely add this to my pantheon of "why Bell is wrong/misguided/etc" links. Each one with a completely different critique, and all equally well accepted*.


*Not.

 

[stevendaryl]

If so, then De Raedt's illustration that I just discussed in post #151 is "non-local"?!

I have to admit that I didn't read that in any kind of detail, so I can't comment. Past efforts on my part to understand papers that claim to refute Bell have all ended in frustration, because the authors almost always end up proving something that is beside the point. But for the sake of the discussion, I guess I can try once again with De Raedt's example.

Is there a definitive statement of what the example is and what it shows? Or can you just summarize it here? The post that you pointed to seems to start in the middle.

 

[stevendaryl]

EPR Challenge

This picture illustrates the challenge for a local hidden-variables explanation for the spin-1/2 twin-pair EPR experiment: Is it possible to simulate the quantum mechanical prediction using nonquantum means?

What would be sufficient to disprove Bell's claims would be to write three computer programs of the following type:

1. Generator(i): computes the ith value for λ, where λ is a floating point number (I'm assuming that any other reasonable type of value can be "encoded" into a real.
2. Detector_A(α, λ): takes a pair α, λ, where α is a detector orientation (chosen by Alice), and λ is the output of Generator.
3. Detector_B(β, λ): takes a pair β, λ, where βis a detector orientation (chosen by Bob), and λ is the output of Generator.

For a large number of rounds i (enough that there are good statistics for various pairs of α and β), have Alice and Bob randomly choose α_i and β_i, respectively, and have the Generator randomly choose λ_i. Record the outputs A_i and B_i. Then compute statistics:

P(A, B | α, β) = N'/N
P(A, \negB | α, β) = N''/N
P(\negA, B | α, β) = N'''/N
P(\negA, \negB | α, β) = N''''/N

where N = the number of rounds i such that α_i = α,
β_i = β, and where

• N' = the number of those rounds such that A_i = +1, B_i = +1,
• N'' = the number of those rounds such that A_i = +1, B_i = -1,
• N''' = the number of those rounds such that A_i = -1, B_i = +1,
• N'''' = the number of those rounds such that A_i = -1, B_i = -1,

The claim is that no matter what programs are used, you will not get

P(A, B | α, β) = 1/2 sin²(θ/2)
P(A, \negB | α, β) = 1/2 cos²(θ/2)
P(\negA, B | α, β) = 1/2 cos²(θ/2)
P(\negA, \negB | α, β) = 1/2 sin²(θ/2)

(If you want, you can add more inputs to the detectors to represent local randomness.)

Mucking about with Bell's inequalities is a waste of time, it seems to me. The bottom line is really the nonexistence of three programs that would reproduce the predictions of QM. And there are no such programs.

Now, you could try messing with the requirements. For instance, you can say that the detectors sometimes output a "null" value, rather than +1 or -1. Or you can say that (as someone, maybe De Raedt, suggested), you can say that occasionally, Alice's detector or Bob's detector gets the wrong λ; maybe Alice gets λ_i while Bob gets λ_i+1. I don't have an opinion about whether such generalizations could allow a better simulation of QM.

 

[harrylin]

I have to admit that I didn't read that in any kind of detail, so I can't comment. Past efforts on my part to understand papers that claim to refute Bell have all ended in frustration, because the authors almost always end up proving something that is beside the point. But for the sake of the discussion, I guess I can try once again with De Raedt's example.

Is there a definitive statement of what the example is and what it shows? Or can you just summarize it here? The post that you pointed to seems to start in the middle.

Sure. First of all, for the context: I gave summary of the paper under discussion here in my first post of this thread:
https://www.physicsforums.com/showthread.php?t=499002

And after you asked me in the other thread, I summarized that simple example for you as follows
(https://www.physicsforums.com/showthread.php?t=697939&page=3):

De Raedt attempted to give a counter example to Bell's derivation method. His simple counter example is given on p.25, 26 of http://arxiv.org/abs/0901.2546 :

In this second variation of the investigation, we let only two
doctors, one in Lille and one in Lyon perform the examina-
tions. The doctor in Lille examines randomly all patients of
types a and b and the one in Lyon all of type b and c each one
patient at a randomly chosen date. The doctors are convinced
that neither the date of examination nor the location (Lille or
Lyon) has any influence and therefore denote the patients only
by their place of birth. After a lengthy period of examination
they find
Γ(w) = Aa (w)Ab (w) + Aa (w)Ac (w) + Ab (w)Ac (w) = −3

They further notice that the single outcomes of Aa (w), Ab (w)
and Ac (w) are randomly equal to ±1. [..]
a single outcome manifests itself randomly in one city and [..]
the outcome in the other city is then always of opposite sign

Perhaps the weakest point of that example is that the freely chosen detector position of Bell tests with anti-correlation is not fully matched by it. And it is still unclear to me if that is impossible to implement in an example, or only difficult to do. Consequently, the question is for me still open if Bell's assumptions about local realism were valid or not.

However, as wie brought up that the inequality in DeRaedt's paper does not exactly match equation 15 of Bell 1964, I re-analyzed that simple illustration with that inequality in post #151 here.
- https://www.physicsforums.com/showthread.php?p=4465579

[..]

This picture illustrates the challenge for a local hidden-variables explanation for the spin-1/2 twin-pair EPR experiment: Is it possible to simulate the quantum mechanical prediction using nonquantum means?

What would be sufficient to disprove Bell's claims would be to write three computer programs of the following type:

[..]

Mucking about with Bell's inequalities is a waste of time, it seems to me. The bottom line is really the nonexistence of three programs that would reproduce the predictions of QM. And there are no such programs.

That it's very difficult to write such a set of computer programs is well known (although Accardi apparently claims to have done it). In fact, it was already known that it's very difficult to come up with a fitting "local realistic" model, and therefore Bell came up with his famous inequality which he claimed cannot be broken by such a model. Searching for such programs is a waste of time if Bell was right.
It would also be sufficient to disprove Bell's claims by giving an example that does what he claims to be impossible: breaking his inequality with an example that uses no "spooky action at a distance". The topic of De Raedt's paper under discussion in this thread happens to relate to that claim about inequalities; efforts to come up with an impossible(?) program are discussed in other papers.

Now, you could try messing with the requirements. For instance, you can say that the detectors sometimes output a "null" value, rather than +1 or -1. Or you can say that (as someone, maybe De Raedt, suggested), you can say that occasionally, Alice's detector or Bob's detector gets the wrong λ; maybe Alice gets λ_i while Bob gets λ_i+1. I don't have an opinion about whether such generalizations could allow a better simulation of QM.

Certainly any simulation about what could be realistic must account for anything that could significantly influence the results in reality. But I also don't know what may matter and what not.

 

[harrylin]

I found two journal articles by other authors that refer to De Raedt et al's Boole/Bell paper (I just found them now):

http://www.ingentaconnect.com/content/asp/jctn/2011/00000008/00000006/art00012

ABSTRACT
We discuss the connection of a violation of Bell's inequality and the non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and "death of realism" are only sufficient, but not necessary conditions for non-Kolmogorovness. Other sufficient conditions for non-Kolmogorovness and, hence, a violation of Bell's inequality can be found. We find one important source of non-Kolmogorovness by analyzing the axiomatics of quantum mechanics. We pay attention to the postulate (due to von Neumann and Dirac) on simultaneous measurement of quantum observables given by commuting operators. This postulate is criticized as nonphysical. We propose a new interpretation of the Born-von Neumann-Dirac rule for the calculation of the joint probability distribution of such observables. A natural physical interpretation of the rule is provided by considering the conditional measurement scheme. We use this argument (i.e., the rejection of the postulate of simultaneous measurement) to provide a motivation for the non-Kolmogorovness of the probabilistic structure of the EPR-Bohm experiment. and
http://iopscience.iop.org/1402-4896/2012/T151/014007

ABSTRACT
In the given controversy, Einstein was right; the Copenhagen quantum mechanics has been based on physically unacceptable assumptions. And also later, Bell's inequalities have been mistakenly interpreted: holding true only in the classically deterministic model and not for the Schrödinger solutions when the initial state of the evolving system is represented by a (not fully known) set of different classical states; and the measured results in individual events are statistically distributed. The structure of Hilbert space formed by the solutions of the corresponding Schrödinger equation cannot be arbitrarily defined; it must be adapted to the corresponding physical system. Any Schrödinger state is then equivalent to a superposition of the solutions of the corresponding Hamilton equations, while all solutions of these equations form a greater set. However, the usual energy quantization approach represents phenomenological characteristics only, and the proper cause should be interpreted on other physical grounds. The actual source of quantum phenomena may hardly be explained without the participation of all interactions between the corresponding physical objects; their not yet fully known properties surely play an important role. The results obtained in experiments when the mutual (mainly elastic) collisions of the corresponding particles are studied might surely be very helpful.

PS I hit a broken link in the second paper, and found the new address:
http://www.cost.eu/domains_actions/mpns/Actions/MP1006

 

[stevendaryl]

Sure. First of all, for the context: I gave summary of the paper under discussion here in my first post of this thread:
https://www.physicsforums.com/showthread.php?t=499002

And after you asked me in the other thread, I summarized that simple example for you as follows
(https://www.physicsforums.com/showthread.php?t=697939&page=3):

De Raedt attempted to give a counter example to Bell's derivation method. His simple counter example is given on p.25, 26 of http://arxiv.org/abs/0901.2546 :

I find De Raedt's writing almost incomprehensible. If he has a point, it'll take me a while to discover it.

 

[harrylin]

I find De Raedt's writing almost incomprehensible. If he has a point, it'll take me a while to discover it.

I find that true for most papers on this topic; however it looks to me that his simple illustration is easy to verify - it's literally as simple as 1+1 (only more elaborated).

 

[stevendaryl]

I find that true for most papers on this topic; however it looks to me that his simple illustration is easy to verify - it's literally as simple as 1+1 (only more elaborated).

Well, what it seems to me is that he is describing a deterministic function

A(x,l,e) = +/- 1

where

• x = a, b, or c (country of the patient's birth)
• l = 1, 2, or 3 (city where the patient is tested),
• e = even or odd, depending on the day the test is given

This seems like a completely straight-forward "hidden variables" model to me. What De Raedt does with this model is to arrange for certain subsets of the triples \langle x, l, e \rangle to produce the appearance of a non-local interaction. Okay. What this shows is that the criterion for what's a non-local interaction has to be formulated in a way that is insensitive to such subsetting. That's sort of an interesting point, but as I have said several times, what's of interest is not whether a particular inequality holds or not, it's whether the predicted QM results can be explained in terms of a local model. I don't see that De Raedt is shedding any light on that.

 

[harrylin]

Well, what it seems to me is that he is describing a deterministic function

A(x,l,e) = +/- 1

where

• x = a, b, or c (country of the patient's birth)
• l = 1, 2, or 3 (city where the patient is tested),
• e = even or odd, depending on the day the test is given

This seems like a completely straight-forward "hidden variables" model to me. What De Raedt does with this model is to arrange for certain subsets of the triples \langle x, l, e \rangle to produce the appearance of a non-local interaction. Okay. What this shows is that the criterion for what's a non-local interaction has to be formulated in a way that is insensitive to such subsetting. That's sort of an interesting point, but as I have said several times, what's of interest is not whether a particular inequality holds or not, it's whether the predicted QM results can be explained in terms of a local model. I don't see that De Raedt is shedding any light on that.

The topic happens to be inequalities, and in particular the one of Bell; however his other two examples shed some light on QM results. I did not (yet) study those simply because it takes some time to do and his particle model of light is not much to my liking.

Meanwhile I suddenly hit on an Arxiv paper that describes a classical (and straightforward) computer simulation of the Malus-law coincidence + breaking of Bell inquality in optical experiments(!); however I don't know if it has been officially published. It refers to a journal paper of 1996 that describes a demonstration of an EPRB-like experiment with LED's, but not breaking Bell's inquality. So it's not clear yet if I found material for a new topic on this forum...

 

[stevendaryl]

The topic happens to be inequalities, and in particular the one of Bell; however his other two examples shed some light on QM results. I did not (yet) study those simply because it takes some time to do and his particle model of light is not much to my liking.

Meanwhile I suddenly hit on an Arxiv paper that describes a classical (and straightforward) computer simulation of the Malus-law coincidence + breaking of Bell inquality in optical experiments(!); however I don't know if it has been officially published. It refers to a journal paper of 1996 that describes a demonstration of an EPRB-like experiment with LED's, but not breaking Bell's inquality. So it's not clear yet if I found material for a new topic on this forum...

De Raedt himself (I think it was him) wrote a paper a few years back about a classical simulation of the quantum EPR experiment. His "trick" was to assume a steady supply of electron/positron pairs, and to assume that, depending on the detector setting, the detection of a particle could be delayed relative to the detection of the twin particle. This allowed the experimenter to occasionally measure pairs of particles that are NOT from the same twin pair, but from different twin pairs. I don't think the details are so important, but he managed to reproduce the predictions of QM with his setup.

To me, that's like a magic trick, where you saw a person in half. It's interesting, but nobody should take it seriously as a new kind of surgery.

 

[harrylin]

De Raedt himself (I think it was him) wrote a paper a few years back about a classical simulation of the quantum EPR experiment. His "trick" was to assume a steady supply of electron/positron pairs, and to assume that, depending on the detector setting, the detection of a particle could be delayed relative to the detection of the twin particle. This allowed the experimenter to occasionally measure pairs of particles that are NOT from the same twin pair, but from different twin pairs. I don't think the details are so important, but he managed to reproduce the predictions of QM with his setup.

To me, that's like a magic trick, where you saw a person in half. It's interesting, but nobody should take it seriously as a new kind of surgery.

That simulation works with rather "traditional surgery". In contrast, I still consider "spooky action at a distance" to be such a magic trick; and nobody takes it seriously as a new kind of communication.

 

[stevendaryl]

That simulation works with rather "traditional surgery". In contrast, I still consider "spooky action at a distance" to be such a magic trick; and nobody takes it seriously as a new kind of communication.

"Spooky action at a distance" is not a mechanism, it's just a description of the experimental evidence.

 

[stevendaryl]

That simulation works with rather "traditional surgery".

I wouldn't say that. I don't find it at all plausible to be an actual explanation of what's going on in EPR type experiments. For one thing, you could generate twin pairs hours or even days apart. It's just not plausible that one of the experimenters might accidentally get a particle from a different twin pair (at least not in any consistent way).

It's a trick, it's not a serious model.

 

[rkastner]

There have been other attempts to get around Bell's theorem by challenging its basic assumptions, but these usually involve redefining 'elements of reality' in ways contrary to that intended by 'local realism'. Dr. Chinese is right: there is nothing wrong with Bell's theorem, which (in view of its violation by QM) demonstrates that 'local realist' interpretations of QM cannot be maintained.

I offer a nonlocal realist account of QM in which I take quantum objects as nonlocal physical possibilities of a specific kind. It includes a solution to the measurement problem and applications to specific experiments such as the quantum eraser. http://www.cambridge.org/us/knowledge/discountpromotion/?site_locale=en_US&code=L2TIQM (Comments welcome)

 

[wle]

Now, it looks to me that your representation here above of Bell's original inequality is still not quite right: an absolute sign is lacking. According to my copy, Bell's eq.15 for locations 1 and 2 is (rearranged):

<br /> \lvert \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle \rvert - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle \leq +1 \,.<br />

This is the same thing as I wrote, simply because if you measure some quantity X in an experiment then either \lvert X \rvert = X or \lvert X \rvert = -X. So the inequality as you write it above is equivalent to two linear inequalities being satisfied:
<br /> \begin{eqnarray}<br /> \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; 1 \,, \\<br /> - \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{b}} \rangle + \langle A^{1}_{\mathbf{a}} A^{2}_{\mathbf{c}} \rangle - \langle A^{1}_{\mathbf{b}} A^{2}_{\mathbf{c}} \rangle &amp;\leq&amp; 1 \,.<br /> \end{eqnarray}<br />
Up to an overall sign these are the same inequalities as the ones I marked (*) in the post you were quoting. For anticorrelated \mathbf{b} outcomes there are two (and only two) additional inequalities that should always be satisfied that are imposed by locality.

Here are the fictive measurement results once more, for locations 1-3 on even and odd days:

... Even ...|.. Odd
L ...1...2...3.|..1...2...3
A_a +1 +1 +1.| -1. -1. -1
A_b +1. -1 +1.| -1 +1. -1
A_c. -1. -1. -1.|+1 +1 +1

Computing from the results for location pair (1,2), I obtain as outcomes: +1, -1.
That location pair does not break Bell's inequality, the average is 0.

Are you sure you've done this correctly? For starters your odd table is the same as the even table except with all the signs flipped, so you should always get the same correlator value in each case simply because you're always taking products of pairs of terms.

As an aside, if you want to apply Bell's inequality the way you wrote it in the quote above, then you shouldn't be calculating the LHS separately for the even and odd days and then averaging them. You calculate the average of the separate terms individually and should only take the absolute value of the first two at the very end (though in this case it shouldn't affect the end result, because you should get the same thing on the even and odd days anyway).

For location pair (1,3), I obtain as outcomes: +3, +3. Average +3.
If I'm not mistaken, this pair very strongly breaks Bell's inequality!

In your table you also always have A^{1}_{\mathbf{b}} = +A^{3}_{\mathbf{b}} while Bell's inequality can only be derived assuming A^{1}_{\mathbf{b}} = - A^{3}_{\mathbf{b}}. So you're violating Bell's inequality in a context where there's no particular reason it should hold in the first place.

 

[harrylin]

"Spooky action at a distance" is not a mechanism, it's just a description of the experimental evidence.

Once more, IMHO it's an illusion, similar to the "experimental evidence" of the doctors in Lille and Lyon.

I wouldn't say that. I don't find it at all plausible to be an actual explanation of what's going on in EPR type experiments. For one thing, you could generate twin pairs hours or even days apart. It's just not plausible that one of the experimenters might accidentally get a particle from a different twin pair (at least not in any consistent way).

It's a trick, it's not a serious model.

Once more, I don't fancy their partilcate models much; such mechanicms look rather articficial to me compared to wave models.

 

[audioloop]

So there are papers saying that Bell is wrong, because it's easy for a local hidden variables theory to violate the inequalities. Then there are other papers saying that Bell is wrong because nothing can violate the inequalities, not even quantum mechanics.

any logical possibility i think.



.

 

[stevendaryl]

Once more, IMHO it's an illusion, similar to the "experimental evidence" of the doctors in Lille and Lyon.

What's an illusion? I see orthodox quantum mechanics as simply a "recipe" for computing results. It's not a mechanism for how those results come about. So I don't know what you are calling an illusion.

 

[harrylin]

What's an illusion? I see orthodox quantum mechanics as simply a "recipe" for computing results. It's not a mechanism for how those results come about. So I don't know what you are calling an illusion.

Yes indeed quantum mechanics is a recipe for computing results. Just as in your magic trick example, the inferred "spooky action at a distance" is an interpretation of the observation of such results, as a consequence of looking at the phenomena in a certain way. The inferred cutting in two of a girl at the stage is an interpretation of the observation of a magic trick; and that interpretation is the result of the illusionist setting the stage and the observer following the line of thinking that the illusionist suggests.

 

[harrylin]

[..]
Are you sure you've done this correctly? For starters your odd table is the same as the even table except with all the signs flipped, so you should always get the same correlator value in each case simply because you're always taking products of pairs of terms.

Well seen! I did it twice but repeated the same error... the very first number is wrong. See next.

As an aside, if you want to apply Bell's inequality the way you wrote it in the quote above, then you shouldn't be calculating the LHS separately for the even and odd days and then averaging them. You calculate the average of the separate terms individually and should only take the absolute value of the first two at the very end (though in this case it shouldn't affect the end result, because you should get the same thing on the even and odd days anyway).

Very right! So, we get then for the average of all locations not 4/3 but 3/3=1. And that means that whille it is broken between two locations, on the average of all locations, DeRaedt's illustration doesn't break that inequality.

In your table you also always have A^{1}_{\mathbf{b}} = +A^{3}_{\mathbf{b}} while Bell's inequality can only be derived assuming A^{1}_{\mathbf{b}} = - A^{3}_{\mathbf{b}}. So you're violating Bell's inequality in a context where there's no particular reason it should hold in the first place.

Ah yes, well seen -again!
Is this particular inequality really "harder" than the other one? That would be surprising for me... I'll have another go at it.

 

[wle]

Very right! So, we get then for the average of all locations not 4/3 but 3/3=1. And that means that whille it is broken between two locations, on the average of all locations, DeRaedt's illustration doesn't break that inequality.

How do you mean? No (relevant) Bell inequality can be violated from the table you gave, whether you condition on the even/odd days or not.

Is this particular inequality really "harder" than the other one?

Which inequality are you talking about? For perfectly correlated or anticorrelated A^{i}_{\mathbf{b}} and A^{j}_{\mathbf{b}}, there are four inequalities imposed by Bell locality that I listed for you in [POST=4459297]this post[/POST]. You just need to be careful that you are testing one of the "right" inequalities, since they differ for A^{i}_{\mathbf{b}} = + A^{j}_{\mathbf{b}} and A^{i}_{\mathbf{b}} = - A^{j}_{\mathbf{b}}.

One way not to make any mistake here, by the way, is simply to test all the possible CHSH inequalities, since the three-term Bell inequalities are just special cases of them anyway:
<br /> \begin{eqnarray}<br /> -2 \leq &amp; +\, \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{b}} \rangle + \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{c}} \rangle - \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle &amp; \leq 2 \,, \\<br /> -2 \leq &amp; +\, \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{b}} \rangle + \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{c}} \rangle - \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle &amp; \leq 2 \,, \\<br /> -2 \leq &amp; +\, \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{b}} \rangle - \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle &amp; \leq 2 \,, \\<br /> -2 \leq &amp; -\, \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{b}} \rangle + \langle A^{i}_{\mathbf{a}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{c}} \rangle + \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle &amp; \leq 2 \,.<br /> \end{eqnarray}<br />
These inequalities are known to be a tight characterisation of the set of correlations compatible with Bell's definition of locality for two parties with binary inputs and outputs. This means that if you have a two-party probability distribution that satisfies all of these inequalities, then a local explanation for it is known to be possible. Conversely, if any one of them is violated, then a local explanation is ruled out.

These inequalities explicitly include the \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle term and always hold regardless of its value (provided, of course, that -1 \leq \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle \leq 1, which is just part of the definition of the correlators). By explicitly setting \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle = +1 or \langle A^{i}_{\mathbf{b}} A^{j}_{\mathbf{b}} \rangle = -1 you can recover the three-term inequalities I listed for you [POST=4459297]here[/POST].

It is pointless to try to violate a relevant three-term inequality with De Raedt's example. This is simply because, as I've just explained, they're special cases of CHSH, and De Raedt et. al. explicitly and openly state that their example never violates a CHSH inequality. Unlike with the three-term inequalities, the CHSH inequalities are always applicable and so De Raedt et. al. never get an opportunity to mislead themselves by testing a "wrong" one.

 

[harrylin]

[..] Which inequality are you talking about?

The original one of Bell, eq.15 compared the one of Boole(?) that De Raedt provided. Once more, you were very right to point out that the two are not identical.

[..]
It is pointless to try to violate a relevant three-term inequality with De Raedt's example. This is simply because, as I've just explained, they're special cases of CHSH, and De Raedt et. al. explicitly and openly state that their example never violates a CHSH inequality. [..]

[Edited]
I doubted your suggestion that it makes an important difference. However, it had escaped my attention that Bell's inquality is a special case of the CHSH inequalites. Consequently according to the paper that illustration (as well as basic variants, as I now verified) cannot break that inequality. In other words, Bell's inequality is stronger than the one illustrated.

That's now perfectly clear to me - thanks again!

 

[morrobay]

While the above probability and statistics is way overhead and while the ± is trivial ( providing it is set up correctly) is this correct ? From (A¹_aA²_b) - (A¹_aA²_c) - (A¹_bA²_c) ≤ +1
With (A¹_bA²_b) = -1 , A¹_b = +1
Then the inequality ; 1 + (A¹_bA²_c) + (A¹_aA²_c ≥ (A¹_aA²_b) is dis proven with 1 + (b+c-) + (a+c-) ≥ (a-b-) values
From [-++ +--] + [+-+ -+-}≥ [ -+- +-+] substituting in above , products equal : 1 - 1 -1 is not ≥ +1

 

[harrylin]

While the above probability and statistics is way overhead and while the ± is trivial ( providing it is set up correctly) is this correct ? From (A¹_aA²_b) - (A¹_aA²_c) - (A¹_bA²_c) ≤ +1
With (A¹_bA²_b) = -1 , A¹_b = +1
Then the inequality ; 1 + (A¹_bA²_c) + (A¹_aA²_c ≥ (A¹_aA²_b) is dis proven with 1 + (b+c-) + (a+c-) ≥ (a-b-) values
From [-++ +--] + [+-+ -+-}≥ [ -+- +-+] substituting in above , products equal : 1 - 1 -1 is not ≥ +1

Sorry, your notation is too cryptic for me. What do you mean with b- if not -b, and what does [-++ +--] stand for?

 

[morrobay]

While the above probability and statistics is way overhead and while the ± is trivial ( providing it is set up correctly) is this correct ? From (A¹_aA²_b) - (A¹_aA²_c) - (A¹_bA²_c) ≤ +1
With (A¹_bA²_b) = -1 , A¹_b = +1
Then the inequality ; 1 + (A¹_bA²_c) + (A¹_aA²_c ≥ (A¹_aA²_b) is dis proven with 1 + (b+c-) + (a+c-) ≥ (a-b-) values
From [-++ +--] + [+-+ -+-}≥ [ -+- +-+] substituting in above , products equal : 1 - 1 -1 is not ≥ +1

::A::::::::::B::
-++... +-- = b+c-
+-+... -+- = a+c-
-+-... +-+ = a-b-
Can the inequality be dis proven from individual case above. If not then what three
streams P₁ P₂ P₃ would disprove it
And how would you apply correlation function to show dis proof.
q(∅₁∅₂) = N same(∅₁∅₂) - N different(∅₁∅₂) / N same + N different

Actually I am trying to follow post # 181 and some other posts by wle and post 151 by harrylin who are showing how inequalities are violated, and I am not sure what the exact steps are, thanks.

 

[harrylin]

::A::::::::::B::
-++... +-- = b+c-
+-+... -+- = a+c-
-+-... +-+ = a-b-
Can the inequality be dis proven from individual case above. If not then what three
streams P₁ P₂ P₃ would disprove it
And how would you apply correlation function to show dis proof.
q(∅₁∅₂) = N same(∅₁∅₂) - N different(∅₁∅₂) / N same + N different

Actually I am trying to follow post # 181 and some other posts by wle and post 151 by harrylin who are showing how inequalities are violated, and I am not sure what the exact steps are, thanks.

A quick first reply: post #151 was corrected in posts #186 - #188.
That simple illustration is useful but not so convincing because it only shows the principle of breaking that kind of inequalities. More is needed to break Bell's inequality.

 

[Ilja]

Yes, I quite agree that is an assumption of Bell. A correct one, of course! And this is not coming from the quantum mechanical side, it is coming from the realism side. As I have said many times before: if the above is NOT a concise requirement, then what DOES IT MEAN TO BE REALISTIC?

Note: virtually anything LESS than the above is essentially returning to the standard QM position.

Bell himself has often clarified that the assumption of realism is much weaker than that the results of the possible spin measurements are predefined. That these results have to be predefined is, instead, a conclusion of the first part of the game, namely of the EPR argument. And the EPR argument already needs not only realism, but also Einstein causality.

What it means to be realistic can be easily explained by the example of the Bohmians. Bohmians are realists. So, if you believe in de Broglie-Bohm theory, you believe in a realistic theory. As a consequence, there cannot be any observable contradiction between quantum theory and realism - dBB in quantum equilibrium and QT make the same predictions.

 

[Ilja]

Here, the illustration that the point made in the last post is not only about DrChinese, but also about Raedt et al themself.

Raedt et al write in http://arxiv.org/pdf/0901.2546v2.pdf:

However, it is well-known that Bell’s assumptions to prove his inequalities are equivalent to the statement that there exists a three-variable joint probability that returns the probabilities of Bell. No additional (metaphysical) assumptions about the nature of the model, other than the assignment of non negative real values to pairs and triples are required to arrive at this conclusion.

The point is that the assumption that there exists a three-variable joint probability that returns these probabilities is not an assumption made by Bell, but a conclusion. The conclusion of the first, EPR part of the argument.

To derive this "assumption" via the EPR argument from something else, we need these additional metaphysical assumptions, not only of classical realism, but also of Einstein causality.

I have not found the exact quote that already Bell has made this point himself too, but found a quite similar point in "Bertlmann's socks and the nature of reality":

It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred.

Together with what follows, this makes the point sufficiently clear.

 

[rkastner]

Bell himself has often clarified that the assumption of realism is much weaker than that the results of the possible spin measurements are predefined. That these results have to be predefined is, instead, a conclusion of the first part of the game, namely of the EPR argument. And the EPR argument already needs not only realism, but also Einstein causality.

What it means to be realistic can be easily explained by the example of the Bohmians. Bohmians are realists. So, if you believe in de Broglie-Bohm theory, you believe in a realistic theory. As a consequence, there cannot be any observable contradiction between quantum theory and realism - dBB in quantum equilibrium and QT make the same predictions.

This is interesting because the traditional Bohmian picture involves 'guiding waves' that are not spacetime entities. Yet these guiding waves somehow steer particles in spacetime. According to this definition of realism, there are real entities that don't live in spacetime that nonlocally steer particles that do. I have never seen an explanation of how this is supposed to be accomplished in realist terms. On the other hand, I do provide a realist account of how pre-spacetime entities can be the basis of spacetime events, in my possibilist extension of Cramer's TI, 'PTI'. It involves embracing the wavelike pre-spacetime reality of quantum objects as offer (and confirmation) waves but letting go of the 'hidden variables' of particle positions. In PTI, particles are just actualized transactions, which give rise to spacetime events. The transactions are where the 'particles' come from -- they are not hidden variables. I think this is more straightforward and it has a smooth transition to the relativistic realm, in contrast to the Bohmian picture which has difficulties with relativistic domain.

 

[bahamagreen]

I'm still back around page 8... but I don't suppose there is such a crystal that always emits six photons at a time, three photons in one direction and three in the opposite direction, each time randomly making the three going one way all have the same spin and opposite of the spin of the three going the other way... to make the triple possibilites actual triplicates... (or maybe pretending such a crystal exists)... would this make the challenge dataset then realistic?

 

[Ilja]

... in my possibilist extension of Cramer's TI, 'PTI'... I think this is more straightforward and it has a smooth transition to the relativistic realm, in contrast to the Bohmian picture which has difficulties with relativistic domain.

Cramer's transactional interpretation gives up classical causality and classical concepts of time. I see no sufficient justifications for this. To give up such really fundamental concepts, one needs really strong evidence. Everything else is, in my humble opinion, mysticism.

The Bohmian picture has only a minor problem with the relativistic domain: It needs a hidden preferred frame. Not a big deal. It was, last but not least, the original "Lorentz ether" interpretation of relativity.

Except for die-hard positivists who reject the existence of everything they cannot observe. In a world where we cannot even observe the NSA with sufficient accuracy this seems to be a quite unnatural restriction.

 

[Dale]

This has degenerated into the usual "my interpretation is better than yours" discussion. Thread closed.