Bell's theorem and the DrChinese Challenge?

[Gordon Watson]

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As I read the situation, DrChinese frequently challenges local realists -- of whatever hue -- here, in the Quantum Physics section of PF.

As I understand the details: The challenge is delivered in the context of Aspect's experiment, the twinned photons are identically correlated (in the spherically symmetric singlet state), and the three Bell-test orientations are, on a clock-face: 12.00, 4.00. 8.00.

Now; as I now understand the situation: A "local realistic response" to the DrChinese Challenge would be viewed as "non-mainstream", a Personal Theory, even if its results were in full accord with QM. So, it seems to me, such a response must be delivered in the Independent Research Forum (IR).


Question 1: Am I correct in thinking that the DrChinese Challenge must be addressed in IR?

Question 2: Irrespective of the answer to Question 1, whatever is required to fully comply with PF Rules: Would someone care to initiate* the DrChinese Challenge formally, in what ever is the correct PF venue**, please?

* Initiation by those who oppose a local realistic world-view, it seems to me, being essential.

** Some avenue for addressing (within PF), the DrChinese PF-found Challenge being also essential (it seems to me).

Many thanks.
..

 

[JesseM]

Now; as I now understand the situation: A "local realistic response" to the DrChinese Challenge would be viewed as "non-mainstream", a Personal Theory, even if its results were in full accord with QM. So, it seems to me, such a response must be delivered in the Independent Research Forum (IR).

The basic laws of arithmetic show it's impossible to meet DrChinese's challenge in a way that gives results "in full accord with QM." If you still can't see this, please tell me which specific step of the following explanation from [post=3213861]post #137 on the other thread[/post] you have doubts about:

1. According to the predetermined results given on the table, it must be true that:
P(a+, b+|ab) = P3 + P4
P(a+, c+|ac) = P2 + P4
P(c+, b+|cb) = P3 + P7

2. Since all the probabilities P1-P8 are real and non-negative, it must be true that:
P3 + P4 ≤ P3 + P4 + P2 + P7

3. Substituting the formulas from 1. into 2. gives:
P(a+, b+|ab) ≤ P(a+, c+|ac) + P(c+, b+|cb)
Therefore, any theory that gives probabilities for P1-P8 and agrees with the formulas in 1. must satisfy this inequality

4. But the QM predictions can violate the inequality in 3. for specific angles a,b,c like a=45, b=22.5 and c=0. So, no theory giving probabilities for P1-P8 can replicate the QM predictions, which are just those given in your Table 2.

In terms of the tables you gave, if we assume P(a+, b+|ab) = P3 + P4, then in Table 1 you had P3=[Sab.Cac + Sab.Sbc + Cac.Sbc]/6 and P4=[Sab.Sac + Sab.Cbc + Sac.Cbc]/6, so P3+P4 would be [Sab.Cac + Sab.Sbc + Cac.Sbc + Sab.Sac + Sab.Cbc + Sac.Cbc]/6, and this is not equal to the QM prediction for P(a+, b+|ab) = Sab/2. Do you disagree?

 

[DrChinese]

As I read the situation, DrChinese frequently challenges local realists -- of whatever hue -- here, in the Quantum Physics section of PF.

This is not quite correct. When someone who is learning about Bell wants to understand better why Local Realism cannot hold - which is the generally accepted result of Bell's Theorem - I often use the dataset challenge as a tool to help them come to a better understanding of the matter. Once one sees that this is impossible, it is usually enough to allow the reader to continue on in more fruitful studies of entanglement.

Because Bell stands and further there are thousands of papers on the experimental and theoretical side of things, there is really no reason to think of the matter in terms of a debate. There isn't any significant debate in the scientific community over the core of Bell that I am aware of! For that matter, over any element of QM. There is a lot of discussion over interpretations and possible extensions, but that is quite another matter.

I believe the moderators here try to be as open (read: lenient) as they can to discussions on Bell because they know it is difficult for many to get comfortable with. Threads on the "correctness" of Bell are very common here, and usually they tend to draw out "doubters" - which is not the same as "local realists", in my experience. But if someone is a local realist (especially one who has written or published in the area), they should NOT be posting arguments in favor of that viewpoint in the Quantum Physics area. Certainly not without identifying it as non-standard science or personal opinion in their posts. This is NOT a forum for anyone to express their unaccepted scientific opinions in front of readers who may not know the difference.

Please be aware that my comments should not be taken as speaking for PF or the dedicated moderators here. It just happens that Bell is an area I have a longstanding interest in and PF is a great venue for me to enhance my understanding.

-DrC

P.S. Lest anyone think I do not look at all sides of issues: the fact is that I also do study LR concepts (although I am obviously not in that camp) and interact with some pretty dedicated LR advocates. But I do that outside of PF.

 

[Dmitry67]

and interact with some pretty dedicated LR advocates. But I do that outside of PF.

I am curious, what loopholes do they explore if the 'dataset' argument closes all options?

 

[DrChinese]

I am curious, what loopholes do they explore if the 'dataset' argument closes all options?

Good question: Fair sampling (detection/efficiency) is about all you can argue (which has its own sets of theoretical issues). Which has been closed by the below experiment, as well as others.

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html

Keep in mind, that to keep the debate going all one needs to do is deny accepted theory and/or experiment. Or argue with definitions. In other words, basically reject good science.

In the past, I have had a number of rather pointless and extended discussions with people (ct, nightlight, etc) who come here to advocate local realism, rather than to learn why local realism is untenable. So when I realize such is the case, I now try to limit my comments to corrections of misstatements and providing relevant citations. An actual debate on the merits does not belong here.

I realize that Gordon is baiting the issue with this thread, so I will be trying to zip it as best I can.

 

[Calrid]

http://www.newscientist.com/article/mg20928011.100-reality-check-closing-the-quantum-loopholes.html

This article on closing loopholes in Bell's Aspect experiment is quite interesting.

Many have now been closed, but the inventiveness of scientists always seems to throw up new ones.

<<quote deleted>>

I'm afraid it's subscription only so I can't post the whole article.

 

[Gordon Watson]

<SNIP>But if someone is a local realist (especially one who has written or published in the area), they should NOT be posting arguments in favor of that viewpoint in the Quantum Physics area. Certainly not without identifying it as non-standard science or personal opinion in their posts. This is NOT a forum for anyone to express their unaccepted scientific opinions in front of readers who may not know the difference.

<SNIP>.

Interim reply only, re the above:

I have expanded my signature and would welcome your comments.

PS: As well, of course, as comments from others.
..

 

[edguy99]

The basic laws of arithmetic show it's impossible to meet DrChinese's challenge in a way that gives results "in full accord with QM." If you still can't see this, please tell me which specific step of the following explanation from [post=3213861]post #137 on the other thread[/post] you have doubts about:

In terms of the tables you gave, if we assume P(a+, b+|ab) = P3 + P4, then in Table 1 you had P3=[Sab.Cac + Sab.Sbc + Cac.Sbc]/6 and P4=[Sab.Sac + Sab.Cbc + Sac.Cbc]/6, so P3+P4 would be [Sab.Cac + Sab.Sbc + Cac.Sbc + Sab.Sac + Sab.Cbc + Sac.Cbc]/6, and this is not equal to the QM prediction for P(a+, b+|ab) = Sab/2. Do you disagree?

I think the applicable reference is: http://en.wikipedia.org/wiki/Sakurai's_Bell_inequality

With respect to this, I have 2 problems:

1/ If you start with the assumptions that your measurements are done at 12, 4 and 8 oclock and labeled as the a, b and c direction, the probability of both P4 and P5 are impossible. For P4 as an example, you cannot have an electron that points down wrt 4 and 8 oclock and up wrt to 12 oclock. Why are P4 and P5 counted as valid probabilities when they cannot happen?

2/ Once the term P(a+, c+) is determined (measurement, thought process or whatever), the term P(c+, b+) is determined to be P3. The term P7 is impossible for P(c+, b+) given the measurement P(a+, c+).

This appears to suggest that the terms that violate the equality are impossible.

 

[JesseM]

I think the applicable reference is: http://en.wikipedia.org/wiki/Sakurai's_Bell_inequality

With respect to this, I have 2 problems:

1/ If you start with the assumptions that your measurements are done at 12, 4 and 8 oclock and labeled as the a, b and c direction, the probability of both P4 and P5 are impossible. For P4 as an example, you cannot have an electron that points down wrt 4 and 8 oclock and up wrt to 12 oclock. Why are P4 and P5 counted as valid probabilities when they cannot happen?

I don't understand, why do you think an electron can't point down wrt to 4 and 8 but up wrt 12? Remember that the hidden variables need not take the form of a vector which is projected onto the the different possible measurement directions or anything like that, the hidden variables could be absolutely anything, all that's important is that they predetermine what response the electron will give to each possible measurement direction. So certainly if we are allowed to invent arbitrary hidden variables and arbitrary laws governing how the hidden variable state determines the electron's response to different measurements, then we could imagine some hidden variable state that predetermines that an electron will give response "down" to 4 and 8 but will give response "up" to 12.

2/ Once the term P(a+, c+) is determined (measurement, thought process or whatever), the term P(c+, b+) is determined to be P3.

Remember that P(a+,c+) refers to the probability that Alice measures "up" on axis a and Bob measures "up" on axis c...in order for Bob to measure "up" on c, the particle that went to Alice must have been predetermined to be "down" on c, so the particles cannot have been in the hidden variables state whose probability is given by P3, it has to be one where Alice's particle has + for a and - for c, i.e. P2 or P4. But this tells you nothing about what the predetermined result on axis b was on that trial, since P2 has + for Alice on axis b while P4 has - for Alice on axis b.

This appears to suggest that the terms that violate the equality are impossible.

Terms that violate the inequality are of course impossible, that's the whole point, although not for the reasons you suggest. Again see my list of conclusions 1-4 in the post to Gordon (which I hope he will respond to) for a quick summary of the reasoning that no local hidden variable theory giving probabilities for P1-P8 can violate the inequality.

 

[edguy99]

I don't understand, why do you think an electron can't point down wrt to 4 and 8 but up wrt 12? ...

The probability of the state "point down wrt to 4 and 8 but up wrt 12" is of fundamental importance. Note from the article:

Alice | Bob | Probability
a b c | a b c
+ + + | − − − P1
+ + − | − − + P2
+ − + | − + − P3
+ − − | − + + P4
− + + | + − − P5
− + − | + − + P6
− − + | + + − P7
− − − | + + + P8

Consider the clock:

All of the probabilites can be found, for instance an axis at 10 oclock would appear to Alice as a+, b+, c- and is P2 in the list above. All the probabilities can be found:

P1 a+, b+, c+ is at 12 oclock
P2 a+, b+, c− is at 10
P3 a+, b−, c+ is at 2

no P4 or P5

P6 a−, b+, c− is at 8
P7 a−, b−, c+ is at 4
P8 a−, b−, c− is at 6

Another way to view the missing P4 a+, b−, c− to consider:

For b to be minus, the axis must be between 1 and 7 oclock. For c to be minus, the axis must be between 5 and 11 oclock making the real axis somewhere between 5 and 7, clearly that is a down with respect to a.

If there is no P4 event you don't carry it into subsequent calculations.

You say: The basic laws of arithmetic show it's impossible to meet DrChinese's challenge in a way that gives results "in full accord with QM."

Perhaps: Removal of P4 and P5 does meet the challenge?

 

[JesseM]

Consider the clock:

All of the probabilites can be found, for instance an axis at 10 oclock would appear to Alice as a+, b+, c- and is P2 in the list above. All the probabilities can be found:

Huh? What is the green "axis at 10 o'clock" supposed to represent? And how is the fact that it points to 10 o'clock supposed to imply anything about whether the particle is deflected "up" or "down" when it encounters a Stern-Gerlach device whose North end points to 12 o'clock or 4 o'clock or 8 o'clock? Did you miss the part in my previous post where I said the following?

Remember that the hidden variables need not take the form of a vector which is projected onto the the different possible measurement directions or anything like that, the hidden variables could be absolutely anything, all that's important is that they predetermine what response the electron will give to each possible measurement direction.

P1 a+, b+, c+ is at 12 oclock
P2 a+, b+, c− is at 10
P3 a+, b−, c+ is at 2

I don't know what you mean here...you say things like "is at 12 oclock", but what is at 12 o'clock in the first line, at 10 o'clock in the second, and at 2 o'clock in the third? The green vector? Again, the probabilities P1-P8 don't tell you anything about the detailed nature of the hidden variables (they certainly don't imply the hidden variables must be a vector pointing in a particular direction), they simply tell you the predetermined results for the three possible SG orientations a=12 o'clock, b=4 o'clock and c=8 o'clock in your diagram.

You say: The basic laws of arithmetic show it's impossible to meet DrChinese's challenge in a way that gives results "in full accord with QM."

Perhaps: Removal of P4 and P5 does meet the challenge?

No, nothing about the argument changes if you set P4 or P5 to zero. Read the 4 steps of the argument I gave again more carefully and you'll see this...for example, in step 2 it still must be true that P3 + P4 ≤ P3 + P4 + P2 + P7 even if P4=0, then it just reduces to P3 ≤ P3 + P2 + P7, and obviously (P3 + P2 + P7) could not be smaller than P3 alone as long as P2 and P7 are non-negative (and 'non-negative' obviously includes the possibility that any of P3, P2, and P7 could be zero as well).

 

[edguy99]

Huh? What is the green "axis at 10 o'clock" supposed to represent? And how is the fact that it points to 10 o'clock supposed to imply anything about whether the particle is deflected "up" or "down" when it encounters a Stern-Gerlach device whose North end points to 12 o'clock or 4 o'clock or 8 o'clock? ...

The green line represents the axis of spin of a particle that is approaching you. If measured in a Stern-Gerlach device whose north is 12, it would go up if its axis was anywhere between 9 through 12 to 3 (as 10 oclock is) and would go down if its axis was pointed down (3 through 6 to 9).

 

[Gordon Watson]

<SNIP>Terms that violate the inequality are of course impossible, that's the whole point, although not for the reasons you suggest. Again see my list of conclusions 1-4 in the post to Gordon (which I hope he will respond to) for a quick summary of the reasoning that no local hidden variable theory giving probabilities for P1-P8 can violate the inequality.

Jesse, Yes; I'll be responding soon. Thanks, GW.

 

[JesseM]

The green line represents the axis of spin of a particle that is approaching you.

Are you suggesting particles have a definite spin even before we measure them, and that this spin determines their response to the Stern-Gerlach device? This would be one type of hidden-variable theory, but it's certainly not the only one possible, and QM alone (without hidden variables) doesn't say anything about particles having definite spins prior to measurement. Also note that even if you propose that particles do have a "hidden spin" prior to measurement, they aren't behaving like classical spinning charged balls in response to a magnetic field...as explained on this page, classical spinning charged balls with a range of different spin axes would be deflected in a range of different directions on passing through a magnetic field like the one created by a Stern-Gerlach device, whereas electrons are only deflected in one of two binary directions, "up" or "down".

If measured in a Stern-Gerlach device whose north is 12, it would go up if its axis was anywhere between 9 through 12 to 3 (as 10 oclock is) and would go down if its axis was pointed down (3 through 6 to 9).

Well, you're free to imagine a hidden-variables theory that works this way, but again there is no reason to think that any local realistic theory would involve a comparison between the electron's own hidden "spin axis" and the north of the SG device; the argument on the Sakurai's Bell inequality page is intended to be more general, covering all possible local realistic theories where the two electrons have predetermined responses to each SG orientation. And as I said, the argument I presented with points 1-4 would certainly cover the type of hidden-variable theory you suggest.

 

[JesseM]

Jesse, Yes; I'll be responding soon. Thanks, GW.

OK, thanks. Please make sure that your response is specific in the sense of telling me precisely which of the four points 1-4 you first have doubts about (i.e. you doubt it follows necessarily from logic and from the previous points...keep in mind the idea from the other thread that I'm assuming we're expressing angles in terms of a fixed coordinate system which doesn't change from one particle pair to another over the course of the experiment). Also please respond to my question about your tables in the pdf from [post=3191024]post #85 on the other thread[/post], and whether you agree or disagree that if we assume P(a+, b+|ab) = P3 + P4 along with the equations for P3 and P4 given in Table 1 in your pdf, then we get a value for P(a+, b+|ab) which is not equal to Sab/2.

 

[zincshow]

... Also note that even if you propose that particles do have a "hidden spin" prior to measurement, they aren't behaving like classical spinning charged balls in response to a magnetic field...as explained on this page, classical spinning charged balls with a range of different spin axes would be deflected in a range of different directions on passing through a magnetic field like the one created by a Stern-Gerlach device, whereas electrons are only deflected in one of two binary directions, "up" or "down"...

I like your page, and you are correct, classical spinning charged balls are not enough to explain what is going on hence it is unlikely that an electron is a classical spinning charged ball. Your ball shows a spin axis, but it does not have an axis that the spin axis can precess around. As those electrons are going through the magnets, in addition to moving either up or down all at the same rate, they will begin to precess since their spin axis is random with respect to the magnetic field the electron finds itself in. It is this precession that will persist after the electron leaves the Stern-Gerlach device and gives very unusual (but predictable) results when they enter a second Stern-Gerlach device.

 

[Gordon Watson]

Jesse, Yes; I'll be responding soon. Thanks, GW.

..

That response has begun at https://www.physicsforums.com/showthread.php?t=488170

GW