Joy Christian, Disproof of Bell's Theorem

[ThomasT]

This is inaccurate. Generating θ randomly around a circle gives us values in the range [0,360]. So how do you get <θ>=45 degrees shouldn't it be 180?

Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate?

Even if your 45 degrees were correct which it is not, <x> is not the same as Sin<θ>.

You defined x = cosθ. I wrote <x> = cos<θ> because you said you're randomly varying θ. If instead you randomly vary x from 0 to 1, then <x> = <cosθ> = .5, but then you're not randomly varying θ, which is what you said you were doing. It was a little confusing. But I now understand what you're doing. Anyway, I don't think we need it, unless you want to contribute to the collection of illustrations showing that qm is incompatible with LR.

The problem is not with the inequality. It is a question of whether bipartite experiments, and QM's predictions for expectation values for bipartite experiments (which do not commute with each other) can be used as legitimate sources of terms to be substituted into the equation for comparisons. I believe not.

Given what's being compared, it's legitimate. And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?

The main point is simply that you can not combine expectation values for non-commuting observables into the same expression as is commonly done when comparing Bell's inequality with QM, and as DrC does in the text I quote.

Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.

If your point is that this doesn't inform us about the underlying reality, then I agree with you. Joy Christian on the other hand is presenting so called LR models of entanglement that agree with qm predictions. Any ideas you have on Christian's offerings, and in particular the one presented in this thread, are most welcome.

 

[Gordon Watson]

..

DrC, ThomasT, billschnieder, and others.Am I mistaken?

We have here, in the "triangles" and "negative probability" discussions, a chance to at least settle these issues with finality. Yes?

And, even if little else were to be resolved: That would be progress. Yes?

So shouldn't someone take the initiative and start a new thread -- leaving this one to the JC discussions, per the OP?

How about: Bell's theorem and negative probabilities versus triangle-inequalities?

??

With some of the discussion, already here, transferred to kick it off?

 

[billschnieder]

Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate?

Why should it? Try to understand the point before you suggest what should be enough or not. The simple fact the <θ> in your "simplification" is different from <θ> in my original example 'should' tell you that it is not the same thing we are talking about.

You defined x = cosθ. I wrote <x> = cos<θ> because you said you're randomly varying θ. If instead you randomly vary x from 0 to 1, then <x> = <cosθ> = .5, but then you're not randomly varying θ, which is what you said you were doing. It was a little confusing.

I also mentioned that x was the length of one side of a triangle. I assumed it will be obvious to most that a length can not be negative which means you should take its absolute value. Which means <x> is not the same as cos<θ> for the same reason that |<v>| does not mean the same thing as <|v|>. You do not deny that randomly varying θ reaches the conclusion I reached so your response here is curious and very surprising.

But I now understand what you're doing. Anyway, I don't think we need it, unless you want to contribute to the collection of illustrations showing that qm is incompatible with LR.

I still do not think you understand it, otherwise you will not conclude that you do not need it.

And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?

No I do not agree. I would instead say that, neither QM not Bell test experiments are legitimate sources of terms for the inequality 1 + P(b,c) ≥ |P(a,b) - P(a,c)|. Simply because all three terms are not defined within the same probability space neither QM nor in Bell test experiments. Non-locality and/or reality are completely peripheral here. There is no P(a,b,c) distribution from which you can extract the three terms, not in QM, not in Bell test experiments and that alone explains why you can not use QM nor Bell test experiments as sources for those three terms.

Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.

This is wrong. There is no conflict with QM until Bell introduces the third angle. Please check his original paper again to confirm that this is correct. I mentioned DrC article because the same error is made in which expectation values from three incompatible non-commuting measurements are combined in the same expression. Are you claiming hereby that it is sound mathematics to do that? This is the question you did not answer.

If your point is that this doesn't inform us about the underlying reality, then I agree with you.

I'm not just interested in stating that. I am explaining WHY any result so obtained can not inform us of anything other than the fact that a subtle mathematical error has been made, ie substituting incompatible expectation values within Bell's inequality.

Joy Christian on the other hand is presenting so called LR models of entanglement that agree with qm predictions. Any ideas you have on Christian's offerings, and in particular the one presented in this thread, are most welcome.

Did you read the one posted in this thread? You seemed to dismiss it earlier based on what you had heard about his other offerings. He presents in 1/2 a page, a LR model which violates Bell's inequality. You may ask how come his LR model could violate the inequallity, and the answer is for the same reasons I have already explained. -- the terms he used are not all defined within the same probability space. It is the same reason why QM violates the inequalities.


He concludes that:

Evidently, the variables A(a, λ) and B(b, λ) defined above respect both the remote parameter independence and the remote outcome independence (which has been checked rigorously [2][3][4][5][6][7]). This contradicts Bell’s theorem.

I haven't seen anybody here argue that his model presented in the above paper is not LR, nor have I seen anyone argue that his model does not reproduce the QM result. All I have seen is discussion around his other papers.

 

[ThomasT]

Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate?

Why should it? Try to understand the point before you suggest what should be enough or not. The simple fact the <θ> in your "simplification" is different from <θ> in my original example 'should' tell you that it is not the same thing we are talking about.

I also mentioned that x was the length of one side of a triangle. I assumed it will be obvious to most that a length can not be negative which means you should take its absolute value. Which means <x> is not the same as cos<θ> for the same reason that |<v>| does not mean the same thing as <|v|>. You do not deny that randomly varying θ reaches the conclusion I reached so your response here is curious and very surprising.

The values I input for 0° --> 90° give roughly <x>2 + <y>2 = .8, which corresponds with what you got. And <x2 + y2> = .975. So, isn't the net effect the same -- you get a contradiction between separable and nonseparable formulations?

I still do not think you understand it, otherwise you will not conclude that you do not need it.

Only that we already have illustrations of the incompatibility between separable and nonseparable formulations. Bell's, for one.

And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?

No I do not agree. I would instead say that, neither QM nor Bell test experiments are legitimate sources of terms for the inequality 1 + P(b,c) ≥ |P(a,b) - P(a,c)|. Simply because all three terms are not defined within the same probability space neither QM nor in Bell test experiments. Non-locality and/or reality are completely peripheral here.

The inequality is based on Bell's LR form. Any model of entanglement taking that form must satisfy his inequality. The question concerns how locality and reality might be explicitly encoded in the same model, while remaining compatible with qm, and Bell shows that they can't be.

There is no P(a,b,c) distribution from which you can extract the three terms, not in QM, not in Bell test experiments and that alone explains why you can not use QM nor Bell test experiments as sources for those three terms.

That's the point of DrC's illustration. (a,b,c) is the LR dataset, based on the idea that underlying predetermined particle parameters exist independent of measurement.
There is no such dataset in qm. Hence, the conflict.

Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.

This is wrong. There is no conflict with QM until Bell introduces the third angle. Please check his original paper again to confirm that this is correct.

The results (10) and (11) are in conflict with qm. The unit vectors a and b in (2) can refer to any θ. The unit vector, c, is introduced after that, specifically to derive the inequality. The whole point of Bell's paper is that the generalized LR form (2) is incompatible with qm.

I mentioned DrC article because the same error is made in which expectation values from three incompatible non-commuting measurements are combined in the same expression. Are you claiming hereby that it is sound mathematics to do that? This is the question you did not answer.

Yes, it's sound mathematics to do that given what he's trying to show. There are limits on how explicit LR models can be formulated. These limits are based on certain assumptions. Based on the assumption of realism, DrC has fashioned a numerical treatment that demonstrates a conflict between that assumption and qm.

If your point is that this doesn't inform us about the underlying reality, then I agree with you.

I'm not just interested in stating that. I am explaining WHY any result so obtained can not inform us of anything other than the fact that a subtle mathematical error has been made, ie. substituting incompatible expectation values within Bell's inequality.

We sort of agree then. The results can't inform us of anything other than the fact that a certain mathematical form can't possibly agree with qm or experiment. But, what Bell did is not a mathematical error. Bell constructed a generalized LR form and compared it with qm. They're incompatible.

If you can present another form that an LR model can take, that meets the the requirements for an explicit LR model, and reproduces qm predictions, then that might be interesting.

Did you read the one posted in this thread?

Sure, but I don't really understand what he did.

You seemed to dismiss it earlier based on what you had heard about his other offerings.

I thought he might be doing essentially the same thing in both, ie., allowing a and b to communicate, but 'locally' in an imaginary space, which wouldn't be an LR model. Then I was wondering if there might be 'any' way to translate what he did into a realistic local view of the underlying mechanics. But, even if so, if it can't be made explicitly LR, that is with a clearly 3D classical LR encoded in the model, then it isn't an LR model.

You may ask how come his LR model could violate the inequality, and the answer is for the same reasons I have already explained. -- the terms he used are not all defined within the same probability space. It is the same reason why QM violates the inequalities.

I don't think this clarifies it fully enough.

The inequality is based on a generalized LR form, the salient feature of which is the separability of the underlying parameter determining coincidental detection. Standard qm and Christian's formalisms violate the inequality because those formalisms don't encode a feature that skews the underlying parameter nonseparability (ie., they don't skew the relationship between the particles) -- qm, 'nonlocally' via the projection, and Christian's Clifford algebraic models by allowing the particles to communicate 'locally' via a null interval in C-space. I'm not sure how Christian's paper in this thread does it.

I haven't seen anybody here argue that his model presented in the above paper is not LR, nor have I seen anyone argue that his model does not reproduce the QM result. All I have seen is discussion around his other papers.

Hence, my call for experts or at least more knowledgeable people than myself. Glad you showed up.

His model does reproduce the qm result. But it doesn't 'look' LR because of the bivectors and the algebra he employs. I'm just plodding along trying to learn as I go, so if you or anybody else has some insights into Christian's stuff to offer then that would be most appreciated. And thanks for your input so far. It's motivating me to think about this a little more and not just set it aside.

 

[DrChinese]

Concerning negative probabilities, Dr C says:

...

Note how he defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.

I think that is precisely my point. The HUP should be applied literally, and that makes realism untenable. Experiment follows this in all respects.

 

[DrChinese]

Now Bell's (1) is essentially A(a)={+1,-1}, B(b)={+1,-1}

Bell later effectively says that realism implies simultaneously C(c)={+1,-1}. This assumption is wrong if QM is correct.

Just to drive the above home, here is a definition of realism from an experimental paper from the past few days:

"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 in hundreds of papers.

 

[billschnieder]

The inequality is based on Bell's LR form. Any model of entanglement taking that form must satisfy his inequality. The question concerns how locality and reality might be explicitly encoded in the same model, while remaining compatible with qm, and Bell shows that they can't be.

I have already shown elsewhere in another thread that you do not need LR or anything other than paired products of three variables to obtain Bell-like inequalities, irrespective of the physics behind the variables. It is a mathematical fact first established by Boole almost a hundred years before Bell, that paired products of three variables will obey Bell-like inequalities. Boole even concluded at the time that if in an experiment the data for three variables did not obey the inequality, it simply meant that those three variables could not possibly exist at the same time. He called them "conditions of possible experience".

That's the point of DrC's illustration. (a,b,c) is the LR dataset, based on the idea that underlying predetermined particle parameters exist independent of measurement.
There is no such dataset in qm. Hence, the conflict.

But there can never be such a dataset for the EPR scenario ever because it is impossible to measure two particles three times. Why would any sane individual expect a joint probability space of P(a,b,c) to exist? We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we? We stop the discussion at the point where we realize that there is no such thing as a square circle.

All I am doing here is highlighting the fact that the lack of a P(a,b,c) in QM and in experiments is sufficient to make it impossible to apply Bell's inequalities to the EPR scenario. They are incompatible. So you can't even talk of a violation yet, because the laws of mathematics and logic prohibit you from using those terms from QM and experiments in the inequality. Find an experimental scenario for which P(a,b,c) is a valid probability distribution and you can discuss all you want about QM and experiments and Bell's inequality and LR etc. Until then such discussion is a waste of time and a weapon for increasing mutual confusion.


EDIT:
I thought the above was too complicated so I thought I should simplify.

Some choose to say: the fact that it is impossible to provide a dataset of triples which obeys Bell's inequality, implies that realism is false.

I say: Duh, in the statement of the problem, the impossibility of measuring two particles three times is almost explicitly recognized by any sane individual. Why then would any such individual expect two particles to actually be measured 3 times to obtain the dataset? It can not be done in QM, nor in any experiment, nor in any LR theory that anyone could cook up. Obviously, the fact that we can not measure two particles three times, says absolutely nothing about locality or realism.

 

[DrChinese]

But there can never be such a dataset for the EPR scenario ever because it is impossible to measure two particles three times. Why would any sane individual expect a joint probability space of P(a,b,c) to exist? We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we? We stop the discussion at the point where we realize that there is no such thing as a square circle.

Well gosh darn, Bill. I have non-brown eyes, non-black hair and light skin. My friend has brown eyes, black hair and dark skin. Funny, groups of people have properties that seem to persist and follow Bell Inequalities all day long. I will gladly show you datasets of these, 3 properties for random pairs of persons (that would be 2). The only samples I know of that don't follow these inequalities are quantum particles that are well described by the HUP.

And that would be: any 2 measurements of 3 properties of 2 particles. Is that too hard for you to follow? I mean, really, when has anyone tried to measure 2 particles 3 times? Basically I am saying you are full of hot air, and I think I have said as much before in our prior discussions. Or perhaps you can provide some experimental support for your position. Perhaps a reputable source other than yourself? Otherwise, you are adding nothing of value here except confusion for folks who have no idea that your views are not standard science.

If you want to add here, please add normal scientific thought. Set up your own site for your personal views.

 

[ThomasT]

We've gotten a bit off topic. But all these considerations are connected. I'll tie it to Christian's stuff at the end.

We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we?

No. And it seems that the discussion here at PF has moved beyond that, and that the physics community at large is moving beyond that as well. We're concerned with the form that models of entanglement can take to be instrumentally viable, and why -- and the why of it has, effectively, only to do with a formalism's correspondence with experimental design and preparation. Realism and localism refer to certain formal requirements or limits.

Einstein thought, and others still think (now, in the face of overwhelming evidence to the contrary), that LR formalisms are possible. Opposing postulates associated with competing formalisms are the basis for theorems (Bell) and 'tautologies' (DrC) which are developed to show a quantitative difference between incompatible formalisms. Incompatibility between LR and qm/experiment doesn't imply that some form of nonlocality exists or that an underlying reality with specific properties doesn't -- in fact there's absolutely no empirical evidence that even suggests those notions. It's unfortunate that so much of the literature, and our understanding, has been clouded by claims to the contrary.

It gets complicated insofar as theories do develop according to certain visions of the underlying reality, but those visions should always be based on empirical evidence, not lack of it. We infer from what's known, not from what isn't. It gets even more complicated when theories are developed primarily via abstract mathematics as opposed to primarily via reasonable inference from empirical evidence and sensory experience -- giving rise to paradoxes, pseudo problems and exotic interpretations. Which is not to say that this could be entirely avoided.

Regarding entanglement, it seems that we can reasonably infer from the experimental designs, preparations and observed correlations, that the relationships between the entangled entities are being produced locally via the various experimental protocols.

So, the interesting question has to do with why certain formalisms correctly model entanglement while others don't. What's the important difference between them? The current focus seems to be on separability vs nonseparability. LR formalisms are separable, while qm and Christian's are nonseparable. It's observed that qm and Christian's Clifford algebraic formalisms allow 'communication' between particles in imaginary spaces. But what does that mean? It's speculated that the real reason these formalisms work is because they don't skew the relationships between entangled entities via formal separation which is at odds with experimental design and preparation. This remains to be sorted out, and may never be fully because the exact characteristics of the underlying relationships (in real 3D space and time) are and will remain a matter of speculation.

I think we can say that Christian's current offering isn't an LR model of entanglement. It remains to sort out why it works -- what the formalism does, and maybe more importantly, what it doesn't do in light of reasonable inference from empirical evidence and sensory experience regarding the nature of entanglement.

I've benefitted from your analyses regarding this stuff, that is, your point regarding Bell and DrC is taken, and while your point helps to clean up the language surrounding Bell stuff, it doesn't diminish the correctness of their (Bell, DrC) math or the usefulness of their analyses, so anything you might want to say specifically about Christian's formalism in the current paper is welcomed.

 

[harrylin]

[..] Incompatibility between LR and qm/experiment doesn't imply that some form of nonlocality exists or that an underlying reality with specific properties doesn't -- in fact there's absolutely no empirical evidence that even suggests those notions. It's unfortunate that so much of the literature, and our understanding, has been clouded by claims to the contrary. [..]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
Harald

 

[ThomasT]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
Harald

Nonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable).

 

[Gordon Watson]

Nonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable).

1. This looks to me like an excellent summary of the two positions: mainstream LR versus more mainstream QM. (Or the beginning of one.)

2. It certainly looks like my view of LR, which I associate with Einstein and EPR.

3. So I'd like to be sure that the summary is OK from the QM point of view.

4. In other words: I'd like to see this summary endorsed by those who believe a LR view of the world to be untenable; or by those who might modify the QM view (expressed above) to a more mainstream (and accurate) expression.

5. In other words: Can we sharpen the current dichotomy between LR and QM, in the way ThomasT has begun here, ENSURING that the views he has captured/initiated are "corrected if necessary" so as to be widely accepted by both camps ... and are similarly compressed?

6. In a nutshell: I personally see no objection to the LR view, as expressed above (at this early hour, for me). Is the QM view equally OK?

 

[DrChinese]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
Harald

You have the option of accepting non-realism and retaining locality.

 

[ThomasT]

You have the option of accepting non-realism and retaining locality.

You mean like QFT? Is that really local in the sense that LR means local, ie., in real space and time? I've not studied it yet.

 

[DrChinese]

1. This looks to me like an excellent summary of the two positions: mainstream LR versus more mainstream QM. (Or the beginning of one.)

I sometimes call it "quantum non-locality" to make it clear that it complies with the QM formalism.

Since you are also a fan of EPR: I would say that EPR would never have contemplated the kind of correlations that today are commonplace in Bell tests. You have to believe that Bell would have altered Einstein's view of things substantially.

 

[DrChinese]

You mean like QFT? Is that really local in the sense that LR means local, ie., in real space and time? I've not studied it yet.

I mean as in MWI, which is considered local non-realistic.

 

[ThomasT]

I mean as in MWI, which is considered local non-realistic.

Ah, thanks. I forgot about that one.

 

[Gordon Watson]

I sometimes call it "quantum non-locality" to make it clear that it complies with the QM formalism.

Since you are also a fan of EPR: I would say that EPR would never have contemplated the kind of correlations that today are commonplace in Bell tests. You have to believe that Bell would have altered Einstein's view of things substantially.

Thanks for added clause, with its emphasis.

Re EPR: MHO is the opposite to yours, entanglement being a commonplace in QM, even in their day. They (in fact) choosing entanglement to emphasize their commitment to local realism.

The final EPR sentence being: "We believe, however, that such a theory is possible."

You and I differing as to whether Bell settles the issue; https://www.physicsforums.com/showpost.php?p=3219776&postcount=153 notwithstanding.



So

Nonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable).

leads to this; Yes, thus far?

...

Nonlocality (NL) in LR and QM refers to different things:

1. In LR, for Einstein, EPR, and local realists, NL refers to instantaneous action at a distance in real space and time. So NL is rejected; it is an unphysical mechanism; an impossibility.

2. In QM, NL refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (i.e., not scientifically ascertainable). Called "quantum non-locality" (QNL) to emphasize its compliance with the QM formalism, there is no connection to any physical mechanism.

...

 

[DrChinese]

Re EPR: MHO is the opposite to yours, entanglement being a commonplace in QM, even in their day. They (in fact) choosing entanglement to emphasize their commitment to local realism.
...

Ah, not so fast! This was my point, entanglement was only coined as a word around that time (1935). And the theoretical elements of entanglement were not at all well understood then. As far as I know, the first physical entanglement was not demonstrated before 1970. So basically Alf and Bet were in their infancy.

 

[Gordon Watson]

Ah, not so fast! This was my point, entanglement was only coined as a word around that time (1935). And the theoretical elements of entanglement were not at all well understood then. As far as I know, the first physical entanglement was not demonstrated before 1970. So basically Alf and Bet were in their infancy.

...

Sorry Doc, I thought twas me that was slowing down.*

Please see Schroedinger (1935), where the term "entanglement" was first introduced: To describe the then-well-known connection between quantum systems (Schroedinger, 1935; p. 555):

"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled." original emphasis by Schroedinger, emphasis added by GW.

PS: We theorists, when theorizing correctly, tend not to wait upon confirmatory experiments.

...
* a possible impossibility that I need more time to think about.

 

[DrChinese]

...

Sorry Doc, I thought twas me that was slowing down.*

Please see Schroedinger (1935), where the term "entanglement" was first introduced: To describe the then-well-known connection between quantum systems (Schroedinger, 1935; p. 555):

"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled." original emphasis by Schroedinger, emphasis added by GW.

PS: We theorists, when theorizing correctly, tend not to wait upon confirmatory experiments.

...
* a possible impossibility that I need more time to think about.

That was actually the exact quote I had in mind, 1935, same year as EPR. So thanks for sharing this.

Obviously, if a system of 2 particles becomes separated spatially, he is saying there is a non-local connection between them. That's the theory, anyway. And yet many theorists rejected this particular element of QM, including Einstein. Having an experiment in hand does matter to many!

And I have absolutely no doubt Einstein would have been very swayed by Bell's reasoning, and completely convinced after Aspect's experiment. In fact, I cannot think of a single influential physicist who does not accept Bell/Aspect as convincing. Of course, the many successes of QM through the years has been quite important to getting folks to this point.

 

[ThomasT]

And I have absolutely no doubt Einstein would have been very swayed by Bell's reasoning, and completely convinced after Aspect's experiment.

Me too. Einstein was, after all, a great physicist. It's just that he was motivated by a desire for a fundamental theory based more on (and developed in accordance with) natural philosophical insights than on abstract mathematical insights. But the evidence following Bell would have convinced him that such an approach meets insurmountable obstacles wrt the formalisms necessary for correspondence with experimental results. At some point(s), there's only the math (which might or might not lead to insights regarding the underlying reality).

In fact, I cannot think of a single influential physicist who does not accept Bell/Aspect as convincing. Of course, the many successes of QM through the years has been quite important to getting folks to this point.

Yes. And to tie this to the Christian offering that's being considered in this thread, my interest is in ascertaining whether it might offer any insights, regardless whether it can be properly called an LR model or not. I think all agree that it isn't an LR model.

So, once again, a call for any observers who can offer some insight into Christian's formalism.

 

[Q-reeus]

...So, once again, a call for any observers who can offer some insight into Christian's formalism.

Have you tried contacting him directly? Email address is listed on most if not all his arXiv papers.

 

[ThomasT]

Obviously, if a system of 2 particles becomes separated spatially, he is saying there is a non-local connection between them.

That's not exactly what Schrodinger said, and since the term nonlocality has different meanings, it might do to clarify.

What Schrodinger said was:

... after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own.

The only connection he refers to is a local one. And that, after that local interaction, neither of the subsystems can be described "by endowing each of them with a representative of its own". In other words, following the interaction, and wrt the system, neither of the subsystems can be described as an entity or function that's separable from the other. Which is in accordance with Bell's theorem and the qm formalism. The standard qm formalism doesn't explicate a nonlocal connection in real space and time. It's acausal.

But, and here's the key point, what Schrodinger said is also in accordance with the understanding that the relationship between the particles can't be represented as a combination of separable and variable λ functions (whether λ is allowed to be continuous or not) , if the underlying parameter determining coincidental detection is constant from pair to pair. It was, apparently, recognized long before Bell, in the development of standard qm, that λ, the determiner of individual detection, was not the determiner of coincidental detection. This understanding is incorporated into the qm formalism in the only way that it could be (via nonseparability) so as to not skew the statistical predictions of the qm formalism.

The qm projection along either of the unit vectors associated with paired detection attributes seems to me to be conceptually based on this understanding, which is compatible with the classical view.

 

[ThomasT]

Have you tried contacting him directly? Email address is listed on most if not all his arXiv papers.

I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

 

[DrChinese]

I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

Nice reference, ThomasT! There is plenty there for anyone who wishes to learn more.

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions. He instead describes topological issues that do not seem to relate to the EPR paradox in any sense I understand. In fact, sort of reminds me of Caroline Thompson's Chaotic Ball example. But you can read all that in the thread. An excerpt of Joy's comments, quote:

In my view Bell’s theorem is based on a serious topological error. The error lies in the very first equation of Bell’s famous paper. He associates numbers +1 and -1 with the end results of an EPR-type experiment, and writes them as A ( a, L ) = +1 or -1. What could be wrong with such an innocent assumption? Well, the problem is that A and B are supposed to represent values of the EPR elements of reality (or spin components). But EPR-Bohm elements of reality have a very specific topological structure---they live on a unit 2-sphere (i.e., on the surface of a unit ball). This topological structure differs from the topological structure presumed by Bell in the functions A ( a, L ) = +1 or -1, which live on a unit 0-sphere, not 2-sphere. Thus Bell’s theorem simply does not apply to the EPR argument, unless one modifies his main assumption by writing his function as A ( a, L ) = +1 or -1 about a. After all, no one has ever observed a “click” in an experiment other than about some experimental direction a. With this simple change the function A now takes on values in a topological 2-sphere, not the real line, thereby correctly representing the EPR elements of reality. The values of the spin components are still +1 or -1, but they now reside on the surface of a unit ball. This, in essence, is the only change I have made in any of my papers. But once this change is made, no contradiction with quantum mechanics arises. In fact I have been able to reproduced many complicated quantum mechanical results by implementing this corrected assumption. And I have done this in a manifestly local and realistic manner. Hence the title “disproof of Bell’s theorem.”

 

[yoda jedi]

I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

it seem that this the essence of one of your objections (interesting).
can be traced it in your posts, but it will take time.

..."But for this claim to be true, Bell must first adapt the EPR premises correctly within his own demonstration. So my first observation is that the very first equation of Bell's famous paper is incompatible with the EPR premises---i.e., with their criteria of locality, reality, and completeness. This becomes evident when one looks at these criteria collectively---not individually as is usually done---within the coherence of the EPR argument. Now an inequality derived using a faulty assumption cannot possibly have relevance for the question of local realism. Therefore, just as von Neumann's theorem could not rule out all hidden variable theories because of its faulty assumption, Bell's theorem cannot---and does not---rule out a local-realistic theory of physics. End of the story!"....

 

[ThomasT]

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions.

It answers the important question of whether it's an LR model (which it isn't), and it tells us that Christian is not understanding fully that the LR program is about producing a viable "LR" model (which is impossible). But it doesn't explore the deeper reasons for why LR models of entanglement are impossible even if the universe and all its subsystems are evolving exclusively in accordance with the principle of local causality and the SR limit.

He instead describes topological issues that do not seem to relate to the EPR paradox in any sense I understand.

I don't understand it either. Yet. It will be interesting to reread his stuff and attempt to translate it into some sort of understanding in classical terms.

In fact, sort of reminds me of Caroline Thompson's Chaotic Ball example.

I never bothered reading that one. Even in my earlier confusions it seemed clear to me that she had the wrong slant on things.

 

[ThomasT]

it seem that this the essence of one of your objections (interesting).
can be traced it in your posts, but it will take time.

..."But for this claim to be true, Bell must first adapt the EPR premises correctly within his own demonstration. So my first observation is that the very first equation of Bell's famous paper is incompatible with the EPR premises---i.e., with their criteria of locality, reality, and completeness. This becomes evident when one looks at these criteria collectively---not individually as is usually done---within the coherence of the EPR argument. Now an inequality derived using a faulty assumption cannot possibly have relevance for the question of local realism. Therefore, just as von Neumann's theorem could not rule out all hidden variable theories because of its faulty assumption, Bell's theorem cannot---and does not---rule out a local-realistic theory of physics. End of the story!"....

Anything that clarifies the discussion is welcomed.

 

[Gordon Watson]

<SNIP>

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions.<SNIP>

Just a reminder: The question of data-sets is being addressed on that other thread. https://www.physicsforums.com/showthread.php?p=3219803#post3219803

PS: Clarification of your "Why" question would ease continuation there. https://www.physicsforums.com/showpost.php?p=3221967&postcount=156

Thanks, as always.

 

[DrChinese]

Just a reminder: The question of data-sets is being addressed on that other thread. https://www.physicsforums.com/showthread.php?p=3219803#post3219803

Joy clearly thinks that a dataset is unnecessary when his reasoning is so sound. Yet no one really follows the logic of the "disproof" while Bell's own reasoning is easy to follow. So a dataset would be a simple way to demonstrate success to those of us unwilling to accept Joy's characterization of the relevant issues.

As a reminder, here are the dataset rules (which should be demanded of any purported LR model):

a) Perfect correlations
b) QM expectation value
c) Simultaneous hidden variable (HV) values for 3 angle settings: 0, 120, 240 degrees
d) A way to map those HV values to a {+1, -1} observation value without reference to a remote setting

 

[Gerhard78]

http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_physicist_joy_christian_collect_nobel_prize-79614" may help.

 

[harrylin]

http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_physicist_joy_christian_collect_nobel_prize-79614" may help.

OMG! ... If those email conversations are true, then I'm afraid that this "alpha male" Sascha is right ("scaling problem"? Why, what scaling?? To me this doesn't make any sense).

PS on second reflection, one should not confuse two very different issues. Take for example if I lived in the middle ages and came with the theorem that it is impossible to make a flying machine because any building material is heavier than air. Comes a guy who says that he derived that it should be possible to fly, thanks to some not-yet understood properties of air. OK then I say, just show us! The guy accepts that challenge but he has a mistaken idea of how to do that and crashes in a cloud of bamboo sticks and feathers. Thus he was wrong and it is impossible to make a flying machine.

 

[DrChinese]

Comments on "Disproof of Bell's theorem", Florin Moldoveanu

http://arxiv.org/abs/1107.1007

"In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory..."

A contextual hidden variable theory is not realistic. (This class of theory flies in the face of the EPR dictate that it is unreasonable for one observer to be able to determine the reality of another who is spacelike separated.) For a number of different reasons, the author is able to demonstrate why the Christian paper does little to Bell.

 

[Delta Kilo]

Wow, just wow. 5 pages of metaphysical discussion and no-one actually bothered to look at the half-a-page of math to see the elephants lurking therein.

Well, let's look at eq (5). I'll copy it down for your convenience:

$E(a,b)=\frac{\lim_{n \to \infty} \{ \frac 1 n \sum_{i=1}^n A(a,\lambda^i) B (b, \lambda^i)\} }{\{-a_j \beta_j\}\{ b_k \beta_k\} }$

I assume the intention was to compute correlation as in

$corr(X,Y)=\frac{E[(X-E[X])(Y-E[Y])]}{\sigma_X\sigma_Y}$

But but look at the denominator ! Note that $\beta_j$ are not real numbers but members of Clifford algebra, and for many $a,b$ they do not cancel each other out! The author says and I quote

where the denominators in (5) are standard deviations.

Err, WHAT ? Does it look like a standard deviation to you? Last time I checked standard deviation was computed as

$\sigma_X=\sqrt{E[(X-E[X])^2]}$.

and it was a non-negative number and most certainly not an element of some fancy Clifford algebra.

Now, just for fun, let's take a closer look at $A(a,\lambda)$:

$A(a,\lambda) = \{ -a_j \beta_j \} \{ a_k \beta_k(\lambda) \}$

written with explicit summation:

$A(a,\lambda) = \underset{\small j}{\Sigma} [ - a_j \beta_j ] \underset{\small k}{\Sigma} [a_k \beta_k (\lambda) ]$

substitute $\beta_j(\lambda)=\lambda\beta_j$:

$A(a,\lambda) = \underset{\small j}{\Sigma} [ - a_j \beta_j ] \underset{\small k}{\Sigma} [a_k (\lambda \beta_k) ]$

move $-\lambda$ outside the sum:

$A(a,\lambda)=-\lambda\underset{\small j}{\Sigma} [a_j \beta_j ] \underset{\small k}{\Sigma} [a_k \beta_k ]$

open the brackets:

$A(a,\lambda) = -\lambda \underset{\small j,k}{\Sigma} (a_j a_k \beta_j \beta_k)$

re-group:

$A(a,\lambda)= -\lambda [\underset{\small j}{\Sigma} (a_j^2 \beta_j \beta_j) + \underset{\small j \ne k}{\Sigma} a_j a_k (\beta_j \beta_k + \beta_k \beta_j)]$

use $\beta_j \beta_j = -1$ and $\beta_j \beta_k = - \beta_k \beta_j, j \ne k$:

$A(a,\lambda)= \lambda \underset{\small j}{\Sigma} a_j^2$

and since $|a|=1$:

$A(a,\lambda) = \lambda$, and similarly $B(b,\lambda) = -\lambda$

Err, WTF?! Hello-o-o?!

From here we have $E_A(a)=E_B(b)=0$, $\sigma_A(a)=\sigma_B(b)=1$, $E(a,b)=-1$ and therefore

$|E(a,b)+E(a,b')+E(a'b)-E(a'b')|=2$ $\forall a,b,a',b'$

Dum dum dum dum another one bites the dust dum-dum

DK