# Do nonlocal entities fulfill assumptions of Bell theorem?

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

1. ### Jarek DudaRegistered Senior Member

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No, as we know physics doesn't fulfill these inequalities, so I have just distinguished what was really proven (Bell inequalities for some assumptions), and what was not (physics situations does not fulfill these assumptions).

Last edited: Nov 12, 2015

3. ### SchmelzerValued Senior Member

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You have proven something, starting from your own assumptions, and made the conclusion that these assumptions are wrong. Nice, but irrelevant for Bell's theorem, which started with different assumptions.

5. ### Q-reeusBannedValued Senior Member

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Reinforced in #38:
Not just superluminal - instantaneous connections over any spatial separation, in dBB. Physics luminaries like Maldacena and Susskind now postulate 'micro-wormholes' as presumably the 1D transmission-lines that entangle particles: http://www.fromquarkstoquasars.com/wacky-physics-are-entangled-particles-connected-by-wormholes/
Superluminal/instantaneous (or for that matter even sub-luminal) signalling via 'wormholes' or anything else is for all the reasons given in #3, no less mystical, no less crackpot, than abandoning realism.

7. ### Jarek DudaRegistered Senior Member

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There are no doubts that:
1) Bell inequalities are fulfilled for some assumptions,
2) physics violates these inequalities.

Hence, physics doesn't fulfill these naturally looking assumptions - we need to localize why.

And this is quite clear - the assumption is having unique binary descriptors - in contrast, in physics these descriptors are probabilistic ... and additionally depend on the order of questioning, like in multistage Stern-Gerlach.

Last edited: Nov 12, 2015
8. ### SchmelzerValued Senior Member

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I do not claim that your error is a new one, it is a well-known one, made by many people, and already Bell himself was tired correcting it. So, here some John Boccio or Lorenzo Maccone is making this same error.

So, again, using the language of that paper: Counterfactuality is not assumed in Bell's theorem, but proven in the first part of the proof. This first part is the EPR argument.

And, therefore, the rejection of counterfactuality is not a solution, because it is not assumed in Bell's version of his theorem.

9. ### Jarek DudaRegistered Senior Member

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Call them as you want, but this assumption isn't fulfilled even for classical analogues of EPR ...

So imagine classical EPR - let say two pencils flying with parallel alignment - we don't know what direction are they pointing, but we know that originally it is the same direction.
We can define Stern-Gerlach-like measurement for them, even simulate the classical Malus law: look at the angle, the "throw a dice" (use random number generator) accordingly to cos^2(theta) using angle from some chosen measurement direction - then fix the angle as parallel or anti-parallel to this measurement direction.

How would you define these ABC binary descriptors for such a pencil?

10. ### SchmelzerValued Senior Member

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Why should I try, given that it is completely irrelevant, once I cannot apply the EPR criterion of reality?

Here it is: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." Can we do this in your example? No? So what is the point of this example? How is it related to Bell's theorem?

11. ### Jarek DudaRegistered Senior Member

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So you are saying that pencils are not real?

Let me be more specific for this classical EPR:
there are two pencils flying in empty space (no gravity) - such that they are parallel ("entangled"): initially pointing the same direction, but we don't know which direction it is.

Now we can simulate Stern-Gerlach type of measurement, for example using Malus-like cos^2(theta) probabilities:
- we look at the angle of the flying pencil and compare it with the chosen measurement direction to calculate the required probability,
- generate a random number and compare it with this calculated probability (e.g. cos^2(theta)),
- accordingly to the result of this comparison, take this pen and set it to parallel or anti-parallel direction along the measurement direction.

Measurement is disturbing the system - both in standard EPR and this classical one.
So how do you define the binary ABC values in both of these cases?

12. ### SchmelzerValued Senior Member

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The point of the EPR criterion is the following: If I decide to measure at A in direction a, then I can predict, with certainty, the result of measurement at B in direction a. This is a prediction of QT, and can be checked by observation. (Ok, an idealization, there would be some error because one cannot choose a exactly, but this is not the point here.) Once the choice of direction of measurement at a cannot influence the measurement result at B, because of Einstein causality, the result of measuring in direction a at B has to be predefined.

It does not look like your experiment with flying and distorted pencils, can reproduce the 100% correlation if the same direction is measured at A and B. Not?

13. ### Fednis48Registered Senior Member

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Three things, Jarek.

First, the proof I sent you is super-compact. As Schmelzer has been alluding to, most proofs of Bell's theorem - including the original - explicitly talk about binary functions of arbitrary variables (ie. functions that map an arbitrarily complex state to a binary measurement outcome), so they don't need to assume anything about the underlying physics. Lorenzo Maccone's version glosses over this step for the sake of simplicity, so if it bothers you, I'd suggest you find a more formal proof, like perhaps Bell's original.

Second, if you actually do the math for your pencil example, you'll find that it doesn't violate Bell's inequality.

Third, it's worth noting that you've changed your argument from the OP. Originally, you were saying solitons can violate Bell's inequality, because they're not localized. Now you've switched to saying that non-binary hidden variables can violate Bell's inequality. To do so without even acknowledging the shift seems a little disingenuous.

14. ### brucepValued Senior Member

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It's been an interesting discussion. I was especially interested in the properties of solitons. In cosmology the inflation event is predicted to originate from a soliton in quantum scalar field. The local gravitational field causes the soliton to inflate because the cosmological constant term in the metric is very dominant resulting in inflation rather than collapse. Anti gravity rather than gravity. Based on that I would tend to think that solitons can't be nonlocal. But I really don't know. Your 'second' is revealing.

15. ### przyksquishyValued Senior Member

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At the risk of beating a dead horse,

That isn't a particularly good explanation of Bell's theorem (the author invokes assumptions like "counterfactual definiteness" that aren't necessary and only make the discussion more confusing than it needs to be). If you want a good understanding of Bell's theorem then a good place to start is the introduction by Travis Norsen (arXiv:0707.0401 [quant-ph]). There's also a Scholarpedia article on the topic which Norsen is a co-author of.

The ArXiv article by Norsen is heavily based on writings by Bell, which are well worth reading in their own right. At least two of them are freely available online:
The "local beables" essay in particular discusses the precise formulation of "locality" that the theorem is derived from.

All four of these sources include a derivation of the CHSH inequality.

That isn't a restriction. The "binary descriptors" can be any macroscopic event (e.g., a particle lands in one or another region on a screen, or this or that photon detector signals a detection) and you can always make a range of possible outcomes binary just by grouping them into two categories*. Representing the outcomes with the values +1 and -1 is also a matter of convention/definition. It is not an assumption or an attempt to model spin.

*One important practical example of this is the handling of losses. In a typical Bell experiment, you would not in practice expect to detect every particle, since some of them get lost in transit and sometimes the detector might not register them. You also can't simply ignore nondetection events (where you were hoping/expecting to detect a particle but didn't), since this opens a loophole in the theorem. One simple way to handle this rigorously is to absorb nondetections into one of the outcomes, so if you're measuring something you call "spin" you might record +1 for whatever you consider a "spin up" result and "-1" for "spin down or nondectection" results.

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17. ### Fednis48Registered Senior Member

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Indeed; thanks for those links. I'm pretty comfortable with Bell's theorem itself, but I'm not very familiar with the literature on it, so it's good to be pointed to a well-written explanation of it.

18. ### Jarek DudaRegistered Senior Member

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I am reading "Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields" from Optica (July 2015) claiming violation of CHSH for classical fields:
https://www.osapublishing.org/view_...7-611.pdf?da=1&id=321243&seq=0&mobile=no&org=
What do you think about it?
Exactly like a single electric charge affects (electric field of) the entire universe, 2/3D topological charge affects the entire space - they are extremely nonlocal entities:

19. ### Fednis48Registered Senior Member

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I remember looking at this work (or maybe some related work) with a few of my colleagues a little while back. Like I said about Sanctuary earlier, this seems to be a case of Eberly getting lost in too much mathematical structure without enough sanity checks. I don't doubt that all of his calculations are right, but what's missing compared to genuine Bell violations is any notion of pairs of measurements. In essence, Eberly writes a 2-D classical field in terms of the intensities of its horizontal and vertical components, $\vec{E}=I_x \vec{e}_x+I_y \vec{e}_y$. This can be formally re-expressed as the dot product of two vectors:
$\vec{I}=\langle I_x, I_y \rangle$, $\vec{u}=\langle \vec{e}_x, \vec{e}_y \rangle$, $\vec{E}=\vec{I}\cdot\vec{u}$.
One can find a correlation function between these vectors over fluctuations in intensity, and Eberly performs an experiment to measure that correlation function. But look for a minute at what the vectors actually are. The first is a pair of scalar intensities, which contains all the information about the fluctuating scalar field. The second is a pair of unit vectors, which is completely defined by our choice of coordinate system. Any correlation function between the two is extremely contrived. For these variables to actually produce quantum nonlocality, Alice and Bob would each have to perform a binary measurement on one of the two. So in some sense, Alice would measure "In what direction is the field's intensity strongest?", while Bob would measure "In what direction is the field's coordinate axis?" If you think Bob's measurement makes no sense, you're not the only one.

20. ### Jarek DudaRegistered Senior Member

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So here is the main part of the experiment:

If I properly understand, the incoming beam (top) has some "Bell's hidden state" - they split it, use polarizers with different angles (a and s/a) to recreate CHSH, and measure correlations as intensities - getting violation of CHSH.

Why do you think that they measure something completely different?

21. ### brucepValued Senior Member

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Exactly like the mass of the soliton effects the gravitational field. Changes in the electromagnetic and gravitational field propagate at the speed of light and the speed of gravity. c. What you seem to be saying is information associated with topological charge can be known instantly throughout the field? And this translates to a possible hidden variable? I'd like to read the link but for some reason I'm linking a blank page.

Last edited: Nov 14, 2015
22. ### Jarek DudaRegistered Senior Member

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No, neither electric nor topological charges require exceeding the field's wave propagation speed (c) - which limits all kind of interactions.
The Gauss (electric) or analogously Gauss-Bonnet (topological) theorem guards the charge conservation - forbid creation of a single charge.
Instead, charge can be created only in charge-anticharge pairs (both electric and topological) - and information about such creation should propagate with c.

Returning to the Bell violation in classical field article, I have take a deeper look and everything looks fine ... and I doubt Optics would accept such a controversial paper without a really throughout verification - but I would gladly discuss eventual problems there(?)
Yesterday I have realized that the classical pencil example was insufficient - I was searching for a soliton/wave way for the violation and thought about a string in 3D - that its horizontal and vertical waves could be entangled ... like in this entanglement of E_x and E_y.

Anyway, this is another strong argument that there might be no fundamental obstacles for searching of the configurations of (e.g. EM) fields of particles, of trying to understand what holds them together (e.g. topology), why charge is quanitzed (e.g. topological charge as electric charge) - looking for soliton particle models:
- while e.g. Feynman didn't believe that interference could be performed/understood classically ... e.g. Couder do it with droplets with wave-particle duality ... also explaining orbit quantization ... the same can be done with breathers: oscillating solitons,
- while classical conductance/diffusion models seemed very wrong for semiconductor (Anderson localization) ... they were based on only approximating the maximal entropy principle (required by statistical physics models) - doing it right (Maximal Entropy Random Walk), we get the same as thermodynamically predicted by QM - also for solitons,
- while QM violates Bell inequalities required by classical mechanics ... now we see that classical field theories also can do it ... like describing vibration of a crystal: we do it classically, or equivalently using quantum description (Fourier transform) with phonons, which can be entangled,
...

What are other counterarguments against asking for the structure of fields of particles - of soliton particle models?
I think the strongest remaining is the belief that electron is a perfect point.
However, looking at electric field of a point charge, its energy integrates to infinity - it makes no sense - we need to regularize it to a finite energy (like 511keVs) and soliton approach does it.
Another argument (of prof. Faber) is running coupling: for very high energies alpha ~ q^2 is decreasing - what is also seen in soliton models: the effective charge drops to zero while going to its center (in high energy collisions).

What other counterarguments can you think of?

23. ### brucepValued Senior Member

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The way I interpret that is Alice's measurement is an invariant spacetime event while Bob makes a choice of how to model the event with a specific set of coordinates. Choice of coordinates is irrelevant to the physics. Beyond making the model easier to use. The contrivance comment seems to be right on.

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