Joy Christian, Disproof of Bell's Theorem

[billschnieder]

Nonseparability has been mentioned but I doubt that it's impact to this discussion has been fully understood. In the the Gordon Watson's linked thread he mentioned "triangle inequality", I have a variation of it which may throw some light in a simple and common sense manner why "nonseparability" is so important to the issue being raised by Joy Christian. DrC may be interested in this because it blows the lid off his "negative probabilities" article.

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.

Concerning negative probabilities, Dr C says:

X is determined by the angle between A and B, a difference of 67.5 degrees X = COS^2(67.5 degrees) = .1464 This prediction of quantum mechanics can be measured experimentally.*
Y is determined by the angle between A and C, a difference 45 degrees Y = SIN^2(45 degrees) = .5000 This prediction of quantum mechanics can be measured experimentally.*
Z is determined by the angle between B and C, a difference 22.5 degrees Z = COS^2(22.5 degrees) = .8536 This prediction of quantum mechanics can be measured experimentally.*

...

(X + Y - Z) / 2

Substituting values from g. above:

= (.1464 + .5000 - .8536)/2

= (-.2072)/2

= -.1036

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.

 

[ThomasT]

["Joy" inserted above for clarity. GW]

1. The thread initiated by me -- https://www.physicsforums.com/showthread.php?t=475076 --

is an off-shoot from another thread discussing Joy Christian's work.2. I make no claim as to whether Joy Christian does or does NOT understand the LR program. But I would be very surprised if he does not understand it exactly, precisely, whatever.

3. IMHO, it is not that difficult; unless I too am missing some extreme subtlety; or there is being inserted a requirement that goes beyond the Einstein and EPR program.

4. I would certainly expect that anyone, critically and carefully studying Bell's theorem, would be trying to ensure that their efforts did not breach the commonsense (the core Einstein and EPR principles) that attaches to the LR program.

5. However, in this widely rejected/neglected area of study (Einstein's baby, IMHO), slips are possible. So a better critique of JC's work, for those concerned by it, would be to identify JC's error specifically; my own critical opinion of JC's efforts not being relevant here.

6. The point that I would like to emphasize is this: The L*R program, discussed in the above thread (https://www.physicsforums.com/showthread.php?t=475076), is most certainly local and realistic, and in full accord with the Einstein and EPR program, as I understand it. (And I doubt that JC understands it any less than I do -- so why not help him find his slip -- IF slip there be. Because my "guess" is: it's fixable!)

See Carlos Castro's, There is no Einstein-Podolsky-Rosen Paradox in Clifford-Spaces . In C-space, the particles can exchange signals encoding their spin measurement values across a null interval, which isn't the sort of locality required by the LR program. Or can it be translated into that because this is essentially the same as specifying a relationship produced via a common source? I don't know.

Because Christian is using tensors (in the papers using Clifford algebra and in the paper currently under discussion with the Kronecker Delta, Levi-Cevita algebra) to deal with a relationship (which is what Bell tests are actually measuring) between vectors, then maybe I was too quick to dismiss his stuff. Or maybe not. Again, I don't know.

These articles might also be relevant:

Bound entanglement and local realism

All the Bell Inequalities

Clearly, we need some input from experts, or at least more knowledgeable, in the field.

 

[Gordon Watson]

Nonseparability has been mentioned but I doubt that it's impact to this discussion has been fully understood. In the the Gordon Watson's linked thread he mentioned "triangle inequality", I have a variation of it which may throw some light in a simple and common sense manner why "nonseparability" is so important to the issue being raised by Joy Christian. DrC may be interested in this because it blows the lid off his "negative probabilities" article.

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.

Concerning negative probabilities, Dr C says:

---Quote---
X is determined by the angle between A and B, a difference of 67.5 degrees X = COS^2(67.5 degrees) = .1464 This prediction of quantum mechanics can be measured experimentally.*
Y is determined by the angle between A and C, a difference 45 degrees Y = SIN^2(45 degrees) = .5000 This prediction of quantum mechanics can be measured experimentally.*
Z is determined by the angle between B and C, a difference 22.5 degrees Z = COS^2(22.5 degrees) = .8536 This prediction of quantum mechanics can be measured experimentally.*

...

(X + Y - Z) / 2

Substituting values from g. above:

= (.1464 + .5000 - .8536)/2

= (-.2072)/2

= -.1036
---End Quote---

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.

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, for one, will be very interested in studying this beautiful example. My current concern is to first show where BT fails. That for me will open the way for me (and others) to assess what I would presently call "analogies." For my job then would be to use examples such as yours; showing how they fit into a "more formal" disproof of BT.

Until that time, I can hear Bell's supporters discussing "loopholes" against you, ad nauseam.

(The boot will be on the other foot, as it were, for them then; considering all the loopholes that EPR-style supporters adduce to ignore BT and related experimental results. Me here wanting to be very clear that LOOPHOLES are not only unnecessary but unwarranted. And have never been considered valid or relevant by me.)

 

[ThomasT]

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.

You say you're varying θ randomly. So, <θ> = 45°, where <x> = cosθ = .707..., <y> = sinθ = .707... , (.707...)² + (.707...)² = 1. No violation.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.

Bell's inequality is based on the fact that for x,y,z = ±1, you have |xz - yz| = 1 - xy. Substituting x = A(b,λ), y = A(c,λ), z = A(a,λ) and integrating wrt the measure ρ, you get 1 + P(b,c) ≥ |P(a,b) - P(a,c)| , (Bell's inequality), in view of Bell's (14), P(a,b) = - ∫dλρ(λ)A(a,λ)B(b,λ) . There's no mathematical error in Bell's stuff.

Note how he (DrC) 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 don't see any mathematical error in DrC's stuff either. It's an interesting numerical treatment based on Einstein realism which demonstrates the incompatibility with qm.

 

[billschnieder]

You say you're varying θ randomly. So, <θ> = 45°, where <x> = cosθ = .707, <y> = sinθ = .707 . (.707)² + (.707)² = 1. No violation.

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? Even if your 45 degrees were correct which it is not, <x> is not the same as Sin<θ>. You may be tempted to say Sin(180) = 0 and Cos(180) = 1 which still adds up to 1 but the error here is that you are assuming that information is present in the experiment which is is not. Remember that x is a length and our experimenter is measuring a length not an angle. He is never given an angle, just a triangle so he can not determine <θ>. He only has the length which is the absolute value of Sin(θ). Secondly, were you to suggest that the mean value for x which he measured were <x> = 0 (cf sin(180)), you will be suggesting that he actually measured negative lengths which is not possible.

In fact <x> is 0.6366.. NOT 0.707 as you stated. You can verify it with a simple calculation, the python code below does that
0.6366^2 + 0.6366^2 = 0.81056.. NOT 1

I hope you see that this simple example is not as stupid as you may have assumed at first. In fact your misunderstanding of this example highlights exactly the point I'm trying to make.

import numpy
# generate 1million angles from 0 to 360
thetas = numpy.linspace(0,2*numpy.pi, 1000000)

# calculating |sin(<theta>)|
x1 = numpy.abs(numpy.sin(thetas.mean())) 
print "%0.4f" % x1
#Output: 0.0000                

# calculating <|sin(theta)|>
x2 = numpy.abs(numpy.sin(thetas)).mean()
print "%0.4f" % x2
#Output 0.6366

Bell's inequality is based on the fact that for x,y,z = ±1, you have |xz - yz| = 1 - xy. Substituting x = A(b,λ), y = A(c,λ), z = A(a,λ) and integrating wrt the measure ρ, you get 1 + P(b,c) ≥ |P(a,b) - P(a,c)| , (Bell's inequality), in view of Bell's (14), P(a,b) = - ∫dλρ(λ)A(a,λ)B(b,λ) . There's no mathematical error in Bell's stuff.

That is not my point. For the valid inequality |xz - yz| = 1 - xy., all three terms xz, yz, and xy are defined within the same probability space. You can not take terms from three different probability spaces and substitute them in the above equation. 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.

I don't see any mathematical error in DrC's stuff either. It's an interesting numerical treatment based on Einstein realism which demonstrates the incompatibility with qm.

Given that you did not understand my original point, I did not expect that you will see the error either. 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. If anybody thinks it is a valid mathematical procedure, let them say so and we can discuss that in a new thread.

 

[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.