# I Bell's Theorem: more general interactions with detector?

1. Aug 29, 2015

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

A quick look at polarised light:
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?!

Last edited by a moderator: Aug 29, 2015
2. Aug 29, 2015

### Staff: Mentor

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]

Last edited: Aug 29, 2015
3. Aug 29, 2015

### Michel_vdg

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?

4. Aug 29, 2015

### 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?

5. Aug 29, 2015

### DrChinese

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.

6. Aug 29, 2015

### DrChinese

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.

7. Aug 30, 2015

### 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 travelled 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

8. Aug 30, 2015

### 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?

9. Aug 30, 2015

### gill1109

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.

10. Aug 30, 2015

### 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.

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

Last edited: Aug 30, 2015
11. Aug 30, 2015

### 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 : )

12. Aug 30, 2015

### Staff: Mentor

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.

13. Aug 30, 2015

### 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?

14. Aug 30, 2015

### gill1109

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.

Last edited: Aug 31, 2015
15. Aug 31, 2015

### Michel_vdg

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.

16. Aug 31, 2015

### gill1109

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.

17. Aug 31, 2015

### 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.

18. Aug 31, 2015

### 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.)

19. Aug 31, 2015

### gill1109

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

20. Aug 31, 2015

### 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°

Last edited: Aug 31, 2015