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

[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...

 

[DrChinese]

a very incoherent friend...

Black the kettle calls the pot?

 

[yoda jedi]

Black the kettle calls the pot?

Acknowledgement from the party make statements non-essential...

 

[Gordon Watson]

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.

Thanks for this. My problem, I know, but I'm still not clear: Is their M function somehow an implication re M for Measurement? Why M?

IMHO, the hidden variables (HVs) are pairwise correlated (per each set of twins), with no pairs having the same HVs (no HVs repeated). So, with HVs being supplied from an infinite set, and the detectors being dichotomic in output, I remain concerned that the paper deals with a restricted view of "Realism" -- a situation all too common, in my limited experience.

Also, imho: The "spokes" that you mention may be taken to be arbitrary orientations in 2-space (for simplicity). So again, supplied from an infinite set.

Speaking of spokes: When I spoke to the twin's mother yesterday, she was again very upset that you referred to them as Alice and Bob. (PS: I've written to you before, on her behalf, about this.) She insists that they be known by the name she gave them: Alf and Bet. (After her grandparents: Alfredo and Alfreda, Bethel and Bethune.)

What especially upsets her, DrC, is this: Alice and Bob (as is well known), independently operate and orientate the detectors which violently, rudely and perturbatively interrogate Alf and Bet - stopping their progress in life, often to the point of death.

Their Mum describes these "interactions" as acts equivalent (at minimum) to "lower body mutilation" (my translation).

So, please, DrC, in their honor: Alf and Bet; noting that they have yet much to teach -- and we yet much to learn.

 

[DrChinese]

Thanks for this. My problem, I know, but I'm still not clear: Is their M function somehow an implication re M for Measurement? Why M?

IMHO, the hidden variables (HVs) are pairwise correlated (per each set of twins), with no pairs having the same HVs (no HVs repeated). So, with HVs being supplied from an infinite set, and the detectors being dichotomic in output, I remain concerned that the paper deals with a restricted view of "Realism" -- a situation all too common, in my limited experience.

Also, imho: The "spokes" that you mention may be taken to be arbitrary orientations in 2-space (for simplicity). So again, supplied from an infinite set.

Speaking of spokes: When I spoke to the twin's mother yesterday, she was again very upset that you referred to them as Alice and Bob. (PS: I've written to you before, on her behalf, about this.) She insists that they be known by the name she gave them: Alf and Bet. (After her grandparents: Alfredo and Alfreda, Bethel and Bethune.)

What especially upsets her, DrC, is this: Alice and Bob (as is well known), independently operate and orientate the detectors which violently, rudely and perturbatively interrogate Alf and Bet - stopping their progress in life, often to the point of death.

Their Mum describes these "interactions" as acts equivalent (at minimum) to "lower body mutilation" (my translation).

So, please, DrC, in their honor: Alf and Bet; noting that they have yet much to teach -- and we yet much to learn.

The M function can be anything, you can treat it a lot of ways. For discussion purposes, suppose Alf and Bet have an internal structure we refer to as DNA. I.e. a set of genes which will result in certain identical expression when observed identically. This is just an analogy, like the spokes.

This analogy would clearly explain everything were it not for Bell. Because it turns out that Alf's genes are themselves bound by a (seemingly) simple but onerous relationship: they must also yield the QM expectation value. This turns everything into a mess.

I think the "spokes" example makes it easier to see this requirement and how difficult it really is. Because the spokes cannot have independently random values. Do you see why?

 

[Gordon Watson]

The M function can be anything, you can treat it a lot of ways. For discussion purposes, suppose Alf and Bet have an internal structure we refer to as DNA. I.e. a set of genes which will result in certain identical expression when observed identically. This is just an analogy, like the spokes.

This analogy would clearly explain everything were it not for Bell. Because it turns out that Alf's genes are themselves bound by a (seemingly) simple but onerous relationship: they must also yield the QM expectation value. This turns everything into a mess.

I think the "spokes" example makes it easier to see this requirement and how difficult it really is. Because the spokes cannot have independently random values. Do you see why?

?

Using "orientations" or "spokes" or "detector settings" -- I'd have thought that the (Alice- and Bob-chosen) detector settings to be allowably independent and random in any valid Bell-test of Alf and Bet.

So, No: I don't yet see this point, re any two detector settings; and am very interested.

Why, indeed? Please elaborate and clarify. Thanks.

PS: As you know, we are currently discussing elsewhere, and are in some disagreement, about "the "mess" -- please stay-tuned on that one.

(Perhaps above you are referring to three settings??)

 

[Gordon Watson]

<SNIP>I think the "spokes" example makes it easier to see this requirement and how difficult it really is. Because the spokes cannot have independently random values. Do you see why?

Emphasis added above, by GW.


DrC: SOS: I don't see why.

I do not see the "difficulty" either, but that explanation can wait for now.

Could you explain "the why" please, now?

Many thanks.

 

[DrChinese]

Emphasis added above, by GW.


DrC: SOS: I don't see why.

I do not see the "difficulty" either, but that explanation can wait for now.

Could you explain "the why" please, now?

Many thanks.

1) The spokes at 0 & 90 must always give opposite results. Same for 1 & 91, 2 & 92, etc.

2) Further, the results at 0 & 45 must be randomly correlated (50% match rate). Also 1 & 46, 2 & 47, etc. Now, random correlation may seem simple to achieve, but this is actually a very severe requirement.

3) Also: the results at 0 & 60 must match 25% of the time. Ditto for 1 & 61, 2 & 62, etc.

When you combine these 3 requirements, everything falls apart. I have played with this plenty of times, and it is like squeezing jelly: you get 1 & 2 working, then 3 is messed up. Or 1 & 3 working, 2 is messed up.

And keep in mind that the purpose for the "spokes" model in the first place was to explain the EPR elements of reality (i.e. perfect correlations). In this case, of course, we apply it to particle spin.

 

[JesseM]

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

Your response below doesn't actually answer my primary question, can you please give a simple yes/no answer to whether you are willing, for the sake of discussion with me (what you do with others is your business), to phrase your arguments in terms of a single fixed coordinate system where each possible orientation of the polarizer/Stern-Gerlach device is assigned a fixed angle which doesn't change from one trial to another? Again, a yes/no answer to this question should take precedence over all other responses, such as responses to my other comments below.

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.

I think it is rather arrogant to assume confidently that you have disproved a theorem that thousands of very smart physicists and mathematicians have looked over and found valid for decades. And I thought you said before you were open to the possibility that there could be a flaw in your reasoning, are you going back on that now? Note that even if you have done "careful checking" in a mathematical sense, that doesn't rule out the possibility that there is some flaw in your conceptualization of the physical significance of your equations. For example, when I said that Table 2 agreed with QM predictions, that was because I was assuming we were using a fixed coordinate system where each possible orientation of the polarizer/SG device was assigned a single angle, if you are instead using some weird scheme where the angles assigned to each orientation can change from one trial to another, then it would probably no longer be true that the predictions of QM, when expressed in terms of this average of different coordinate systems, would match the equations of Table 2. Did your "careful checking" involve figuring out exactly what QM predictions would look like when not expressed in terms of a single fixed coordinate system? If not you have missed something crucial due to concentrating too much on reproducing the mathematical form of the QM equations without thinking about the assumptions under which those equations are expected to hold.

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.

By "singlet state" do you just mean the state they were in when the source emitted them? (singlet state means something rather different in QM, your comment doesn't really make sense to me with the standard meaning of that phrase). If so that would have to be true in a local realist theory, though of course under non-local interpretations like Bohmian mechanics it's not true that "any correlations in the outcomes" arise from correlations in their original states on emission.

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.

Yes, that'd be true under a local realist theory with the no-conspiracy assumption. But hopefully you don't think that this fact in itself requires us to use different coordinate systems on different trials, any physical fact like this can be expressed using whatever coordinate system we please, including a fixed coordinate system which doesn't vary from one trial to another.

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.

No, not in the experiment that Bell was describing. Again, the idea is that the two experimenters agree in advance to set their polarizers or SG devices at one of three possible orientations on each trial (one of three possible angles relative to a fixed coordinate system), not that they have agreed in advance that the angle between their two polarizers/SG devices should take one of 3 values but they don't care about the orientation (in the latter case, how would they enforce the condition that the relative angle can only take one of three values, given that they have no idea what orientation the other experimenter chose on each trial due to the spacelike separation between them?) If you aren't dealing with this specific scenario, you aren't dealing with Bell's proposed experiment, so you can't possibly be giving a counter-example to Bell's theorem.

 

[Gordon Watson]

The M function can be anything, you can treat it a lot of ways. For discussion purposes, suppose Alf and Bet have an internal structure we refer to as DNA. I.e. a set of genes which will result in certain identical expression when observed identically. This is just an analogy, like the spokes.

This analogy would clearly explain everything were it not for Bell. Because it turns out that Alf's genes are themselves bound by a (seemingly) simple but onerous relationship: they must also yield the QM expectation value. This turns everything into a mess.

I think the "spokes" example makes it easier to see this requirement and how difficult it really is. Because the spokes cannot have independently random values. Do you see why?

Emphasis added above; GW.

Sorry DrC, looks like big misunderstanding on my part: I took it that the spokes (orientations, detector settings; as I understood them) could take on independent random values, from the infinite set of orientations in 2-space.

Your reply (I see, below) relates to the outcomes recorded at those orientations. And I agree:

The recorded outcomes at ANY independently random or arbitrary detector-orientation chosen by Alice, are NOT independent of the paired-outcomes recorded by Bob at his arbitrarily selected detector-orientation. Because the twinned particles are pairwise correlated by the conditions accompanying their birth.

That is: The pairs are Alf1 & Bet1, Alf2 & Bet2, Alf3 & Bet3, etc; with no two pairs the same -- since the orientation of the pairwise-conserved total angular momentum may be delivered from the infinite set of orientations in 3-space.

No problem.

1) The spokes at 0 & 90 must always give opposite results. Same for 1 & 91, 2 & 92, etc.

2) Further, the results at 0 & 45 must be randomly correlated (50% match rate). Also 1 & 46, 2 & 47, etc. Now, random correlation may seem simple to achieve, but this is actually a very severe requirement.

3) Also: the results at 0 & 60 must match 25% of the time. Ditto for 1 & 61, 2 & 62, etc.

When you combine these 3 requirements, everything falls apart. I have played with this plenty of times, and it is like squeezing jelly: you get 1 & 2 working, then 3 is messed up. Or 1 & 3 working, 2 is messed up.

And keep in mind that the purpose for the "spokes" model in the first place was to explain the EPR elements of reality (i.e. perfect correlations). In this case, of course, we apply it to particle spin.

No problem, DrC -- These requirements are well-understood (and covered) in any work that I do.

However, having been advised that Personal Theories (even those that accord with QM, and so are not overly speculative) must be addressed in the IR section, I'll head there to respond in detail. May take a while, with (of course) no guarantee of approval there.

Please contact me directly if you'd like to comment on my draft submission; your advice would, I'm sure, be very helpful. [Working title: LRQ -- A local realistic interpretation of quantum mechanics; with special reference to Bell's Theorem.]

 

[DrChinese]

Sorry DrC, looks like big misunderstanding on my part: I took it that the spokes (orientations, detector settings; as I understood them) could take on independent random values, from the infinite set of orientations in 2-space.

Your reply (I see, below) relates to the outcomes recorded at those orientations. And I agree:

The recorded outcomes at ANY independently random or arbitrary detector-orientation chosen by Alice, are NOT independent of the paired-outcomes recorded by Bob at his arbitrarily selected detector-orientation. Because the twinned particles are pairwise correlated by the conditions accompanying their birth.

The spokes could generate a set of values:

0: 139, 87, 1401
1: 458, 64, 9472
2: etc.

As long as they evaluate to {+1, -1} according to some formula. Those results must then follow the cos^2 rule ON THE AVERAGE. But why bother with the sets of values when you can make up any data set you want to yield any result you want? Extra work for nothing. I'm not asking you to tell me HOW you can up with the dataset. I don't care what formula you use. I just want it to provide the "answer" values for 0, 120, 240 which average to a 25% match rate. (But clearly that is not possible, and I assume you can see that.)

The spokes example is intended to get you to see that there is a relationship between the spokes, on the average. That relationship, for 2 spokes, is cos^2(a-b). And again, it should be obvious that spokes cannot simultaneously maintain this relationship for any more than 2, generally.

 

[Gordon Watson]

[Originally Posted by Gordon Watson

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.]

I think it is rather arrogant to assume confidently that you have disproved a theorem that thousands of very smart physicists and mathematicians have looked over and found valid for decades. And I thought you said before you were open to the possibility that there could be a flaw in your reasoning, are you going back on that now? Note that even if you have done "careful checking" in a mathematical sense, that doesn't rule out the possibility that there is some flaw in your conceptualization of the physical significance of your equations. For example, when I said that Table 2 agreed with QM predictions, that was because I was assuming we were using a fixed coordinate system where each possible orientation of the polarizer/SG device was assigned a single angle, if you are instead using some weird scheme where the angles assigned to each orientation can change from one trial to another, then it would probably no longer be true that the predictions of QM, when expressed in terms of this average of different coordinate systems, would match the equations of Table 2. Did your "careful checking" involve figuring out exactly what QM predictions would look like when not expressed in terms of a single fixed coordinate system? If not you have missed something crucial due to concentrating too much on reproducing the mathematical form of the QM equations without thinking about the assumptions under which those equations are expected to hold.

..

Just to clarify this important point (above), to prevent it clouding the important matters that we expect to discuss (and hopefully resolve between us) this month:

My claim relates to what the model does, mathematically. Every related equation being detailed in PDF2. That was the intended message.

The real question at issue is then (once this mathematical aspect of the model is properly established): Is it truly local and realistic?

It is the combination of these two facts that is required to deliver the overall situation that you refer to. That combination must cover such issues as: Physical significance, any possible combination of detector-settings, realistic pristine-particle-correlations, valid interpretations of orientations in 2- and 3-space, etc.

To put it bluntly and all-inclusively: NO TRICKS!

To move us in that direction, and searching for flaws, I expect to answer all your previous key questions today (my time).

Thanks.

PS: Just checking this point, to ensure that I am clear about it:

"Did your "careful checking" involve figuring out exactly what QM predictions would look like when not expressed in terms of a single fixed coordinate system? If not you have missed something crucial due to concentrating too much on reproducing the mathematical form of the QM equations without thinking about the assumptions under which those equations are expected to hold."

This is, as I understand it, the general case that the model addresses in PDF2, Table2. That is, the model delivers the correct QM outcomes for any combination of Alice-Bob detector-orientations. I take this last underlined phrase of mine to include detector-setting combinations "not expressed in terms of a single fixed coordinate system".

By this I mean that some settings could be nested within other settings; like testing across 12-3 on a clock-face, then testing across 1-2; there being no limit on valid, physically testable, combinations.

Is that what you mean? By the expression "not expressed in terms of a single fixed coordinate system"?

[Noting that more advanced calculations may be adduced when the detectors settings equally (and validly) range over 3-space. For another time!]

Thanks.

..

 

[Gordon Watson]

Your response [STRIKE]below[/STRIKE] doesn't actually answer my primary question, can you please give a simple yes/no answer to whether you are willing, for the sake of discussion with me (what you do with others is your business), to phrase your arguments in terms of a single fixed coordinate system where each possible orientation of the polarizer/Stern-Gerlach device is assigned a fixed angle which doesn't change from one trial to another? Again, a yes/no answer to this question should take precedence over all other responses, such as responses to my other comments below.

Strike-out inserted by GW; for clarity.

Sorry Jesse, should have done this first:

YES: I am willing, for the sake of discussion with you (JesseM) (what I do with others is my business), to phrase my arguments in terms of a single fixed coordinate system where each possible orientation of the polarizer/Stern-Gerlach device is assigned a fixed angle which doesn't change from one trial to another.

One "trial" being a set of tests, 2 Alice-Bob orientations at a time, across the 3 (arbitrary, but fixed for a given trial) orientations typically associated with Bell's theorem.

Jesse: Is this addendum correctly worded; in your terms? Thanks.

 

[DrChinese]

...One "trial" being a set of tests, 2 Alice-Bob orientations at a time, across the 3 (arbitrary, but fixed for a given trial) orientations typically associated with Bell's theorem...

If you are a realist, you believe that a single particle has outcome values for all possible "spokes" simultaneously. What are they?

You don't even need to talk about entangled particles to get started - since ALL particles have the attribute of realism. I just don't get what there is to think about here. Certainly you have tried to put together your own dataset as part of your reading on Bell. Or?

 

[Gordon Watson]

The spokes could generate a set of values:

0: 139, 87, 1401
1: 458, 64, 9472
2: etc.

As long as they evaluate to {+1, -1} according to some formula. Those results must then follow the cos^2 rule ON THE AVERAGE. But why bother with the sets of values when you can make up any data set you want to yield any result you want? Extra work for nothing. I'm not asking you to tell me HOW you can up with the dataset. I don't care what formula you use. I just want it to provide the "answer" values for 0, 120, 240 which average to a 25% match rate. (But clearly that is not possible, and I assume you can see that.)

The spokes example is intended to get you to see that there is a relationship between the spokes, on the average. That relationship, for 2 spokes, is cos^2(a-b). And again, it should be obvious that spokes cannot simultaneously maintain this relationship for any more than 2, generally.

Doc, with respect. I find your wording to be a little confusing for me, at times; so I am always concerned that, in such cases, it's my fault and that I may be missing some important subtlety.

A. I would say, in my terms: "The spokes/orientations could [STRIKE]generate a set of values[/STRIKE] be oriented at the following angles (in degrees), with reference to a fixed Reference Orientation:

0: 139, 87, 1401
1: 458, 64, 9472
2: etc."

B. The relationship[STRIKE], for 2 spokes, is cos^2(a-b)[/STRIKE], between 2 spokes/orientations (oriented a and b) is the angle (a – b).

C. The relationships -- for the normalized outcomes -- measured across the above 2 spokes/orientations (a, b), are cos^2(a – b) for the sum of ++ and –– outcomes; and sin^2(a – b) for the sum of +– and –+ outcomes: for similarly correlated photons.

D. As for the other items (of great interest to me), I must (for the moment) refer you to the signature below.
..

 

[Gordon Watson]

1) The spokes at 0 & 90 must always give opposite results. Same for 1 & 91, 2 & 92, etc.

2) Further, the results at 0 & 45 must be randomly correlated (50% match rate). Also 1 & 46, 2 & 47, etc. Now, random correlation may seem simple to achieve, but this is actually a very severe requirement.

3) Also: the results at 0 & 60 must match 25% of the time. Ditto for 1 & 61, 2 & 62, etc.

An L*R model can (and must) deliver all of this.

Otherwise the L*R here (PDF2), would not have been offered for comment and critical evaluation here, at PF.

BUT NB, please: PDF2 provides the L*R model for the EPRB example given by vanesch and Zakurai and Bell (1964) -- (as specified in the OP).

It relates to two anti-correlated spin-1/2 particles.

Now, with respect, you keep referring to the simpler example of correlated photons, which can be confusing.

I believe that it would be best if you (in this thread) framed all your examples in terms of the OP example.

I will happily address your preferred example in another thread, if you'd care to open it.

Your example (from Aspect) is, by far, the best example for beginners -- in understanding Bell's theorem and the L*R response.

But (originating with Bohm), Bell (1964), vanesch and Zakurai: the OP addresses the somewhat more complex spin-half case -- so that it may be seen by purists to address Bell (1964).

Alas: With its greater complexity (this original case-study by Bell in 1964), there are associated -- and pretty-much guaranteed -- "head-spinners for beginners".

When you combine these 3 requirements, everything falls apart. I have played with this plenty of times, and it is like squeezing jelly: you get 1 & 2 working, then 3 is messed up. Or 1 & 3 working, 2 is messed up.

Please; stay tuned; me being more into the concrete (as opposed to the jelly-like) of this world.

And keep in mind that the purpose for the "spokes" model in the first place was to explain the EPR elements of reality (i.e. perfect correlations).

Ah! The old "EPR-epr"! They can involve much discussion (as you probably know).

But that discussion may be quite independent of any "perfect correlation" requirements.

WHATEVER: L*R delivers the required perfect correlations. Otherwise, it would not be offered ... etc.

In this case, of course, we apply it to particle spin.

Well: L*R generalizes across intrinsic particle spin (s), via the inclusion of s in all relevant trigonometric arguments; e.g., (sab).

..

 

[Gordon Watson]

If you are a realist, you believe that a single particle has outcome values for all possible "spokes" simultaneously. What are they?

You don't even need to talk about entangled particles to get started - since ALL particles have the attribute of realism. I just don't get what there is to think about here. Certainly you have tried to put together your own dataset as part of your reading on Bell. Or?

I would hope that I'm among many realists here, at PF.

I hope that we'll soon be mostly local realists, together; local and realist understood in Einstein's terms.

What is there to think about? Local Realism -- the combination!

"Certainly"? Certainly I have done many things; my life-long signature not lightly chosen.

"Or?" L*R!

..

 

[Gordon Watson]

Your response below doesn't actually answer my primary question, can you please give a simple yes/no ... <SNIP>.

Addressed above.

I think it is rather arrogant to assume confidently that you have disproved a theorem that thousands of very smart physicists and mathematicians have looked over and found valid for decades. ... <SNIP>

Addressed above.

By "singlet state" do you just mean the state they were in when the source emitted them? (singlet state means something rather different in QM, your comment doesn't really make sense to me with the standard meaning of that phrase). If so that would have to be true in a local realist theory, though of course under non-local interpretations like Bohmian mechanics it's not true that "any correlations in the outcomes" arise from correlations in their original states on emission.

I remain a steadfast local realist, in the full Einsteinian sense, as I interpret him. That fact notwithstanding, Bohm remains another hero of mine -- though I am not in his camp re anything to do with non-locality (NL).

From http://en.wikipedia.org/wiki/Singlet_state: "In theoretical physics, a singlet ... may also refer to two or more particles prepared in a correlated state, such that the total angular momentum of the state is zero. ... The singlet state formed from a pair of electrons has many peculiar properties, and plays a fundamental role in the EPR paradox and quantum entanglement."

I think that I use the term similar to most physicists who study Bell; I have no need to reject any aspect of QM in this regard.

That is, for me and in my terms:

1. The singlet state (used in most tests of Bell's theorem) is invariant
under rotations (not just about the line of flight).

2. However: The "Hardy state" -- if it's based on spin or polarization -- is not.​

Yes, that'd be true under a local realist theory with the no-conspiracy assumption. But hopefully you don't think that this fact in itself requires us to use different coordinate systems on different trials, any physical fact like this can be expressed using whatever coordinate system we please, including a fixed coordinate system which doesn't vary from one trial to another.

I expect that we do not differ here. I require no loopholes, conspiracies, ++. (In fact, I counsel Bell's critics NOT to use them -- they are irrelevant.)

No, not in the experiment that Bell was describing. Again, the idea is that the two experimenters agree in advance to set their polarizers or SG devices at one of three possible orientations on each trial (one of three possible angles relative to a fixed coordinate system), not that they have agreed in advance that the angle between their two polarizers/SG devices should take one of 3 values but they don't care about the orientation (in the latter case, how would they enforce the condition that the relative angle can only take one of three values, given that they have no idea what orientation the other experimenter chose on each trial due to the spacelike separation between them?) If you aren't dealing with this specific scenario, you aren't dealing with Bell's proposed experiment, so you can't possibly be giving a counter-example to Bell's theorem.

I'm dealing with Bell and anything to do with "Bell's proposed experiments" -- please rest assured of that fact.

[But, in passing and requiring no comment to distract us from the main path here -- just for the record: I did not invent BI-angles.

I discovered them in my data. While we are focussing on the QM results of Table 2, PDF2, they are irrelevant.]

On the other hand, to be very clear: My use of "frames of reference" is helpful to me -- they provide different accounts of the same phenomena, as they should. See Bell (How to teach special relativity ..), Mermin (It's about time ...).

PS: I very much appreciate your attention to detail, and most sincerely thank you for it.
..

 

[Gordon Watson]

.

So can you please address my point that the formulas in Table 1 are clearly incompatible with those in Table 2, ...

Based on earlier responses from me, and more detail below: I trust this perceived "incompatibility" is now resolved?

There is NO incompatibility. Are we now in agreement on this point?

as shown by my numerical example in [post=3159151]post 71[/post] (which you never responded to, ...

As I recall: Your post #71 came in on the day JenniT was urgently to go bush. JenniT had delayed her departure to address some earlier matters, and planned to reply to #71 before she left. Vanesch then pointed out that she'd written 0.732 for 0.0732, so at that she went bush ...

... having realized her mistake in responding to posts while in meetings, and under other pressures, in an effort to keep her (perceived) responsibility to this thread moving ... to a helpful conclusion.

Post #78 refers [https://www.physicsforums.com/showpost.php?p=3159608&postcount=78]

Then, on her return: Most outstanding matters were cleared up in PDF2: With its complete derivation, via L*R, of every relevant EPRB probability. All in full accord with QM. That is: In full accord with the point of view repeatedly emphasized here; as one with QM.

... and you also didn't respond to my specific request to address this in post 90)?

Sorry: I thought that Post #91 responded to the matters raised in your post #90?

Please bring forward any outstanding matters that remain unresolved between us -- taking PDF2 into account, please.

More generally, your formulas in Table 1 [sic] are simply the ones predicted by QM, ... [GW emphasis and "sic" added.]

I suspect this is a typo and should read ... More generally, your formulas in Table 2 are simply the ones predicted by QM,

YES, but they are wholly derived from within L*R; so that "simply" of yours would be better written as "in full accord with".

So, with these understandings, we'd then have: Your formulas in Table 2 are [STRIKE]simply[/STRIKE] in full accord with the ones predicted by QM.

My response would then be:

Yes, because that QM-ACCORD was a boundary condition on the model and on its submission for discussion here.

NB: I am not in dispute with QM. I am in dispute with Bell's theorem ... in the same way that QM is in dispute with Bell's theorem:

BT cannot be formulated from within QM, nor from within the local realism of L*R. That's the point here.

... 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: ...

Sorry, I thought that PDF2 made it clear: Regarding "Zakurai's Bell Inequality page" -- I accepted his 8 equivalence classes (ECs) as valid (+++ –––, etc.), then derived the relevant P1-P8 (the RHS of Table 1 in PDF2) that are applicable under L*R.

That is: Going beyond Zakurai and QM: I give specific values for every probability; not some generalized notion that such (in some form) exist, under some form of local realism (perhaps of the naive variety, for all I know).

So: PDF2, Table 1, shows the normalized distribution of all 8 ECs: under the local realism of L*R.

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

From PDF2, using the notation therein (which is wholly equivalent to yours above), with the PDF2 equation numbers in Appendix A:


(A0a) P(ab++|ab) = [P(ab++|a) + P(ab++|b)]/2 = Sab/2.

(A0b) P(ab++|abc) = [P(ab++|a) + P(ab++|b) + P(ab++|c)]/3 = [2P(ab++|ab) + P(ab++|c)]/3.

(A0c) ∴ P(ab++|ab) = [3P(ab++|abc) – P(ab++|c)]/2 = Sab/2.

Note that you write:

(1X) P(a+, b+|ab) = P3 + P4. X
(2X) P(a+, c+|ac) = P2 + P4. X
(3X) P(c+, b+|cb) = P3 + P7. X

But these are all incorrect: The conditioning space is NOT variously ab, ac, cb (respectively), as you have written; but abc for all. That is, retaining your notation here for comparison, but correcting the conditioning space:

(1) P(a+, b+|abc) = P3 + P4.
(2) P(a+, c+|abc) = P2 + P4.
(3) P(c+, b+|abc) = P3 + P7.

Then: Since these are Normalized Probabilities from L*R (and NOT from QM), they must be reduced to deliver the corresponding QM Normalized Probabilities.

The result is shown in PDF2, Table 2; with every calculation detailed in Appendix A: IN FULL ACCORD WITH QM.

Please check your P(a+, b+|ab), P(a+, c+|ac), P(c+, b+|cb) there, in Table 2.

NB: The need for reduction arises because L*R does what many evidently believe QM cannot do; i.e., L*R goes beyond what many evidently believe to be QM's limit. [A diversionary point not addressed here because QM is not under attack here. It's a point for another day.] That is, and importantly: The reduction DOES NOT arise from any dispute with QM!

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

This is NO MORE true in L*R than it is in QM! It is a nonsense in both.

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

Clearly, this is not the case; this is just not so: Let us see, in your notation --

P(a+, b+|ab) = Sab/2.

P(a+, c+|ac) = Sac/2.

P(c+, b+|cb) = Scb/2.

The inequality -- that you insist must exist -- CANNOT be formulated.

As in QM, so on L*R: Bell Inequalities cannot be formulated; BT non est in both!

Reason: In part due to critical analysis; in part because L*R supplies a physically-significant, local-realistic, specific-valued, normalized distribution that sums to unity: And not some unspecified (perhaps misunderstood) non-specific Probabilities; perhaps attaching to a naive view of local realism? -- which is not relevant (at this time) to our discussions here.

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.

As stated above: The inequality cannot be constructed in L*R; just as it cannot be constructed in QM.

Please: Such a result should not be held against L*R; no more than it is held against QM.

In your words: The QM predictions can violate the inequality in 3.

In my words: Agreeing with QM, the L*R predictions can violate the inequality in 3.​

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:

In haste, trusting these matters are clarified by PDF2 and the above.

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.

Now resolved, understood, and agreed between us: I trust?

With thanks again,

GW

 

[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?

<SNIP>

ThomasT, the SNIP part was answered earlier.

My formula for the singlet state expectation value in the context of the EPR-Bohm (EPRB) experiment under discussion, and in reasonably common terms and usage, is:

E(a, b)_EPRB = P(ab++|ab) – P(ab+–|ab) – P(ab–+|ab) + P(ab– –|ab) = 2P(ab++|ab) – 2P(ab+–|ab) = Sab – Cab. (1)

Each term, per Table 2 of PDF2, in accord with QM and non-naive local realism. The reductions in (1) follow from Table 2 of PDF2; substituting s = 1/2 (since we are discussing the original EPRB), we have the correct QM expectation:

E(a, b)_EPRB = – cos(ab) = – a.b. (2)

So far, no problem: As I often say in the thread, L*R delivers all QM results correctly.

However, from some other questions of yours, your real interest appears to relate to:

"What and where is the HV in GW's formulation of L*R? Or, to put it another way: Where's Bell's lambda in L*R?"

I use λ for Alf (the particle on its way to Alice), and a separate λ' for particle Bet (the one on its way to Bob). The general linking formula is then:

F(λ, λ') = 0. (3)

This allows the respective conservation law to link λ and λ' appropriately; whether for photons or spin-half particles. For example, in the EPRB case mostly under discussion here:

λ + λ' = 0. (4)

Which is: λ = – λ'. (5)

This yields the familiar EPRB anti-parallel correlations.

But to go into depth here, on these deeper issues, will be in breach of PF Rules re Personal Theories: as I see them. So you might care to wait until an IR application is approved -- the current point here, now, being:

1. Does L*R deliver all the QM results, correctly?

2. Is it possible to formulate a Bell Inequality, from within L*R?

OR: Is it impossible to formulate a Bell Inequality, from within L*R (just as it is impossible from within QM)?

Answers to these questions would lead us to the theory underlying L*R -- which, as I see it, takes us to IR.

PS: From some of your old posts, I'm thinking that you were for local realism? Well, if it helps restore your faith: I am very confident that L*R will be found to be local and realistic (in Einstein's terms, as I read him) at its deepest level -- its grass-roots.

 

[Jonathan Scott]

I haven't followed all the details of this thread, but for what it's worth I discussed this idea with Gordon Watson by e-mail about three years ago and at the time the specific flaw I found in his idea was as follows:

If the set-up happens to be such that at least one of the pair of analyzers will obtain a pure state, then it is well known that quantum theory and classical physics give the same result for the correlations, and this was the mathematical essence of his assertions.

It is not possible for this condition to be true for all of the measurements needed to show Bell inequalities, but he was apparently trying to get round this by implicitly assuming a rotation of the reference direction (on the grounds that it's all relative) so that the calculation which assumes a pure state at one end could still be used. This is however a physical constraint which is not present in the original system, and means that the particles in the rotated experiment effectively have to be prepared in a different way from the way in which they would have been prepared for the original experiment.

Personally, I always consider the following result when I want to be reminded that there's no simple way round the Bell inequalities (taking sqrt(1/2) as approx 70%):

Experiment 1: Analyzers are correlated, QM results at both ends are 100% same.
Experiment 2: If one analyzer was changed, QM results would be 15% different.
Experiment 3: If other analyzer was changed, QM results would be 15% different.
Experiment 4: If both analyzers are changed, QM results would be 50% different.

It is not possible for the differences introduced by changing the two analyzers independently to add up to the overall difference, so no local realistic theory can simulate this (except via cheats such as detection loopholes).

 

[DrChinese]

It relates to two anti-correlated spin-1/2 particles.

Now, with respect, you keep referring to the simpler example of correlated photons, which can be confusing.

I believe that it would be best if you (in this thread) framed all your examples in terms of the OP example.

It's your example, I can't help but believe the reason you don't want to use Type I entangled photons is because you want to obscure what you are doing. Of course you get the same results either way.

I will simply wait for a dataset, I don't expect you can or will produce one - ever. So you will be explaining - as nearly all local realists do - why it isn't necessary. You don't even need to explain why you won't provide this, as this is all I am really interested in seeing. The reason I ask for a dataset is that it makes all the handwaving over the math unnecessary and cuts to the chase. It's really quite simple: how local realistic can a model be if you cannot produce simultaneous values for 0, 120 and 240 degrees?

I think you know my answer, which is why local realistic arguments are no longer taken too seriously (except as something of an exercise in how to dispose of them). Here again, nothing is forthcoming. As I have said many times before: WHERE IS THE BEEF?

:yawn:

 

[DrChinese]

Personally, I always consider the following result when I want to be reminded that there's no simple way round the Bell inequalities (taking sqrt(1/2) as approx 70%):

Experiment 1: Analyzers are correlated, QM results at both ends are 100% same.
Experiment 2: If one analyzer was changed, QM results would be 15% different.
Experiment 3: If other analyzer was changed, QM results would be 15% different.
Experiment 4: If both analyzers are changed, QM results would be 50% different.

It is not possible for the differences introduced by changing the two analyzers independently to add up to the overall difference, so no local realistic theory can simulate this (except via cheats such as detection loopholes).

Thank you for a note of sanity. Although the values are different for spin 1/2 particles and spin 1 particles, the same relationship applies to both as to the above. Only a linear relationship on the difference resolves the problem, and obviously that is different than the QM expectation value.

 

[Gordon Watson]

Originally Posted by Gordon Watson AS CUT BY DrChinese

...

"It relates to two anti-correlated spin-1/2 particles.

Now, with respect, you keep referring to the simpler example of correlated photons, which can be confusing.

I believe that it would be best if you (in this thread) framed all your examples in terms of the OP example."

...

It's your example, I can't help but believe the reason you don't want to use Type I entangled photons is because you want to obscure what you are doing. Of course you get the same results either way.

I will simply wait for a dataset, I don't expect you can or will produce one - ever. So you will be explaining - as nearly all local realists do - why it isn't necessary. You don't even need to explain why you won't provide this, as this is all I am really interested in seeing. The reason I ask for a dataset is that it makes all the handwaving over the math unnecessary and cuts to the chase. It's really quite simple: how local realistic can a model be if you cannot produce simultaneous values for 0, 120 and 240 degrees?

I think you know my answer, which is why local realistic arguments are no longer taken too seriously (except as something of an exercise in how to dispose of them). Here again, nothing is forthcoming. As I have said many times before: WHERE IS THE BEEF?

:yawn:

DrChinese,

I am currently drafting detailed replies to JesseM and vanesch, who have properly engaged here with the original EPR-Bohm and Bell (1964) example. And who deserve detailed replies as we get down to the nitty gritty of this thread.

So your latest disparaging innuendo is an unfortunate distraction.

However, believing it important to have my reply appear close to yours, here it is.

Here is what I wrote:

An L*R model can (and must) deliver all of this.

Otherwise the L*R here (PDF2), would not have been offered for comment and critical evaluation here, at PF.

BUT NB, please: PDF2 provides the L*R model for the EPRB example given by vanesch and Zakurai and Bell (1964) -- (as specified in the OP).

It relates to two anti-correlated spin-1/2 particles.

Now, with respect, you keep referring to the simpler example of correlated photons, which can be confusing.

I believe that it would be best if you (in this thread) framed all your examples in terms of the OP example.

I will happily address your preferred example in another thread, if you'd care to open it.

(NB: Bold emphasis here is by GW, not in the original. DrChinese chose to delete this continuation!)

Your example (from Aspect) is, by far, the best example for beginners -- in understanding Bell's theorem and the L*R response.

But (originating with Bohm), Bell (1964), vanesch and Zakurai: the OP addresses the somewhat more complex spin-half case -- so that it may be seen by purists to address Bell (1964).

Alas: With its greater complexity (this original case-study by Bell in 1964), there are associated -- and pretty-much guaranteed -- "head-spinners for beginners".​

DrChinese: Interesting? That you chose to cut above the critical continuation!?[PS deleted. GW]


[Footnote deleted. GW]
..

 

[Gordon Watson]

..

Jesse, this is your Post #71, with my reply.

It is based on the expanded and rigorous formulae given in PDF2; not the misleading short-cuts that are to be found in that rushed first draft (from "JenniT" - as you know). The corrective second-draft (PDF2) was uploaded soon after her return.

Please accept my apologies for this unfortunate side-track -- JenniT, having in-part served her purpose, is no longer posting here (I trust); leaving me to carry the can (and not tip it).

Yes, I checked it, and it was wrong.

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

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

The expanded formula is given in PDF2, Appendix A; equations (A0b) and (A0c) and notes thereto. That is:

P(ab++|ab) = [P(ab++|a) + P(ab++|b)]/2 = Sab/2. (A0a)

P(ab++|abc) = [P(ab++|a) + P(ab++|b) + P(ab++|c)]/3 = [2P(ab++|ab) + P(ab++|c)]/3. (A0b)

∴ P(ab++|ab) = [3P(ab++|abc) – P(ab++|c)]/2 = Sab/2. (A0c)

In this regard, the second draft (PDF2) was meant to be a global corrective.

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

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

Sab/2=0.375

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

So, in their expanded form:

P(ab++|abc) = (2Sab + Cac.Sbc + Sac.Cbc)/6 = 0.3125. (W)

P(ab++|ab) = Sab/2 = 0.375. (X)

This confirms the correctness of your calculations, but properly assigns them to the correctly specified Probabilities. By which I mean: with correctly completed conditioning spaces.

So, under L*R, equations (W) and (X) are correct; and the basis for discussion as required.

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

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

whereas

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

and neither of these are equal to

Sab/2 = 0.375

Again (and again with apologies), the confusion arises from the short-cut [due to me] of not inserting the conditioning-space data.

Your -- "Pab++ = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2 from post #33" --

expands to (per PDF2, from Table A3.c):

P(ab++|c) = P3 + P4 = (Cac.Sbc + Sac.Cbc)/2 = 0.1875. (Y)

Your -- "the [first-draft] PDF's equation of Pab++ = P3+P4 =(2Sab + Cac.Sbc + Sac.Cbc)/6" --

expands to (per PDF2, equation (A0b) and from Table 1):

Pab(++|abc) = P3 + P4 (from Table 1) = (2Sab + Cac.Sbc + Sac.Cbc)/6 = 0.3125. (Z)

This again confirms the correctness of your calculations, but again properly assigns them to the correctly specified Probabilities. By which I mean: with correctly completed conditioning spaces.

So, under L*R, equations (Y) and (Z) are correct; and (again) the basis for discussion as required.

... and neither of these are equal to

Sab/2 = 0.375

But Sab/2 =

P(ab++|ab) = 0.375. (J);

whereas the comparative numbers relate to

P(ab++|c) = 0.1875. (Y)

Pab(++|abc) = 0.3125. (Z)

So (again), under L*R, equations (J), (Y) and (Z) are correct; and (again) the basis for discussion as required.

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

Agreed.

And now made explicitly correct in L*R terms, via the inclusion of the correct conditioning data.

PS: It is clearly my mistake: I should have more comprehensively pointed out that the (second-draft) PDF2 was a global antidote to what had gone before. The "arrogant" mathematical message (as you assessed it), was also meant to be a global corrective, suggesting that analyses such as yours should be re-assessed under the PDF2.

All of which, IMHO, moves us closer to the nitty gritty conclusion of this thread.

I next plan to respond in detail to vanesch's EPR-Bohm + Bell (1964) example.

In closing: Please accept my apologies; and, as always, my thanks.

And, though I'm sure many questions remain, PDF2 (with its accompanying Errata) remains the L*R model.
GW
..

 

[DrChinese]

DrChinese,

I am currently drafting detailed replies to JesseM and vanesch, who have properly engaged here with the original EPR-Bohm and Bell (1964) example. And who deserve detailed replies as we get down to the nitty gritty of this thread.

So your latest disparaging innuendo is an unfortunate distraction...

You keep teasing us with comments to the effect of "Local Realistic Models can simulate QM expectation values". And yet you have shown absolutely nothing so far that backs up this wild claim. So I ask you to refrain from hinting at such assertions BEFORE you can back them up.

Further, it is quite disappointing that you have yet to demonstrate any understanding whatsoever of the critical difficulties you are facing. I am not saying you don't understand them, but you certainly seem to brush them off without the slightest comment. So my guess is that you have no idea what you are up against. I would guess that there are perhaps hundreds of purported disproofs of Bell to date by some quite enthusiatic persons. None of these have yet to gain any traction because they cannot answer the simple question I ask: where is the LR dataset? That instantly separates all disproofs into one of several categories and shows everyone what is being asserted.

So that is why I keep asking for some substance rather than sizzle. You are about to provide a proof which is a complete waste of time unless you realize the issues the scientific community is interested in. A useful theory is good. QM is such. And while you and others are asserting local realism, experimentalists have repeatedly demonstrated - following QM - that reality is NOT local in hundreds of ways that you deny should be possible. So it fairly silly to offer local realistic "proofs" which are violated every day in practice. Hows about you explain why the future appears to affect the past, for example, and that particles that have never even existed in the same locality can violate Bell Inequalities. QM can do this, LR - by definition - cannot.