Bell's Theorem: more general interactions with detector?

[Michel_vdg]

[Mentor's note: split off from the thread https://www.physicsforums.com/threads/first-loophole-free-bell-test.829586/ as this is a general question about Bell's Theorem, not the specific experiment discussed in that thread]

It says in the paper ...

We perform 245 trials testing the CHSH-Bell inequality S ≤ 2 and find S = 2.42 ± 0.20.

... and the 'CHSH-Bell inequality' all revolves around the use of filters to polarise light:

In order to adapt it to real situations, which at the time meant the use of polarised light and single-channel polarisers, they had to interpret '−' as meaning "non-detection in the '+' channel", i.e. either '−' or nothing. http://www.phy.pku.edu.cn/~qiongyihe/content/download/2-13.pdf

A quick look at polarised light:

A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector E (red) oscillating in the vertical direction. The magnetic field B (or H) is always at right angles to it (blue), and both are perpendicular to the direction of propagation (z). - wiki

Now to jump to Bells Theorem, it is often presented as a ven diagram with 3 clearly defined sets:

Now to raise a question ... let's imagine something wild and suppose that a polarised Photon is not just some straight wave in reality, but possibly more like a string in the shape of a constant curvature knot (8) that spirals forward, which can squeeze its way through the slated polarisation filter with more or less leeway. If so, than there should be more variables than just those 3 ABC-options and the *Spookiness* has more to do with how light passes through a filter than 'locality'. My point is that we always look at a hidden variable ONLY within the Photon, but not in the Photon-Filter interaction, why?!

 

[Nugatory]

Now to jump to Bells Theorem, it is often presented as a ven diagram with 3 clearly defined sets:
...
Let's imagine..., than there should be more variables than just those 3 ABC-options and the *Spookiness* has more to do with how light passes through a filter than 'locality'. My point is that we always look at a hidden variable ONLY within the Photon, but not in the Photon-Filter interaction, why?

Bell's theorem is often presented using that three-way Venn diagram, but that's just a convenient way of outlining the basic argument. If you look at Bell's actual paper, you'll see that his proof allows for arbitrary interactions between the particle and the detector.

[edit: the paper is here: http://www.drchinese.com/David/Bell_Compact.pdf and the relevant part is the discussion of the parameter $\lambda$ in section 2]

 

[Michel_vdg]

If you look at Bell's actual paper, you'll see that his proof allows for arbitrary interactions between the particle and the detector.

I guess that relates to what was mentioned in the OP First loophole-free Bell test? where the detection loophole was mentioned from the start. But I was talking about Photon-Filter interaction or is the Filter included in the detector?

 

[Michel_vdg]

A small addition: I found this video on YouTube of the 'Spooky action at a distance'. Here it looks straight forward: turn one polarisation trigger (filter?) and the other result changes also; but I guess in both case the separate polarisation triggers are moved simultaneously and not just one side ... it looks a little misleading no ... or am I overlooking something?

 

[DrChinese]

My point is that we always look at a hidden variable ONLY within the Photon, but not in the Photon-Filter interaction, why?!

There is an excellent reason.

1. A photon polarized at theta will always pass through another polarizer set at theta, and you can add more polarizers at theta and it will pass all of them. So the extra polarizers do nothing in this case. That fits your model loosely.

2. A photon polarized at theta will pass through another polarizer set at theta+delta with probability cos^2(delta). So the polarizer does something, but it is probabilistic. That fits your model loosely.

3. With Bell pairs, there is a special case: when both polarizers are set at ANY identical angle, you get the so-called perfect correlations. This does NOT fit your model because the angle can be varied across 360 degrees (on both sides), and the results are always a perfect correlation. That wouldn't happen if the polarization was preset per your model and the interaction with the polarizer was probabilistic. There would be different probabilities on each side.

Obviously, both sides instead know to "act" the same way independent of the polarizers. This is usually cited as proof instead that the outcomes are predetermined at ALL angles due to hidden variables. The Bell proof then goes on to show that assumption (hidden variables) is inconsistent with quantum mechanics.

 

[DrChinese]

I guess that relates to what was mentioned in the OP First loophole-free Bell test? where the detection loophole was mentioned from the start. But I was talking about Photon-Filter interaction or is the Filter included in the detector?

Please note that in the referenced experiment, there are no pairs of photons being entangled. There is instead measurement of electron spins (spin-spin) at various angles.

The photons in this experiment are originally entangled as spin-polarization (spin being the electron, polarization being the photon). The photons are then using to swap their entanglement.

The Bell pairs being measured are entangled electron spins.

 

[gill1109]

Do look at Figure 7 from Bell's (1981) "Bertlmann's socks". The detectors and everything are all *inside* the big long box in the middle. It's literally a black box, we don't care what is inside. In Delft, it is 4000 feet wide and 4 microseconds high. (Time goes from bottom to top). The derivation of the CHSH inequality doesn't care what goes on there. What kind of interactions between "detectors" and "particles" or "waves" or whatever. The derivation depends on macroscopic binary inputs (measurement settings) being picked freely by the experimenter (a and b on bottom line), and macroscopic binary outputs coming out on the top line (yes/no). The yes/no outputs have to appear before the input settings could possibly have traveled the distance from left to right and vice-versa. In the middle is basically a clock to synchronise the whole thing and to say which pairs of measurements and outcomes are worth looking at. Bell envisaged a three particle atomic decay with the third particle giving a signal that the first two were on their way. This has now been turned around using entanglement swapping to signals being sent from Alice and Bob's labs, meeting half way, and a measurement there telling us that everyone is set up nicely (and that the next pair of settings and outcomes can go into the statistics of the CHSH inequality). See Zukowski, Zeilinger, Horne and Ekert (1993) https://vcq.quantum.at/fileadmin/Publications/1993-06.pdf Physics Review Letters vol 71, 4287-4290

 

[Michel_vdg]

... and what about chirality wouldn't that have an influence on the spin, if one particle goes to the right while the other moves to the left, or at least in the opposite directions?

 

[gill1109]

... and what about chirality wouldn't that have an influence on the spin, if one particle goes to the right while the other moves to the left, or at least in the opposite directions?

Who cares? It's all in the black-box. Assuming local hidden variables and freedom (no-conspiracy) we can write down bounds for the correlations which we could observe in the macroscopic experimental set-up described in the figure.

QM has some predictions for what the correlations (a set of four correlations, one for each of the four setting pairs) would be, or could be, assuming a particular content of the black box.

According to LHV, some of the sets of correlations allowed by QM are impossible.

Now they have done the experiment in Delft and observed a set of four correlations which is allowed by QM but forbidden by LHV. To be precise, correlations +0.6, -0.6, -0.6 and -0.6. The first minus the sum of the other three is S = 2.4. According to LHV you can't get S bigger than 2. According to QM it can be up to 2.8. (Tsirelson's bound). This is also the bound according to Pawlowski et al (2009) "information causality" http://arxiv.org/abs/0905.2292. Appeared in Nature. Not only can Alice not see what Bob is doing: even if Bob starts sending classical information to Alice, it doesn't help. Alice can't learn more than 1 bit of new information about what Bob is doing, per classical bit of information sent by Bob. So the quantum entanglement and the "spooky correlations" can't be used to communicate, and they can't be used to speed up communication either.

 

[Michel_vdg]

I care ... just want to understand it all better, and since the particles are moving in opposite directions ... and there is not only spin but also chirality ... Anyway I need to read all the papers and let it sink in, thanks.

The direction along which an electron propagates and the amplitude of its wave function are not independent, so the electrons are said to possesses the property of chirality, or handedness. Pinning down fundamental details about these exotic electron states is important for developing graphene-based devices, but measuring this property directly has, however, remained elusive.
https://physics.aps.org/articles/v4/79

Edit: there's also light radiated back from the filter so it isn't a 100% oneway street ...

 

[Michel_vdg]

Ok, perhaps a stupid question ...

The setup is based on 3 filters and QM makes the output a 50% chance being spin up on one side and 50 % chance being spin down on the other. It has to be because they are entangled ... or at least opposite of each other.

But what if Chirality causes the particles in one box to be 50% up and 50% down in the opposite box just like it would be when flipping coins in front of a mirror because light travels in the opposite direction ... an its sort of a 4th filter?

The reaction it he mirror is also instantaneously ... and entangled : )

 

[Nugatory]

But what if Chirality causes the particles in one box to be 50% up and 50% down in the opposite box just like it would be when flipping coins in front of a mirror because light travels in the opposite direction ... an its sort of a 4th filter?

What if it does? You're proposing a different $\lambda$, the interactions that eventually lead to the results that we've measured. But Bell's proof is a statement about the results of the measurements and it does not depend on $\lambda$: No matter what is going on the experiment, the quantum mechanical correlations can only be produced if $\lambda$ is such that the results at one detector are affected by changing the setting at the other.

 

[Michel_vdg]

I made a rough sketch to check if I understood the setup correctly of the opposite particles and the series of filters; and I was wondering if one goes Clockwise and the other Counter-Clockwise, with chirality, do they arrange the order of the filters ABC differently to match (ABC vs. ACB) ... or is this unimportant?

 

[gill1109]

I made a rough sketch to check if I understood the setup correctly of the opposite particles and the series of filters; and I was wondering if one goes Clockwise and the other Counter-Clockwise, with chirality, do they arrange the order of the filters ABC differently to match (ABC vs. ACB) ... or is this unimportant?

View attachment 88019

What they do is important to understand from the point of view of quantum mechanics. From the point of view of testing local realism, it is unimportant. However you can say that the fact that the experimental results are in violation of local realism means in a very definite way that we have no hope of understanding what actually goes on at the particle by particle level. Particle-by-particle, deterministic/mechanical explanations, are forced to be non-local or worse.

 

[Michel_vdg]

What they do is important to understand from the point of view of quantum mechanics. From the point of view of testing local realism, it is unimportant. However you can say that the fact that the experimental results are in violation of local realism means in a very definite way that we have no hope of understanding what actually goes on at the particle by particle level. Particle-by-particle, deterministic/mechanical explanations, are forced to be non-local or worse.

Why? Aren't that kind of details important for each view? When looking at those pathways there is a rotation difference of 120° steps vs. 240° the other way around.

 

[gill1109]

Why? Aren't that kind of details important for each view? When looking at those pathways there is a rotation difference of 120° steps vs. 240° the other way around.

I'm trying to say that the logic of the Bell experiment does not require us to understand what goes on inside the big long black box. Of course as physicists we would like to understand what goes on. The experimenters designed the experiment using their knowledge of quantum mechanics and skills at actually engineering certain quantum states, quantum measurements, etc.

 

[Michel_vdg]

When the 'long black box' produces automatically 50/50 mirrored results because of the 240/120 rotation differences than the test is proving something differently.

 

[gill1109]

The long black box generates results like this:

Alice setting 1, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.4, 0.1, 0.1, 0.4
Alice setting 1, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1
Alice setting 2, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1
Alice setting 2, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1

Corresponding to correlations = Prob(equal) - Prob(unequal) of 0.6, -0.6, -0.6, -0.6 and hence S = corr(1, 1) - corr(1, 2) - corr(2, 1) - corr (2, 2) = 2.4 with a standard error of 0.2, by routine statistics computations, since there are approximately 245/4 pairs of measurements for each pair of settings.

(I am reverse-engineering the numbers from what is published in the arXiv preprint. Hopefully the full paper will get accepted and will contain full data.)

 

[gill1109]

The long black box generates results like this:

Alice setting 1, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.4, 0.1, 0.1, 0.4
Alice setting 1, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1
Alice setting 2, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1
Alice setting 2, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.1, 0.4, 0.4, 0.1

Corresponding to correlations = Prob(equal) - Prob(unequal) of 0.6, -0.6, -0.6, -0.6 and hence S = corr(1, 1) - corr(1, 2) - corr(2, 1) - corr (2, 2) = 2.4 with a standard error of 0.2, by routine statistics computations, since there are approximately 245/4 pairs of measurements for each pair of settings.

(I am reverse-engineering the numbers from what is published in the arXiv preprint. Hopefully the full paper will get accepted and will contain full data.)

PS local realism predicts that the most extreme these statistics could have been would be

Alice setting 1, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.375, 0.125, 0.125, 0.375
Alice setting 1, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.125, 0.375, 0.375, 0.125
Alice setting 2, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.125, 0.375, 0.375, 0.125
Alice setting 2, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.125, 0.375, 0.375, 0.125

Quantum mechanics actually allows a bit more extreme still (Tsirelson's bound), approximately

Alice setting 1, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.425, 0.075, 0.075, 0.425
Alice setting 1, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.075, 0.425, 0.425, 0.075
Alice setting 2, Bob setting 1: outcomes ++, +-, -+, -- with relative frequency 0.075, 0.425, 0.425, 0.075
Alice setting 2, Bob setting 2: outcomes ++, +-, -+, -- with relative frequency 0.075, 0.425, 0.425, 0.075

 

[Michel_vdg]

I’m not saying that the results are wrong, and this is not specifically about the newly published test in Nature, I’m just trying to understand Bell’s Theorem, and see how that works in practice with rotation and chirality. It looks to me that the order of the filters plays a role. Here’s a cleaner drawing to show how I’m looking at things ... this might help figure out where I'm wrong:

For Bell's ‘predeterministic’ particles you can have 2 options: one where Alice and Bob have all their arrows-spin outwards vs. inwards, which gives you 100% differences; the other option is like in the sketch where there’s 1/3 different.

With filters A:0°, B:120°, C:240° you get 9 possible combinations of which 5/9 form a matching pair (+/-).

Now let’s add rotation: Alice = Clockwise (CW) vs. Bob = Counter-Clockwise (C-CW) and they keep rotating in-between the filters.

Both particles arrive equally at the first filter A:0° and can check if they match; than for CW the next filter ‘B’ is at 120° rotation steps, while for C-CW that same filter ‘B’ is at 240° distance.

Thus Bob has to take twice as many steps as Alice to align with the same filter to find out if there’s a match or not.

CW: A:0°, B:120°, C:240°
C-CW: A:0°, B:240°, C:480°

Conclusion: if you change the order of filters B:120° and C:240° for one of them, mirror, than Alice and Bob would be rotationally synchronised and encounter those filters at the same time, and you might get the 5/9 logical match.

CW: A:0°, B:120°, C:240°
C-CW: A:0°, B:-120°, C:-240°

 

[gill1109]

I’m not saying that the results are wrong, and this is not specifically about the newly published test in Nature, I’m just trying to understand Bell’s Theorem, and see how that works in practice with rotation and chirality. It looks to me that the order of the filters plays a role. Here’s a cleaner drawing to show how I’m looking at things ... this might help figure out where I'm wrong:

View attachment 88034

For Bell's ‘predeterministic’ particles you can have 2 options: one where Alice and Bob have all their arrows-spin outwards vs. inwards, which gives you 100% differences; the other option is like in the sketch where there’s 1/3 different.

With filters A:0°, B:120°, C:240° you get 9 possible combinations of which 5/9 form a matching pair (+/-).

Now let’s add rotation: Alice = Clockwise (CW) vs. Bob = Counter-Clockwise (C-CW) and they keep rotating in-between the filters.

Both particles arrive equally at the first filter A:0° and can check if they match; than for CW the next filter ‘B’ is at 120° rotation steps, while for C-CW that same filter ‘B’ is at 240° distance.

Thus Bob has to take twice as many steps as Alice to align with the same filter to find out if there’s a match or not.

CW: A:0°, B:120°, C:240°
C-CW: A:0°, B:240°, C:480°

Conclusion: if you change the order of filters B:120° and C:240° for one of them, mirror, than Alice and Bob would be rotationally synchronised and encounter those filters at the same time, and you might get the 5/9 logical match.

CW: A:0°, B:120°, C:240°
C-CW: A:0°, B:-120°, C:-240°

The CHSH experiment uses two different filter directions for Alice, and two different filter directions for Bob. Alice chooses between 0 and 90 degrees, Bob between 45 and 135.

 

[DrChinese]

I made a rough sketch to check if I understood the setup correctly of the opposite particles and the series of filters; and I was wondering if one goes Clockwise and the other Counter-Clockwise, with chirality, do they arrange the order of the filters ABC differently to match (ABC vs. ACB) ... or is this unimportant?

View attachment 88019

If I understand your diagram correctly, you are far off. The order of filters after the first on each side is definitely not related to "chirality" or anything other than the setting of the first.

 

[Michel_vdg]

The CHSH experiment uses two different filter directions for Alice, and two different filter directions for Bob. Alice chooses between 0 and 90 degrees, Bob between 45 and 135.

All I could find in the paper regarding the polarisation was that it was "passing a fibre-based polarizer (POL)."

If I understand your diagram correctly, you are far off. The order of filters after the first on each side is definitely not related to "chirality" or anything other than the setting of the first.

What you know for sure is that a polariser can start to dim and eventually completely block the light passing through at a certain angle, but light that passes through can still have lots of variable properties ... so why not chirality and CW vs. C-CW?

Check this video of light passing through a polariser and next through an optic fiber:

 

[DrChinese]

What you know for sure is that a polariser can start to dim and eventually completely block the light passing through at a certain angle, but light that passes through can still have lots of variable properties ... so why not chirality and CW vs. C-CW?

Light passing through a linear polarizer is linearly polarized.

Further, the Heisenberg Uncertainty Principle essentially assures us that any measurement causes non-commuting properties to lose any previous values and take on indeterminate values. There are no known "prior histories" attached to quantum particles after measurements*

*except for bases not being measured. If you measure spin but not position/momentum, position/momentum is not affected.

 

[Michel_vdg]

Light passing through a linear polarizer is linearly polarized.

Further, the Heisenberg Uncertainty Principle essentially assures us that any measurement causes non-commuting properties to lose any previous values and take on indeterminate values. There are no known "prior histories" attached to quantum particles after measurements*

*except for bases not being measured. If you measure spin but not position/momentum, position/momentum is not affected.

Ok. I thought added this:

Orbital angular momentum of light
(https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light)

The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum.
...
The helical modes are characterized by an integer number [PLAIN]https://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png, positive or negative. If [PLAIN]https://upload.wikimedia.org/math/e/6/7/e6753e61990bc639ae1869683cb421b7.png, the mode is not helical and the wavefronts are multiple disconnected surfaces, for example, a sequence of parallel planes (from which the name "plane wave"). If [PLAIN]https://upload.wikimedia.org/math/7/8/3/783cc658a9a9237061983a383b467aae.png, the handedness determined by the sign of [PLAIN]https://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png, the wavefront is shaped as a single helical surface, with a step length equal to the wavelength[PLAIN]https://upload.wikimedia.org/math/e/0/5/e05a30d96800384dd38b22851322a6b5.png. If [PLAIN]https://upload.wikimedia.org/math/4/7/1/4712cd2e5e56dc931b330475cbe69ca4.png, the wavefront is composed of https://upload.wikimedia.org/math/a/7/4/a74d57c803194092ca5e0780138fab66.png distinct but intertwined helices, with the step length of each helix surface equal to [PLAIN]https://upload.wikimedia.org/math/a/d/7/ad70db9028e6a40684c6e64834ed3326.png, and a handedness given by the sign of [PLAIN]https://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png. The integer https://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png is also the so-called "topological charge" of the optical vortex.

 

[DrChinese]

Ok. I thought added this:

...Which has nothing to do with linear polarization of photons, nor with going through a series of linear polarizers.

Not really sure what you are trying to say. You can entangle photons on basis E and basis F and then measure each basis independently. Then it would not matter if Alice did a measurement of first E, then F; while Bob did a measurement of first F, then E.

I have to admit that I know little about OAM, and I don't exactly see how you would entangle photons on that basis (which apparently can be done). But the above should still apply. Regardless, your example - A/B/C filter sequence on entangled photons - does not work as (I think) you intend.

 

[Michel_vdg]

Not really sure what you are trying to say.

The video below of Bell's Inequality explains it all more clearly ... I'm adding a couple of screenshots:

Here it shows how a particle could twist & turn after the 1st filter and thus being able to also pass the 2nd filter, like in my sketch:

- This twist & turn possibility is pointed out in the first row, where we no longer know if 'x' is still 'x' after the first filter.
- To solve this they used for the second test the entangled particles of which they know it is the opposite of the other and used a mirrored filter.
- Thus we are also sure that the 1st and 2nd test on the particle 'x' are 100% correct even when the distance is 'hundred of meters', but there's is nothing 'spooky' about that since the particles can be deterministic ...

... because to proof Bell's Inequality and determinism you need 3 tests (ABC) on the same particle 'x' and you have only 2 test possibilities that are 100% safe ...

... next there is the CHSH experiment where they redirect the two results A+B for the 3rd test but there's always interference; the particles could have turned CW or C-CW, and you can't know how they started at point 'S'. Of course the results will always be complementary like a mirror, but it doesn't tell us anything about determinism and locality the whole point of Bell's Theorem ... or what am I missing here?

 

[DrChinese]

1. ... because to proof Bell's Inequality and determinism you need 3 tests (ABC) on the same particle 'x' and you have only 2 test possibilities that are 100% safe ...

2. ... next there is the CHSH experiment where they redirect the two results A+B for the 3rd test but there's always interference; the particles could have turned CW or C-CW, and you can't know how they started at point 'S'. Of course the results will always be complementary like a mirror, but it doesn't tell us anything about determinism and locality the whole point of Bell's Theorem ... or what am I missing here?

1. A Bell test consists of a single measurement on one of the entangled pair, and a single measurement on other of the pair. There is no ABC on the same particle. Period. This is true as well for CHSH.

http://arxiv.org/abs/quant-ph/9810080

2. There is no CW or C-CW in a CHSH type Bell test. Period. These are done with linear polarization, as I have said several times. If you would care to produce a reference to a suitable paper (not a video which does not meet the standard here), please feel free. This will be needed to continue the discussion in a meaningful manner.

You are mixing several concepts which are not related. While photons can go through a series of polarizers at different angles, this really has nothing to do with entanglement or handedness.

 

[Michel_vdg]

There is no CW or C-CW in a CHSH type Bell test. Period. These are done with linear polarization, as I have said several times. If you would care to produce a reference to a suitable paper (not a video which does not meet the standard here), please feel free. This will be needed to continue the discussion in a meaningful manner.

Found some:

Realising high-dimensional quantum entanglement with orbital angular momentum:
http://arxiv.org/pdf/1305.7102.pdf

Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces:
https://www.osapublishing.org/...
"We observe entanglement between photons in controlled super- position states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality."

Complementarity reveals bound entanglement of two twisted photons:
http://iopscience.iop.org/article/10.1088/1367-2630/15/8/083036/pdf

And a video just for fun : P

 

[DrChinese]

Found some:

Realising high-dimensional quantum entanglement with orbital angular momentum:
http://arxiv.org/pdf/1305.7102.pdf

Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces:
https://www.osapublishing.org/...
"We observe entanglement between photons in controlled super- position states of orbital angular momentum (OAM). By drawing a direct analogy between OAM and polarization states of light, we demonstrate the entangled nature of high order OAM states generated by spontaneous downconversion through violation of a suitable Clauser Horne Shimony Holt (CHSH)-Bell inequality."

Complementarity reveals bound entanglement of two twisted photons:
http://iopscience.iop.org/article/10.1088/1367-2630/15/8/083036/pdf

And as I keep saying, none of these support your "hypothesis" regarding a series of linear polarizers. Again, if you have a reference to that, it would be helpful. Otherwise, it is quite unclear where this is going.

 

[Michel_vdg]

And as I keep saying, none of these support your "hypothesis" regarding a series of linear polarizers.

What you said was: "There is no CW or C-CW in a CHSH type Bell test. Period."

My comment was only intended to disprove only that.

 

[Michel_vdg]

Otherwise, it is quite unclear where this is going.

I guess this quote from Murphy explains it best:

"The Bell inequality arises because Bell included an ad-hoc assumption taken from quantum interpretations (that the wave-function represents a complete description of particle alone, and that when interacting with a passive instrument, it is like a wave encountering a passive barrier). That assumption is then used to place a constraint on the 'hidden variable' model. Bell constrained the hidden variable model so that the selection of the outcome is solely on the basis of the disposition of orientation variables (for spin/polarization measurement) internal to the particle, relative to the axis of the of the analyzer. The outcome of the interaction supposedly depends on the orientation of internal properties of the particle alone, the analyzer is required to be a passive marker.

Spatial symmetry means that such a model must operate within the Bell limits, which is essentially a straight-line correlation curve from analyzers aligned to counter-aligned/right-angles.

In the case of spin/polarization interactions, if the encounter with the instrument spatially distorts the probability distributions along the axes of the analyzer, then there is no surprise that the correlation between one analyzer and another depends on the relative angle of the analyzers. The answer is stunningly simple, and idea that non-locality is required is a fallacy. This is consistent with the QM prediction that the expectation function for the density of a polarization state of a particle while interacting with a polarization analyzer, is a Cos^2(theta) curve. The spatial orientation of the expectation functions depends on the orientation of the analyzers. When this is modeled by discrete hidden variables mapping onto a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory."

 

[gill1109]

I guess this quote from Murphy explains it best:

"The Bell inequality arises because Bell included an ad-hoc assumption taken from quantum interpretations (that the wave-function represents a complete description of particle alone, and that when interacting with a passive instrument, it is like a wave encountering a passive barrier). That assumption is then used to place a constraint on the 'hidden variable' model. Bell constrained the hidden variable model so that the selection of the outcome is solely on the basis of the disposition of orientation variables (for spin/polarization measurement) internal to the particle, relative to the axis of the of the analyzer. The outcome of the interaction supposedly depends on the orientation of internal properties of the particle alone, the analyzer is required to be a passive marker.

Spatial symmetry means that such a model must operate within the Bell limits, which is essentially a straight-line correlation curve from analyzers aligned to counter-aligned/right-angles.

In the case of spin/polarization interactions, if the encounter with the instrument spatially distorts the probability distributions along the axes of the analyzer, then there is no surprise that the correlation between one analyzer and another depends on the relative angle of the analyzers. The answer is stunningly simple, and idea that non-locality is required is a fallacy. This is consistent with the QM prediction that the expectation function for the density of a polarization state of a particle while interacting with a polarization analyzer, is a Cos^2(theta) curve. The spatial orientation of the expectation functions depends on the orientation of the analyzers. When this is modeled by discrete hidden variables mapping onto a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory."

I think this shows that Murphy (whoever that is) does not understand Bell. But his misinterpretation is common. http://filosothots.blogspot.ca/2015/09/talking-about-bell.html

 

[Michel_vdg]

I think this shows that Murphy (whoever that is) does not understand Bell. But his misinterpretation is common. http://filosothots.blogspot.ca/2015/09/talking-about-bell.html

Thanks, I will have to give this some more thought.

But for instance a fish can slip individually through the net (of filters) vs. the whole wave of a flock that has to obey a different set of physical rules, because individually it has more freedom eg rotation ...

 

[Michel_vdg]

http://filosothots.blogspot.ca/2015/09/talking-about-bell.html

I've been looking at Wayne Myrvold's blogpost and paper (Lessons of Bell’s Theorem Nonlocality, yes; Action at a distance, not necessarily), and I can't see what you are referring to regarding the misinterpretation of Murphy; when the autor even says that action at a distance isn't needed to violate Bell inequalities:

"But I think that, at the very least, one should not take for granted that every sort of nonlocality involves spooky action at a distance." - http://www.ijqf.org/archives/1875 (blogpost)

"As many have pointed out, there is more than one way for a nonlocal theory to be nonlocal. I have defended the view that the difference makes a difference; for appropriate set-ups, Parameter Dependence involves a departure from relativistic causal structure, whereas theories, such dynamical collapse theories, that satisfy Parameter Independence and exhibit only Outcome Dependence, can satisfy the requirement that Bell hoped for, namely compatibility with relativistic causal structure at a truly fundamental level." - http://www.ijqf.org/wps/wp-content/uploads/2015/01/Myrvold-Bell-paper.pdf