# Do nonlocal entities fulfill assumptions of Bell theorem?

Discussion in 'Physics & Math' started by Jarek Duda, Nov 3, 2015.

1. ### brucepValued Senior Member

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Thanks for your explanation. It probably makes sense for me to read the paper published in optics. Could you try the link again? The argument Fednes48 makes with respect to the measurements.

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3. ### Fednis48Registered Senior Member

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Because at the top of page 4, they clarify that they're encoding the correlation function $c_{11}$ in the output intensity of one beam. They arrange things such that their beam intensities can be formally expressed in terms the correlations between two vectors, but they don't show that it would be possible (or even meaningful) to measure the vectors separately.

I had the same problem, but if you run a google search for the title, the arXiv version shows up immediately.

The fact that it's in Optica tells me they had a hard time finding a journal that would publish them; this kind of thing is a primary focus of Physical Review A (or Physical Review Letters, if it's especially interesting). It's doubly telling that they had to go with a journal that doesn't specialize in the quantum information side of things, which is where their error lies. But journal quality is a little beside the point; even in Nature and other top-tier journals, you sometimes get papers (especially speculative theory+experiment papers) that are mathematically sound yet physically vacuous. This is one such paper. To convince me otherwise, you would have to explain how, at least in principle, the correlations they talk about could be realized as actual correlations between separate measurements.

You're starting to sounds a bit like Farsight, here. If you want to talk about whether a soliton model can or can't explain electron behavior, feel free to start another thread. But even if there were no affirmative argument against soliton electrons, they still wouldn't violate Bell's inequality.

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5. ### brucepValued Senior Member

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That was Jareks comment to me. I wouldn't give a crap except you invoked Farsight. LOL.

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7. ### Jarek DudaRegistered Senior Member

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Not true - by using one of the shutters, they measure the vectors independently - with detector on the bottom or on the top-left.
The final coincidence formula (10) uses all three intensities.

Ok, let's take a closer look at the line of thinking as it is nontrivial.
c_11 indeed corresponds to P_11(a,b) - measurement of two properties of the incoming beam, which should fulfill CHSH in Bell's line of thinking.
b appears in (9) formula, but haven't been used in the experimental setting earlier - (9) is a general decomposition and s/a are chosen to remove c_12 due to interference.
The supplement is indeed in the arxiv version: http://arxiv.org/pdf/1506.01305v2.pdf
Are you saying that Optica wouldn't use reviewers who are specialists in Bell inequality for article of this weight?
If the problem is as obvious as you say, wouldn't at least one of reviewers make an alert?
Additionally, there would be articles criticizing it - do any of 6 citing papers do it?
Instead, here is one them: as you want PsyRevA paper ... claiming classical teleportation: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.023827

The discussed article from a good journal says that classical field theories can violate Bell's inequality.
Remember that for solitons we are not talking about classical mechanics, where they are fulfilled, but about classical field theories - where you have superposition of multiple modes/DOFs, which behave like entangled.
Like phonos in crystal - we use quantum description for them, so they may violate Bell's inequalties ... but they can be also seen as normal modes of classical oscillations.

There are lots of people who are trying to understand the structure of fields of particles, like Penrose twistors, Volovik's Universe in a helium deroplet ... please don't put all of us into one bag.
I am mainly referring to the view of prof. Manfried Faber from Vienna, whose main line of work is QCD.
His lecture: http://www.emqm13.org/abstracts/presentation-videos/video-manfried-faber/

Last edited: Nov 15, 2015
8. ### brucepValued Senior Member

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I wouldn't put you in a bag with anybody else. As far as public science forums go this has been one of the better discussions. Where arguments are published is revealing. This is the abstract [in arxiv] for the paper you're reading. They're are no citations accessible from this source. Assuming 6 citations exist.
http://arxiv.org/abs/1506.01305

Last edited: Nov 15, 2015
9. ### Fednis48Registered Senior Member

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Labeling that as your quote was an editing error on my part. My response was directed to Jareck, at least in my head.

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You're right that the coincidence formula uses all three intensities; my mistake. I also realized that I was mistaken in interpreting the two degrees of freedom of the experiment, and I think I was overly harsh on Eberly as a result. (This understanding is largely as a result of reading http://arxiv.org/pdf/1406.3338v1.pdf, which appears to be an unpublished, pre-experiment version of the paper in question that I actually find easier to follow.) What's really going on is that the beam's polarization and amplitude are correlated, such that the total field can be written as the sum of two linearly polarized fields whose spatial amplitude functions are orthogonal. The principle is even more clearly distilled in http://journals.aps.org/pra/abstract/10.1103/PhysRevA.82.033833, which is unfortunately behind a paywall; in it, Borges takes a laser whose polarization components are in different angular momentum modes and shows that its interferometry statistics violate Bell-like inequalities.

What's still missing, though, is the idea that the correlation measured could actually be expressed as the correlation between two separate measurements. It is certainly not the case that one output beam measures the intensity while the other measures polarization, and equation (10) does not take the form of a standard correlation calculation. Instead, interferometry is used in such a way as to access the intensity-polarization correlation more or less directly. Even if everything is classical, the step of running beams through polarizers and then re-merging them at a beamsplitter causes interactions between the two degrees of freedom that simply cannot be captured by postprocessing of independent measurements. As a result, the experiment might highlight what the essential properties of Bell's theorem really are, but those essential properties still stand.

Sorry if I came across as bashing Optica; Optics Letters is a perfectly good journal. Especially in light of my misunderstanding the degrees of freedom at play, Eberly's only "mistake" in my opinion is that he overstates his conclusions about how this demonstrates a classical Bell violation. (Incidentally, the overstatement is much more pronounced in the earlier, unpublished paper I linked above.) And if any journal would let him get away with overstating the information-theoretic side of his experiment, it would be a journal focused on the optical side.

That PRA paper is actually really cool - thanks for linking it! Here's the arXiv version. For those who don't want to read through it, the authors set up an intensity-polarization correlation as above, but go one step further by performing a teleportation-like transfer of coherence between the two. The result is a setup that maps orbital angular momentum modes of the laser to different polarizations. I don't know how practically useful it is, but it's certainly intriguing, and the reverse process would definitely be groundbreaking if someone ever pulled it off. Moreover, I think the authors got their conclusion just right, noting that a laser's formally entanglement-like structure allowed them to take "inspiration" from quantum information processes to pull off something cool, but without really downplaying the quantum nature of Bell violations.

Again, tell me what measurements are made and I'll tell you why they don't work. Part of the reason Bell's theorem is such a celebrated result is that it's not at all intuitively obvious; even knowing the theorem, there's no qualitative argument that makes one think "Oh, of course no classical theory can ever match the predictions of quantum mechanics!" Rather, the devil is in the details, and those details can't be sussed out by something as vague as appealing to the superposition structure of field theories or the "nonlocality" of solitons. As for phonons, one phonon is a normal mode of a classical oscillator, and cannot violate Bell's inequality. A general classical oscillator is described by a sum of phonons with real coefficients, and still cannot violate Bell's inequality. Quantum mechanics allows a superposition of phonons with complex coefficients, and that makes all the difference.

Fair enough. My essential point is just that the viability of a soliton electron model is a separate question from whether such a model could violate Bell's inequality without quantum superposition.

I don't doubt there are 6 citations, although you're right that tracking them down takes some doing. The one Jareck specifically linked is behind a paywall, but it's on the arXiv here.

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10. ### Jarek DudaRegistered Senior Member

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Let's imagine a regular crystal lattice - we can describe it classically as positions of atoms.
Alternatively, we can go to normal modes (Fourier transform), getting phonons - described by quantum formalism, their superposition acts as entanglement - can violate Bell inequalities.

Soliton models (some nonlinear potential) additionally allow for stable localized field configurations in such (continuous limit of ) a crystal - there are these corpuscles/solitons surrounded by superposition of all kinds of waves (also pilot) in this (viscosity-free) field.
While pair creation, soliton doesn't just travel alone, but it is among other accompanied by ("is in superposition with") a delocalized wave guarding Noether angular momentum conservation (from pair creation) - is entangled with kind of a ghost of the second particle.

11. ### brucepValued Senior Member

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Thanks for the link. Interesting experiment model. Would you call that an analog experiment? Very informative post. Thanks.

12. ### przyksquishyValued Senior Member

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That isn't a Bell experiment. I'm not so well versed in classical optics but, if I understand the article correctly, they define their "CHSH correlator" in terms of "probabilities" $P_{ij}(a, b)$ that are ultimately just functions of a (for practical purposes) local field state. In a Bell test you have (usually discrete) "events" and the probabilities are the actual joint probabilities of obtaining those events, estimated experimentally by coincidence counting, i.e., $P_{ij}(a, b) \approx N_{ij} / N_{\text{total}}$, where $N_{ij}$ is the number of $(i, j)$ coincidence events and $N_{\text{total}} = \sum_{ij} N_{ij}$ is the total number of events. Also, the "events" in a Bell test are supposed to be spatially separated so that if causal influences are limited by the speed of light then they shouldn't be able to directly influence each other.

I previously linked to material explaining Bell's theorem for a reason: the explanations I linked to are very clear about what type of scenario Bell's theorem is concerned with (correlations between spacelike separated parties) and what type of model is ruled out (roughly, models where events can be fully understood in terms of initial conditions in their past light cones).

Incidentally, the published Optica article (which is open access) can be linked to via its DOI: http://dx.doi.org/10.1364/OPTICA.2.000611.

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14. ### Fednis48Registered Senior Member

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Glad you found it interesting! I guess I would call it an analog experiment, in the sense that they're working with function spaces rather than discrete ladders of states. Not sure what that implies, if anything.

I couldn't get the link to work when Jarek posted it, but yours seems to work fine. Weird.

15. ### Jarek DudaRegistered Senior Member

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Let me explain the experiment one more time - the measurement of correlations is here:

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So beam of light comes from the top - assuming some "hidden variables" describing it, they should fulfill Bell inequalities (CHSH) - they ask about two such hidden parameters at a time: P(a or a', b or b'), expressed by intensities of all three detectors (10), and their correlations violate CHSH.

We can see Mach-Zehnder interferometer - its path with 'a' polarizer corresponds to encoding 'a' for P(a,b) correlation by choice of the angle of the polarizer.
The 's-a' path is chosen such that the interference will remove mixed term (c_12 in (9)).
Finally the remaining 'c_11' term corresponding to P(a,b) correlation can be retrieved from all three intensities - formula (10) ... and these correlations violate CHSH.

CHSH allows for maximal value B = 2, quantum mechanics allows for at most B = 2.828.
They have reached only B = 2.54, but they explain that it is caused by imperfection of polarization:
"To be careful, we note that in our experiments the field was almost but not quite completely unpolarized; thus, not quite the same field was sketched in the Background Theory section."

Hence, this classical field situation cannot be imagined as having hidden variables a, a', b, b.

16. ### przyksquishyValued Senior Member

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Is this supposed to address what I said somehow? The "$P(a, b)$"s in Bell experiments are joint probabilities of spacelike separated events. So the authors of this paper did something that isn't a Bell experiment and they ruled out a type of "hidden variable model" that they made up and that nobody cared about before. Like Fednis48 pointed out, they appear to have taken some of the mathematics associated with Bell's theorem and applied it out of context.

When arguing about Bell's theorem it is worth keeping in mind that Bell was originally inspired by and responding to the Einstein-Podolsky-Rosen argument (the EPR article is freely available here), which explains the motivation for looking for hidden variable models in the first place. Relativistic causality -- the idea that effects shouldn't propagate faster than light -- is a crucial part of that argument. In the experiment described in the Optica article, there are no spatially-separated events or correlations between them, so the EPR argument doesn't apply and the EPR/Bell motivation for considering hidden variable models is gone.

17. ### Jarek DudaRegistered Senior Member

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Sure, this experiment has nothing to do with nonlocality.
It only tests if we can assume Bell-like hidden variables to a classical field - and, like for QM, the answer is: no.

It shows that in contrast to classical mechanics, both QM and field theories are much more complex, they can be seen/decomposed as a superposition of waves.
Like seeing a crystal lattice through classical positions of balls-and-springs ... or through normal modes - phonons, described by quantum mechanics.

18. ### Farsight

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For the record, I'm with Einstein. And I'm afraid I find the "spooky at a distance" experiments utterly unconvincing. You fight through the media hype and grand claims to read the paper, all you find is a graph and sigmas. There's never any substance.

19. ### przyksquishyValued Senior Member

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It's not just locality vs. nonlocality. The CHSH correlator is also defined in terms of discrete binary events, e.g., "spin up"/"spin down", "particle detected"/"particle not detected", "yes"/"no", "accept"/"reject", etc., while in the Optica paper their correlator is ultimately defined in terms of certain field intensities. This is a second way in which what they're measuring is quite different from what's measured in a Bell experiment.

20. ### Jarek DudaRegistered Senior Member

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Sure, it is not EPR - nobody says that it is.
It is just testing some correlations which should fulfill CHSH ... while they don't - saying that violation of Bell inequalities is not restricted to QM.

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22. ### brucepValued Senior Member

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How do you convince a crank bullshit artist? Most likely you don't. Why is that ?

23. ### przyksquishyValued Senior Member

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I disagree. Why should anything vaguely resembling the CHSH inequality be fulfilled by anything you feel like calling "classical correlation"? That isn't even well defined.