Bell's theorem and local realism

[stevendaryl]

For instance explanations of the statistical correlations based just in geometry are not usually mentioned, I guess because currently background independence is more fashionable and many have given up on finding a purely geometrical theory.

What geometry-based explanations are you talking about?

 

[TrickyDicky]

What geometry-based explanations are you talking about?

I'm talking about a geometrical approach in the most general sense. I don't know of any specific purely geometrical explanation that can account for QM predictions.

I refer to the fact that a geometrical object, say like the one you draw in #10, has obvious nonlocal correlations between distant parts that are not correlated based in any local causation, it's just the instantaneous, spacelike geometrical relations.

Or the way any specific physical problem can be better solved by exploiting its symmetries and choosing a geometry as boundary condition to treat it that has those symmetries, or the way in which in the macroscopic experiments in fluids discussed in parallel threads, just the inclusion of a geometrical boundary like a circular corral produces certain apparently nonlocal correlations.

 

[TrickyDicky]

I wouldn't say so. There is one aspect of differential geometry that is nonlocal, which is the topology of a manifold. You can't tell the topology of a manifold just by making local measurements. But topology is not likely to be important in something an EPR type experiment (in spite of Joy Christian's claims to the contrary).

No I'm referring to the geometry in the sense explained in the above post.

 

[DrChinese]

Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory."

I agree with that. It is almost circular, true enough.

 

[bhobba]

I'm talking about a geometrical approach in the most general sense. I don't know of any specific purely geometrical explanation that can account for QM predictions.

Well actually it can:
http://en.wikipedia.org/wiki/Quantum_geometry

In that approach Gleason's theorem plays a very significant role meaning its simply not possible for it to be deterministic.

Further detail can be found in Geometry of Quantum Theory by Varadarajan.

Be warned however. It's a highly mathematical approach, and is described by mathematicians as highly non trival. That's a mathematics codeword for it's HARD. It's right at the limit of my mathematical competency - meaning I can understand it - but only with a lot of effort.

Thanks
Bill

 

[TrickyDicky]

Well actually it can:
http://en.wikipedia.org/wiki/Quantum_geometry

Yes, there are multiple attempts at quantum gravity theories that use more or less geometrical methods.
I didn't mean that, I was just giving an example of an obvious(at least to me, but I have never seen it mentioned) type of hidden variables theories (nonlocal but at this point I'm not really sure if they would be considered nonlocal by all experts) just relying on a spacetime geometry which spacelike separated events are obviously correlated by the metric relations and would therefore give correlated outcomes that are not causally related for the measurements of geometrical properties(i.e. say quantum spin was such a geometrical feature).

 

[nikman]

"When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects."

You can't go wrong going with Zeilinger, a Bellmeister who goes this far and no farther: "A photon is a click in a photon detector." Now, we can probably agree that a photon detector is a real object and a click is a real sound (if we all indicate synchronously, intersubjectively, that we hear it). Could a real-not entity affect a real one in that manner, probably not imo. Although that may be way too naively classical.

 

[bhobba]

Could a real-not entity affect a real one in that manner, probably not imo. Although that may be way too naively classical.

We know what QFT says it is.

Why not simply say that's the reality - sounds simple to me instead of getting caught up in this semantic quagmire of what a real object is yada yada yada. Its what I do.

Such is generally a philosophers game and they really haven't gotten anywhere - physicists will likely not either.

The real import of Bell's theorem is we have a precise definition of naive reality - and we know what the theorem says. You won't get anywhere with questions like what a photon is without similar definitions and then you have the problem of getting people to agree.

Thanks
Bill

 

[nikman]

I didn't want to diss the post that began the thread. And you're right, that's exactly what BT is: the concise expression of classical realism. Although it's not really naive in the macroworld we live in (unless, like say the dreadful Joy Christian, one is a hopeless crackpot) because you can't violate it with ordinary macroscopic objects. It's the world life and our brains evolved in. That truth needs to be accepted if it's to be in any sense transcended.

You can't have too much philosophical reflection about this stuff if it's sophisticated and knowledgeable philosophy. You want to get humanists into the game or just shunt them aside and snark at them? Screw, with respect, your yada yada. That attitude's a serious part of the problem. Ever read, for example, Jeffrey Bub's SEP article on quantum entanglement and information? It's called Philosophy of Science.

 

[bhobba]

You can't have too much philosophical reflection about this stuff if it's sophisticated and knowledgeable philosophy. You want to get humanists into the game or just shunt them aside and snark at them? Screw, with respect, your yada yada. That attitude's a serious part of the problem. Ever read, for example, Jeffrey Bub's SEP article on quantum entanglement and information? It's called Philosophy of Science.

Well I think if that's what interests you a forum whose rules specifically preclude philosophy may not be the appropriate place to discuss your issues.

My view is very similar to Wienberg:
http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc
'Physicists do of course carry around with them a working philosophy. For most of us, it is a rough-and-ready realism, a belief in the objective reality of the ingredients of our scientific theories. But this has been learned through the experience of scientific research and rarely from the teachings of philosophers'.

If you want to chat about it at that level start a thread over at philosophy forums and drop me a line linking to it. Happy to comment over there. But I have to say from my forays over on that forum I find I speak a different language, the language of applied math, and we talk past one another. That's why I prefer here because the rough and ready view of Weinberg suits me better.

And of course humanists under no circumstances should be excluded, I can go down that path with you and any anyone else that wants to participate if you want - just not here. My only concern, like I said, is I speak the language of applied math - not philosophy. Applied mathematicians have a very rough and ready view of such things.

Thanks
Bill

 

[nikman]

Sorry. I suspect I shouldn't have said "screw your ..." However, the first post on this thread asked a certifiably, purely, quintessentially metaphysical question (go ahead, deny that):

"When drawing conclusions from this most important and profound theorem, I wonder if somebody has interpreted its proof of the falseness of local realism as implicitly referring to elementary particles as realistic objects."

Bit of a double standard you're employing here but hey. Anyway I've spent a fair amount of time over the years explaining or trying to explain Bell, Wigner-d'Espagnat, CHSH, Dirk Aerts' macroworld Bell isomorphisms, Joy Christian's pathology, the Quantum Randi Challenge, why "Shut Up and Calculate" isn't entirely indefensible etc. to liberal arts types in informal discussions and a few times I've encountered variations of the above question. JSB himself took it up at least obliquely in "Bertlmann's Socks". The point of that last being he was a competent applied mathematician with an adequate understanding of QFT who didn't dodge issues Weinberg cocks a snoot at. However I'm outtahere.

 

[morrobay]

Bell's theorem refers to correlations between "classical" or "macroscopic" experimental outcomes. So as long as one believes that the experimental outcomes in a Bell test are "classical", then the violation of the inequality does rule out local realism.

There are some assumptions that go into this conclusion. For example, it assumes that each measurement produces only one outcome. In many-worlds each measurement has more than one outcome, so the Bell test don't rule out that many-worlds is a local realistic theory.

With the assumption that one measurement produces one outcome can a Bell inequality violation be numerically shown
(non statistically) with the two forms of the inequality below ?
Given that ø between detectors is 0⁰,120⁰and 240⁰
So that the inequality violation is function of + or - signs in the inequality alone.
P ++ = P-- = 1/2 sin²ø/2
P+- = P-+ = 1/2cos²ø/2

(1) M = AB + AB' - A'B + A'B' = (A-A')B + (A+A')B' .... -2 ≤ M ≤ 2
(2) C(a,b) - C(a,c)|+|C(a',b) + C(a',a) ≤ 2 ...... A₁ and A₂ (+ or -) 1

 

[jk22]

Since the function for the result in A is a one point function, it depends only on the angle in a, this formula should in fact modelize the following experiment : we have a single polarized photon beam and we generate 4 time series for the four direction of measurement ? So Bell's experiment does not need a bbo crystal nor an entangled pair ?

To see this we take simply the initial state a single qbit along z and the tensor product becomes the matrix product (which represent in som sense the time ordering i think) and we get the same result.

 

[stevendaryl]

With the assumption that one measurement produces one outcome can a Bell inequality violation be numerically shown
(non statistically) with the two forms of the inequality below ?
Given that ø between detectors is 0⁰,120⁰and 240⁰
So that the inequality violation is function of + or - signs in the inequality alone.
P ++ = P-- = 1/2 sin²ø/2
P+- = P-+ = 1/2cos²ø/2

(1) M = AB + AB' - A'B + A'B' = (A-A')B + (A+A')B' .... -2 ≤ M ≤ 2
(2) C(a,b) - C(a,c)|+|C(a',b) + C(a',a) ≤ 2 ...... A₁ and A₂ (+ or -) 1

I don't know if the three angles 0, 120, 240 provide an example of a violation of Bell's inequality. It actually looks like you're using the CHSH inequality above. If so, I think you have a sign error. According to Wikipedia, it should be:

C(a,b) + C(a,b') + C(a', b) - C(a',b') \leq 2

For spin-1/2, the correlation is given by:

C(a,b) = - cos(\theta)

where \theta is the relative angle between the two detector orientations. So we have:

• \theta = 0 \Rightarrow C = -1
• \theta = 60 \Rightarrow C = -0.5
• \theta = 120 \Rightarrow C = +0.5
• \theta = 180 \Rightarrow C = +1
• \theta = 240 \Rightarrow C = +0.5

So here's a choice for a, b, a', b' that violates the inequality:

• a = 0
• b = 180
• a' = 60
• b' = 120

Then:

• C(a,b) = +1
• C(a, b') = +0.5
• C(a',b) = +0.5
• C(a',b') = -0.5

Then C(a,b) + C(a,b') + C(a',b) - C(a',b') = 1 + 0.5 + 0.5 - (-0.5) = 2.5

I don't think you can get a violation with just 0, 120, 240.

 

[morrobay]

Thanks for the clarification on CHSH with P(a,b)_QM = -cos ø.
While P++ = P-- = 1/2 sin²ø/2 and P-+ = P+- = 1/2 cos²ø/2 do not seem to apply to CHSH inequality.
They can show violations when spin 1/2 particles are measured with Stern - Gerlach apparatuses oriented along a and b when ø is angle difference with detectors at three settings :
A.....B
a=0....a'=0
b=120.....b'=120
c=240.....c'=240

With this form of inequality: P(a+b'+) ∠ P(a-c'+) + P(c+b'-) with expected outcomes taken from measurements when detector settings at A and B are aligned at 0⁰,120⁰,240⁰ ( ++-...--+) one of eight

Then the inequality violation is 1/2sin²120/2 ∠ 1/2cos²240/2 + 1/2cos²120/2 = .375 ∠ .125 + .125

 

[gill1109]

No particles in Bell's theorem

I think it is worth pointing out that Bell (1981) himself argued forcibly that his "theorem" (by which he meant his inequality - an elementary probability and calculus exercise) is not about particles or even about quantum theory. It is about what you would expect to see according to a completely conventional picture of the macroscopic physical world about a completely macroscopic experimental set-up. The following is quoted from his (IMHO) masterpiece, "Bertlmann's socks and the nature of reality". Ch. 16 of "Speakable and unspeakable". But you can also find it on internet.

You might suspect that there is something specially peculiar about spin-1/2 particles. In fact there are many other ways of creating the troublesome correlations. So the following argument makes no reference to spin-1/2 particles, or any other particular particles.
Finally you might suspect that the very notion of particle, and particle orbit, freely used above in introducing the problem, has somehow led us astray. Indeed did not Einstein think that fields rather than particles are at the bottom of everything? So the following argument will not mention particles, nor indeed fields, nor any other particular picture of what goes on at the microscopic level. Nor will it involve any use of the words ‘quantum mechanical system’, which can have an unfortunate effect on the discussion. The difficulty is not created by any such picture or any such terminology. It is created by the predictions about the correlations in the visible outputs of certain conceivable experimental set-ups.
Consider the general experimental set-up of Fig. 7

To avoid inessential details it is represented just as a long box of unspecified equipment, with three inputs and three outputs. The outputs, above in the figure, can be three pieces of paper, each with either ‘yes’ or ‘no’ printed on it. The central input is just a ‘go’ signal which sets the experiment off at time t1. Shortly after that the central output says ‘yes’ or ‘no’. We are only interested in the ‘yes’s, which confirm that everything has got off to a good start (e.g., there are no ‘particles’ going in the wrong directions, and so on). At time t1 + T the other outputs appear, each with ‘yes’ or ‘no’ (depending for example on whether or not a signal has appeared on the ‘up’ side of a detecting screen behind a local Stern–Gerlach magnet). The apparatus then rests and recovers internally in preparation for a subsequent repetition of the experiment. But just before time t1 + T, say at time t1 + T – δ, signals a and b are injected at the two ends. (They might for example dictate that Stern–Gerlach magnets be rotated by angles a and b away from some standard position). We can arrange that cδ << L, where c is the velocity of light and L the length of the box; we would not then expect the signal at one end to have any influence on the output at the other, for lack of time, whatever hidden connections there might be between the two ends.
Sufficiently many repetitions of the experiment will allow tests of hypotheses about the joint conditional probability distribution P(A,B|a, b) for results A and B at the two ends for given signals a and b.​

 

[TrickyDicky]

I think it is worth pointing out that Bell (1981) himself argued forcibly that his "theorem" (by which he meant his inequality - an elementary probability and calculus exercise) is not about particles or even about quantum theory. It is about what you would expect to see according to a completely conventional picture of the macroscopic physical world about a completely macroscopic experimental set-up. The following is quoted from his (IMHO) masterpiece, "Bertlmann's socks and the nature of reality". Ch. 16 of "Speakable and unspeakable". But you can also find it on internet.

I was actually aware of that particular chapter, but even if Bell himself clearly made an effort to distance his theorem from interpretations related specifically to particles, be it classical , or quantum (whatever the latter are, which sometimes seems like it is not clear even for experts, but let's agree on whatever experts mean when they use the word particle in the context of quantum theory), I think it is reasonable that some kind of more general object or what I referred above from a reference on the theorem as local "individual entity" is implicit in Bell's own interpretation of his theorem, calling these objects "particles" and whether this leads to further confusion is just a semantic issue.

Consider this comment by Bell in the quote above:
"We are only interested in the ‘yes’s, which confirm that everything has got off to a good start (e.g., there are no ‘particles’ going in the wrong directions, and so on)."

It seems obvious we are still implicitly concerned by certain objects(in scare quotes).

 

[gill1109]

Consider this comment by Bell in the quote above:
"We are only interested in the ‘yes’s, which confirm that everything has got off to a good start (e.g., there are no ‘particles’ going in the wrong directions, and so on)."

It seems obvious we are still implicitly concerned by certain objects (in scare quotes).

Bell puts the word "particles" in quotes for a very good reason. They are not *scare* quotes. They are quotes indicating that we are briefly talking another language, assuming some particular physical theory, which we want to test in this experiment.

Suppose a quantum physicist tries to engineer this experiment. He wants to win the Nobel prize by doing the first ever succesfull loophole-free Bell type experiment (it seems that this might happen without a year from now - so it will have only taken a bit more than 50 years to achieve). The quantum physicist does have the word "particle" in his vocabulary. Bell was thinking of an experiment in which three particles are emitted simultaneously and registering one of them is used to "announce" that there are another two on their way. He did this because he was thinking of experiment where you try to "excite" some "molecule" but you may or many not have success in causing the desired emission of "particles".

Nowadays we think more often of pulsed experiments where we make sure that per short time window there is only one emission of "particles". Then we don't need to have a third particle emitted in order to tell us that the other two are successfully launched.

You can read about the experiment he had in mind in chapter 13 of "Speakable and unspeakable". This was before people started having success with the photon polarisation type experiments (Aspect et al ...). Different physical systems.

People still talk about experiments with "event ready detectors". Possibly we could get two atoms very far apart entangled, by doing entanglement swapping with photons. But photons are slippery creatures and this often doesn't succeed. So you have to make sure you know you have succeeded e.g. by successful detection of another "particle"

 

[gill1109]

Interesting remark that there may be no philosophy in this forum. Nowadays Bell's theorem is called part of "experimental metaphysics". The experiment allows one to distinguish between whole classes of physical theories. It's not about testing one particular theory.

Even if philosophy is not allowed, I hope that metaphysics is allowed. If not, then Bell's theorem is .a not-allowed topic

 

[TrickyDicky]

You seem to be missing my point, you are describing experiments that involve particles aren't you?

 

[gill1109]

You seem to be missing my point, you are describing experiments that involve particles aren't you?

The experiments don't have to involve particles. The experiments might be experiments in which theories are tested/implemented in which the word particle occurs. But they could also be experiments in which theories are tested/implemented in which there are only waves. It depends what the physicist puts inside (or rather: thinks he or she is putting inside) that big long box drawn in the figure from "Bertlmann". There is no particle drawn in the picture. There was no need whatever to use the word "particle" in the description of the experiment. There are three inputs and three outputs on a long box, and there is some time schedule which needs to be adhered to.

For instance, *inside* that long box one could place a network of three computers. The one in the middle sends some messages to the ones at each end, and also delivers an output saying "I did it". The ones at each end do some local computation based on their respective inputs and the message that came from the central computer.

What we very well understand, is that if we put three classical computers in the box, and do the experiment, the resulting statistics will satisfy the Bell-CHSH inequality. We imagine that if instead we put some quantum source and some quantum detectors inside the box and are really smart with our quantum engineering (creating some "particles" in a desired "state" and implementing certain "quantum measurements" on those "particles") then we would violate the Bell-CHSH inequality. (It hasn't been done yet, but maybe it will be done soon).

 

[TrickyDicky]

I was using the word particle in a broadest sense, as quantum objects that are local(interact at points) and have defined properties as individual or countable entities, in other words local realistic objects, you may call them particles, waves, messages from computers...

 

[gill1109]

I was using the word particle in a broadest sense, as quantum objects that are local(interact at points) and have defined properties as individual or countable entities, in other words local realistic objects, you may call them particles, waves, messages from computers...

The words "quantum" and "particle" are not needed to describe the experiment. We can put in that box whatever we like, and we can use whatever theory we like to describe our understanding of what we goes on inside. If you want to say that two "particles" go from the source to the measurement stations while another has just let the experimenter know that the two particles are on their ways, that's fine.

 

[TrickyDicky]

The words "quantum" and "particle" are not needed to describe the experiment. We can put in that box whatever we like, and we can use whatever theory we like to describe our understanding of what we goes on inside. If you want to say that two "particles" go from the source to the measurement stations while another has just let the experimenter know that the two particles are on their ways, that's fine.

The words used are irrelevant, it is quite clear the kind of objects you are putting in the box, they are the local agents I described in my previous post and what Bell's theorem claims that any physical theory based on them cannot reproduce Quantum experiments correlations.

 

[gill1109]

The words used are irrelevant, it is quite clear the kind of objects you are putting in the box, they are the local agents I described in my previous post and what Bell's theorem claims that any physical theory based on them cannot reproduce Quantum experiments correlations.

Bell's theorem shows indeed that what Bell considered as local realist agents cannot reproduce quantum correlations. One could also say "local realist agents" = "what can be simulated by classical computers communicating one-way".

Of course there is another question whether or not Nature can exhibit quantum correlations in the rather restricted context of the long box experiment. So far it has not been observed in Nature (ie in the Lab).

 

[TrickyDicky]

I could use an analogy to clarify what I meant above by a spacetime geometry as an obvious way to get a "nonlocal" hidden variables theory compatible with quantum correlations. (I'll explain later why I put nonlocal in quotes.)

Consider the amplituhedron, here we have a geometric object with certain properties that give rise to probability distributions of the outcomes of QFT experiments that are usually understood in terms of 'particles' interactions.

I would say this would be an example of nonlocality, since it is claimed that locality is removed and it would only appear as emergent property.

Similarly in an actual spacetime geometry that putatively were able to give the right probabilistic distributions of outcomes observed in quantum experiments, we'd either consider the physical theory based on it as nonlocal, or consider that such geometry exploits a "conceptual loophole" in Bell's theorem if it was viewed as local.

Of course here the difficult part is to find such a geometry, which many physicists probably will think doesn't exist. However the amplituhedron seems to hint that it might.


See also this reference that uses the geometric Malus law in the context of Bell's theorem:
J. of Nonlinear Math. Phys. Volume 11, Supplement (2004), 104–109
"EPR-B correlations: non-locality or geometry?" Kracklauer A F

 

[gill1109]

See also this reference that uses the geometric Malus law in the context of Bell's theorem:
J. of Nonlinear Math. Phys. Volume 11, Supplement (2004), 104–109
"EPR-B correlations: non-locality or geometry?" Kracklauer A F

That 2004 paper has so far only been cited once ... and that was in another paper by the same author (according to Google scholar).

Now this paper by de Raedt and others attempts to show that the quantum correlations of the singlet state can de deduced from some geometric and informational principles: http://arxiv.org/abs/1303.4574

Quantum mechanics is not in conflict with locality. There is no action at a distance, no "Bell telephone", no way to use the quantum correlations to communicate instantaneously over some distance. It is only when one hypothesizes an otherwise invisible hidden layer which "explains" those correlations in a classical (mechanistic, deterministic) way that one runs into locality issues.

 

[harrylin]

[..]
See also this reference that uses the geometric Malus law in the context of Bell's theorem:
J. of Nonlinear Math. Phys. Volume 11, Supplement (2004), 104–109
"EPR-B correlations: non-locality or geometry?" Kracklauer A F

Found it: http://iopscience.iop.org/1464-4266/6/6/012
As far as I am aware, Kracklauer did not really "crack" the problem: as a matter of fact I have tested his simulation program and also studied the "laboratory confirmation", but found both of those wanting (of course, I could have made a mistake).

However, perhaps he was thinking in the right direction.
It reminds me of an old thread on this forum, which IMHO left some intriguing questions wide open: https://www.physicsforums.com/showthread.php?t=490571.

Neumaier argued that from the perspective of QFT the problem is caused by the "particle" concept (that is: countable, unalterable objects), and that in contrast, classical (Maxwellian) EM can break Bell's inequality.

A recently published paper on classical optics seems to make similar suggestions, if I understand correctly what the authors are saying:

" [..] we have presented the first study of nonlocal correlations in classical optical beams with topological singularities. These nonlocal correlations between two different light modes are manifested through the violation of a Bell inequality using the Wigner function for this system of classical vortex beams. [..]
Clearly, the violation of the Bell inequality for classical light fields and the existence of nonlocal correlations bring out totally new statistical features of the optical beams. [..] "
Phys. Rev. A 88, 013830 (2013) - http://arxiv.org/abs/1307.2981

PS. Note that according to Bell his theorem does not depend on "local hidden variables":
"It is notable that in this argument nothing is said about the locality, or even localizability, of the variables λ."
- Bertlmann's socks and the nature of reality

 

[TrickyDicky]

Found it: http://iopscience.iop.org/1464-4266/6/6/012
As far as I am aware, Kracklauer did not really "crack" the problem: as a matter of fact I have tested his simulation program and also studied the "laboratory confirmation", but found both of those wanting (of course, I could have made a mistake).

I found the paper googling a couple of keywords, and some paragraph in page 106 seemed an example of what I was talking about wrt to geometry and nonlocality, on rereading it is probably not the most relevant reference I could find.

However, perhaps he was thinking in the right direction.
It reminds me of an old thread on this forum, which IMHO left some intriguing questions wide open: https://www.physicsforums.com/showthread.php?t=490571.

Neumaier argued that from the perspective of QFT the problem is caused by the "particle" concept (that is: countable, unalterable objects), and that in contrast, classical (Maxwellian) EM can break Bell's inequality.

Thanks for pointing me to that thread, it answers what I asked in the OP about others interpreting Bell's theorem in that way.

 

[gill1109]

Found it: http://iopscience.iop.org/1464-4266/6/6/012
As far as I am aware, Kracklauer did not really "crack" the problem: as a matter of fact I have tested his simulation program and also studied the "laboratory confirmation", but found both of those wanting (of course, I could have made a mistake).

However, perhaps he was thinking in the right direction.
It reminds me of an old thread on this forum, which IMHO left some intriguing questions wide open: https://www.physicsforums.com/showthread.php?t=490571.

Neumaier argued that from the perspective of QFT the problem is caused by the "particle" concept (that is: countable, unalterable objects), and that in contrast, classical (Maxwellian) EM can break Bell's inequality.

A recently published paper on classical optics seems to make similar suggestions, if I understand correctly what the authors are saying:

" [..] we have presented the first study of nonlocal correlations in classical optical beams with topological singularities. These nonlocal correlations between two different light modes are manifested through the violation of a Bell inequality using the Wigner function for this system of classical vortex beams. [..]
Clearly, the violation of the Bell inequality for classical light fields and the existence of nonlocal correlations bring out totally new statistical features of the optical beams. [..] "
Phys. Rev. A 88, 013830 (2013) - http://arxiv.org/abs/1307.2981

PS. Note that according to Bell his theorem does not depend on "local hidden variables":
"It is notable that in this argument nothing is said about the locality, or even localizability, of the variables λ."
- Bertlmann's socks and the nature of reality

It is easy to create *half* the cosine curve by LHV. It is easy to create the cosine curve by the detection loophole or by the coincidence loophole. I forget which one Kraklauer was using in his simulation, but it was one or the ither.

The problem is not the " particle" concept in the hidden layer, in the physics behind the scenes, it is the discreteness of the manifest outcomes. Click or no-click. +1 or -1. Within a time interval of fixed duration.

The recent paper needs more looking at http://arxiv.org/abs/1307.2981. They don't talk about regular CHSH but some generalization for continuous outcomes. And as far as I can see there is no spatial dimension. They are measuring at the same time different observables "in the same place". Bell is about "same time different places". The paper is hard and one thing is clear to me: the authors don't actually know much about / understand the conventional Bell story.

Note that *if* they had found a classical physical system violating Bell-CHSH within a rigorous time-space no-loopholes Bell type experimental framework, they would have disproved Bell's theorem. And someone could win the quantum Randi challenge by programming the math. And get famous and win the Nobel prize: loophole-free experimental violation of Bell-CHSH by a classical physical system (network of classical computers). Hell, it hasn't even yet been done in the quantum lab...