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

[Gordon Watson]

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.

A reference orientation is any pre-agreed orientation of a detector in a Bell-test experiment, the experimenters (Alice and Bob) having here pre-agreed to three such orientations. (Thank you.)

The conditioning space in P(X|C) is C; as usual. And, as usual, the boundary conditions on the experiment are implied. So, as I believe is customary, only special conditions are included specifically. Since P(ab++|ab) differs from P(ab++|c), the model includes both. P(ab++|ab) is the probability of ab++ when correlated across the angle ab. P(ab++|c) arises from the use of frames of reference in the model, as in my reply to vanesch. I'll address this when I revise; in that I will be removing the Bell-test objection that you raise with regard to multiple tests.

I honestly expected no resistance to ADDITIONAL tests, over all 3 reference orientations. And thought it (for present purposes), better, less novel, than introducing the local-realistic basis for L*R. Will fix.

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

PDF2, Page 7.

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.

PDF2 was written to correct the hurried mess that was the first PDF, with its short-cuts; including short-cutting the conditioning space on any P; noting that all P are conditional to me, in that some conditions are inevitably implied or explicit. So, with apologies, PDF2 now spells out every calculation. Which will bring you to those darned angles.

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".

I thought that, when the L*R tests are conducted over every Bell-test detector setting (as they are; see Tables A1-A3), all we would have (and agree upon) is a more complete set of Bell-tests. I did not expect an objection to MORE tests; any component of which is a component of a Bell-test.

As for tigers: I thought that I was breeding Bell-tests.

So, for me, the question remains: Given that Table 2, PDF2, will remain unchanged, and since it applies to any Bell-test that you might nominate, how will a Bell Inequality be constructed?

To take a common example: How will P(ab++|ab) be yoked to P(ac++|ac) and P(bc++|bc)? The model being as one with QM in this respect?

It seems to me that these considerations will eventually move us to enquire: Is the model truly local and realistic?

That is: Local and realistic in line with Einstein's ideas and expectations? Me believing that he was not happy with the EPR elements of reality (too naive, imho), me understanding that he makes no mention of them in his work?

 

[JesseM]

A reference orientation is any pre-agreed orientation of a detector in a Bell-test experiment, the experimenters (Alice and Bob) having here pre-agreed to three such orientations. (Thank you.)

The conditioning space in P(X|C) is C; as usual. And, as usual, the boundary conditions on the experiment are implied. So, as I believe is customary, only special conditions are included specifically.

Yes, that's how conditional probability normally works, you don't include conditions which are present in all trials (like facts about the experimental setup which don't change), you only include conditions which can vary from one trial to another. But then I don't understand why you write:

Since P(ab++|ab) differs from P(ab++|c), the model includes both.

P(ab++|ab) means we are looking at only the subset of trials where Alice chose angle "a" and Bob chose angle "b", correct? But then what does P(ab++|c) mean? If c is supposed to be the "reference orientation", you just said the "reference orientation" was "pre-agreed", so it shouldn't change from one trial to another. Does c here not represent the choice of which orientation to call the "reference orientation" but rather the actual detector setting chosen by Alice or Bob on a trial? If so, who chose c, Alice or Bob? Or both? You really need to explain your notation more when it departs from the standard notation.

P(ab++|ab) is the probability of ab++ when correlated across the angle ab.

"correlated across angle ab" is an odd way of phrasing it, do you mean the same thing as I meant, i.e. the probability they both get result "+" in the subset of trials where Alice chose to set her SG device at the orientation "a" and Bob chose to set his SG device at the orientation "b"?

P(ab++|c) arises from the use of frames of reference in the model, as in my reply to vanesch.

There is no need to consider multiple "frames of reference", we can just use a single physical standard for labeling the three possible orientations, as I said in this comment:

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)

I'll address this when I revise; in that I will be removing the Bell-test objection that you raise with regard to multiple tests.

I honestly expected no resistance to ADDITIONAL tests, over all 3 reference orientations.

I have no idea what you mean by "over all 3 reference orientations", is this something to do with your bizarre notions about "bi-angles" and multiple "coordinate systems"? You seem to want to play a weird shell game where you try to "win" by using different labels for the same physical orientations on different trials, but surely you understand that a mere re-labeling is not going to change the actual results of any physical experiment. Why not accept the standard practice in physics of using a single scheme for labeling angles of physical objects, rather than developing some completely weird and idiosyncratic labeling scheme that makes everything far more complicated for no apparent reason?

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

Page 7; it's safe; no tigers lurking.

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?

PDF2 was written to correct the hurried mess that was the first PDF, with its short-cuts; including short-cutting the conditioning space on any P; noting that all P are conditional to me, in that some conditions are inevitably implied or explicit. So, with apologies, PDF2 now spells out every calculation. Which will bring you to those darned angles.

PDF2 involves a lot of incomprehensible notation and terminology such as "bi-angles" and "P(ab++|c)". In your reply to me, assuming we are using a fixed coordinate system where the angles assigned to each orientation are a=240,b=120,c=0, can you please show what values you would calculate for P3, P4 and P(ab++|ab) given these angles?

I thought that, when the L*R tests are conducted over every Bell-test detector setting (as they are; see Tables A1-A3), all we would have (and agree upon) is a more complete set of Bell-tests. I did not expect an objection to MORE tests; any component of which is a component of a Bell-test.

This is all totally incomprehensible to me, as I did not object to "more tests", I objected to the notion (which seemed implicit in your "bi-angles" terminology and in Fig. 1) that in a single series of trials the physical meaning of a given label like "b" might be different on some trials than others (on some it might mean the SG device was aligned with 2 o'clock, on some it might mean it was aligned with 10 o'clock...again, that's what Fig. 1 seems to show). Bell inequalities are only meant to apply to a series of trials where the experimenters were picking between a set of three physical orientations which are labeled in a consistent way, of course you could first do a series of trials #1 where the orientations were a=240,b=120,c=0 and a series of trials #2 where the orientations were a=30,b=20,c=0, but each series would have a separate Bell inequality it would be expected to satisfy under local realism, Bell wouldn't say that local realism demands that when you combine the data from both series that the combined dataset must still satisfy a Bell inequality.

So, for me, the question remains: Given that Table 2, PDF2, will remain unchanged, and since it applies to any Bell-test that you might nominate, how will a Bell Inequality be constructed?

Table 2 simply gives the standard QM probabilities, what I don't believe is that you can derive Table 2 from any table like Table 1 that gives specific values for P1-P8 and is thus compatible with local realism. If you disagree, please address my specific example of a=240,b=120,c=0, and tell me what values you would get for P3 and P4 given these angles. From Table 1 it seems you should get P3=0.9375/6=0.15625 and P4=0.15625, so that if P(ab++|ab)=P3+P4 this would imply P(ab++|ab)=0.15625 + 0.15625 = 0.3125, but Table 2 says that P(ab++|ab)=Sab/2 which for these angles is equal to 0.375.

To take a common example: How will P(ab++|ab) be yoked to P(ac++|ac) and P(bc++|bc)? The model being as one with QM in this respect?

Um, the whole point of the argument is that none of us believe you can come up with a local realist model that gives probabilities for P1-P8 which is "as one with QM". Do you really not understand the really really basic point that all Bell inequalities are supposed to be claims about what must be true under local realism, not about what is predicted by the QM probabilities?

It seems to me that these considerations will eventually move us to enquire: Is the model truly local and realistic?

That is: Local and realistic in line with Einstein's ideas and expectations? Me believing that he was not happy with the EPR elements of reality (too naive, imho), me understanding that he makes no mention of them in his work?

I have my doubts that you understand either "the EPR elements of reality" or the standard notion of "local realism"--perhaps you could explain what aspects you find "naive" so we could see if you are addressing what these ideas actually mean or just some strawman version.

 

[Gordon Watson]

I have my doubts that you understand either "the EPR elements of reality" or the standard notion of "local realism"--perhaps you could explain what aspects you find "naive" so we could see if you are addressing what these ideas actually mean or just some strawman version.

Excuse me for chopping up you last post here. All points will be answered. I just want to separate out some non-mathematical issues first.

I call "naive" any local realism that does not allow that a measurement may perturb the measured system. My view makes me wary of the way some interpret the EPR paper; i.e., when they conclude that if particle 1 is measured to be spin-UP, then particle 2 is spin-UP prior to its measurement. (In my view, a measurement of one reveals an equivalence class for the other -- which is quite a different statement -- and one which I trust will not side-track us here from moving to a focus on my maths.)

By "locality", I follow Einstein (1949): " ... the real factual situation of the system S2 is independent of what is done with system S1, which is spatially separated from the former."

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.

Does this remove your concern in this area?

 

[JesseM]

Excuse me for chopping up you last post here. All points will be answered. I just want to separate out some non-mathematical issues first.

I call "naive" any local realism that does not allow that a measurement may perturb the measured system. My view makes me wary of the way some interpret the EPR paper; i.e., when they conclude that if particle 1 is measured to be spin-UP, then particle 2 is spin-UP prior to its measurement. (In my view, a measurement of one reveals an equivalence class for the other -- which is quite a different statement -- and one which I trust will not side-track us here from moving to a focus on my maths.)

I agree with you, there's no need to take this "naive" view that measurements are simply revealing properties of the particle that were exactly the same before measurement. I haven't looked at the EPR paper lately so I can't say for sure that they avoid this naive view, but from my reading of Bell's own work I'm confident that his version of local realism did not take such a naive view. In post #20 I gave my summary of how I understand "local realism", which I think matches Bell's conception:

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).

Then in post #83 I offered the following clarification to ThomasT about the meaning of 1):

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.

The "local facts" referred to in 1) might or might not be facts about the values of measurable quantities like position and spin, there is no requirement that they correspond in any such direct way to measurable quantities (and if they do, there is certainly no requirement that the value of this quantity at a point on the particle's worldline immediately before measurement is the same as its value at a point immediately after measurement). All that's required in my clarification to ThomasT is that a fact about a measurement performed in some finite region of spacetime, like "we measured the particle and got result spin-up", would be in principle deducible from the complete set of all local facts about points in spacetime within that finite region, there should be no "irreducibly nonlocal" facts in the universe which cannot even in principle be deduced from the complete set of local facts.

By "locality", I follow Einstein (1949): " ... the real factual situation of the system S2 is independent of what is done with system S1, which is spatially separated from the former."

And would you agree that the "real factual situation" cannot be "irreducibly nonlocal" as I defined it above? That whatever the "real factual situation" about some well-defined region of spacetime, it must ultimately boil down to a collection of real factual situations about each point in spacetime within that region?

Also, Einstein's statement requires some clarification, it's not just that they are "spatially separated" in the ordinary sense of being at different positions in space, but that we are talking about two regions of spacetime with a spacelike separation, so that we are not talking about the factual situation about one system in a region of spacetime that's in the past light cone of the region of spacetime of the other system. After all, if S1 was in the past light cone of S2 then facts about S1 could have a causal influence on facts about S2, so they wouldn't necessarily be statistically "independent". That's why I defined point 2) in terms of light cones above.

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.

As long as you agree with the above point that this external reality can in principle be boiled down to a collection of local facts about each point in spacetime, and the other point that there must be a spacelike separation between two sets of local facts for them to be considered truly independent, then I think your definition shouldn't be any different from mine above. But please tell me if you have any objections to (or questions about) my definition of local realism (which I'm pretty sure matches up with Bell's notion), if you think there's any way in which it differs from your own.

 

[Gordon Watson]

I agree with you, there's no need to take this "naive" view that measurements are simply revealing properties of the particle that were exactly the same before measurement. I haven't looked at the EPR paper lately so I can't say for sure that they avoid this naive view, but from my reading of Bell's own work I'm confident that his version of local realism did not take such a naive view. In post #20 I gave my summary of how I understand "local realism", which I think matches Bell's conception:

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).

Then in post #83 I offered the following clarification to ThomasT about the meaning of 1):

The "local facts" referred to in 1) might or might not be facts about the values of measurable quantities like position and spin, there is no requirement that they correspond in any such direct way to measurable quantities (and if they do, there is certainly no requirement that the value of this quantity at a point on the particle's worldline immediately before measurement is the same as its value at a point immediately after measurement). All that's required in my clarification to ThomasT is that a fact about a measurement performed in some finite region of spacetime, like "we measured the particle and got result spin-up", would be in principle deducible from the complete set of all local facts about points in spacetime within that finite region, there should be no "irreducibly nonlocal" facts in the universe which cannot even in principle be deduced from the complete set of local facts.

And would you agree that the "real factual situation" cannot be "irreducibly nonlocal" as I defined it above? That whatever the "real factual situation" about some well-defined region of spacetime, it must ultimately boil down to a collection of real factual situations about each point in spacetime within that region?

Also, Einstein's statement requires some clarification, it's not just that they are "spatially separated" in the ordinary sense of being at different positions in space, but that we are talking about two regions of spacetime with a spacelike separation, so that we are not talking about the factual situation about one system in a region of spacetime that's in the past light cone of the region of spacetime of the other system. After all, if S1 was in the past light cone of S2 then facts about S1 could have a causal influence on facts about S2, so they wouldn't necessarily be statistically "independent". That's why I defined point 2) in terms of light cones above.

As long as you agree with the above point that this external reality can in principle be boiled down to a collection of local facts about each point in spacetime, and the other point that there must be a spacelike separation between two sets of local facts for them to be considered truly independent, then I think your definition shouldn't be any different from mine above. But please tell me if you have any objections to (or questions about) my definition of local realism (which I'm pretty sure matches up with Bell's notion), if you think there's any way in which it differs from your own.

Jesse, this is fantastic stuff for me, and I want to do all that I can to keep it coming -- hopefully to the point of a full consensus between us. And I continue to marvel at your "fluency" (efficiency) across various threads. (I need to lift my game in that area.)

But here's my problem: I neatly began to "itemize" your prior post, to begin developing the clearest possible answers (having nothing to hide, and keen to learn). Then BANG, another set of "itemizations" required, and I haven't finished with the first post!

NOW, that's my problem, so please do not change your style. Keep pumping the info and questions out; and chase me up on any point not clear or missed.

I just want to be clear why I will sometimes appear to be guarded in my answers; why I may appear to be over-cautious in some replies: I want to reassure you that my ideas are grounded in a great deal of good sense, so that that you will move ahead with more facts and probing questions.

I will cover them all, as the thread progresses. And, for me, seeing the consequences that might be (improperly) associated with some of my early answers, I can clarify such points as I go.

SO, to the point, on your latest post:

I cannot immediately see where we disagree; or might disagree.

I certainly accept that added "space-like" requirement without question. And if I'd found an old paper of mine (as I now have), I would simply have cut and pasted this (re photons, hence the nu):

"That is, following Einstein: The real factual situation of a system v [nu] is independent of what is done to system v' that is space-like separated from it," (Einstein 1949).

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.

 

[Gordon Watson]

THIS IS THE LAST POST BY JenniT

This will be my last post at PF.

As some of you know, from private communications, I am the tentative alter ego of a keen PF supporter.

That supporter, my boyfriend, struggles with his writing. So I represent his attempt to develop a suitable "social-networking" style of expression and correspondence

That same boyfriend (it's our 4th anniversary on April 9) has proposed that we live together. And I've accepted.

We've been allocating duties, jobs, etc, via coin-tosses (and no funny-business ...) ever since, with these results:

Here's where I won: He moves into my flat next Saturday. I am to have lots of babies. I am to find affordable land in a happy valley by the sea to continue our research into developing heirloom fruit and vegetables that grow like weeds. I am to sort out his research in this area.

Here's where he lost: He is to be the bread-winner. He is to make lots of babies, starting next Saturday. (Yes, truly; we start then!) He, poor boy, is to sort out my messy interests in physics.

In closing: I would like to sincerely thank every PF participant that has contributed to my knowledge and experience and learning here; especially those who might have thought that we were squabbling; or me too cheeky ... sometimes. I apologize for such shortcomings, though I do believe that I learn best when it's fun.

I thank Greg for creating PF, and for his efficient administration. (I have advised him of my departure.)

I thank DrC and ThomasT for their informative inputs, and for their mutual goings-on; me seemingly at odds with them both.

I thank vanesch for sharing his knowledge, and the way he brings mathematics into his answers.

I especially thank JesseM for his patience, diligence and all-round competence and knowledge. He has helped me very much! "One day with a great teacher beats a thousand days studying solo."

I have learned a great deal at PF, and will watch from afar, now and then, with great interest.

Ciao, for now,

XOXOXOXOX

JenniT

 

[Gordon Watson]

This is the first post by Gordon Watson.

Symbolically turning over a new leaf, as a reminder to myself, I would like to assure readers of this thread re two things:

1. All questions will be answered in due course.

2. I will certainly acknowledge that penultimate post, should there be such, that sinks the model definitively.

With best regards,

Gordon Watson

 

[ThomasT]

The "local facts" referred to in 1) might or might not be facts about the values of measurable quantities like position and spin, there is no requirement that they correspond in any such direct way to measurable quantities (and if they do, there is certainly no requirement that the value of this quantity at a point on the particle's worldline immediately before measurement is the same as its value at a point immediately after measurement). All that's required in my clarification to ThomasT is that a fact about a measurement performed in some finite region of spacetime, like "we measured the particle and got result spin-up", would be in principle deducible from the complete set of all local facts about points in spacetime within that finite region, there should be no "irreducibly nonlocal" facts in the universe which cannot even in principle be deduced from the complete set of local facts.

And would you agree that the "real factual situation" cannot be "irreducibly nonlocal" as I defined it above? That whatever the "real factual situation" about some well-defined region of spacetime, it must ultimately boil down to a collection of real factual situations about each point in spacetime within that region?

so, Einstein's statement requires some clarification, it's not just that they are "spatially separated" in the ordinary sense of being at different positions in space, but that we are talking about two regions of spacetime with a spacelike separation, so that we are not talking about the factual situation about one system in a region of spacetime that's in the past light cone of the region of spacetime of the other system. After all, if S1 was in the past light cone of S2 then facts about S1 could have a causal influence on facts about S2, so they wouldn't necessarily be statistically "independent". That's why I defined point 2) in terms of light cones above.

Wrt my current understanding, Bell codifies your 1) via his 'continuous λ', and codifies your 2) via his locality condition.

Regarding 1):

The inclusion of a λ variable is necessary for the realism part of a Local Realistic (LR) model to be clearly evident in the model. That is, if it isn't explicitly realistic in that it includes explicit reference to a local hidden variable (λ), then by what criterion might the model be said to be realistic? I think the answer is that there is no other way to do it than by inclusion of λ. Without λ, then a proposed LR model lacks R. (Unless Gordon Watson is proposing some sort of non-Bell-like R, and can demonstrate why it should be considered R.) And it has therefore failed the first test in determining whether it's an LR model of entanglement.

The reason I said in an earlier post that 1) is not necessary wrt effective modelling of entanglement (whether everything is actually evolving according to local causality or not -- and of course we have no way of ascertaining that) is that we know that λ is irrelevant wrt determining coincidental photon flux. λ determines individual photon flux. A continuous λ allows us to trace the production of a relationship between λ_a and λ_b back to the emission process and codifies the assumption that this relationship had a local, common cause (eg., wrt Aspect, two photons are entangled, via conservation of angular momentum, via their emission by the same atom during the same atomic transition).

One hypothesis is that the inclusion of λ in a model of entanglement skews the range of statistical results that will be predicted by such a model independent of whether the evolution of the underlying reality excludes nonlocal transmissions.

But if no λ, then the model isn't LR. And if it includes R, then either L is encoded via R or an additional locality condition is required. Sort of a Catch-22 for LR diehards if the above hypothesis is correct -- since it's untestable.Regarding 2):

The inclusion of a λ variable still doesn't codify the causal independence of S1 and S2. For that we need some sort of locality condition. Bell's reduces to an expression of both causal and simple statistical independence. Hence, we have no way of knowing whether BIs are effectively experimentally violated via one or the other.Regarding Gordon Watson's (GW) proposed LR model:

What I would like to see is a clear exposition and explanation of GW's LR ansatz. If, at that stage, it's ascertained to be nonrealistic, then whether it reproduces qm results is moot, because it wouldn't be an LR model.

That is, I still don't understand exactly how GW's LR model is encoding realism and locality (ie., how it is making your, JesseM's, 1 and 2 explicit).

I also don't understand how realism and locality could be encoded (made clearly explicit) in any way other than the way Bell did it. In more or less recent threads this is what my fiddling with some way to specify the relationship between λ_a and λ_b without skewing the range of predictions had to do with.

So, unless GW is able to answer these questions, or demonstrate why a non-Bell-like LR formulation should be considered an LR formulation, then I'm compelled to take Bell's formulation as the archetypal LR model of entanglement -- thus, via Bell's demonstration, ruling out any and all LR models of entanglement.
[Note: The above considerations should make it clear why I think that Bell's theorem doesn't rule out the possibility that nature, including Bell tests and other realizations of quantum entanglement, is evolving locally. The fact that a viable model can be made which causally (via FTL or AAD) relates events in S1 and S2 is meaningless wrt what is actually happening at level(s) underlying instrumental results. Bottom line, we have no way of knowing, and assumptions/inferences of nonlocality aren't reasonable given the current situation in physics.]

 

[Gordon Watson]

Um, the whole point of the argument is that none of us believe you can come up with a local realist model that gives probabilities for P1-P8 which is "as one with QM".

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"?

Let me explain: Table 1 is NOT based on QM; it is based solely on local realism of the L*R variety. So it must be interpreted in that context. Table 1 cannot be based on current understandings in QM, because the conditioning space (CS) includes three orientations (a, b, c).

[Aside (which is where my writing too often goes astray): Are you happy to have the space C in P(X|C) called the conditioning space; CS, for short?]

Further, any sum over Table 1 must be (initially, until the sum is reduced), a sum of of Ps with CSs abc. Thus SUM = P(X|abc) + P(Y|abc) + ... .

Since QM tests currently range over only two orientations, these summations cannot be QM results. They are L*R results. The QM results are delivered by reducing the CS to any two orientations.

PDF2: Table 2 gives every possible 2-orientation outcome. Appendix A has everyone worked out in full detail. All agree with QM.

To be clear here: The first Boundary Condition (B/C) on L*R is local realism. The second B/C is that all testable results must accord with QM. If one or both of these B/Cs is not met, the model fails.

PS:

QM can test over two orientations and one angle.

L*R can test over three orientations and two angles -- via a thought-experiment. For that is how L*R was developed.

I trust this might help to remove some of our "Table 1 and 2 and QM-outcome" differences?

Do you really not understand the really really basic point that all Bell inequalities are supposed to be claims about what must be true under local realism, not about what is predicted by the QM probabilities?

I do understand this point. I am wondering where I appeared to not understand?

The predicted QM probabilities are simply a B/C on the L*R predictions. If they are not "as one", then the model fails.

But look at your second point: "all Bell inequalities are supposed to be claims about what must be true under local realism." Again, where do we differ? They are supposed to be.

They are "supposed to be, and are widely believed to be" claims about what must be true under local realism.

Hence my bringing L*R here to see where it fails. FOR L*R is a local realistic model about what MUST be true about local realism.

And, just as in QM, L*R says Bell's inequalities cannot be constructed from within this local realistic world-view.

Tentative conclusion by GW (which is under test here at PF now): All Bell inequalities are supposed to be claims about what must be true under local realism. BUT L*R is definitely derived from local realism, local realism in its most general form, and Bell inequalities cannot be formulated therein.

Implied conclusions:

1. All Bell inequalities are supposed to be claims about what must be true under local realism, but they are not.

2. All Bell inequalities may (perhaps) be true under a naive form of local realism.

I will be follow-up on these matters, using the PDF2 material and expanded clarifying notes. I know there are many more questions that need to be answered.

 

[Gordon Watson]

the P

<snip>

regarding gordon watson's (gw) proposed lr model:

What i would like to see is a clear exposition and explanation of gw's lr ansatz. If, at that stage, it's ascertained to be nonrealistic, then whether it reproduces qm results is moot, because it wouldn't be an lr model.

That is, i still don't understand exactly how gw's lr model is encoding realism and locality (ie., how it is making your, jessem's, 1 and 2 explicit).

<snip>

[Note to Admins: If this expansion on the model is not permissible here, under PF guidelines, I'd be happy to lodge an application for it to go under Independent Research.]

ThomasT,

Does this help? I think it properly gets us to the nitty-gritty, and what I write might help others understand the simplicity beneath L*R. Or locate the defect, which is our goal!

1. In L*R there are no abstract entities; we work with real elements of physical reality, and every relevant element of such must appear in the relevant equations. Such elements include trajectories and angular momenta before any test. In the discussion here, we can proceed by considering test outcomes only. The WHY for our maneuvers needs some discussion of HVs, total-momentum orientations and perturbed trajectories in 3-space, projected onto 2-space.

2. In L*R there are just two types of spin-half particles in the world: Those that would yield + and those that would yield – when tested via an appropriate detector oriented a. Same for photons.

3. How come there are only two types? Well, in L*R, any test reveals an equivalence class (EC) to which that particle belongs.

4. So when we select a frame of reference (FoR), say a, we know that there are only two particle types that require consideration at that orientation: Those that will, or did, or could, yield +; those that will, or did, or could, yield – at this orientation.

5. Since the pristine-particle orientations are pairwise correlated, but otherwise random, the P(a+|a) from one set of twins to the next is 1/2. BUT, as a consequence of the pair-wise correlations of twins at their creation, if one twin (by test) belongs to a specific EC, the other twin belongs to a related EC, depending on the particlar correlation existing at their creation. In PDF2, the correlations are OPPOSITE. So if one particle EC-qualifies a+, its twin will qualify a–.

6. So here, if you are ready to maintain the discipline enforced by FoRs, you are now ready to derive Tables A1-A3 in PDF2. NB: Your readiness implies that you understand this fact: As you fill up the cells in your blank Table, you are repeatedly answering a question like this:

If this pristine particle would yield a + outcome if tested at a, what is the probability that its pristine twin would yield a + outcome if it were tested at b? And so on. Does this next comment help? Imagine the pristine twins to be stable correlated gyroscopes. We are going to perturb each, independently, via a measurement interaction. We are allowing that the perturbed 3-space orientation-based trajectories of both particles do this: They pass through a on their way to b; or vice versa; or they start between a and b and go their own correlated ways accordingly. In thought-testing many pairs, across many orientations, I know of no evidence that negates this trajectory-centric-view.

7. For the frame of reference selected (and you will be going through a, b, c in turn), the first number to write is 1/2; the Probability, for the outcome you are analyzing, occurring at that orientation. For the next orientation (say b), in this FoR-a Table (A1), you will write Cab if the sign is the same at that for the a frame; or Sab if the signs are different. For these are the related Ps that apply over the relevant trajectories. (We are just using Malus' Law, generalized.)

8. You will do the same for c in the a-FoR Table (A1).

9. Table A1 is now complete. So next do A2, then A3. Table 1 is the average over these 3 Tables. Table 2 (the crucial desideratum) follows, as per detailed equations in Appendix A, if you get lost.

10. Tip: The process is so straight-forward and robotic that I usually derive the results afresh each time that they're required. To get a flying start, copy the tables from PDF2 and blank out the answers only.

HOMEWORK: Since we are only dealing with squared cosines and sines, there is no excuse for not doing this as a way to begin answering the excellent point (imho) that you raise:

Time yourself over the above exercise, please. For this will be helpful info. I'm guessing that it takes maybe two hours max; especially with PDF2 to bail you out.

Please see if you differ from any result given in PDF2. This, of course, does not validate the model completely. There could be two wrongs making a supposed right.

But it will at least show the simplicity involved in L*R. You will have derived every possible QM outcome, in full accord with the QM-approved result. (The method, of course, not yet approved.) You will have followed the discipline which I believe FoRs bring to bear on the subject: Remembering that FoRs provide different accounts of the same phenomena.

So, seems to me like a fair investment for (maybe) two hours work.

I might even send you a PF subscription, if you find the defect:

Or you buy a 5-year one when you don't?

 

[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.