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

[Gordon Watson]

Here, things bug. Maybe this comes about because of a misunderstanding of the exact set-up, or about what exactly we are talking about, I don't know. There's no "double-valuedness" of any angle.

Consider the set-up as follows:

On Monday, Alice puts her analyser vertically and her detector clicks when she gets an "up" result. Bob puts his analyser at 45 degrees with the vertical (s times angle is then 22.5 degrees, right) towards the window of the room, and his detector clicks also when he gets an "up" result. An electronic circuit links Alice's and Bob's detector signals to a counter, which counts each time there is a simultaneous click on both detectors.
Carol starts the electron-pair source in the middle, and let's it generate 1 million electron-pairs during the afternoon.
Quantum mechanics predicts that at the end of the afternoon, the counter will read something like 73 000 counts.

On Tuesday, Alice leaves her installation in place, but Bob rotates his axis until it is horizontal (so s times angle is 45 degrees), with his "up" direction pointing towards the window.
When Carol starts the 1 million electron pair source again, quantum theory predicts that the counter will read 250 000 at the end of the afternoon.

On Wednesday, Alice, Bob and Carol go to a party.

On Thursday, Bob leaves his installation in the horizontal direction, but now Alice rotates her axis also in the direction of the window, over 45 degrees. Carol makes the source again run and produce 1 million electron pairs. Quantum mechanics predicts that the counter will read 73 000 counts.

The whole point is that the statistical mixture of the 1 million electron pairs is each time the same ; that the source didn't suffer any influence from the choice of settings.

So if on Friday, Alice and Bob randomly change their axes and we take data until we have 1 million events where Alice and Bob had aligned their axes as on Monday (so only considering those results when by coincidence Alice and Bob had their axes as on Monday), we expect to find statistically the same result as on Monday ; if we take data until we have 1 million events where Alice and Bob had aligned their axes as on Tuesday (so considering only those results where by coincidence Alice and Bob had their axes as on Tuesday), we expect to find the same result statistically as on Tuesday. And same for Thursday. Also, if by coincidence Alice and Bob put their axes parallel, we find that the counter reads 0.
The results will be the same if the source is generating statistically identical sets of events, independently of how the axes are set.Now, if we are to explain the results of Alice and Bob in a LR way, we have to assume that each pair sent out by the source must fall in 1 of 8 categories.

In the first category are the pairs which would give us a click in Alice's counter when it is vertical, and no click in Bob's counter when it is vertical ; that it would give us a click in Alice's counter when it was at 45 degrees, and no click in Bob's counter when it was at 45 degrees, and again that it would give a click in Alice's counter when at 90 degrees, and no click in Bob's counter when it was at 45 degrees. We write it as (+ + +). So events in this category will always give a click in Alice's counter and never one in Bob's counter.

and so on for the 7 other categories.

Note that there are no other possibilities: the 8 categories cover entirely the possibilities of the electron pair behaviour. It is for instance not possible that a pair wouldn't give a click in any Alice counter nor in any Bob counter. If a pair doesn't give a click in a vertical Alice counter, then it MUST give a click in a vertical Bob counter. So if we know the behaviour of a pair at Alice, we know that the behaviour at Bob's is complementary.

So the 1 million events must be subdivided in these 8 categories, with:

P1 * 1000000 = N1 the number of pairs in the first class,
P2 * 1000000 = N2 the number of pairs in the second class

etc...

Well, the number of pairs that belong to those that were counted on Monday are those in class 2 AND those in class 4. Each of the pairs in one of these classes will make the counter count, so we have that:

N2 + N4 = 73 000 up to statistical errors.

The counts on Tuesday are N3 + N4 = 250 000 up to statistical errors

The counts on Thursday are N3 + N7 = 73 000 up to statistical errors.

Well, you can't find such (positive) numbers N2, N3, N4, and N7.

Simply because if you add the counts on Monday and those on Thursday,

N2 + N3 + N4 + N7 = 146 000

and the counts on Tuesday are only N3 + N4 and they are LARGER: 250 000.

There's no "double angledness" or whatever here. There are specific measurements, with specific outcomes, and you CAN'T explain them with a pre-determined mixture of events. That's the point.

Excuse delayed reply here. I answered a related post earlier, but wanted to be sure that the issues here were clearly covered.

I didn't understand the reference to windows, and some settings pointing to them. For example, this confused me: "with his "up" direction pointing towards the window."

However, I believe that the outcomes relate to QM outcomes, as given in that other reply. So, per Table 2 in PDF2, we are not disagreeing about valid QM results.

However: With the numbers that were meant to be "pedagogical" -- they are numbers derived from L*R. Such numbers do not deliver the QM numbers directly. Instead they deliver the numbers that correctly relate to the "L*R 3-orientations, 2-angles, 1 bi-angle" thought-experiments that characterize L*R.

To get the QM numbers that you seek to check, the "L*R 3-orientations, 2-angles, 1 bi-angle" results must be reduced to a result that QM relates to. QM results involve and relate to "2-orientations, 1-angle" tests.

These reductions are fully detailed in Appendix A of PDF2. They yield (as shown in Table 2 of PDF2), correctly, every possible QM number that relates to the experiment.

On this basis, I'd be pleased if you would reconsider the "pedagogical" merits of my P1-P8 L*R-based numbers.

Many thanks.

 

[ThomasT]

Thanks GW.

Ok, we're only interested in predicting coincidental photon flux (++), so your LR formula for the expectation value in, say, the Aspect experimental setting reduces, in conventional notation, to,

P(A,B) = (cos²θ)/2,

Is that correct?

If so, then in this form it doesn't qualify as an LR model. The various 'Cab', etc. in your Tables also don't qualify as LR.

I mean, it looks as if you've just added λ (your s) to the qm formula to define 'Cab' etc., and then just omitted it (presumably because λ is continuous from a to b, and a randomly occurring value) to calculate the values for various θ.
If so, then your model isn't an LR model.

So if you could take us back to some point in your derivation where your formulation encodes realism and locality (that is, where λ, your s, and a locality condition actually have something to do with the calculations), then that would be helpful in evaluating your claim.

Without that, it doesn't matter whether or not your tables are able to reproduce qm results.

 

[Gordon Watson]

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.

As far as I can see, JenniT has offered only ONE proposal involving the "8 numbers" referred to above.

Those numbers are as given in Table 1 of PDF2; as general functions of C and S.

I believe the alleged impossibility derives from a serious misunderstanding.

That misunderstanding is this: The 8 numbers in PDF2, the 8 numbers provided by JenniT, are numbers within L*R. See Table 1 of PDF2.

They are not QM numbers. The numbers that relate to QM are derived from the L*R numbers. These QM numbers are given in Table 2; there are more than 8 of them, and all agree with QM.

I further address this issue below.

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.

Here the above-mentioned misunderstanding is explicit. The numbers 0.25, 0.073, 0.073 are the correct QM numbers. They are equally derived from QM and L*R.

The numbers 0.125, 0.073 and 0.073 are L*R numbers. Two (0.073) are equally QM numbers. The 0.125 number is specifically L*R. Let us see what it relates to; then if it is correct:

The L*R model states that, in the calculation delivering 0.125, 0.073 and 0.073, the 0.125 is an average over two values. In the given example, the two values are 0 and 90. (And to be noted in passing, the experiment was carried out on the 90 setting, and L*R gave the correct result: 0.25.)

But is 0.125 the average of an 0 and a 90 setting; calling them ab-1 and ab-2 respectively?

Average = [S(ab-1)/2 + S(ab-2)/2]/2 = [0 + 0.25]/2 = 0.125.

I trust this goes some way to clearing up the "two angles" that L*R deals with correctly. For we have this FACT: L*R gives numbers BEYOND QM, plus every possible QM number. L*R said that this would be the case from day one.

In that the QM numbers are correctly delivered, it seems to me that the real question remains: Is L*R truly local and realistic? This seems to me to be the question that ThomasT seeks to address.

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.

As stated above: As far as I can see, JenniT has offered only ONE proposal involving the "8 numbers" referred to above.

Those numbers are as given in Table 1 of PDF2; as general functions of C and S.

Further: The requisite algebra, to derive the 3 numbers above, is spelled out in Appendix A of PDF2, and summarized in Table 2.

As I interpret your example with the window, let us take: ab = 90, ac = bc = 45.

From PDF2, from the given worked example but inserting specific numbers:

Pab(++|ab) = Sab/2 = 0.25.

In similar manner, we also have:

P(ac++|ac) = Sac/2 = 0.0732

P(bc++|bc) = Sbc/2 = 0.0732

These are the correct QM and L*R predictions!

I see no algebraic impossibilities here.

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

Somebody who is happily and openly checking and learning within the PF community, to find possible errors. Someone who is very appreciative of your contributions, and many others.

Thus far, with many questions yet to be answered, I find unfortunate misunderstandings (about the L*R model, which is thus far unchanged), and I accept my role in many such. But unfortunate misunderstandings do not constitute errors; though errors there may be.

 

[Gordon Watson]

Thanks GW.


Ok, we're only interested in predicting coincidental photon flux (++), so your LR formula for the expectation value in, say, the Aspect experimental setting reduces, in conventional notation, to,

P(A,B) = (cos²θ)/2,

Is that correct?

I'm confused. The L*R example deals with an example in Zakurai, originally introduced by vanesch, with spin-half particles.

OK, Aspect deals with photons; s = 1 for photons.

And as you can see, L*R deals with both. But I suggest we stick with that s = 1/2 example for now.

If so, then in this form it doesn't qualify as an LR model. The various 'Cab', etc. in your Tables also don't qualify as LR.

Could you carefully elaborate this please. You may be on the right track, but I don't yet see it from these brief remarks. Thanks.

I mean, it looks as if you've just added λ (your s) to the qm formula to define 'Cab' etc., and then just omitted it (presumably because λ is continuous from a to b, and a randomly occurring value) to calculate the values for various θ.
If so, then your model isn't an LR model.

You write: λ (your s) ?

My s = intrinsic spin, as defined from day one.

Could you carefully elaborate this please. You may be on the right track, but I don't yet see it from these brief remarks. Thanks.

So if you could take us back to some point in your derivation where your formulation encodes realism and locality (that is, where λ, your s, and a locality condition actually have something to do with the calculations), then that would be helpful in evaluating your claim.

There's wrong bits here; they may be clouding your valid point of view; and my view of it!

You write: "where λ, your s," ?

My s = intrinsic spin, as defined from day one.

Without that, it doesn't matter whether or not your tables are able to reproduce qm results.

Let us see; after you've clarified and expanded your text. OK? And thanks.

 

[ThomasT]

I'm confused. The L*R example deals with an example in Zakurai, originally introduced by vanesch, with spin-half particles.

OK, Aspect deals with photons; s = 1 for photons.

And as you can see, L*R deals with both. But I suggest we stick with that s = 1/2 example for now.

Ok, Bell's LR formula for the singlet state expectation value is,

P(a,b) = ∫dλρ(λ)A(a,λ)B(b,λ),

and the qm formula is,

< σ₁ ∙ a σ₂ ∙ b > = - a ∙ b = - cosθ, where θ is equivalent to your ab.


What is your LR formula for the singlet state expectation value?

Could you carefully elaborate this please. You may be on the right track, but I don't yet see it from these brief remarks. Thanks.

According to your paper, Cab; etc. = cos²sab; etc. Sab; etc. = sin²sab; etc. ab = angle between orientations a and b; etc. s = intrinsic particle spin.

So, how is Cab, Sab (etc.) to be evaluated?

You write: λ (your s) ?

My s = intrinsic spin, as defined from day one.

Could you carefully elaborate this please. You may be on the right track, but I don't yet see it from these brief remarks. Thanks.

λ is the conventional notation for the hidden variable. Isn't s your hidden variable? Is it affecting the value of Cab? How? If not, then I don't understand what s is doing in Cab.

 

[Gordon Watson]

Ok, Bell's LR formula for the singlet state expectation value is,

P(a,b) = ∫dλρ(λ)A(a,λ)B(b,λ),

and the qm formula is,

< σ₁ ∙ a σ₂ ∙ b > = - a ∙ b = - cosθ, where θ is equivalent to your ab.


What is your LR formula for the singlet state expectation value?


According to your paper, Cab; etc. = cos²sab; etc. Sab; etc. = sin²sab; etc. ab = angle between orientations a and b; etc. s = intrinsic particle spin.

So, how is Cab, Sab (etc.) to be evaluated?


λ is the conventional notation for the hidden variable. Isn't s your hidden variable? Is it affecting the value of Cab? How? If not, then I don't understand what s is doing in Cab.

Some small confusions continue; so let's address them, then see what's left.


1. You ask: So, how is Cab, Sab (etc.) to be evaluated?

I suspect that you are in the process of formulating a deeper, more critical and important question. So let's see how that emerges; I'm looking forward to it.

For now, as I interpret the above question:

Cab = cos^2 (ab/2) = a number; given s = 1/2, and given ab.

Sab = sin^2 (ab/2) = a number; given s = 1/2, and given ab.


2. You ask: Isn't s your hidden variable? Is it affecting the value of Cab? How?

Answer: s = intrinsic spin of the particle under test. So it affects the value of Cab as we move from testing spin-1/2 particles to photons (spin-1). It is included to provide the generality that L*R seeks to deliver: one formulation, as you see, covering many Bell-tests and examples.


3. That leaves just one neat question remaining.

It deserves a similar answer.

I'll try to type it up as soon as I get through a day of meetings. Thanks.

 

[ThomasT]

Some small confusions continue; so let's address them, then see what's left.


1. You ask: So, how is Cab, Sab (etc.) to be evaluated?

I suspect that you are in the process of formulating a deeper, more critical and important question. So let's see how that emerges; I'm looking forward to it.

For now, as I interpret the above question:

Cab = cos^2 (ab/2) = a number; given s = 1/2, and given ab.

Sab = sin^2 (ab/2) = a number; given s = 1/2, and given ab.


2. You ask: Isn't s your hidden variable? Is it affecting the value of Cab? How?

Answer: s = intrinsic spin of the particle under test. So it affects the value of Cab as we move from testing spin-1/2 particles to photons (spin-1). It is included to provide the generality that L*R seeks to deliver: one formulation, as you see, covering many Bell-tests and examples.

Your s isn't a hidden variable. I didn't see anything else that might possibly qualify as your hidden variable. Thus, your model is, as far as I can tell, nonrealistic.

 

[Gordon Watson]

Your s isn't a hidden variable. I didn't see anything else that might possibly qualify as your hidden variable. Thus, your model is, as far as I can tell, nonrealistic.

Sorry for delay in replying; but to be very clear:

Intrinsic spin (s) is NOT a hidden-variable (HV) in my model.

Just as you do NOT see any HV in the QM formulation that you gave above, so you do NOT see any HV in the L*R model.

See your formula posted above: < σ₁ ∙ a σ₂ ∙ b > = – a ∙ b = – cosθ,

where θ is equivalent to my ab.

So in many ways it is good that you "did NOT see" anything that looked like a HV.

HOWEVER, in the work that leads to L*R, the local-realistic counter-example to Bell's theorem that is offered here for discussion, THAT is where you will find Bell's LAMBDA.

TWICE!

As λ and λ'.

I personally find it difficult to analyze Bell's writings with his single lambda. OK, we can all do it; but I wish he had written up the version of his theorem that he was using in his last lectures; for I then hoped that my two lambdas would more easily be introduced.

The reason that I use two lambdas is this: I provide λ (lambda-plain) for Alice's particles and λ' (lambda-prime) for Bob's particles. I then allow

(1) F(λ, λ') = 0,

to represent the applicable conservation of angular momentum; for the applicable singlet state, F being the applicable function. This, it seems to me, is the correct way to go, especially as a convinced local realist. As such a one, I want to ensure (in theory and in practice) that there is no linkage between the separating particles: EXCEPT for that established by equation (1) above: the conservation law that applies to the birth of each set of twins in any EPR-Bohm (EPRB) experiment.

Hoping this puts to rest your concern that my L*R model is not realistic, or not local, or both.

The L*R model is both local and realistic -- with locality and realism defined rigorously and acceptably for most physicists.

And it delivers every EPRB result in full accord with QM.

That remains my claim for the model.

With many questions yet to be answered.

 

[yoda jedi]

that all Bell inequalities are supposed to be claims about what must be true under local realism

good point.
but i add:

that all Bell inequalities are supposed to be claims about what [STRIKE]must[/STRIKE] should be true under some concept of local REALISM

Realism by:

With "realism", I follow Clauser and Shimony (1978): "Realism is a philosophical view, according to which external reality is assumed to exist and have definite properties, whether or not they are observed by someone."

but properties are just qualities, not existence per se.
something is real just because of its existence and not because of any qualities it has.

 

[DrChinese]

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.)

"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."

So, using the "model" in the PDF, just give me a set of sample values (+/-) for some series of runs, perhaps 8 or 16, something like:


a b c
-----

+ + -
- + -
- + +
+ - +
etc.

Then we can see if the ab, bc, ac coincidences average about 25% (QM expectation value) or are closer to 33% as I say they will be. I mean, this is a futile exercise as we all know the answer.

 

[ThomasT]

Sorry for delay in replying; but to be very clear:

Intrinsic spin (s) is NOT a hidden-variable (HV) in my model.

Ok.

Just as you do NOT see any HV in the QM formulation that you gave above, so you do NOT see any HV in the L*R model.

See your formula posted above: < σ₁ ∙ a σ₂ ∙ b > = – a ∙ b = – cosθ,

where θ is equivalent to my ab.

So in many ways it is good that you "did NOT see" anything that looked like a HV.

HOWEVER, in the work that leads to L*R, the local-realistic counter-example to Bell's theorem that is offered here for discussion, THAT is where you will find Bell's LAMBDA.

TWICE!

As λ and λ'.

OK, I neglected your stuff previous to the latest pdf. If you could show how your λ and λ' are associated with events at stations S₁ and S2, respectively, via functions A and B, respectively, incorporating unit vectors a and b, respectively, then that would be helpful.

I personally find it difficult to analyze Bell's writings with his single lambda. OK, we can all do it; but I wish he had written up the version of his theorem that he was using in his last lectures; for I then hoped that my two lambdas would more easily be introduced.

The reason that I use two lambdas is this: I provide λ (lambda-plain) for Alice's particles and λ' (lambda-prime) for Bob's particles. I then allow

(1) F(λ, λ') = 0,

to represent the applicable conservation of angular momentum; for the applicable singlet state, F being the applicable function.

It would help me to evaluate your LR model, and we can (hopefully) render it in its simplest complete form (using conventional notation), if you lay out its development, step by step, in this thread, in a manner somewhat akin to, but perhaps not exactly, the way Bell did it in his paper, ON THE EINSTEIN PODOLSKY ROSEN PARADOX.

As such a one, I want to ensure (in theory and in practice) that there is no linkage between the separating particles: EXCEPT for that established by equation (1) above: the conservation law that applies to the birth of each set of twins in any EPR-Bohm (EPRB) experiment.

A single λ, vis Bell, denotes hidden parameters carried by the particles from the source.

Hoping this puts to rest your concern that my L*R model is not realistic, or not local, or both.

Not yet. A step by step development, a la Bell, is necessary.

The L*R model is both local and realistic -- with locality and realism defined rigorously and acceptably for most physicists.

We'll see. Your model might turn out to pass the realism test. But it has to be both explicitly realistic, and explicitly local.

 

[Gordon Watson]

Ok.

OK, I neglected your stuff previous to the latest pdf. If you could show how your λ and λ' are associated with events at stations S₁ and S2, respectively, via functions A and B, respectively, incorporating unit vectors a and b, respectively, then that would be helpful.

It would help me to evaluate your LR model, and we can (hopefully) render it in its simplest complete form (using conventional notation), if you lay out its development, step by step, in this thread, in a manner somewhat akin to, but perhaps not exactly, the way Bell did it in his paper, ON THE EINSTEIN PODOLSKY ROSEN PARADOX.

A single λ, vis Bell, denotes hidden parameters carried by the particles from the source.

Not yet. A step by step development, a la Bell, is necessary.

We'll see. Your model might turn out to pass the realism test. But it has to be both explicitly realistic, and explicitly local.

Well, OK: As long as you are being reasonable above, as to what it is that a rational local realist must deliver.

Would you therefore comment on my next post, to see if it meets most of your requirements; AND tell me those that it does not. Thanks.

 

[Gordon Watson]

Dear DrC:

As always, DrC, many thanks for engaging with L*R: My local realistic model of EVERY EPRB experiment and EVERY EPRB-Bell test.

But please excuse my directness here: You appear to misunderstand the issue.

Dare I say, as a result of this misunderstanding, you appear to be avoiding a real test of my L*R model: One that IMHO would affirm my position and claims, cast serious doubts on yours, and provide points where we each might need to clarify our positions?

Here's what I posted:

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.

You replied:

"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."

So, using the "model" in the PDF, just give me a set of sample values (+/-) for some series of runs, perhaps 8 or 16, something like:a b c
-----

+ + -
- + -
- + +
+ - +
etc.

Then we can see if the ab, bc, ac coincidences average about 25% (QM expectation value) or are closer to 33% as I say they will be. I mean, this is a futile exercise as we all know the answer.

Do you not see that this is a repeat of your original challenge: WITH NO protocol on how your challenge is to be met?

My L*R model yields EVERY correct (i.e., QM-validated) result for ANY EPRB EXPERIMENT that you wish to nominate.

So let us put it to a TEST:

Your challenge mentions three (3) orientations. OK; that's up to you.

To be conducted openly on PF, the protocol requires simply this:

1a: You tell me the FIRST test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

1b: I will send you the full results for this first test. OK?

2a. You next tell me the SECOND test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

2b: I will send you the full results for this second test. OK?

NB: I will also send to a fair neutral party of your choosing -- you will provide me privately with their direct email address -- the following:

2c: The predicted results of ONE experiment that you might perform, but will NOT seek to have analyzed in your next request.

2d: The predicted results of THE experiment that you will perform, and seek to have analyzed in your next request.3a. You next tell me the THIRD test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

3b: I will not send you the full results for this third test. OK?

Because the neutral party will already have the results, and will post them here, on PF: Simply by posting the contents of my email.PS: DrC, a certain absurdity attaches to the above: Time-pressured, I have given no consideration as to whether L*R can do as I hope. So if it cannot, it will require modification. However: In that I expect a rational local realist can deliver the correct results for any fair challenge involving EPRB, then all should be well -- for me. ;-)

DrC: This PS was added to contrast my position with yours above. You say above: "I mean, this is a futile exercise as we all know the answer."

But I don't know the answer. I don't yet know the formal question. But if "the answer" relates somehow to your confidence in that 33% figure of yours, then I know this: That 33% of yours does not relate to the three orientations that you foreshadowed: 0, 120, 240. So we at least need to test our difference on this small point. Though I am confident that more than that will emerge from the protocol and my responses. The idea being that, collectively, we will get closer to the crux of the matter, or at least be able to point to some improvement in our understanding. Thanks DrC.

PPS: I guess you are discussing photons in your example; but your 33% still does not emerge.

Please note that Tables 1 & 2 in PDF2 relate to particles satisfying the +/– distributions in Table 1.

 

[ThomasT]

So let us put it to a TEST:

Your challenge mentions three (3) orientations. OK; that's up to you.

To be conducted openly on PF, the protocol requires simply this:

1a: You tell me the FIRST test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

1b: I will send you the full results for this first test. OK?

2a. You next tell me the SECOND test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

2b: I will send you the full results for this second test. OK?

NB: I will also send to a fair neutral party of your choosing -- you will provide me privately with their direct email address -- the following:

2c: The predicted results of ONE experiment that you will NOT seek to have analyzed in your next request.

2d: The predicted results of THE experiment that you will CERTAINLY seek to have analyzed in your next request.


3a. You next tell me the THIRD test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?

3b: I will not send you the full results for this third test. OK?

Because the neutral party will already have the results, and will post them here, on PF: Simply by posting the contents of my email.


PS: DrC, a certain absurdity attaches to the above: Time-pressured, I have given no consideration as to whether L*R can do as I hope. So if it cannot, it will require modification. However: In that I expect a rational local realist can deliver the correct results for any fair challenge involving EPRB, then all should be well -- for me. ;)

I don't get why all this is necessary. Why not just lay out the development of your model and we can assess whether it's explicitly realistic and local? You've already presented a reduced form for calculating expectation values that matches qm for certain experiments. What we need to see is how you got there. Specific developmental steps and the rationale behind them. These 'dataset requirements' are superfluous, imho.

 

[zonde]

DrC: This PS was added to contrast my position with yours above. You say above: "I mean, this is a futile exercise as we all know the answer."

But I don't know the answer.

Maybe example with polarizers at 0°, 30° and -30° angles is easier to understand:
see DevilsAvocado https://www.physicsforums.com/showthread.php?p=3024316#post3024316"
or in alternative form in my https://www.physicsforums.com/showthread.php?p=3024641#post3024641"

You have made a post in that thread near the end but maybe you have skipped over particular example.

For me it seems that this example shows the problem as clear as possible.

 

[DrChinese]

Your challenge mentions three (3) orientations. OK; that's up to you.

To be conducted openly on PF, the protocol requires simply this:

1a: You tell me the FIRST test that you'd like results for. That is: You send me sufficient data, data that you think is fair, enabling that test to be conducted. OK?
...

You must be kidding. Ace, the burden is entirely on you. Perhaps you don't realize that you position violates mainstream science. Unless you can back up your statements, I would say your claims violate PF guidelines.

You say you have the example formula to generate the dataset. Great, so apply it and give the results to us. I will tell you if I consider it suitable. The angle settings have been laid out. (Of course I already know you cannot deliver what you claim.)

 

[DrChinese]

Maybe example with polarizers at 0°, 30° and -30° angles is easier to understand:
see DevilsAvocado https://www.physicsforums.com/showthread.php?p=3024316#post3024316"
or in alternative form in my https://www.physicsforums.com/showthread.php?p=3024641#post3024641"

You have made a post in that thread near the end but maybe you have skipped over particular example.

For me it seems that this example shows the problem as clear as possible.

As zonde mentions, this is a good example too. The point is to have consistency (i.e. following the cos^2 rule) for a, b, AND c where you provide +/- or 0/1 values for a dataset consisting of a, b and c values. If you only provide 2 values per dataset, you are simply following the QM formalism (which describes the results of experimental observation) but are not including the Realism assumption.

To sum up the Realism requirement, as Einstein said: "I think that a particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it." You measure a (from Alice) and b (from Bob), but ASSUME there must be a c (third) spin component value which exists - although not itself measured. Turns out c values don't fit.

 

[ThomasT]

As zonde mentions, this is a good example too. The point is to have consistency (i.e. following the cos^2 rule) for a, b, AND c where you provide +/- or 0/1 values for a dataset consisting of a, b and c values. If you only provide 2 values per dataset, you are simply following the QM formalism (which describes the results of experimental observation) but are not including the Realism assumption.

To sum up the Realism requirement, as Einstein said: "I think that a particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it." You measure a (from Alice) and b (from Bob), but ASSUME there must be a c (third) spin component value which exists - although not itself measured. Turns out c values don't fit.

What you're calling Bell's realism assumption isn't, "You measure a (from Alice) and b (from Bob), but ASSUME there must be a c (third) spin component value which exists - although not itself measured."

Apparently you think Bell's introduction of c has something to do with an abc dataset.

However, Bell's introduction of c is simply to have the three datasets (ab, ac, and bc) necessary to produce his inequality.

Anyway, it's now clear to me what your 'realistic dataset requirement' is based on, and why you might think that it's an insight into 'what Bell is all about' as well as a quantitative shortcut wrt assessing proposed LR models. It's neither. It's based on a misunderstanding of the role that c plays in Bell's exposition.

The first step in evaluating a proposed LR model of entanglement is:
Does the model reproduce qm predictions for a given setup?
If it doesn't, then it's not a viable model and is dismissed.
If it does, then it remains to determine whether it's suitably, explicitly realistic and local via its notational content and form, and the rationale underlying those.
If GW's model reduces to the qm expectation value, then it will pass the first test.
My guess is that it will, but will fail one or both of the realism and locality tests.

 

[yoda jedi]

With "realism", I follow Clauser and Shimony (1978): "Realism is a philosophical view, according to which external reality is assumed to exist and have definite properties, whether or not they are observed by someone." This means that I talk about trajectories and total angular momenta before they are measured.

clauser and shymony (and escorts) are wrong, that is not realism !
that is essentialism...
essentialism is the view that, for any entity (electrons, for example), there are properties (qualities) all of which any entity of that kind possess.
Essentialism, is any philosophy that acknowledges the primacy of Essence (properties). Unlike Existentialism (Realism), which posits "being" as the fundamental reality,
essentialism stands diametrically opposed to existential realism because Realism postulate that something is real just because of its existence and not because of any qualities it has.

same thing for this one:

To sum up the Realism requirement, as Einstein said: "I think that a particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it." You measure a (from Alice) and b (from Bob), but ASSUME there must be a c (third) spin component value which exists - although not itself measured. Turns out c values don't fit.

has to be written
"To sum up the counterfactual definiteness requirement...a particle must have a value independent of the measurements"


.

 

[DrChinese]

clauser and shymony (and escorts) are wrong, that is not realism !
that is essentialism...

We are venturing into the world of semantics with this one. By Realism we of course mean "Quantum Realism". You can define that several different and, for most purposes, equivalent ways. I agree that Counterfactual Definiteness - as you mention - might be a better term. I like noncontextual myself (because I believe the context of the measurement is essential within QM). Some also replace Realism with Hidden Variables, also a pretty good concept. Of course there are differences between these terms, but that won't change too much as to the Bell result.

 

[DrChinese]

What you're calling Bell's realism assumption isn't, "You measure a (from Alice) and b (from Bob), but ASSUME there must be a c (third) spin component value which exists - although not itself measured."

Apparently you think Bell's introduction of c has something to do with an abc dataset.

However, Bell's introduction of c is simply to have the three datasets (ab, ac, and bc) necessary to produce his inequality.

Well, it's really not that hard. I assume you agree that Alice and Bob will give identical results when each are measured at any c. I assume you agree that Alice and Bob will give results following the cos^2 rule when each are measured at any a and b respectively. If you believe that Alice and Bob are independent (locality holds) and the prior 2 statements are simultaneously correct, then clearly I can come up with a/b/c setting for which there are no stream of values which average to the cos^2 rule.

Alice is a clone of Bob, therefore Alice(a)=Bob(a); Alice(b)=Bob(b); Alice(c)=Bob(c). As well:

Alice(a)=+
Alice(b)=+
Alice(c)=-
Alice(d)=-
Alice(e)=+
Alice(f)=+
... simultaneously to infinity


You agree with the above, correct? If you do, you are a realist. And if you do, you will find that for a=0, b=120 and c=240, you have problems. Big problems. Of course, you can always say you are a realist and then simply abandon or ignore the above.

 

[ThomasT]

Well, it's really not that hard. I assume you agree that Alice and Bob will give identical results when each are measured at any c. I assume you agree that Alice and Bob will give results following the cos^2 rule when each are measured at any a and b respectively. If you believe that Alice and Bob are independent (locality holds) and the prior 2 statements are simultaneously correct, then clearly I can come up with a/b/c setting for which there are no stream of values which average to the cos^2 rule.

Alice is a clone of Bob, therefore Alice(a)=Bob(a); Alice(b)=Bob(b); Alice(c)=Bob(c). As well:

Alice(a)=+
Alice(b)=+
Alice(c)=-
Alice(d)=-
Alice(e)=+
Alice(f)=+
... simultaneously to infinity


You agree with the above, correct? If you do, you are a realist. And if you do, you will find that for a=0, b=120 and c=240, you have problems. Big problems. Of course, you can always say you are a realist and then simply abandon or ignore the above.

What does any of this have to do with my post #118, to which you're ostensibly replying?

 

[DrChinese]

What does any of this have to do with my post #118, to which you're ostensibly replying?

You are simply mouthing words which basically have no meaning. Clearly, I am asking you to provide an actual realistic example. You just say something is realistic without providing support, as does JenniT and Gordon. Hey folks, realism means that the attributes DON'T have to be measured to exist. So provide putative values for these, will ya? That would be a and b AND c! Get this, c is NOT measured, a and b are.

I have a chair. It has simultaneous leg1, leg2, leg3 and leg4 each which have a position. The positions are relative to each other, each a foot apart forming a square at the base. If I observe the positions of any 2, without measuring the other 2, I can make the statement that the legs are realistic. That is because there are values for the 2 legs I don't observe that are not inconsistent with the relative positions of the 2 legs I do measure.

This analogy does NOT hold for quantum objects, specifically entangled particle pairs. They are not realistic! And neither are any objects which follow the HUP at the microscopic level.

Here is an example (settings 0/120/240 for a/b/c):

a/b/c
+ - +
- + -
+ + -
- + +

Note that the ab coincidence rate is 25%, exactly as predicted by QM. The bc rate should also be 25%, and it is in fact 25%. But the ac rate should also be 25%, and it is instead 50%. Oops! This is not consistent. Go to progressively larger datasets and you get no closer than this. The averages always ends up around 33% instead of the QM expectation of 25%.

W H E R E I S T H E B E E F ?

(And I don't mean DEADBEEF :)

So my point is that how *realistic* is an example that cannot show us that there are unobserved values which, if measured, would be consistent? Everything else being said is simply empty words.

 

[Gordon Watson]

You must be kidding. Ace, the burden is entirely on you. Perhaps you don't realize that you position violates mainstream science. Unless you can back up your statements, I would say your claims violate PF guidelines.

You say you have the example formula to generate the dataset. Great, so apply it and give the results to us. I will tell you if I consider it suitable. The angle settings have been laid out. (Of course I already know you cannot deliver what you claim.)

DrC and Admins: I have neither the intention nor the desire to breach any PF guide-line. I am here for the long-haul; I am here to learn, and I am learning. So I would welcome explicit directions and guidance if a possible breach of PF Guidleines ever seems to be the case. I am happy to lodge an application to the "Independent Research" section of PF, should that be required. I have been restrained in what I said in some posts above; and am still restrained in preparing some of the replies that I am yet to deliver. ThomasT raises questions that I believe I will need to answer in IR. (They relate to what I term LRQ -- a local realistic interpretation of QM -- which combines a widely-accepted view of the wave-function with equivalence classes.)

So DrC, that said, and with respect, there seems to be a lot of bias, innuendo, intimidation, misinformation and (still) misunderstanding in your response. Especially read in the light of the simple request that triggered your response.

1. I am not kidding. Why do you say that I must be?

2. You use the term "Ace". (I at first thought you were referring to someone else, maybe a friend of yours, an earlier poster.) But I understand the "dog-whistle" in this seemingly innocuous expression, as used in American English. Best I bite my tongue.

3. You say the burden is entirely on me. I thought this was a collaborative effort (all I asked for was the test-settings), but I will accept my share of the burden, and more, quite happily.

4. To that end: If you accept that the burden is entirely on me, I will post to you my interpretation of vanesch's example, and I will use the settings therein. I trust that you will not judge vanesch's example UNSUITABLE?

5. You say: "Perhaps you don't realize that your position violates mainstream science. Unless you can back up your statements, I would say your claims violate PF guidelines." This confuses me, so I'll let it pass for now. Except when I offered to back up my statements, you chose not to supply the test data? Very confusing to me; especially with me having no wish to breach the PF rules; and my OP question approved for its possible pedagogic merit.

6. I do not know where I said this: "I have the example formula to generate the data-set"? I want to demonstrate the formula that I have on test-settings provided by you. In the absence of such settings from you, I will now use vanesch's example, but in your context.

7. The IT here is not clear to me. "I (DrC) will tell you if I consider it suitable." ? I'll push on anyway.

8. You say: "The angle settings have been laid out. (Of course I already know you cannot deliver what you claim.)" Well I cannot deliver any claim based on angles only. I need more than angles to run a test; I need to know the particles (since my formula includes s for intrinsic spin); and the specific singlet correlation that you have chosen. So I will use the vanesch example, which is EPRB as used in Bell's 1964 paper; and which is the experiment addressed in L*R's Table 1 (PDF2) etc. This way, it will be clear that I have not "cooked" any formulae; so that is the way for me to go.

9. You say: "(Of course I already know you cannot deliver what you claim.)" Then (it seems to me) "my claim" is wrong, or you misunderstand it, or you are wrong. Are there other choices? Let's see.

10. To that end, I will first revise PDF2 to PDF3, to correct the typos already signaled; and to be specific about my definition of local realism (as spelled out in a reply to JesseM).

With best regards, and not too many hard feelings,

GW

PS: The example chosen has this merit: It will tie in with issues already raised in this thread, and with some questions that I have not yet answered.

 

[DrChinese]

DrC and Admins: I have neither the intention nor the desire to breach any PF guide-line. I am here for the long-haul; I am here to learn, and I am learning. So I would welcome explicit directions and guidance if a possible breach of PF Guidleines ever seems to be the case. I am happy to lodge an application to the "Independent Research" section of PF, should that be required. I have been restrained in what I said in some posts above; and am still restrained in preparing some of the replies that I am yet to deliver. ThomasT raises questions that I believe I will need to answer in IR. (They relate to what I term LRQ -- a local realistic interpretation of QM -- which combines a widely-accepted view of the wave-function with equivalence classes.)

So DrC, that said, and with respect, there seems to be a lot of bias, innuendo, intimidation, misinformation and (still) misunderstanding in your response. Especially read in the light of the simple request that triggered your response.

1. I am not kidding. Why do you say that I must be?...

Anyone who researches the area should know that LR theories have been definitively ruled out. This is mainstream science. See for example Aspect, Zeilinger, etc. Shimony, the S in CHSH, said "...the incompatibility of Local Realistic Theories with Quantum Mechanics permits adjudication by experiments..." and hundreds have confirmed QM over LR. So if you want to learn about the area, great, perhaps I can help. But if you are here to attempt to persuade readers that LR theories are viable, you are making a mistake. This is not a forum for alternative views of science or personal theories. This is a moderated discussion area with guidelines. I believe you have been around here enough to understand how this place works, so I have to admit I am a bit confused.

On the other hand, if you want to learn WHY LR theories are ruled out, this is an excellent place to come! And I have been trying to explain just that.

As to the setup: a suitable PDC Type I source can produce photon pairs which have identical polarization. This is easily the best way to discuss entangled pairs because they are polarization clones and you don't need to adjust for opposite spin (which can be unnecessarily confusing in nomenclature). Use a=0, b=120 and c=240 degrees. The QM prediction for correlation at any differing pair of these (ab, bc, ac) will be 25%, and will be 100% for any identical pair (aa, bb, cc). I would expect that + and - values would be more or less equal and random, but that is not something I am too strict about. Is that specific enough?

You have a black box "LR" formula you want to test. It has some internal workings, the nature of which does not concern me. All I want to know is what the values are for a, b and c - they will be the same for Alice and Bob obviously - for some run. You should actually be able to provide me with values for 0 degrees, 1, 2, 3... 359. Or for that matter, .1, .2, .3... 359.9 degrees just as easily. But all I ask is for the a/b/c I requested above. You see, if there is only a and b from your model, then you are saying NOTHING more than QM! The realist asserts that there are values even when not measured. OK, if so, what are they? Because it should be clear very quickly that the experimental correlation results ALWAYS depend on the relative angle between Alice and Bob and NOTHING else. Which is exactly what QM asserts, and no more.

Good luck.

 

[yoda jedi]

We are venturing into the world of semantics with this one. By Realism we of course mean "Quantum Realism". You can define that several different and, for most purposes, equivalent ways. I agree that Counterfactual Definiteness - as you mention - might be a better term. I like noncontextual myself (because I believe the context of the measurement is essential within QM). Some also replace Realism with Hidden Variables, also a pretty good concept. Of course there are differences between these terms, but that won't change too much as to the Bell result.

Realism is the idea that ALL particle properties are independent of an actual measurement.

So if Realism ...hold, particle properties are predetermined.
So presumably the unmeasured properties have values.

is not semantics, we are talking about the existence, you are arguing that
the moon is not there if nobody observes it (someone has to watch it to exist, for be there).

you state: the electron need have a spin value, if not, the electron is not real.
there are two very different things, is not semantics.
I say the electron exists, have or not a definite spin value.


.

 

[ThomasT]

You are simply mouthing words which basically have no meaning.

Where? I just indirectly asked you to reply to my statements in post #118 of this thread. I've pointed out to you (in the Joy Christian thread) what constitutes explicit realism in Bell's formulation, and noted (in this thread) that your conception/translation of Bell's realism seems to be based on a misunderstanding of the role that the analyzer setting, c, plays in his exposition.

Not that your 'realistic dataset requirement' (based on your "... realism means that the attributes DON'T have to be measured to exist.") isn't insightful in a way. But it isn't Bell's realism, which is defined by the functions (which determine individual datasets) in his (1). Bell's realism, per se, is compatible with qm. What qm is incompatible with is the separability of those functions (1) in Bell's (2) -- a consequence of the application of Bell's locality condition.

Your dataset requirement seems to be more than just a realism requirement. Since it requires multiple datasets, and since it's incompatible with qm, it seems more of a realism + localism requirement. Maybe I'm wrong about that, and we can discuss it in another thread. Anyway, as I'll try to show below, it isn't the most efficient way to approach assessing proposed LR models.

Clearly, I am asking you to provide an actual realistic example.

Clearly ... and repeatedly. Ok, it's one way to approach assessing an LR model. If the model meets your dataset requirement, then it isn't a viable model and we can discard it.

But what if it's a viable model (which is the only sort of LR models that we're interested in)? We don't really need a numerical test to determine this. If the LR formulation reduces to the qm expectation value, then it's viable, and we also then know that it has to be a non-Bell-like LR model. But, that in itself, in the absence of a logical proof that Bell's (2) is the generalized LR form, doesn't automatically disqualify it. (Note that I do think that Bell's stuff is general, but I don't know how to prove it. If you're aware of anybody who has proved it, then that would certainly save us some time.)

Whether or not it might be deemed explicitly local and realistic (and it has to be explicitly local and realistic -- not just a weird algebraic workaround of the sort that Christian offers, and not just an interpretation of the qm formalism that ultimately offers the qm expectation value without an ansatz whose content is explicitly realistic and whose form is explicitly local) requires looking at the content and form of the proposed LR formalism, and not just plugging numbers into a qm-compatible reduced version of it.

You just say something is realistic without providing support, as does JenniT and Gordon.

Where?

As for Gordon, we'll be holding him to task regarding the viability, realism and locality of his model. I have no doubt at this time that it's going to fail at least one of those tests.

 

[Gordon Watson]

is not semantics, we are talking about the existence, you are arguing that
the moon is not there if nobody observes it (someone has to watch it to exist, for be there).

you state: the electron need have a spin value, if not, the electron is not real.
there are two very different things, is not semantics.
I say the electron exists, have or not a definite spin value.

There's an important subtlety here, imho, which I endorse in the context of the following quote from Bell (re spin-1/2 particles being unpolarized):

"Some people ... may have come to think of the result of a spin measurement on an unpolarized particle (and each particle, considered separately IS unpolarized here) as utterly indefinite until it has happened." Bell's emphasis, in Einstein-Podolsky-Rosen experiments (1976).

So, for me: Particles exist, with or without a definite polarization; entangled particles in the singlet state being unpolarized.

When discussing L*R, with its generality across spin-1/2 and spin-1, I speak of both the photon-polarizers and the SGMs as polarizers. And in L*R, all pristine entangled particles are taken to be unpolarized. I therefore speak of each particle's total spin (total angular momentum), involving the intrinsic and extrinsic spin.

The mental picture that I have is this: On interaction with a polarizer, such pristine particles ("gyroscopic" in nature) have their extrinsic spin burnt off (as envisaged in macroscopic micro-wave polarizers) and their intrinsic spin re-oriented. (It works for me. But is this view-point -- with its mental picture and dynamics -- anathema to a quantum-physicist?)

But two things re terminology:

1. Whatever ones view, particles exist!

2. Though unpolarized, the pristine singlet-entangled particles still have definite properties!

I take the realism (in "local realism") to be the combination of these two facts. Which, I suspect, goes beyond the "strict realism" that we might find in philosophy.

So maybe the question is this: Can we, or should we, non-philosophers improve our terminology? To bring philosophers into the discourse more easily? To thus enlighten them. Certainly I take the view: The moon exists, even if no one looks.

 

[DrChinese]

is not semantics, we are talking about the existence, you are arguing that
the moon is not there if nobody observes it (someone has to watch it to exist, for be there).

I never argued the moon isn't there when it is not being observed. Sheesh!

The Moon analogy is Einstein's, and is just an analogy! QM makes no statement about the existence of particle properties beyond the context of the Heisenberg Uncertainty Principle. Generally, the idea is that properties do not exist outside of an observation.

 

[DrChinese]

So maybe the question is this: Can we, or should we, non-philosophers improve our terminology? To bring philosophers into the discourse more easily? To thus enlighten them. Certainly I take the view: The moon exists, even if no one looks.

I think a closer reading of the literature will make clear: this is an analogy only, and no one is supposed to doubt the existence of a moon or a particle when it is not being observed. The only question is whether particles have definite properties outside of the context of an observation. The accepted answer to this is: NO, and the Heisenberg Uncertainty Principle correctly details the limits of particle properties.

 

[yoda jedi]

the idea is that properties do not exist outside of an observation.

Thats All.

PROPERTIES.



Realism:
Real because of its existence and not because of any properties it has.






.

 

[Maui]

Thats All.

PROPERTIES.



Realism:
Real because of its existence and not because of any properties it has.






.

When you made that claim, were you aware that that claim was cast out of iron and was consistent with everything we've come to know from experiments? It's impossible to argue against becuase the experiments directly support it(see the SQUID macroscopic quantum superposition experiment for a new definition of existence).

It's time physicists turn their attention to the very notion of existence, as the old ideas are plain wrong. There is no requirement that existence be local-realistic, is there? And it all comes down to why there is something instead of nothing, doesn't it?

 

[Maui]

I never argued the moon isn't there when it is not being observed. Sheesh!

The question is - Would you be willing to bet more than $1 that it is? All this talk that separates real from non-real and existing from non-existing is entirely human-made, isn't it?

 

[ThomasT]

I never argued the moon isn't there when it is not being observed. Sheesh!

The Moon analogy is Einstein's, and is just an analogy! QM makes no statement about the existence of particle properties beyond the context of the Heisenberg Uncertainty Principle. Generally, the idea is that properties do not exist outside of an observation.

I think a closer reading of the literature will make clear: this is an analogy only, and no one is supposed to doubt the existence of a moon or a particle when it is not being observed. The only question is whether particles have definite properties outside of the context of an observation. The accepted answer to this is: NO, and the Heisenberg uncertainty principle correctly details the limits of particle properties.

I agree with this. Obviously, something exists independent of measurement. But to what extent do we instrumentally (including our own sensory 'instrumentation') create/fashion the 'properties' that we talk and make theories about?

Anyway, I'm engaged in closer, more extensive reading of the literature on Bell, etc., after not being able to shake the feeling that I'm missing something. I see you haven't replied to my latest posts in this thread. Good. No need to until I rethink things. Also, read your Bell's Theorem and Negative Probabilities. Looks ok, and somewhat unique, though I prefer more, er, conventional treatments of BT. Found some literature that seems pertinent to it, and an old thread on it. If I decide to nitpick because not sure of some part of your rationale is it ok to necropost in that thread (nice discussion by the way), or should I start a new one?

Anything I might have said about Gordon's LR proposal is thus put on hold, but will watch this thread for interesting developments. Thanks to all.

 

[JesseM]

Hi Gordon, I've been on a trip for the last week without a lot of time to post here, should be back to regular posting by the beginning of April. In the meantime I'll give a brief comment on your question here:

My immediate question relates to this: there should be no "irreducibly nonlocal" facts in the universe which cannot even in principle be deduced from the complete set of local facts.

It is not an impediment to any analysis of my model, but it seems to me that it could be worded more clearly? Could you put it another way? Some clarifying punctuation, maybe?

Many thanks, as always; and henceforth to be understood.

When I referred to "irreducibly nonlocal" facts it was in reference to this comment to ThomasT elaborating on my definitions 1) and 2):

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.

A physical that is not specifically associated with a single point in space and time, like the magnetic flux through an extended surface or the state vector of a multiparticle system, would be what I call a "nonlocal fact". But some nonlocal facts are reducible to a collection of local facts in the sense above--that if you know some set of local facts in an extended region, the nonlocal fact is simply a function of these local facts, so in principle the nonlocal fact could always be determined from the local facts without any additional information being required. An "irreducibly nonlocal" fact would just be a fact that is not reducible to a collection of local facts in this sense. Whether or not there are any such nonlocal facts in physics is something we can't know for sure without knowing the most fundamental laws of physics, but one can at least imagine a universe in which there are irreducibly nonlocal facts which evolve according to their own rules and which influence the local facts, but the state of the nonlocal variables at any given moment can't be determined from the local facts alone. I am assuming in 1) that there aren't any irreducibly nonlocal facts in this sense, that all nonlocal facts must be in principle reducible to sets of local ones.

 

[yoda jedi]

...Particles exist, with or without a definite polarization...

Right, Realism have nothing to do with properties, qualities, values.

 

[JesseM]

There seems to be a major misunderstanding here. Not about my understanding of current beliefs, but about the next bit, which I'll rephrase as a question:

Q: Does GW really believe that he can come up with a local realist model that gives probabilities for P1-P8 which is "as one with QM"?

A: Yes; as has been shown in PDF2 (Table 1, Table 2, and notes thereto). So, in fact, GW believes that he has (beyond can) already come up with a local realist model that gives probabilities for P1-P8 which is "as one with QM"?

So can you please address my point that the formulas in Table 1 are clearly incompatible with those in Table 2, as shown by my numerical example in [post=3159151]post 71[/post] (which you never responded to, and you also didn't respond to my specific request to address this in post 90)?

More generally, your formulas in Table 1 are simply the ones predicted by QM, there is no possible way you could ever come up with a list of probabilities P1-P8 that reproduce the QM probabilities, based simply on the argument on the Bell inequality page[/url] which you have never really addressed:

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.

Is there some part of this argument you don't understand? If you understand it but think the logic is flawed, can you tell me which of these points 1-4 you disagree with? Also, please note here that the angles are considered to be defined relative to some fixed coordinate system, so there can be no notion that any of the probabilities P(a+, b+|ab), P(a+, c+|ac), P(c+, b+|cb) are defined as "averages" of different pairs in P1-P8 as opposed to the simple formulas in 1. If you want to dispute this point and continue to talk about "bi-angles", "reference frames" and other such nonsense, please reread my post #88, and respond to this section in post #92:

OK, as noted above I don't know what terms like P(ab++|a) even mean, and if it's something to do with changing how you label angles from one trial to another, I don't really want to know. Unless you are making the totally crackpot argument that proving Bell wrong requires this sort of relabeling (in which case I really have no interest in trying to reason with you), please just adopt the standard practice of picking a single way to label angles and sticking with it through all trials. Note that I already asked you to do this in two separate posts...in post #25 I said:

Look, if you want to talk about angles there's no need for some convoluted notion of defining them relative to one another and picking one as a "reference angle", just do what is always done when talking about angles in physics, and define them relative to some fixed coordinate system! You could have a long straight rod stretching from one experimenter to the other whose position never changes and which is taken to define the x-axis of your coordinate system, and then the angle of the polarizer could just be defined as the angle relative to the rod, and then if you started the polarizer out parallel to the rod you could just see how many degrees you have to rotate it counterclockwise before it reaches the desired orientation, and call that the "angle" of the desired orientation. In this case every orientation would have a well defined angle, like a=70, b=30 and c=10, and then a difference between two angles like ac could just be defined as one minus the other, so ac=a-c while ca=c-a and so forth. In this case it's clear that ac=ab+bc is true since (a-c)=(a-b)+(b-c), while ac=ab-bc is false since (a-c)=(a-b)-(b-c)=a-2b+c which doesn't work. Given my example angles above you can see that ac=70-10=60, ab=70-30=40, and bc=30-10=20, so clearly ac=ab+bc does work since 60=40+20, but ac=ab-bc doesn't since 60 is not equal to 40-20.

I really hope your entire argument doesn't reduce to an incoherent notation for labeling angles...if not, then please just phrase your argument in terms of the standard type of coordinate-based angular notation I describe above.

And in post #29 I said:

I would like you to use the standard type of notation for angles, where individual angles are defined relative to some fixed coordinate angles and differences between two angles are defined in some fixed way, like ab=a-b. If you think the terminology of "bi-angles" still makes sense in this context, then please explain clearly what you mean, hopefully using a numerical example where we have definite angles for a,b,c and can thus calculate any angles like ab and ac.

...

Your notion of "focusing" on 2 angles or "reference angles" are similarly incomprehensible to me, I'm just talking about angles in the standard way that physicists always talk about angles, defining them relative to some fixed coordinate system, see post #25. As I requested there, I would like you to start using this sort of standard definition of angles as well, if your argument really revolves around saying there is something fundamentally flawed about defining angles relative to a fixed coordinate system and that we must use your incomprehensible alternative definitions, then your argument really is hopelessly crackpot and I am not interested in continuing.

Will you agree to this, and not refer me to any arguments or equations involving changing definitions of which orientation is at an angle of 0 and what the angles of the other two orientations are?

Please respond to that question at the end ("Will you agree to this..."): this should take precedence over all other responses to questions in my post. I really, really, don't want to continue to hear arguments involving "bi-angles", using different "reference frames" on different trials which label the three possible orientations with different angles, and so forth; if you cannot restate your argument in terms of a fixed coordinate system, then clearly what you are talking about has nothing to do with refuting Bell's own argument since he (and every other physicist who uses the same type of notation) was assuming a fixed coordinate system where the angles associated with each of the three physical orientations are constant from trial to trial.

 

[DrChinese]

Right, Realism have nothing to do with properties, qualities, values.

That might be OK for a philosophy forum. Here, we are discussing local realism and that definition does not apply. All you need is to read Einstein's definition:

"I think that a particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it."

He is talking about particle properties: spin, location and so forth...

Hopefully this makes it clear. No one - in the discussion of realism (in the quantum sense used here) - is debating whether particles themselves exist independently of observation. It is a matter of applying the HUP.

 

[yoda jedi]

That might be OK for a philosophy forum. Here, we are discussing local realism and that definition does not apply. All you need is to read Einstein's definition:

"I think that a particle must have a separate reality independent of the measurements. That is: an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it."

He is talking about particle properties: spin, location and so forth...

completely wrong.
values are defined by
Counterfactual Definiteness.
i.e the definiteness of the results of measurements that have not been performed.


.

 

[DrChinese]

values are defined by
Counterfactual Definiteness.
i.e the definiteness of the results of measurements that have not been performed.

.

You can also say a dog is a cat. Here is a definition of Realism from an experimental paper from the past few days (I started a separate thread on the paper itself because it supplies strong evidence against Realism):

"Reality": The state of any physical system is always well defined, i.e. the dichotomic variable Mi(t), which tells us whether (Mi(t) = 1) or not (Mi(t) = 0) the system is in state i, is, at any time, Mi(t) = {0, 1}.

This from Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations. And you could find similar definitions or Realism in hundreds of papers. Not that the definition would be much different than that of Counterfactual Definiteness.

But you ARE using the term "Realism" incorrectly in this forum. If you would care to provide a quote from an authoritative quantum physics source to back up your view, go for it.

 

[yoda jedi]

You can also say a dog is a cat.

But you ARE using the term "Realism" incorrectly

I agree that Counterfactual Definiteness - as you mention - might be a better term.

....

 

[DrChinese]

....

Yes, that's correct: you added nothing to my quotes.

Hopefully, that ends this useless rabbit trail.

 

[Gordon Watson]

Hi Gordon, I've been on a trip for the last week without a lot of time to post here, should be back to regular posting by the beginning of April. In the meantime I'll give a brief comment on your question here:

When I referred to "irreducibly nonlocal" facts it was in reference to this comment to ThomasT elaborating on my definitions 1) and 2):

A physical that is not specifically associated with a single point in space and time, like the magnetic flux through an extended surface or the state vector of a multiparticle system, would be what I call a "nonlocal fact". But some nonlocal facts are reducible to a collection of local facts in the sense above--that if you know some set of local facts in an extended region, the nonlocal fact is simply a function of these local facts, so in principle the nonlocal fact could always be determined from the local facts without any additional information being required. An "irreducibly nonlocal" fact would just be a fact that is not reducible to a collection of local facts in this sense. Whether or not there are any such nonlocal facts in physics is something we can't know for sure without knowing the most fundamental laws of physics, but one can at least imagine a universe in which there are irreducibly nonlocal facts which evolve according to their own rules and which influence the local facts, but the state of the nonlocal variables at any given moment can't be determined from the local facts alone. I am assuming in 1) that there aren't any irreducibly nonlocal facts in this sense, that all nonlocal facts must be in principle reducible to sets of local ones.

Welcome back. I too am constrained somewhat until early April, so let's look forward to some real progress then.

And thanks for the above clarification. Personally, I see no need anywhere to use any word associated with "nonlocal" concepts.

Your reply above, it seems to me, shows that we should get along just fine. Me not using such terms; and me understanding what you mean might mean in such contexts.

Thanks again.

 

[Gordon Watson]

You can also say a dog is a cat. Here is a definition of Realism from an experimental paper from the past few days (I started a separate thread on the paper itself because it supplies strong evidence against Realism):

"Reality": The state of any physical system is always well defined, i.e. the dichotomic variable Mi(t), which tells us whether (Mi(t) = 1) or not (Mi(t) = 0) the system is in state i, is, at any time, Mi(t) = {0, 1}.

This from Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations. And you could find similar definitions or Realism in hundreds of papers. Not that the definition would be much different than that of Counterfactual Definiteness.

But you ARE using the term "Realism" incorrectly in this forum. If you would care to provide a quote from an authoritative quantum physics source to back up your view, go for it.

DrC, with respect to this bit:

<"Reality": The state of any physical system is always well defined, i.e. the dichotomic variable Mi(t), which tells us whether (Mi(t) = 1) or not (Mi(t) = 0) the system is in state i, is, at any time, Mi(t) = {0, 1}.>

How would this apply to EPRB systems where the 2 pristine particles are pair-wise correlated by conservation of total angular momentum? With no two pairs the same?

In Bell's terms, as I understand him: they are unpolarized.

And when Einstein refers to their spin, he no doubt refers to their intrinsic spin. It being a giant leap to think that he referred to total spin?

So what dichotomic variable are we discussing in the context of the above quote and EPRB?

Thanks.

 

[Gordon Watson]

So can you please address my point that the formulas in Table 1 are clearly incompatible with those in Table 2, as shown by my numerical example in [post=3159151]post 71[/post] (which you never responded to, and you also didn't respond to my specific request to address this in post 90)?

More generally, your formulas in Table 1 are simply the ones predicted by QM, there is no possible way you could ever come up with a list of probabilities P1-P8 that reproduce the QM probabilities, based simply on the argument on the Bell inequality page[/url] which you have never really addressed:

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.

Is there some part of this argument you don't understand? If you understand it but think the logic is flawed, can you tell me which of these points 1-4 you disagree with? Also, please note here that the angles are considered to be defined relative to some fixed coordinate system, so there can be no notion that any of the probabilities P(a+, b+|ab), P(a+, c+|ac), P(c+, b+|cb) are defined as "averages" of different pairs in P1-P8 as opposed to the simple formulas in 1. If you want to dispute this point and continue to talk about "bi-angles", "reference frames" and other such nonsense, please reread my post #88, and respond to this section in post #92:

Please respond to that question at the end ("Will you agree to this..."): this should take precedence over all other responses to questions in my post. I really, really, don't want to continue to hear arguments involving "bi-angles", using different "reference frames" on different trials which label the three possible orientations with different angles, and so forth; if you cannot restate your argument in terms of a fixed coordinate system, then clearly what you are talking about has nothing to do with refuting Bell's own argument since he (and every other physicist who uses the same type of notation) was assuming a fixed coordinate system where the angles associated with each of the three physical orientations are constant from trial to trial.

Jesse, in response to your primary question: This is interim only, but it bears repeating to keep hopes alive:

1. If you derive any contradiction with QM, you have made a mistake.

2. If you derive a contradiction, any contradiction, you have made a mistake.

3. These claims are not from arrogance, but from careful checking.

4. Each particle faces, and responds to, a detector ORIENTATION. Each independently responding to whatever setting Alice and Bob may have chosen, respectively; any correlations in the outcomes arise from their pristine correlation in the singlet state.

5. The Source has no memory of, nor info re any orientation. The particles are absorbed after responding to a particular orientation; they pass no info on. Angles, between the respective two orientations in each test on a particle pair, are clearly defined.

6. The angle ab (say 90 degrees) may be oriented any which way, in an infinity of orientations. Examples on a clock-face: 12-3, 1-4, 2-5, 3-6, 6-9, 12-9, 9-6.

7. The correlations for such are always the same, being functions of sab only.

This simply to reassure you for now that there are no games being played. And that all questions will be answered. Thanks.

PS: I will respond in complete detail -- ASAP -- early April.

 

[DrChinese]

DrC, with respect to this bit:

<"Reality": The state of any physical system is always well defined, i.e. the dichotomic variable Mi(t), which tells us whether (Mi(t) = 1) or not (Mi(t) = 0) the system is in state i, is, at any time, Mi(t) = {0, 1}.>

How would this apply to EPRB systems where the 2 pristine particles are pair-wise correlated by conservation of total angular momentum? With no two pairs the same?

In Bell's terms, as I understand him: they are unpolarized.

And when Einstein refers to their spin, he no doubt refers to their intrinsic spin. It being a giant leap to think that he referred to total spin?

So what dichotomic variable are we discussing in the context of the above quote and EPRB?

Thanks.

Electron Alice and electron Bob are entangled. Therefore if you measure the spin of Alice and Bob at 0 degrees with a suitable apparatus, you will obtain as results from {0,1} for Alice and {1,0} for Bob. I.e. Alice+Bob=1, that follows the conservation rule. In fact, if you measure this pair at the same angle for any angle within 360 degrees, you obtain the same. However, the values for a stream of Alices will appear purely random, as will those for a stream of Bobs.

One might naturally conclude that in a local realistic world, this is simply due to the fact that the outcomes of the measurements at any angle setting are effectively predetermined. So if we imagined the angle settings as a wheel with many spokes: each spoke for Alice is paired with a matching spoke for Bob, such that a +1 for Alice matches a 0 for Bob - and vice versa. Perhaps there are 360 "spokes", who knows. At any rate, the spoke values would presumably be different from pair to pair, which explains the random results.

With that analogy in mind, I would conclude that the spokes are arranged in some manner such that the cos(theta) rule emerges over a sufficiently large sample. I have no idea how such would be constructed, but I simply have "faith" that such a mechanism is possible. Prior to Bell, this analogy - and vision of Realism - would have been held by many if not most physicists.

 

[yoda jedi]

Yes, that's correct: you added nothing to my quotes.

of course, just exposing your madness...

 

[ThomasT]

of course, just exposing your madness...

I've come to find DrC's madness rather enlightening ... at least when he takes the time to elaborate and clarify.

 

[DrChinese]

of course, just exposing your madness...

I have come to live with it, sort of like a little friend...

 

[yoda jedi]

I have come to live with it, sort of like a little friend...

a very incoherent friend...