What's wrong with this local realistic counter-example to Bell's theorem?

[Gordon Watson]

Jesse, my replies will be spasmodic for a week or more. I will try to keep in touch because I think that we are getting to the meat of the differences between us.

XO, JenniT

 

[JesseM]

Could you just use your formula; or the evident formula that I used in the worked example.

Why not do Pac++ and Pcb++?

Here's my answer: Sac/2, Scb/2. The QM results, I believe?

And how did you calculate these answers?? I just want a yes or no answer to the question of whether you use the formulas Pab++ = P3 + P4 and Pac++ = P2 + P4 and Pcb++ = P3 + P7, I won't discuss any further issues if you continue to be evasive on this simple question. It's obvious that if you do use these formulas, you will not get the QM predictions of Pab++=Sab/2, Pac++=Sac/2, and Pcb++=Scb/2 (if you think you will, you have made a math error somewhere)

edit: and speaking of math errors, your derivation in the PDF for Pab++=P3+P4=Sab/2 doesn't work. I'm fine up to the step where P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6, but how do figure that this would be equal to (2Sab + 2Pab++)/6? That's clearly wrong if you substitute some actual angles, like the earlier example of a=240,b=120 and c=0. In this case we have:

Sab=sin^2 ((a-b)/2) = sin^2 (60) = 0.75
Cac=cos^2 ((a-c)/2) = cos^2 (120) = 0.25
Sbc = sin^2 ((b-c)/2) = sin^2 (60) = 0.75
Sac = sin^2 ((a-c)/2) = sin^2 (120) = 0.75
Cbc = cos^2 ((b-c)/2) = cos^2 (60) = 0.25

So, Pab++=P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6=(2*0.75 + 0.25*0.75 + 0.75*0.25)/6 = 1.875/6 = 0.3125

But if Pab++ = 0.3125 using your formulas with the specified angles, then clearly it is not true that Pab++=Sab/2 according to your formulas, since Sab/2 = 0.75/2 = 0.375 (and this would be the answer predicted by QM, so if Pab++=P3+P4 and we use the values of P3 and P4 in your table, we get an answer which differs from QM here). Nor are either of these equal to (2Sab + 2Pab++)/6, this would be equal to (2*0.75 + 2*0.3125)/6 = (1.5 + 0.625)/6 = 2.125/6 = 0.3541666... So, you must have goofed in the step where you equated (2Sab + Cac.Sbc + Sac.Cbc)/6 to (2Sab + 2Pab++)/6.

edit #2: Perhaps the reason for this erroneous substitution of Cac.Sbc + Sac.Cbc = 2Pab++ is that you were using 2Pab++=2P3 + 2P4 combined with the original definitions of P3 and P4 in your original post on this thread? But that will not do, because the definitions of P3 and P4 in your original post are incompatible with the definitions of P3 and P4 in the PDF table. For example, in the original post you define P3 = Cac.Sbc/2, which for the angles a=240, b=120 and c=0 is equal to 0.25*0.75/2 = 0.09375...whereas in the PDF table you define P3 = [Sab.Cac + Sab.Sbc + Cac.Sbc]/6, which for the same angles is equal to [0.75*0.25 + 0.75*0.75 + 0.25*0.75]/6 = 0.15625. So you have to pick one or the other, you can't use both definitions for P3.

 

[vanesch]

I would not be OK with this, I think you are using this forum as a platform for advertising a crackpot theory that you are already totally confident is right, rather than just exploring the issue in an open-minded way that acknowledges the strong likelihood that it is you who have made an error somewhere in your analysis, and making a sincere effort to listen to critiques in order to identify likely errors.

Indeed, I fully agree with this. Remember that there was "permission to post your 8 numbers" for pedagogical reasons, but there seems not to be much pedagogy happening.

So, to be clear: NO, JenniT, you are NOT allowed to open yet another thread on this same subject.

 

[ThomasT]

I've been following this thread and haven't wanted to post in it so as not to disrupt it's thematic flow (such as it was), however since JenniT has said that she will be off the internet for several days, then I hope it's ok. Nothing Earth'shaking, but some progress in my understanding -- I think.

I hadn't until recently understood the significance of DrChinese's Local Realistic (LR) dataset requirement wrt evaluating proposed LR models of entanglement. Comments in this and other recent threads have helped to clarify my thinking on this subject -- which has led me to a better understanding of why explicitly local hidden variable models of entanglement can't possibly reproduce the range of the qm statistical predictions.

Wrt what constitutes an LR model, it might be phrased that it's the explicit representation of locality (which entails an explicit representation of the local hidden variables that are relevant wrt the production of the local facts of individual measurements, which in turn imposes a constraint on the range of the predictions that any such model of entanglement can produce) that defines a model as LR, and not only whether the model satisfies Bell's inequality (BI).

However, insofar as Bell's LR model is the archetypal LR model¹ of entanglement, a necessary condition for a model to be considered LR is that it must satisfy BI.

Hence, any proposed LR model that violates BI is, by definition, not an LR model. On the other hand, it's been definitively shown that any proposed LR model that satisfies BI can't possibly reproduce the qm predictions (or, as has also been definitively demonstrated², be in agreement with experimental results).

So, there doesn't seem to be any point in considering any proposed LR model of entanglement.

Exactly what BI is implying or has to do with the deep reality underlying instrumental results is another question, the answer to which is, imho ... nothing. BIs are statements about the constraints on the relationship between joint polarizer settings and joint detection attributes (where individual detection attributes are limited to values of 0 and 1) given certain formal, LR, requirements.

-----------------------------------------

¹Bell's ansatz is the archetypal LR model of entanglement because it encodes both an explicit expression of locality and an explicit expression of the hidden variables which produce the local experimental facts.

²There's some disagreement about this, but the experimental loophole considerations have, imho, turned out to be strawman or superfluous considerations wrt the correct interpretation of the physical meaning of Bell's theorem.

 

[vanesch]

OK; thank you; your post came in as I was posting my last.

Q: Do you not see that all the sums that you could possibly require are included in -- or easily derived from -- the base-data in the PDF.

Q: I left many more sums for the reader to complete. Do you want to see any of them?

NB: I ABSOLUTELY REJECT:

P(a+, b+) = P3 + P4 and P(a+, c+) = P2 + P4 and P(c+, b+) = P3 + P7

IF IT IMPLIES: P3 + P4 = P3 + P4 + (POSITIVE NUMBER)! (XXX)

Q: Seriously: In case I misinterpret: Is equation (XXX) what you want me to accept?

Of course not.
That is NOT what the Bell inequalities imply.

What the Bell inequalities imply is the following:

IF YOU ASSUME that all of the emitted the pairs have PREDESTINED responses to 3 possible measurements on both sides independent of which of these three measurements is actually going to be performed (this is the LOCAL REALISM ASSUMPTION), THEN there exist 8 numbers P1...P8 such that
P(a+,b+) = P3 + P4
P(a+,c+) = P2 + P4
and P(c+,b+) = P3 + P7

The 8 numbers P1...P8 come from the 8 different possibilities to predestine responses.

IF that is the case, then it is simple arithmetic to show that:

P(a+,c+) + P(c+,b+) = (P2 + P4) + (P3 + P7) = P3 + P4 + P2 + P7
= P(a+,b+) + P2 + P7.

And from this follows that IT WILL BE IMPOSSIBLE to find 8 such numbers and to obtain that P(a+,b+) is larger than P(a+,c+) + P(c+,b+), no matter what funny theory GENERATES these numbers. You cannot have that P3 + P4 is LARGER than P3 + P4 + positive number.

Now, quantum mechanics DOES NOT assume that the pairs are predestined, so in quantum mechanics there is no such a priori existence for 8 such numbers.
AND it turns out that for specific experiments with pairs of electrons, we can find 3 measurements on both sides such that the QM predictions for P(a+,c+), P(c+,b+) and P(a+,b+) are such that P(a+,b+) is larger than the sum of P(a+,c+) and P(c+,b+).

Note that in QM, P(a+,b+) must not be equal to some P3 + P4. It is only if you claim that you have an EQUIVALENT LOCAL REALISTIC THEORY which predestines the pairs that these numbers P1...P8 have a meaning, and then you run in the impossibility that you should have that these numbers satisfy that P3 + P4 > P3 + P4 + positive number (namely P2 + P7).

Now, YOU CLAIMED that you could provide us with 8 such numbers. Clearly you haven't. (and clearly it is impossible). You asked if you could show them. For sake of pedagogy, you were allowed to "show" us those impossible numbers (I told you so).

Your numbers do NOT reproduce the QM predictions. They do so for 2 out of 3 (you can ALWAYS do it for 2 out of 3) and they fail (of course) for the 3rd prediction, because if they wouldn't, they'd satisfy impossible conditions.

Now, you have been talking A LOT here, not learning a lot.

PS: I believe in my theory; and QM; and I will answer every question.

Up to now, you haven't.

You mentioned a game, which had me confused. I had hoped that the PDF showed my response to ANY game played with EPRB?

Your PDF doesn't show anything, except for a specific calculation of 8 numbers, 8 numbers which DO NOT correspond to the predictions of QM.

 

[Gordon Watson]

Of course not.
That is NOT what the Bell inequalities imply.

What the Bell inequalities imply is the following:

IF YOU ASSUME that all of the emitted the pairs have PREDESTINED responses to 3 possible measurements on both sides independent of which of these three measurements is actually going to be performed (this is the LOCAL REALISM ASSUMPTION), THEN there exist 8 numbers P1...P8 such that
P(a+,b+) = P3 + P4
P(a+,c+) = P2 + P4
and P(c+,b+) = P3 + P7

The 8 numbers P1...P8 come from the 8 different possibilities to predestine responses.

IF that is the case, then it is simple arithmetic to show that:

P(a+,c+) + P(c+,b+) = (P2 + P4) + (P3 + P7) = P3 + P4 + P2 + P7
= P(a+,b+) + P2 + P7.

And from this follows that IT WILL BE IMPOSSIBLE to find 8 such numbers and to obtain that P(a+,b+) is larger than P(a+,c+) + P(c+,b+), no matter what funny theory GENERATES these numbers. You cannot have that P3 + P4 is LARGER than P3 + P4 + positive number.

Now, quantum mechanics DOES NOT assume that the pairs are predestined, so in quantum mechanics there is no such a priori existence for 8 such numbers.
AND it turns out that for specific experiments with pairs of electrons, we can find 3 measurements on both sides such that the QM predictions for P(a+,c+), P(c+,b+) and P(a+,b+) are such that P(a+,b+) is larger than the sum of P(a+,c+) and P(c+,b+).

Note that in QM, P(a+,b+) must not be equal to some P3 + P4. It is only if you claim that you have an EQUIVALENT LOCAL REALISTIC THEORY which predestines the pairs that these numbers P1...P8 have a meaning, and then you run in the impossibility that you should have that these numbers satisfy that P3 + P4 > P3 + P4 + positive number (namely P2 + P7).

Now, YOU CLAIMED that you could provide us with 8 such numbers. Clearly you haven't. (and clearly it is impossible). You asked if you could show them. For sake of pedagogy, you were allowed to "show" us those impossible numbers (I told you so).

Your numbers do NOT reproduce the QM predictions. They do so for 2 out of 3 (you can ALWAYS do it for 2 out of 3) and they fail (of course) for the 3rd prediction, because if they wouldn't, they'd satisfy impossible conditions.

Now, you have been talking A LOT here, not learning a lot.
Up to now, you haven't.
Your PDF doesn't show anything, except for a specific calculation of 8 numbers, 8 numbers which DO NOT correspond to the predictions of QM.

I hope this addresses the issues above:

Let us take: ab = 90, ac = bc = 45.

From the PDF, I derive in the given worked example:

Pab++ = Sab/2 = 0.25.

In similar manner, I derive (and will add as an addendum when I get back)

Pac++ = Sac/2 = 0.0732

Sbc++ = Sbc/2 = 0.0732

I thought that these were the QM predictions?

PS: I'm learning a great deal, and am sorry if I'm trying your patience. But can you see here why I must ask another question?

So please: Let me have the next specific question that now arises from you, re the above. For it seems to me that the problem must be somewhere else.

PS: If you doubt my calculations; well, when I put them into an Appendix you will see the same method as in the PDF example, and the same answers that I have given above.

Q: I might ask: Why do you say that the PDF numbers are wrong? I thought that QM had no such predictions for the table?

I've asked to see them, but so far have not.

Thank you.

 

[Gordon Watson]

And how did you calculate these answers?? I just want a yes or no answer to the question of whether you use the formulas Pab++ = P3 + P4 and Pac++ = P2 + P4 and Pcb++ = P3 + P7, I won't discuss any further issues if you continue to be evasive on this simple question. It's obvious that if you do use these formulas, you will not get the QM predictions of Pab++=Sab/2, Pac++=Sac/2, and Pcb++=Scb/2 (if you think you will, you have made a math error somewhere)

The Pab++ example can be checked right now. It is the worked example in the PDF.

A math error there will be repeated in an addendum that I'll add when I get back; giving the other workings, and those values I have already given to you.

edit: and speaking of math errors, your derivation in the PDF for Pab++=P3+P4=Sab/2 doesn't work. I'm fine up to the step where P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6, but how do figure that this would be equal to (2Sab + 2Pab++)/6? That's clearly wrong if you substitute some actual angles, like the earlier example of a=240,b=120 and c=0. In this case we have:

Sab=sin^2 ((a-b)/2) = sin^2 (60) = 0.75
Cac=cos^2 ((a-c)/2) = cos^2 (120) = 0.25
Sbc = sin^2 ((b-c)/2) = sin^2 (60) = 0.75
Sac = sin^2 ((a-c)/2) = sin^2 (120) = 0.75
Cbc = cos^2 ((b-c)/2) = cos^2 (60) = 0.25

So, Pab++=P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6=(2*0.75 + 0.25*0.75 + 0.75*0.25)/6 = 1.875/6 = 0.3125

But if Pab++ = 0.3125 using your formulas with the specified angles, then clearly it is not true that Pab++=Sab/2 according to your formulas, since Sab/2 = 0.75/2 = 0.375 (and this would be the answer predicted by QM, so if Pab++=P3+P4 and we use the values of P3 and P4 in your table, we get an answer which differs from QM here). Nor are either of these equal to (2Sab + 2Pab++)/6, this would be equal to (2*0.75 + 2*0.3125)/6 = (1.5 + 0.625)/6 = 2.125/6 = 0.3541666... So, you must have goofed in the step where you equated (2Sab + Cac.Sbc + Sac.Cbc)/6 to (2Sab + 2Pab++)/6

.

This is rushed, but are you looking at the right table. The PDF has the correct result. The 3 earlier labels, as explained, had one angle not specifically specified. A problem resolved when the 3 were amalgamated to give the PDF.

The PDF amalgamates the 3 earlier tables; all angles are there specific.

edit #2: Perhaps the reason for this erroneous substitution of Cac.Sbc + Sac.Cbc = 2Pab++ is that you were using 2Pab++=2P3 + 2P4 combined with the original definitions of P3 and P4 in your original post on this thread? But that will not do, because the definitions of P3 and P4 in your original post are incompatible with the definitions of P3 and P4 in the PDF table. For example, in the original post you define P3 = Cac.Sbc/2, which for the angles a=240, b=120 and c=0 is equal to 0.25*0.75/2 = 0.09375...whereas in the PDF table you define P3 = [Sab.Cac + Sab.Sbc + Cac.Sbc]/6, which for the same angles is equal to [0.75*0.25 + 0.75*0.75 + 0.25*0.75]/6 = 0.15625. So you have to pick one or the other, you can't use both definitions for P3.

Just off the cuff, [for now] as above, the 3 earlier tables were required by my model to produce the PDF. The PDF is the model; the others were steps in the model building because I could not handle my "angle" problem any other way.

The substitutions that you query are given in post #33.

There you will see: Pab++ = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2.

And all the other such.

That is where the queried substitution comes from.

Excuse rush.

 

[ThomasT]

I must interject here. Either the mentors and science advisors are capable of explaining clearly and succincltly why prospective LR theories are pointless, or they aren't capable of doing that. There's nothing to be learned by this nitpicking -- imho.

Refer back to DrC's post. (#2?, iirc)

If the proposed LR model doesn't produce an LR dataset (and therefore satisfy BI), then it isn't an LR model. Period.

And if it does produce an LR dataset then it can't agree with qm (and, so far and presumably, with experimental results). Period.

There's nothing else to consider. LR models of entanglement are impossible. Period.

What does this tell us of the underlying reality? Nothing. Period.

 

[vanesch]

I hope this addresses the issues above:

Let us take: ab = 90, ac = bc = 45.

From the PDF, I derive in the given worked example:

Pab++ = Sab/2 = 0.25.

In similar manner, I derive (and will add as an addendum when I get back)

Pac++ = Sac/2 = 0.732

Sbc++ = Sbc/2 = 0.732

I thought that these were the QM predictions?

Clearly, it can't. (there's a typo for Pac++ and Pbc++ where the values are 0.0732, but I guess this is a typo).

I didn't check your pdf in detail, but in your pdf, you (correctly) define:

Pab++ = P3 + P4

You work this out to something (I didn't check the goniometric algebra), but it equals P3 + P4.

You didn't work out the rest, but if it is done correctly, you should also have:

Pcb++ = P3 + P7

and

Pac++ = P2 + P4.

It is a pity that you didn't work it out.

Now, I can assume that the numerical value of P3 + P7 doesn't change between when you write it as P3 + P7, and when you work out the goniometric algebra
(otherwise you made a mistake in your algebra, right ?)

Now, give me please the NUMERICAL VALUES for a vertically, c 45 degrees towards the window, and b horizontal towards the window (so 90 degrees), for all 8 values P1, ... P8 and then for your calculation of Pab++ , Pac++ and Pcb++.

Because it should be obvious that if all your values P1...P8 are positive numbers, and if Pab++ = P3 + P4 and so on as you claim (correctly), that you CANNOT obtain numerically Pab++ = 0.25 and Pac++ = Pcb++ = 0.073...

So in order to show you this, you should work out, for the given angles, the numbers P1 up to P8, and then Pab++ = P3 + P4 and also according to your algebra Sab/2 and Pcb++ and Pac++.

 

[vanesch]

I must interject here. Either the mentors and science advisors are capable of explaining clearly and succincltly why prospective LR theories are pointless, or they aren't capable of doing that. There's nothing to be learned by this nitpicking -- imho.

Well this thread is the result of a request by JenniT that he/she COULD generate 8 numbers P1...P8 such that it corresponded to the quantum predictions. This is clearly impossible, but up to now JenniT has been claiming otherwise.

His/her first attempt gave:

QM: 0.25, 0.073, 0.073 (for spin-1/2 particles and axes 0 degrees, 45 degrees and 90 degrees) and JenniT produced a first set of 8 numbers such that the numbers that came out were 0.125, 0.073 and 0.073, and there was a lot of hot air about a claim that these WERE the right results because of "an average that had to be taken over two different angles" without ever having cleared this up.

Now we seem to have ANOTHER proposal by JenniT where he/she claims this time to HAVE produced 8 numbers such that the predictions come out to be:

0.25, 0.073 and 0.073

after some algebra.

As this is algebraically impossible, we ask him to give us the 8 numerical values, and show how they comply with the above calculation.

There's nothing else to consider. LR models of entanglement are impossible. Period.

You're right, but we're dealing with somebody who claims he knows how to make one.

 

[JesseM]

The Pab++ example can be checked right now. It is the worked example in the PDF.

Yes, I checked it, and it was wrong.

This is rushed, but are you looking at the right table. The PDF has the correct result.

Yes, I was looking just at the PDF. There you write that

Pab++=P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6=(2Sab + 2Pab++)/6=Sab/2

But with the specific examples I gave of a=240,b=120,c=0 it is trivial to see that they are not equal:

(2Sab + Cac.Sbc + Sac.Cbc)/6=0.3125

Sab/2=0.375

So these are not equal to one another, and if we use Pab++=0.3125 neither of these is equal to (2Sab + 2Pab++)/6=0.3541666... If we use Pab++=0.375 then it is true that (2Sab + 2Pab++)/6 = Pab++, but neither of these is consistent with the earlier equation in the PDF saying that Pab++=P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6.

The substitutions that you query are given in post #33.

There you will see: Pab++ = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2.

In post #33 you continue to use the incomprehensible language of "bi-angles", but in any case it's clear that the equation Pab++ = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2 from post #33 is inconsistent with the PDF's equation of Pab++=P3+P4=(2Sab + Cac.Sbc + Sac.Cbc)/6, because with a=240,b=120,c=0 we have:

(Cac.Sbc + Sac.Cbc)/2 = (0.25*0.75 + 0.75*0.25)/2 = 0.1875

whereas

(2Sab + Cac.Sbc + Sac.Cbc)/6=(2*0.75 + 0.25*0.75 + 0.75*0.25)/6 = 1.875/6 = 0.3125

and neither of these are equal to

Sab/2 = 0.375

Please check this numerical example yourself before responding, you'll see that what I say is correct.

 

[JesseM]

Refer back to DrC's post. (#2?, iirc)

If the proposed LR model doesn't produce an LR dataset (and therefore satisfy BI), then it isn't an LR model. Period.

And if it does produce an LR dataset then it can't agree with qm (and, so far and presumably, with experimental results). Period.

There's nothing else to consider. LR models of entanglement are impossible. Period.

What does this tell us of the underlying reality? Nothing. Period.

Thomas, you seem to be arguing as if "local realist" is defined to mean you must have a dataset of predetermined values, but this isn't true. As I said in post #20 to Avodyne:

Not all Bell inequalities assume that the hidden variables totally determine what the response to any given angle will be, see the CHSH inequality for example where the angles a,a' used on one side may be different from the angles b,b' on the other in which case there'd be no combination of settings where knowledge of the result on one side gives you total certainty about the result on the other. I like to think of the definition of local realism this way:

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

From this it follows that if two experimenters making measurements at a spacelike separation are guaranteed to get the same result when they choose the same angle, despite the fact that they pick which angle to use at random, then the results for each possible angle must have already predetermined by facts in their past light cone (like facts about the hidden variables associated with each particle) at some time T after the particles had been emitted but before they picked their angles. But this is just a derived consequence of the notion of local realism above, not a definition of local realism.

Do you agree that no theory with characteristics 1 and 2 above (regardless of whether it involves datasets of predetermined results, and regardless of whether the local variables are hidden or measurable as in classical electromagnetism which does satisfy 1 and 2) could reproduce the statistics predicted by QM?

 

[ThomasT]

Thomas, you seem to be arguing as if "local realist" is defined to mean you must have a dataset of predetermined values, but this isn't true.

I agree, see my post #64 in this thread. However, the LR dataset (ie., agreement with BI) is a necessary condition that any proposed LR model has to satisfy.

That's the beauty of DrC's LR dataset requirement and the math of Bell's theorem. It cuts through, ie. obviates, what you're going through here. I just didn't appreciate or understand it before because I was lost in the trees so to speak. If Jennit's model of entanglement agrees with qm and violates Bell's inequality, then, via the definition of an LR model a la Bell's archetype and your 1 and 2 (which entails that an LR model will satisfy Bell's inequality), it can't be an LR model of entanglement. The same holds for Christian's Clifford algebra C-space model, or Unnikrishnan's static phase relation (iirc) model or any other model that reproduces qm results and violates Bell's inequality.

Do you agree that no theory with characteristics 1 and 2 above (regardless of whether it involves datasets of predetermined results, and regardless of whether the local variables are hidden or measurable as in classical electromagnetism which does satisfy 1 and 2) could reproduce the statistics predicted by QM?

Yes. The point is that a necessary condition for a theory to be called LR is that it has to produce datasets that don't agree with the qm predicted datasets -- ie., that it satisfies Bell's inequality.

And now I think I should probably delete my second, rather terse, post in this thread. I just had to savor the irony (recalling the countless interchanges that we've had on this subject). Or should I leave it? Your call.

 

[JesseM]

Yes. The point is that a necessary condition for a theory to be called LR is that it has to produce datasets that don't agree with the qm predicted datasets -- ie., that it satisfies Bell's inequality.

OK good, I just wanted to make sure you understood that although satisfying Bell's inequality is a necessary consequence of the basic definition of LR, it isn't part of the definition itself (otherwise Bell would have no need for a "proof" that local realism implies the inequality is satisfied!) So I would disagree with your earlier statement "What does this tell us of the underlying reality? Nothing. Period." It tells us that QM is incompatible with any theory satisfying point 1) and 2) from my post to Avodyne, I would say that's a strong negative result ruling out a broad class of theories about the "underlying reality", although perhaps you just meant that it doesn't give us a positive answer to what the underlying reality actually is.

And now I think I should probably delete my second, rather terse, post in this thread. I just had to savor the irony (recalling the countless interchanges that we've had on this subject). Or should I leave it? Your call.

I don't think there's a need to delete it, perhaps the resulting discussion could clarify some things for people reading the thread.

 

[ThomasT]

OK good, I just wanted to make sure you understood that although satisfying Bell's inequality is a necessary consequence of the basic definition of LR, it isn't part of the definition itself (otherwise Bell would have no need for a "proof" that local realism implies the inequality is satisfied!)

Yes, I get this -- it just took a while.

So I would disagree with your earlier statement "What does this tell us of the underlying reality? Nothing. Period." It tells us that QM is incompatible with any theory satisfying point 1) and 2) from my post to Avodyne, I would say that's a strong negative result ruling out a broad class of theories about the "underlying reality", although perhaps you just meant that it doesn't give us a positive answer to what the underlying reality actually is.

I mean that it doesn't tell us whether what's happening in the underlying reality is due to exclusively local interactions and transmissions or not. So, it doesn't contradict the general assumptions of locality and the existence of local hidden variables. It just tells us that explicitly LR formulations of entanglement must produce a reduced range of statistical predictions, and are therefore ruled out.

Why this is so is what Hess, Michielsen, and De Raedt are talking about in their recent paper on the subject.

 

[JesseM]

I mean that it doesn't tell us whether what's happening in the underlying reality is due to exclusively local interactions and transmissions or not.

How do you figure? Wouldn't any theory about the underlying reality which involves "exclusively local interactions and transmissions" satisfy 1) and 2) in my description of local realism?

So, it doesn't contradict the general assumptions of locality and the existence of local hidden variables.

I don't understand why you would distinguish "the general assumptions of locality and the existence of local hidden variables" from "local realism" as described by 1) and 2). Are you imagining there could be a local theory involving local hidden variables which violated either 1) or 2) (or both)? If so which would it violate?

 

[Dmitry67]

Sorry for jumping in,
but (on a psycological level) why "die hard local realists" (c) Dr. Chinese
never consider just using MWI to obtain the result they want?

 

[Gordon Watson]

Clearly, it can't. (there's a typo for Pac++ and Pbc++ where the values are 0.0732, but I guess this is a typo).

I didn't check your pdf in detail, but in your pdf, you (correctly) define:

Pab++ = P3 + P4

You work this out to something (I didn't check the goniometric algebra), but it equals P3 + P4.

You didn't work out the rest, but if it is done correctly, you should also have:

Pcb++ = P3 + P7

and

Pac++ = P2 + P4.

It is a pity that you didn't work it out.

Now, I can assume that the numerical value of P3 + P7 doesn't change between when you write it as P3 + P7, and when you work out the goniometric algebra
(otherwise you made a mistake in your algebra, right ?)

Now, give me please the NUMERICAL VALUES for a vertically, c 45 degrees towards the window, and b horizontal towards the window (so 90 degrees), for all 8 values P1, ... P8 and then for your calculation of Pab++ , Pac++ and Pcb++.

Because it should be obvious that if all your values P1...P8 are positive numbers, and if Pab++ = P3 + P4 and so on as you claim (correctly), that you CANNOT obtain numerically Pab++ = 0.25 and Pac++ = Pcb++ = 0.073...

So in order to show you this, you should work out, for the given angles, the numbers P1 up to P8, and then Pab++ = P3 + P4 and also according to your algebra Sab/2 and Pcb++ and Pac++.

Thanks for your patience and blunder-identification (which I've corrected via an edit). Time-pressure is the excuse; trying to hold up my end of this thread.

That blunder is the message for now:

I've made a big mistake in trying to do my bit here and keep my end of the thread moving while snowed-under with other critical commitments: because I am lapping up the teaching and I'm keen to get to the end.

I even delayed my departure, that's how I'm here, to get some further calcs and answers out.

So: Thanks again; I shall return; your specific questions addressed; quick calcs and answers to follow later -- now to be happily reviewed more carefully first.

The hope for us all, if I may add some hope, is that the arguments will be resolved via maths, not words. That I am happy with; that I learn best from. XO

 

[ThomasT]

How do you figure? Wouldn't any theory about the underlying reality which involves "exclusively local interactions and transmissions" satisfy 1) and 2) in my description of local realism?

Yes, but that doesn't imply that the constraints on statistical predictions associated with the formal LR requirements are due to an underlying nonlocality. I mean, you can interpret it that way, but I don't think you have to. Isn't it at least possible that the effective determiner of BI violations has to do with some more mundane conflict between the LR formalism and the experimental design and preparation of Bell tests than with the existence of nonlocal signals or the nonexistence of local hidden variables?

I don't understand why you would distinguish "the general assumptions of locality and the existence of local hidden variables" from "local realism" as described by 1) and 2).

As DrC's signature quotes from Korzybski, "The map is not the territory." (Did I get that right?)

Are you imagining there could be a local theory involving local hidden variables which violated either 1) or 2) (or both)?

No. I'm just holding out for a more parsimonious explanation for BI violation (that I fully understand) than that it's due to nonlocality. Who knows, maybe I'll eventually think that Bell's theorem proves nonlocality, but right now that doesn't seem likely.

Edit: Apologies to JenniT for somewhat off topic posts. I thought you were going to be away for a while and I wanted to express and clarify my thinking on this. Anyway, I'll post no more in this thread so that you might continue your presentation and argument.

 

[JesseM]

Yes, but that doesn't imply that the constraints on statistical predictions associated with the formal LR requirements are due to an underlying nonlocality.

I didn't use the word "nonlocality", I just said that a theory of the type described by 1) and 2) was ruled out. As you know from previous discussions there are certain "loopholes", for example I was implicitly assuming in 1) that there is a unique set of physical facts about each point in spacetime and so a unique result to any specific measurement, if you drop this and imagine multiple parallel versions of a measurement occurring in the same region of spacetime as in the MWI, then you may be able to explain the quantum statistics without violating locality. Similarly if you imagine the experimenter's choice of what detector setting to use on each trial is not actually uncorrelated with the local variables associated with the particle immediately after emission, so that you have a sort of retrocausal effect where the particle "anticipates" what the future detector setting will be, then one might argue that this would be compatible with locality as well (though some might argue that retrocausal influences don't count as "local").

As DrC's signature quotes from Korzybski, "The map is not the territory." (Did I get that right?)

I don't see how that statement is applicable here. Would you describe statements 1) and 2) about the nature of physics as "map" or "territory"? Whichever you'd choose, I don't see why you'd say that "the general assumptions of locality and the existence of local hidden variables" was any different. And logically, if you agree that "the general assumptions of locality and the existence of local hidden variables" (or 'exclusively local interactions and transmissions") would be false if 1) and 2) were false, then if QM is incompatible with 1) and 2) that shows it's also incompatible with "the general assumptions of locality and the existence of local hidden variables" regardless of what you call "map" and what you call "territory".

 

[ThomasT]

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

I don't understand why you would distinguish "the general assumptions of locality and the existence of local hidden variables" from "local realism" as described by 1) and 2).

My current thinking is that 1) is obviated by the experimental design of Bell tests. Accurately predicting entanglement correlations simply doesn't require breaking things down into sets of local facts. It's because of the inclusion of a local hidden variable lambda in the formulation that the range of statistical predictions is reduced.

2) entails a formalism that contradicts both parameter and outcome dependence. But outcome dependence doesn't contradict locality, thus facilitating a more parsimonious explanation for why BIs are violated than the existence of underlying nonlocal transmissions.

 

[ThomasT]

... I just said that a theory of the type described by 1) and 2) was ruled out.

And we're in agreement on that, which represents progress in my understanding. Maybe we should just leave it at that for the time being and I'll stay out of the thread.

 

[JesseM]

My current thinking is that 1) is obviated by the experimental design of Bell tests.

Purely by the design of the tests, or by the resulting statistics? If you just think that the design itself is enough to obviate 1) you are misunderstanding something, you could certainly do the same sort of tests in a universe where classical electromagnetism was exactly correct and 1) and 2) would both be correct there, you just wouldn't get any statistics that violated Bell inequalities in this case. Keep in mind that 1) doesn't forbid you from talking about "facts" that involve an extended region of spacetime, it just says that these facts must be possible to deduce as a function of all the local facts in that region. For example, in classical electromagnetism we can talk about the magnetic flux through an extended 2D surface of arbitrary size, this is not itself a local quantity, but the total flux is simply a function of all the local magnetic vectors at each point on the surface, that's the sort of thing I meant when I said in 1) that all physical facts "can be broken down into a set of local facts". Similarly in certain Bell inequalities one considers the expectation values for the product of the two results (each one represented as either +1 or -1), obviously this product is not itself a local fact, but it's a trivial function of the two local facts about the result each experimenter got.

2) entails a formalism that contradicts both parameter and outcome dependence. But outcome dependence doesn't contradict locality, thus facilitating a more parsimonious explanation for why BIs are violated than the existence of underlying nonlocal transmissions.

Not sure what you mean by "parameter and outcome dependence", can you be more specific? Again, 1) and 2) are definitely true of classical electromagnetism, if you think they aren't (for any conceivable experiment in a universe where classical electromagnetism was exactly true) then you are misunderstanding something (do you think any possible experiment in such a universe would display parameter and/or outcome dependence?)

 

[Gordon Watson]

I'm back. And happy to be so.

Apologies for my absence; me recognizing my part in this tread. And many thanks to all participants.

Absences will continue sporadically. But there's no need for me to signal them: In that I am committed to answer every question here, you can rest assured that I have not quit ... until I say so.

If a final post sinks my model, then you can expect me to acknowledge that, and move happily on.

I have no problem correcting my wrong beliefs and moving on to new (and better) ones.

I trust the above is a satisfactory part-reply to TomT. Note that my maths is elementary, and supports what I would have thought to be a reasonable LR position for you. More re DrC's position soon, that might interest you.

To Avodyne, OK, and fair enough. But I hope to go beyond semantics and hand-waving.

To Dmitry67, thanks for your post! I'm very happy to spar with physicists who have neither knuckle-dusters, nor FTL, not NL, in their gloves. If I survive this warm-up bout, I might be ready for this one: What's wrong with this One World Interpretation of MWI? Until then, thanks again.

More soon, with a focus on technical issues raised by DrC, JesseM, vanesch.

XO-s and thanks again to all,

JenniT

 

[Gordon Watson]

The criticism is the same for all such: it isn't realistic! ("So any inference to a third side will be misleading. ")

If it is, simply provide a dataset for us to look at. 0, 120, 240 degrees is always a good combo to supply. We will see if the QM predictions hold.

I will repeat my main objection again: it's not realistic if you do not provide values for measurements which cannot be performed. That is the definition of "realistic".

The "confusion" issue is: to the extent anyone agrees with you, we are simply talking about the usual approach to Bell or a closely related equivalent variation. To the extent you assert you have provided a LR counter-example, we keep explaining that actually you have violated the requirement of L locality or R realism despite your words. You cannot just wave your hands and say you have accomplished this without pointing us to some new revelation. I see nothing novel in your approach at all, and it seems to follow your arguments presented in other threads.

Where's the beef? It would really be nice if you would show us something new to discuss rather than just say "I'm right unless you show me where am I wrong".

I have tidied up the presentation, in the attached PDF, in the hope of minimising confusion: and would welcome your comments on it; plus:

Do most of the Tables give results for experiments that cannot be performed? (I think that they do.)

Can you point to any hand-waving in the PDF please? (I am keen to delete any such.)

Could we discuss a protocol for studying your 0, 120, 240 example; along the lines of Figure 1 in the PDF, and related commentary thereunder? (I would be happy to derive the subsequent results.)

PS: For JesseM and vanesch: I am working on replies to your welcome technical queries; please don't despair.

And thank you, as always, DrC.

 

[Gordon Watson]

I have tidied up the presentation, in the attached PDF, in the hope of minimising confusion: and would welcome your comments on it; plus:

Do most of the Tables give results for experiments that cannot be performed? (I think that they do.)

Can you point to any hand-waving in the PDF please? (I am keen to delete any such.)

Could we discuss a protocol for studying your 0, 120, 240 example; along the lines of Figure 1 in the PDF, and related commentary thereunder? (I would be happy to derive the subsequent results.)

PS: For JesseM and vanesch: I am working on replies to your welcome technical queries; please don't despair.

And thank you, as always, DrC.

Re the above post by me:

A. I suggest that we refer to the PDF (attached to the above post) as PDF2.

B. CORRECTIONS to PDF2:

1. Equation (A3a); the last term should read [Sbc + P(bc++|a)]/3.

2. In the second line of the Headings to Tables A1.a, A2.b, A3.c: delete the 2.

 

[Gordon Watson]

I highlighted what we need: Pac++, Pab++ and Pcb++=Pbc--

Pac++ is what is measured on monday, and equals 0.073... in agreement with your numbers
Pab++ is what is measured on tuesday, and equals 0.25. Your number gives 0.125
Pcb++=Pbc-- is what is measured on thursday, and equals 0.073 in agreement with your numbers.

You will NEVER be able to get Pab++ equal to 0.25 (you actually have 0.125), simply because it can't be larger than (Pac++) + (Pbc--) which equals 0.146...
Note that indeed, your number (0.125) is, as it can't be otherwise, smaller than 0.146.
Simply because this 0.146 is made up of your 4 positive numbers P2 + P3 + P4 + P7 as you give it yourself, and Pab++ is equal to only P3+P4 (your 0.125). You ADD to your 0.125 still your P2 and P7 to obtain 0.146, so it has to be smaller (as indeed it is).

Now, QM predicts not 0.125, but rather 0.25. It is bigger. So it can't come from numbers P1...P8 in this way.

There's nothing more to say about this.

Please refer to PDF2, attached at this post

In PDF2 (see above), I have clarified the notation by including the conditioning space in every Probability function. That conditioning, now explicit, was implicit (as you will see) in the example that you cite. The RO was given as c, and the output statement was explicit in referring Pab to = the average over the bi-angle. [2Pab corrected to Pab.]

That is, as also in PDF2: Pab(++|c) = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2.

So we now examine your relations with the implicit conditioning space now explicit (as in PDF2, Table A3.c):

A: P(ac++|c) is what is measured on Monday, and equals 0.073 in agreement with my numbers.

B: P(ab++|c) [SIC] is what is measured on Tuesday, and equals 0.25. [I agree with 0.25. BUT you say that my number gives 0.125: Your statement is incorrect -- as shown below.]

C: P(cb++|c) =P(bc--|c) is what is measured on Thursday, and equals 0.073 in agreement with my numbers.

So our disagreement is at B only ... and, I believe, readily turned to agreement:

Please note that what is measured on Tuesday is P(ab++|ab) or P(ab++|a) or P(ab++|b)! With my model, you have three choices as to how you define it. And from PDF2, all equal Sab/2 = 0.25. In full agreement with YOUR calculation.

The one choice that you cannot make (with my model) is this: That on Tuesday we measured P(ab++|c).

Reason: Orientation c was nowhere evident in Tuesday's test.

Tuesday's test used orientation a, orientation b, and angle ab; the model can work with any of these. BUT orientation c CANNOT appear in the conditioning space for Tuesday's test.

With this correction, which I trust you understand and accept, there is nothing more to say beyond this: We agree with the QM numbers that apply to the subject tests.

In that I said that my model correctly delivered all the QM results, this agreement was to be expected.

So let me now see if we can reach agreement re bi-angles: According to the model, Tuesdays bi-angles are 0 and 90, and the experimenters chose to measure over the 90 value: No problem whatsoever for the model. But note: One bi-angle value yields (S0)/2 = 0. The other bi-angle value yields (S45)/2 = 0.25. The average of these results is 0.125.

That is the origin of that 0.125 number; which is not the number applicable to the actual measurement made on Tuesday. The model gives BOTH numbers, and both correctly: The measured result is 0.25 (in full agreement with QM), and the average over the bi-angle 0.125.

Where we still differ is in the numbers that you invoke re the (supposedly) related Bell-inequality. But as PDF2 states: In agreement with QM (so in agreement between you and me, I'm sure), my model will disagree on numbers to do with BT.

So I will now move to reply to the post where you gave such numbers and, from memory, related them to an impossibility that is unrelated to my model. [The model does not fail when it comes to BT-based impossibilities. Rather, it shows that they cannot be rationally constructed from within. This is shown in PDF2, equation (?). Yes, equation(?), foot of page 4.]

I seek to show you that the L*R model again agrees with QM; here re the futility of any attempt to construct BT from within L*R.

In closing: I very much appreciate your attention to detail, and your engagement with the model. At the end of the day, I expect us both to agree on all the QM numbers. AND on QM's position that BT cannot be constructed from within QM.

I go on to say that BT cannot be constructed from within L*R ("advanced local realism"). So I see that that is where our discussion will head; e.g., is L*R truly L + R. In that MWI beats BT too, as I (preliminarily) understand it, it might boil down to us uniting L*R and MWI -- who knows --

With many thanks, as always; more soon.

 

[JesseM]

You still seem to be talking about "bi-angles" in your pdf, and the diagram shows an experimental setup where, if "a" is an orientation pointing vertically, then there are two possible choices for the direction of "b" and two possible choices for the direction of "c". Please understand that this is not the experimental setup envisioned by Bell or the one that's used in actual Bell test experiments. In a Bell test experiment, the experimenters have pre-agreed on only three possible orientations for the Stern-Gerlach devices or polarizers--imagine that there's a clock face on the wall in front of the SG device used by one of the experimenters, and that experimenter must arrange his device so that the North end of the North-South axis of his device is either pointing in the same direction as 12 o'clock, 2 o'clock, or 4 o'clock, no other orientations are permitted (meanwhile the other experimenter is only allowed to pick orientations which would match up with the same readings in a mirror image of the first experimenter's clock). It is in this specific experiment that Bell said it would be impossible for a local realist theory to violate the Bell inequality, not the alternate setup you seem to be imagining where if "a" points at 12 o'clock "b" could either point at 2 o'clock or 12-2 = 8 o'clock. So, I hope you will take this into consideration and avoid all reference to "bi-angles" in any future response to me.

 

[Gordon Watson]

You still seem to be talking about "bi-angles" in your pdf, and the diagram shows an experimental setup where, if "a" is an orientation pointing vertically, then there are two possible choices for the direction of "b" and two possible choices for the direction of "c". Please understand that this is not the experimental setup envisioned by Bell or the one that's used in actual Bell test experiments. In a Bell test experiment, the experimenters have pre-agreed on only three possible orientations for the Stern-Gerlach devices or polarizers--imagine that there's a clock face on the wall in front of the SG device used by one of the experimenters, and that experimenter must arrange his device so that the North end of the North-South axis of his device is either pointing in the same direction as 12 o'clock, 2 o'clock, or 4 o'clock, no other orientations are permitted (meanwhile the other experimenter is only allowed to pick orientations which would match up with the same readings in a mirror image of the first experimenter's clock). It is in this specific experiment that Bell said it would be impossible for a local realist theory to violate the Bell inequality, not the alternate setup you seem to be imagining where if "a" points at 12 o'clock "b" could either point at 2 o'clock or 12-2 = 8 o'clock. So, I hope you will take this into consideration and avoid all reference to "bi-angles" in any future response to me.

OK; fair enough. But please see my most recent reply to vanesch re the conditioning spaces (of the probability functions), that must be applied to any real experiment carried out over 3 orientations. Also, equations (A0a) - (A0c), exemplifying the derivation of the QM results, make no mention of those angles. Do you see a problem with this equation set?

1. Without reference to any angles, other than those specifically tested (as requested), Table 2 in PDF2 provides all the testable probabilities; all in accord with QM. Do we agree on that? Does this Table, with supporting equations, answer some of your earlier questions re what it is that Table 1 delivers.

2. Note that the alternative "test-arrangements" were given in PDF2 as a way of illustrating what it is that L*R does. Do you believe that the allowance of these additional tests would somehow be the way that L*R breaches BT? (They are not.) Remember that Alice and Bob can move on to any RO, and L*R will still deliver the correct outcome distributions; see Table 2.

3. Moreover, from those correct distributions, L*R delivers precise values for any test set-up. As shown in PDF2, equation (?), there is no basis for a BI in L*R, anymore than there is such a basis within QM.

Many thanks.

 

[JesseM]

OK; fair enough. But please see my most recent reply to vanesch re the conditioning spaces (of the probability functions), that must be applied to any real experiment carried out over 3 orientations.

Since I don't understand the meaning of your "reference orientation" I don't understand what type of "conditioning space" you are using, as in your response to vanesch you say "The RO was given as c" and then condition all your probabilities on c. Normally a probability like Pab(++) would be conditioned on the fact that Alice chose angle "a", Bob chose angle "b", while the specific values of "a", "b" and "c" would be assumed as part of the conditions of the experiment. Indeed that seems to be what you do in Table 2 of the pdf when you write conditional probabilities like P(ab++|ab), but elsewhere in the pdf (and in your response to vanesch) you condition on other things besides the choice of two detector settings on a given trial, I don't understand the reason for that.

Also, equations (A0a) - (A0c), exemplifying the derivation of the QM results, make no mention of those angles. Do you see a problem with this equation set?

Where are equations (A0a) - (A0c)? If they're in the PDF, what page?

1. Without reference to any angles, other than those specifically tested (as requested), Table 2 in PDF2 provides all the testable probabilities; all in accord with QM. Do we agree on that? Does this Table, with supporting equations, answer some of your earlier questions re what it is that Table 1 delivers.

No, I already showed the math for getting Table 2 from the probabilities in Table 1 doesn't work in [post=3159151]post 71[/post] which I hope you will review and respond to. If P(ab++|ab)=P3+P4, then according to Table 1 this will be:

[Sab.Cac + Sab.Sbc + Cac.Sbc]/6 + [Sab.Sac + Sab.Cbc + Sac.Cbc]/6 =
[Sab*(Cac + Sac) + Sab*(Sbc + Cbc) + Cac.Sbc + Sac.Cbc]/6 =
[2Sab + Cac.Sbc + Sac.Cbc]/6

And as I showed in post #71, for the angles a=240,b=120,c=0, this would be equal to 0.3125. But Table 2 claims that P(ab++|ab)=Sab/2, and for these angles Sab/2=0.375. So, the equations in Table 1 are inconsistent with Table 2, assuming you accept equations such as P(ab++|ab)=P3+P4.

2. Note that the alternative "test-arrangements" were given in PDF2 as a way of illustrating what it is that L*R does. Do you believe that the allowance of these additional tests would somehow be the way that L*R breaches BT? (They are not.)

Your question makes no sense to me. The BT deal with a specific type of experiment, how would could the "allowance of additional tests" involving a totally different type of experiment be a way of breaching a theorem which doesn't address the second type of experiment at all? This is kind of like asking whether the "allowance" of an experiment on the breeding habits of Bengal tigers would "be the way that L*R breaches BT".