Binney's interpretation of Violation of Bell Inequalities

[TrickyDicky]

What difference would it make? His theory doesn't work because his geometrical calculation is wrong, not because of any assumptions about locality.

I haven't found anything about Binney's geometrical calculations in the thread and Binney has no theory that I know of. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, did you not read the Wiseman paper linked by atyy?

 

[atyy]

I haven't found anything about Binney's geometrical calculations in the thread. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, did you not read the Wiseman paper linked by atyy?

To be honest, I didn't join the discussion till now because I have no idea what Binney is saying, let alone whether it is right or wrong, so I don't know if Binney is simply using locality as defined by Wiseman. Locality as defined by Wiseman is uncontroversially a property of quantum mechanics.

 

[Derek Potter]

I haven't found anything about Binney's geometrical calculations in the thread and Binney has no theory that I know of. Reading again the first posts Binney's quotes seem perfectly compatible with the indeterministic and local QM view of Bell's theorem, and all the comments about his "not even considering nonlocality" look like misled over-reactions, ...

I agree he does not set out his calculation, but he does spell out his model and asserts that it produces a result. So it is charitable to assume that there is a calculation and it is is based on the situation he describes:

Hence the most Alice can know about the orientation of the spin vector is that it lies in a particular hemisphere. Whatever hemisphere Alice determines, she can argue that the positron's spin lies in the opposite hemisphere. So if Alice finds the electron's spin to lie in the northern hemisphere, she concludes that the positron's spin lies in the southern hemisphere. This knowledge excludes only one result from the myriad of possibilities open to Bob: namely he cannot find Sz = +1/2. He is unlikely to find +1/2 if he measures the component of spin along a vector b that lies close to the z axis because the hemisphere associated with this result has a small overlap with the southern hemisphere, but since there is an overlap, the result +1/2 is not excluded.

Post #25 is my calculation based on what he says:
Construct a plane through a and b. Draw a circle and split it for the two "given" hemispheres. Choose a direction for a. This determines Alice's hemisphere and thus her result. Choose a direction for b, pointing the other way. Obviously b goes into the other hemisphere. Now allow b to swing round to some other angle. Recall that the electron spins are evenly distributed around 360 degrees. So the probabilty of a and b both lying in the same semicircle is proportional to the angle between them. No trigonometrical functions involved. Hence the anti-correlation will follow a linear rule, not the required [cosine] rule.

Unfortunately, although it produces a result, it is the wrong result. For small angles, the overlap of two hemispheres is proportional to the overlap. The quantum correlation is proportional to the overlap squared. Of course, if his words admit of another geometrical interpretation the exact kind of locality might be relevant but I cannot see how any other meaning is possible so it's pretty pointless discussing the finer details of a model which is simply wrong.

 

[Derek Potter]

Post #25

not the required cos^((b-a)/2) rule

Oops! Just say "cosine rule"

 

[TrickyDicky]

Here is my take on what Binney means just by the quotes in the OP, (I must say I don't care if he is right or wrong, had never heard about him):
There are two key points in what he says that I'm guiding my opinión on, he says literallythat no hidden variables can explain violations of BI, which I take as a clear rejection of determinism, and in the example used by Derek in #25 he doesn't say one can predict or calculate anything based simply on anything fixed at the outset, if one did like Derek did would find wrong results but he only talks about "consistence", by which I understand he means that the indeterminism he endorses allows the principle of locality to hold.

 

[Derek Potter]

Here is my take on what Binney means just by the quotes in the OP, (I must say I don't care if he is right or wrong, had never heard about him):
There are two key points in what he says that I'm guiding my opinión on, he says literallythat no hidden variables can explain violations of BI, which I take as a clear rejection of determinism, and in the example used by Derek in #25 he doesn't say one can predict or calculate anything based simply on anything fixed at the outset, if one did like Derek did would find wrong results but he only talks about "consistence", by which I understand he means that the indeterminism he endorses allows the principle of locality to hold.

They're consistent with there being a g in my middle name too but that is just as irrelevant.

 

[TrickyDicky]

They're consistent with there being a g in my middle name too but that is just as irrelevant.

Do you see the difference between claiming one can calcule the results of Bob from knowing that the hemisphere containing the positron's spin is fixed at the outset vs claiming that "a posteriori" (after the fact) the results are consistent with it being fixed at the outset and unaffected by Alice's measurement?

 

[stevendaryl]

Locality (Eq 2) doesn't have Alice's measurement outcome on the LHS, whereas local causality (Eq 4) does. So Eq 2 is just the reduced density matrix, which means that Bob's results don't depend on what Alice does. But Eq 4 is the nonlocal correlation, which means that if Bob knows Alice's results, he can sort his results and find perfect correlation.

Thanks! I stared at the two equations and didn't see that difference.

But now I'm having the opposite problem. It seems to me that if locality is violated that that would imply the possibility of signaling. If Bob's result depends on Alice's detector setting, then wouldn't Alice be able to signal to Bob by varying her setting?

Ah, nevermind. I see the difference: Equation 2 is this:

$P_\theta(B|a,b,c,\lambda) = P_\theta(B|b,c,\lambda)$

If that is violated, then Alice's setting affects Bob's result, but only if $\lambda$ is kept fixed. Since $\lambda$ is a hidden variable, Alice has no way of taking $\lambda$ into account in signalling to Bob, and Bob has no way of taking $\lambda$ into account in interpreting Alice's signal. So as far as signalling, it's sort of like cryptography using a one-time pad of random bits. If you have an independent way of knowing the pad, then you could use it to send messages. But if you don't know the pad, then messages will look like random noise.

 

[Derek Potter]

Do you see the difference between claiming one can calcule the results of Bob from knowing that the hemisphere containing the positron's spin is fixed at the outset vs claiming that "a posteriori" (after the fact) the results are consistent with it being fixed at the outset and unaffected by Alice's measurement?

Yes.

 

[Derek Potter]

the overlap of two hemispheres is proportional to the overlap. The quantum correlation is proportional to the overlap squared.

I mean the Binney correlation is proportional to the overlap!

 

[Derek Potter]

Anyway, fascinating as the hair-splitting about calculability and determinism may be, Binney actually does claim "Contrary to the claims of EPR, the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement."

There is no way he can make that claim unless the model allows calculation of Bob's results AND they agree with EPR/QM. The fact that the model allows some sort of results ("Binney correlations") may be consistent with determinism but EPR does not claim that all correlations are inconsistent with determinism only that quantum correlations are inconsistent with local determinism.

Binney correlations, if you do calculate them, are not quantum correlations. If you don't calculate them then his claim is meaningless.

 

[TrickyDicky]

Anyway, fascinating as the hair-splitting about calculability and determinism may be, Binney actually does claim "Contrary to the claims of EPR, the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement."

There is no way he can make that claim unless the model allows calculation of Bob's results AND they agree with EPR/QM. The fact that the model allows some sort of results ("Binney correlations") may be consistent with determinism but EPR does not claim that all correlations are inconsistent with determinism only that quantum correlations are inconsistent with local determinism.

Binney correlations, if you do calculate them, are not quantum correlations. If you don't calculate them then his claim is meaningless.

Hint: Calculation and measurement are different conceptually and practically.

 

[Derek Potter]

Exactly. I rest my case.

 

[TrickyDicky]

Exactly. I rest my case.

Technically you had no case from the start IMO, you made a straw man argument with Binney's words, he simply is not saying what you think he is saying, he's clearly on Bell's side and opposing EPR determinism.