Is Bell's Logic Aimed at Decoupling Correlated Outcomes in Quantum Mechanics?

[DrChinese]

Again you are putting words in the "mouth" of EPR. They never provided a definition reality like the one you are suggesting. They said:... [snip]

...Note that they do not say the physical quantity being predicted, is itself an element of reality, just that it corresponds to one.

"If, without in any way disturbing a system, we can predict with certainty (i.e, with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way, whenever the conditions set down in it occur. Regarded not as a necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality..."

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."

Funny. That sounds pretty, pretty, pretty, pretty, pretty close to:

"Two or more physical quantities can be regarded as simultaneous elements of reality when they can be predicted with certainty without disturbing the particle in any way - regardless of whether those elements can be simultaneously predicted."

Yes, I do agree that the phrase "corresponding to" is much much different from "regarded as". Oh gosh now, they actually said both didn't they...

And please, don't chop up poor ol' Bell any more than you already have. You're the one who thinks his work is "fatally flawed" or whatever you called it. As I have said many times, you're the local realist - why don't you define realism and then we can move on. Either your definition will agree with EPR or it won't. Obviously, if you are in the group that thinks the EPR is not sufficiently restrictive, then you don't agree with the EPR conclusion. If you do agree with their definition, then you should agree with the Bell conclusion. Go for it!

 

[DrChinese]

I'm just curious to see how DrC will manage to distort EPR and Bell this time.

I like to distort them by using verbatim, in context quotes. Insidious!

 

[Maaneli]

And please, don't chop up poor ol' Bell any more than you already have.

Actually, you're the one who consistently misrepresents Bell's argument, regardless of all the contrary evidence right in front of your face.

 

[Maaneli]

I like to distort them by using verbatim, in context quotes. Insidious!

Actually, you have not quoted Bell on anything.

 

[Maaneli]

Realism is defined a la EPR. And if you don't think Bell used that exactly, read Bell again. I will be glad to supply the reference quotes (which can then be suitably ignored in favor of something else). But I am operating nearly verbatim at this point, both for EPR and Bell.

In my post #25, I showed you exactly how Bell defined realism, in relation to his local causality criterion. *You* are the one who has refused to acknowledge Bell's own definitions, instead saying some dismissive nonsense like "Bell said many things in many different ways" or something like that.

 

[DrChinese]

Actually, you have not quoted Bell on anything.

I'm stung!

Well, how about these:

ON THE EINSTEIN PODOLSKY ROSEN PARADOX
==================================
"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote."

That pretty much is a direct contradiction to the conclusion of EPR. And yet based on their very definition of realism.

 

[nismaratwork]

I'm stung!

Well, how about these:

ON THE EINSTEIN PODOLSKY ROSEN PARADOX
==================================
"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote."

That pretty much is a direct contradiction to the conclusion of EPR. And yet based on their very definition of realism.

Oh Maaneli, I hate to add fuel to the fire that is consuming you, but one of the best treatment of this very subject is on a website named (and I presume owned) by Dr. Chinese. It seems very rigorous to me.

http://www.drchinese.com/David/EPR_Bell_Aspect.htm

I might add, I didn't look for it, this was the #3 result when I googled: "bell definition of reality epr quote"

 

[nismaratwork]

Oh, and this: http://www.springerlink.com/content/j17l7457p2357154/

 

[morrobay]

If the assumption is that a single particle has three such elements of reality at three different angles, then the fact that no experiment has ever been performed in which a single particle was measured at three angles, let alone 2, should be a relevant omission, shouldn't it?

billshnieder, instead of waiting for a perfect experiment, could you derive an inequality
as simple as the original Bell inequality.
That is based on and comports with the existing experiments.

 

[Maaneli]

I'm stung!

Well, how about these:

ON THE EINSTEIN PODOLSKY ROSEN PARADOX
==================================
"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote."

That pretty much is a direct contradiction to the conclusion of EPR. And yet based on their very definition of realism.

That quote does nothing to support your claim, and once again you fail to recognize that the EPR argument is an argument FROM locality TO outcome determining hidden-variables. In other words, the notion of realism that EPR propose already includes a notion of locality and causality. What Bell did was to make mathematically precise these notions in the EPR argument, via his use of a theory of local beables satisfying his principle of local causality (as I explained in post #25). Bell *himself* also explains this in the quote that Bill posted. And for your information, Bill's quote of Bell is not taken out of context. You would see that if you read the paper (from which the quote was taken) in full.

By the way, I am still waiting for you to read Bell's La Nouvelle Cuisine and to get back to me, as you promised that you would.

 

[DrChinese]

By the way, I am still waiting for you to read Bell's La Nouvelle Cuisine and to get back to me, as you promised that you would.

I read it long ago, just want to refresh so I can properly mangle some context.

I think it is fairly funny that you think EPR is about locality. That relativity was to be respected was assumed.

 

[Maaneli]

I read it long ago, just want to refresh so I can properly mangle some context.

OK, so did you understand Bell's reasoning? Do you now see how he uses the assumptions of locality and causality in the derivation of his inequality?

I think it is fairly funny that you think EPR is about locality. That relativity was to be respected was assumed.

I'm sure you do, but that's because you haven't understood the EPR argument.

 

[ThomasT]

Maaneli, I understand that you're PhD physicist. Is this correct? What is your primary field? What is your motivation for being interested in the Bell stuff?

I'm asking this because you seem to be qualified to evaluate the statements presented in this thread, and also because I still don't understand what DrC is talking about. So, is it just me (I am an ignorant layperson -- with a riduculously high IQ and a knowledge of Fourier analysis), or is he, so far as you can ascertain, not making any sense wrt his requirement(s) for LR models of entanglement?

 

[Maaneli]

Maaneli, I understand that you're PhD physicist. Is this correct? What is your primary field? What is your motivation for being interested in the Bell stuff?

I'm asking this because you seem to be qualified to evaluate the statements presented in this thread, and also because I still don't understand what DrC is talking about. So, is it just me (I am an ignorant layperson -- with a riduculously high IQ and a knowledge of Fourier analysis), or is he, so far as you can ascertain, not making any sense wrt his requirement(s) for LR models of entanglement?

ThomasT,

I don't yet have a PhD. Only a BS in physics in 2008. But I will begin my graduate studies at Clemson this upcoming year, with the intent to be advised by Dr. Antony Valentini for my PhD. My 'primary field' centers around a few areas, namely, the foundations of quantum mechanics, stochastic quantization theories, the de Broglie-Bohm theory and its variants, and designing experimental tests of hidden-variables theories. Recently, I've also developed hidden-variable versions of semiclassical gravity and quantum gravity. I'm interested in Bell stuff because as an undergraduate, I was enamored with the possibility of local and nonlocal hidden variable theories underlying QM, and it was important for me to understand Bell's theorem in order to evaluate the physical possibility of said hidden variable theories.

As for evaluating statements in this thread, I haven't been following your exchange with DrC, so I can't comment on that. But my exchange with DrC has been over his misunderstanding of the assumptions used in Bell's theorem, his faith in the authority of Aspect and Zeilinger quotes, and what the implications are of experimental Bell inequality violations. DrC thinks (as, admittedly, do most people in physics) that Bell assumed something like "Local Realism", and that Bell's theorem shows that QM is inconsistent with either the assumption of Realism or Locality (though DrC says his own preference is to conclude that QM is inconsistent with Realism). By contrast, I am trying to point out to him that not only is the phrase Local Realism vague and misleading (it gives the impression that Locality and Realism are two separated assumptions of Bell's theorem, and it is unclear what Realism is intended to mean (independently of Bell's definition of Locality) in Bell's theorem), but Bell himself never used such a phrase to characterize the assumptions in his own theorem - rather, Bell spoke of Local Causality, and showed clearly how his definition of Locality relies on a specific notion of realism involving 'beables', the implication being that it makes no sense to claim that the QM violation of Bell's inequality implies that QM is inconsistent with Realism (as Bell defined it) but consistent with Locality (as Bell defined it). Also, I think that DrC has misinterpreted the EPR argument, both on its own terms, and as it relates to Bell's theorem.

 

[ThomasT]

Thanks Maaneli, I'll sit back and read the exchanges between you and DrC and I'm sure I'll learn something -- probably a lot that I haven't already considered. I hope that others as qualified as you will contribute to these threads on Bell's theorem, nonlocality, etc. I certainly appreciate DrC's contributions, but I just don't understand what he's saying sometimes.

I'm fascinated by the possible implications of Bell's work, but I don't want to jump on the 'nonlocality bandwagon', so to speak, until I'm satisfied that I've investigated, and understand, it thoroughly.

 

[DrChinese]

I certainly appreciate DrC's contributions, but I just don't understand what he's saying sometimes.

Neither do I!

 

[DrChinese]

... his faith in the authority of Aspect and Zeilinger quotes, and what the implications are of experimental Bell inequality violations. DrC thinks (as, admittedly, do most people in physics) that Bell assumed something like "Local Realism", and that Bell's theorem shows that QM is inconsistent with either the assumption of Realism or Locality (though DrC says his own preference is to conclude that QM is inconsistent with Realism)...

First, I think it is awesome that you will be studying with Valentini. I wish you the best, and am looking forward to seeing some papers from you in a few years.

Second, I don't rely at all on secondary quotes or work. I do all of my analytical work against primary sources. Secondary sources, such as the quotes by Zeilinger, are not authoritative in my book. The only reason I quote them - ever - is just to provide some background which supports ideas that are better expressed in the original but may be long and involved. So something like the Aspect/Zeilinger quotes from summary type articles often cut to the chase and indicate the standard view of the community at large.

Which I why I usually resist discussing Bell's book "Speakable and Unspeakable in Quantum Mechanics", although I am interested in discussing this with you.

 

[Maaneli]

First, I think it is awesome that you will be studying with Valentini. I wish you the best,

Thanks, that's kind of you.

and am looking forward to seeing some papers from you in a few years.

Hopefully sooner than that! :)

Second, I don't rely at all on secondary quotes or work. I do all of my analytical work against primary sources.

Oh, I don't doubt that your work involves primary sources from certain authors. But in this thread, I have only seen you post quotes of Zeilinger and Aspect.

Edit: And sections of EPR as well.

Secondary sources, such as the quotes by Zeilinger, are not authoritative in my book. The only reason I quote them - ever - is just to provide some background which supports ideas that are better expressed in the original but may be long and involved. So something like the Aspect/Zeilinger quotes from summary type articles often cut to the chase and indicate the standard view of the community at large.

That's fair enough. But if someone asks you (as I did previously) for a primary source which discusses in detail a claim of the standard view (such as what constitutes the Realism assumption in the Bell inequality derivation), it helps if you can also post the primary source.

Which I why I usually resist discussing Bell's book "Speakable and Unspeakable in Quantum Mechanics", although I am interested in discussing this with you.

But if you say that your analytical work involves primary sources, then, as far as primary sources go, it is indispensable to study the papers in Bell's book! After all, many of the papers include his (exceptionally clear) elaborations on the mathematical and physical assumptions that went into his own theorem! And at the very least, I think it is a good idea to study those papers, so that you can compare Bell's understanding of his own theorem against the understandings of other people.

With that said, I'm glad that you're interested in discussing this with me. I hope we can follow through.

 

[Maaneli]

Thanks Maaneli, I'll sit back and read the exchanges between you and DrC and I'm sure I'll learn something -- probably a lot that I haven't already considered. I hope that others as qualified as you will contribute to these threads on Bell's theorem, nonlocality, etc. I certainly appreciate DrC's contributions, but I just don't understand what he's saying sometimes.

You're welcome, Thomas. Let me know if you have any questions or comments about the exchange.

I'm fascinated by the possible implications of Bell's work, but I don't want to jump on the 'nonlocality bandwagon', so to speak, until I'm satisfied that I've investigated, and understand, it thoroughly.

Edit: Let me start over.

An unavoidable conclusion of Bell's theorem is that standard QM is a nonlocal theory. Now, you might wonder whether by rejecting other (non locality) assumptions in Bell's theorem, one can construct a local hidden variables theory which can also violate the Bell inequalities, and perhaps be empirically equivalent to standard QM. For example, one might consider rejecting Bell's assumption that detector settings and measurement outcomes are "free variables" (in the sense that they only have physical implications on their future light cones). Typically, proposals which attempt to implement this possibility make use of some form of "backwards causation" along the past light cones of detectors. Local hidden variables theories and toy models along these lines have been extensively developed by the likes of Aharonov and Vaidman, O. Costa de Beauregard, Huw Price, Roderick Sutherland, Ken Wharton, and Steven Weinstein, just to name a few. At the moment, this backwards causation approach seems to be the only viable alternative to nonlocality. But even so, it should be emphasized that it is still considerably less developed than nonlocal theories such as standard QM and deBB theory.

 

[billschnieder]

There is a strong argument to be made though that nonlocality is by far the most theoretically plausible, but it's certainly not yet a done deal.

Jaynes wrote the following concerning this "nonlocality" (http://bayes.wustl.edu/etj/articles/cmystery.pdf):
Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal, ' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1

The spooky superluminal stuff [...] disappears as soon as we recognize, with Jeffreys and Bohr, that what is traveling faster than light is not a physical causal influence, but only a logical inference. Here is Bohr's quoted statement:
"Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical phase of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system."

In other words, "nonlocality" is not a strange concept in epistemology, it is only strange in ontology. The following analogy illustrates this (from http://arxiv.org/abs/0812.4506):

suppose that a demon rolls a pair of dice in a distant planet around Betelgeuse and that the outcome is a double-six. This nice result is immediately true on the Earth. Nevertheless, in accordance with Lorentz covariance, we will have to wait for at least 427 years before we could learn this good news. Therefore, on the one hand, we may consider that the instantaneous event is purely fictitious on the Earth. But on the other hand, the same instantaneous event may be considered as real since afterwards, we will be able to derive exactly its date and its location. In other words, the score of the demon may be considered as instantaneously valid at a distance.

The problem is, those suffering from the "Mind Projection Fallacy" do not appreciate the difference between epistemology and ontology. Jaynes describes it as follows:
Jaynes, E. T., 1990, `Probability in Quantum Theory,' in Complexity, Entropy, and the Physics of Information, W. H. Zurek (ed.), Addison-Wesley, Redwood City, CA, p. 381 (http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf)

The failure of quantum theorists to distinguish in calculations between several quite different meanings of 'probability', between expectation values and actual values, makes us do things that don't need to be done; and to fail to do things that do need to be done. We fail to distinguish in our verbiage between prediction and measurement. For example, the famous vague phrases: 'It is impossible to specify ... '; or 'It is impossible to define ... ' can be interpreted equally well as statements about prediction or statements about measurement. Thus the demonstrably correct statement that the present formalism cannot predict something becomes perverted into the logically unjustified and almost certainly false claim that the experimentalist cannot measure it!
We routinely commit the Mind Projection Fallacy: supposing that creations of our own imagination are real properties of Nature, or that our own ignorance signifies some indecision on the part of Nature. It is then impossible to agree on the proper place of information in physics. This muddying up of the distinction between reality and our knowledge of reality is carried to the point where we find some otherwise rational physicists, on the basis of the Bell inequality experiments, asserting the objective reality of probabilities, while denying the objective reality of atoms! These sloppy habits of language have tricked us into mystical, pre scientific standards of logic, and leave the meaning of any QM result ambiguous. Yet from decades of trial and error we have managed to learn how to calculate with enough art and tact so that we come out with the right numbers!

 

[Maaneli]

Jaynes wrote the following concerning this "nonlocality" (http://bayes.wustl.edu/etj/articles/cmystery.pdf):
Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal, ' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1

In other words, "nonlocality" is not a strange concept in epistemology, it is only strange in ontology. The following analogy illustrates this (from http://arxiv.org/abs/0812.4506):

The problem is, those suffering from the "Mind Projection Fallacy" do not appreciate the difference between epistemology and ontology. Jaynes describes it as follows:
Jaynes, E. T., 1990, `Probability in Quantum Theory,' in Complexity, Entropy, and the Physics of Information, W. H. Zurek (ed.), Addison-Wesley, Redwood City, CA, p. 381 (http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf)

Thanks, Bill. I've always found Jaynes' writings on the foundations of probability to be ground-breaking for its time.

Nonlocality is certainly "strange" (in the sense of being counter-intuitive to classical relativistic intuitions) with respect to ontology, but it should be emphasized that it is not a logically inconsistent part of the construction of certain versions of quantum theory, namely, ontological quantum theories such as de Broglie-Bohm, stochastic mechanics, and GRW collapse, where the ontology explicitly has a nonlocal dynamics.

 

[billschnieder]

Thanks, Bill. I've always found Jaynes' writings on the foundations of probability to be ground-breaking for its time.

Nonlocality is certainly "strange" (in the sense of being counter-intuitive to classical relativistic intuitions) with respect to ontology, but it should be emphasized that it is not a logically inconsistent part of the construction of certain versions of quantum theory, namely, ontological quantum theories such as de Broglie-Bohm, stochastic mechanics, and GRW collapse, where the ontology explicitly has a nonlocal dynamics.

But that is the thing, those theories are not ontological just because they are called that. For example dBB starts off by assigning ontology to a configuration. A configuration, is just a collection of information about a physical system. The configuration itself is not physical but epistemic. The so called "nonlocality" of dBB comes from the fact that this configuration contains information about the whole universe at once. It is not an ontological nonlocality but an epistemic one, even though the dBB theory also has clearer ontic components.

One thing that dBB theory shows clearly is the fact that QM is a mixture of both ontological and epistemological aspects, the problem is nobody has been able to clearly disentangle them yet. dBB came closest to doing that.

Many in the field seem to believe that quantum events have no physical causes, only probabilistic laws, but
"instantaneous action at a distance" or nonlocality, if it is ontological as is also often claimed, will qualify as physical cause. What gives?

 

[Maaneli]

But that is the thing, those theories are not ontological just because they are called that. For example dBB starts off by assigning ontology to a configuration. A configuration, is just a collection of information about a physical system. The configuration itself is not physical but epistemic. The so called "nonlocality" of dBB comes from the fact that this configuration contains information about the whole universe at once. It is not an ontological nonlocality but an epistemic one, even though the dBB theory also has clearer ontic components.

One thing that dBB theory shows clearly is the fact that QM is a mixture of both ontological and epistemological aspects, the problem is nobody has been able to clearly disentangle them yet. dBB came closest to doing that.

Many in the field seem to believe that quantum events have no physical causes, only probabilistic laws, but
"instantaneous action at a distance" or nonlocality, if it is ontological as is also often claimed, will qualify as physical cause. What gives?

I think I should clarify what is meant when it is said that deBB theory is an "ontological" theory. Roughly speaking, it means simply that the theory gives an observer-independent account of what fundamental objects *might* compose the real physical world. In other words, the ontology of deBB theory is a *hypothesis* of the ontology of the real physical world.

And to state it more accurately, the proposed ontology in deBB theory is not just a configuration of point particles, but rather a configuration of point particles whose dynamics supervenes on an ontological causal agent in configuration space, namely, the quantum wavefunction; and all the empirical predictions of the deBB theory (in other words, the epistemic aspect of the deBB theory) supervene on the dynamics of the particle configuration. So there is in fact both an ontological and epistemic aspect to the deBB theory, and the distinction and relation between the two is clear.

Regarding how nonlocality arises in deBB theory, what you said is not correct. The nonlocality in (standard) deBB theory is in fact ontological (as well as epistemic in the sense of how the nonlocality manifests in the empirical predictions of the deBB theory), because it is a consequence of the fact that the ontological quantum wavefunction (on which the dynamics of the particle configuration supervenes) is a field that lives on a 3N-dimensional configuration space, and which is in general not factorizable into tensor products of wavefunctions in 3-space.

Now, I should say that there do exist other ontological theories to which the standard deBB dynamics is an approximation. Examples of such theories are Nelson's stochastic mechanics, and Norsen's Theory of Exclusively Local Beables - in both of these theories, the quantum wavefunction in configuration space is neither ontological nor fundamental; rather, the wavefunction in configuration space plays a very specific epistemic role in encoding the (hypothesized) ontological fields that determine the dynamics of the particle configuration in those theories. But again, these are *different* theories from standard deBB, and the latter certainly has its own self-consistent interpretation involving both ontological and epistemic aspects.

As for why "many in the field seem to believe that quantum events have no physical causes, only probabilistic laws, but 'instantaneous action at a distance' or nonlocality, if it is ontological as is also often claimed, will qualify as physical cause", I quite agree with you that the physicists in the field who think that way are simply being inconsistent. And I think the reason for the inconsistency is a failure to fully grasp the implications of EPR and Bell's theorem.

 

[billschnieder]

And to state it more accurately, the proposed ontology in deBB theory is not just a configuration of point particles, but rather a configuration of point particles whose dynamics supervenes on an ontological causal agent in configuration space, namely, the quantum wavefunction;
...
Regarding how nonlocality arises in deBB theory, what you said is not correct. The nonlocality in (standard) deBB theory is in fact ontological (as well as epistemic in the sense of how the nonlocality manifests in the empirical predictions of the deBB theory), because it is a consequence of the fact that the ontological quantum wavefunction (on which the dynamics of the particle configuration supervenes) is a field that lives on a 3N-dimensional configuration space and which is in general not factorizable into tensor products of wavefunctions in 3-space.

I won't say I have an thorough understanding of deBB, but I'm not convinced that the wavefunction defined in configuration space, is necessarily ontological. The fact that the number of dimensions increases with number of particles is suggestive that at least for more than 1 particle, the wavefunction is not entirely ontological but includes epistemic aspects. So I do not doubt the fact that the wavefunction is nonlocal, just the idea that it is ontological.

EDIT:
David Bohm seemed to agree when he said the following:

While our theory can be extended formally in a logically consistent way by introducing the concept of a wave in a 3N-dimensional space, it is evident that this procedure is not really acceptable in a physical theory.
* Bohm, David (1957), Causality and Chance in Modern Physics. London: Routledge & Kegan Paul.

 

[Maaneli]

I won't say I have an thorough understanding of deBB, but I'm not convinced that the wavefunction defined in configuration space, is necessarily ontological. The fact that the number of dimensions increases with number of particles is suggestive that at least for more than 1 particle, the wavefunction is not entirely ontological but includes epistemic aspects. So I do not doubt the fact that the wavefunction is nonlocal, just the idea that it is ontological.

But my point is that in the *standard* deBB theory, all that there is is this nonlocal wavefunction and particle configuration, and the dynamical laws relating the two. And if the standard deBB theory is to be understood consistently on its own terms, the wavefunction can only be understood as ontological. (Maybe I should qualify this by mentioning that there are some Bohmians who think that the wavefunction can be understood as nomological (in other words, as something like a physical law); but I think there is overwhelming evidence which shows that such a view is untenable). Now, you may (reasonably) think that the standard deBB view of the nonlocal wavefunction being ontological is physically implausible, such as for the reason you just gave. But if you take that route, then you're implying a different theory than the standard deBB theory. And again, examples of theories along the lines of what you probably have in mind are those of Nelson and Norsen, where the nonlocal wavefunction is just epistemic, and the standard deBB theory is in some sense an approximation.

 

[Maaneli]

I won't say I have an thorough understanding of deBB, but I'm not convinced that the wavefunction defined in configuration space, is necessarily ontological. The fact that the number of dimensions increases with number of particles is suggestive that at least for more than 1 particle, the wavefunction is not entirely ontological but includes epistemic aspects. So I do not doubt the fact that the wavefunction is nonlocal, just the idea that it is ontological.

EDIT:
David Bohm seemed to agree when he said the following:

Bohm changed his mind about that later in life, btw.

 

[DrChinese]

Saw a nice article about Bell today from someone who knew him (Jeremy Bernstein):

http://arxiv.org/abs/1007.0769

From the article (in the author's words), regarding the Theorem: "Quite generally no local hidden variable theory can reproduce all the results of quantum mechanics."

He gives this as a short description of EPR: "Some mechanism produces a pair of spin-1/2 particles in a singlet state. They fly off in opposite directions to a pair of Stern-Gerlach magnets. Let us say that one of the magnets is oriented in the z-direction and let us say that it measures the spin of one of the particles to be “up.” Because of the correlation we have already discussed we would predict that, when measured, the spin of the other particle will be “down.” EPR go a step further. They would argue that in this set up the z-component of the spin of the other particle has been implicitly measured and that this implicit measurement has conferred “reality” on this quantity. One can then set about to measure the x-component by rotating the magnet. This having been done we have both components measured which quantum mechanics says is impossible. The solution to this problem, if it is a problem, is to insist that “implicit measurements” in the quantum theory don’t count. Either you measure something or you don’t. You cannot measure the x and z components simultaneously. You need two different experiments. Bell of course understood this, but I think that it was thinking about double Stern-Gerlach experiments in this context that set him off."

He discusses Bell's thoughts on dBB as well, as well as Bell's regret that in spite of Einstein's position on EPR being reasonable, he considered it wrong. He also discusses the von Neumann's no-go theorem as Bell saw it.

If you want to understand Bell's logic, this will probably assist.

 

[andrewr]

Dr.Chineese,

Glad to see someone else who notices the double experiment of symmetrical particles vs. two experiments on the same electron issue.

I am not sure that Bohm is right on the hidden variables theory, though, and that is because of an assumption that everyone (Einstein included) makes concerning the nature of a moment of inertia; vis that the magnetic analog is equivalent to a solid object spinning in space and thus its momentum (pseudo) vector angle with respect to an arbitrary fixed axis does not evolve in time.

A moments thought (pun intended) shows that this assumption is not justified in any way or sense -- and that even a double (or perhaps especially) Stern Gerlach experiment would fail to yield the proper result.

No one knows what is rotating, spinning, making a circuit, when they say an "electron" has angular momentum. The Bohr magneton value itself only tells one how much a coulomb charge would have to move spatially in order to generate the magnetic field -- but this is part of the crux; any moving coulomb charge/field necessarily involves two dimensions. The effective charge, no matter what the cause, has to translate along two axii in order to generate a looping effect which is required to form a dipole moment. There is then, some kind of radius in an inertial plane which a charge moves around.

The relation of moment value = current times area enclosed, or equivalently velocity of a point charge multiplied by a value equivalent to the "radius" of the object enclosing area does not give one the same rigidity as a solid sphere idea might.

There is no known external cause for this curvature of motion of coulomb charge/wave propagation in an EM field, but saying that an electron has it regardless of why still implies that there is an unknown (hidden) variable causing it (Einstein POV). What is certain is that space itself does not translate "spin" in the mathematical treatments of EM fields (or even the A field from Einstein) but upon thoughtful consideration microscopic and vaguely helix-like shapes of time retarded coulomb motion are what I picture propagating.
.
If one were to imagine an electron as coulomb charge orbiting empty space even if for no detectable reason at all -- then it is clear that at any given moment in time in the plane of rotation -- regardless of whether the path is truly circular -- that the charge would be changing its direction back and forth periodically. In an equivalent note, since electrons precess in a magnetic field if they don't happen to be perfectly aligned angular momentum wise with the magnetic field -- that the precession angle would change with time. Given that no two magnetic devices are going to have "EXACTLY" the same magnetic field structure -- that even if an experiment with two magnets were constructed, it could not guarantee the needed symmetry to remove the random fluctuation caused by precession. Since the electron at any given moment can be moving in one of two directions in the plane perpendicular to its moment -- attempting to measure its angular momentum with respect to a detector 90 degrees out of phase with the other one is going to produce results which vary randomly.

I am not sure it is meaningful to base the idea of "locality" on the angular momentum vector itself for in effect, even classically -- given the unknown nature or even radius of an electron -- there is simply a degree of freedom in the mathematics which is being glossed over by the standard practice of treating magnetic fields as if they existed at points. Einstein himself, taking the magnetic effect as nothing more than a time delay effect of the electric field propagation in space, ought to have noticed the contradictory nature of assuming the magnetic moment pseudo-vector to be anything but a convenient average.

I don't see how (perhaps you do?) that one can really say a particle whose direction of travel reverses 50% of the time in any axis except the one where its magnetic pole shows up the strongest -- has a value; it certainly isn't truly "zero" in the sense that a magnetic inertia vector would suggest -- for the coulomb charge moves orthogonally at least some of the time to every possible axis of measurement.

If one tries to imagine the magnetic vector pointing "purely" in Z, hypothetically, then it must simultaneously cause a movement of charge in both X and Y axii. Since that is the case, If one tries to measure the Y axis -- then, the electron could be moving in either of two directions in the X axis causing a magnetic field to appear at that instant in time for the Y axis ... the same applies to measuring in the X axis for the electron must move at least occasionally the coulomb charge in the Y direction. In effect, for a single or minimal magnetic field -- there is no way to really say that it's vector points purely and only in one direction. In effect, if it points in z -- then it must simultaneously give up a static definition of the direction in x and y. Essentially, unless on can build two distinct magnets which have EXACTLY the same values -- and get an electron to follow the field strength EXACTLY the same -- I think that one might as well assume the x and y magnitudes of the field are randomly fluctuating. There is no reason to even believe that the coulomb charge effectively moves at a fixed radius or speed ; for many such combinations can give the same value for the dipole moment of the electron which is the only thing being measured.

Einstein's brilliant simplification of the EM field to a time delayed A (vector potential) also comes at a price -- for one can't distribute charge evenly around any geometric shape and then say that it's motion causes a magnetic field. It is the discreet nature of the charges which give rise to the magnetic effect -- for if the charges are perfectly spread out in a line charge; one is left to say that the E field does not change in the *SLIGHTEST* when the the charge moves. If that is the case, then there is no such thing as a change in the E field to propagate the magnetic effect of motion.

Although, arguing based on the average and idealized mathematical model may prove bell correct -- the fact is that Einstein himself did not fully exploit his own theory in the argument and the idealized mathematical model of the magnetic field, I am told, is overly simplified. Knowing E and B at every point in space is not the same as knowing A -- and there is an experimental difference detectable where E and B fields give no information.

If you think that bell's theory still proves non-locality, regardless of all the variations and degrees of freedom that I am outlining -- I would be curious as to why something which would statistically predict that knowledge of a magnetic moment in one direction simultaneously obscures the knowledge of that same information in two other axii is any different than the quantum mechanical assertion of the Heisenberg principle -- which I think does the same thing.

I enjoy reading your posts.

--Andrew.

 

[DrChinese]

...

If you think that bell's theory still proves non-locality, regardless of all the variations and degrees of freedom that I am outlining -- I would be curious as to why something which would statistically predict that knowledge of a magnetic moment in one direction simultaneously obscures the knowledge of that same information in two other axii is any different than the quantum mechanical assertion of the Heisenberg principle -- which I think does the same thing.

I enjoy reading your posts.

--Andrew.

I liked what you were saying about spin by the way, interesting stuff and really shows up issues in classical thought.

EPR was formulated based on ideas around the HUP. They say that the HUP, depending on your precise definition of elements of reality, leads either to an observer dependent reality or QM is incomplete. The QM is incomplete school is not looking too strong lately, so it appears we live in an observer dependent reality. And one which is consistent with the HUP.

With entanglement, you can have more than 1 observer to consider. So I guess that implies a form of nonlocality. I choose to think that traces back to the HUP. And that however the HUP works with 1 particle - if we really understood it - would also explain how entanglement works.

You mention degrees of freedom. It seems to me that entangled particles share degrees of freedom. They must have fewer, in a sense, than unentangled particles.

 

[Maaneli]

I liked what you were saying about spin by the way, interesting stuff and really shows up issues in classical thought.

EPR was formulated based on ideas around the HUP. They say that the HUP, depending on your precise definition of elements of reality, leads either to an observer dependent reality or QM is incomplete. The QM is incomplete school is not looking too strong lately, so it appears we live in an observer dependent reality. And one which is consistent with the HUP.

With entanglement, you can have more than 1 observer to consider. So I guess that implies a form of nonlocality. I choose to think that traces back to the HUP. And that however the HUP works with 1 particle - if we really understood it - would also explain how entanglement works.

You mention degrees of freedom. It seems to me that entangled particles share degrees of freedom. They must have fewer, in a sense, than unentangled particles.

OK, DrC, I am ready to resume our discussion of Bell. What do you think of Bell's La Nouvelle Cuisine paper after reading it? Do you see how his definition of Local Causality is inseparable from the notion of realism used in his theory of Local Beables?

 

[DrChinese]

OK, DrC, I am ready to resume our discussion of Bell. What do you think of Bell's La Nouvelle Cuisine paper after reading it? Do you see how his definition of Local Causality is inseparable from the notion of realism used in his theory of Local Beables?

Hi Maaneli, I am ready to discuss. Mostly I follow (i.e. agree with) the argument he is making here. I would not say it is the same as the original paper but certainly very similar.

Also, you have probably already seen this but if not:

M.P. Seevinck, J. Uffink, "Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean' " (2010)

"The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality. "

Nicely references both Norsen and La Nouvelle Cuisine (LNC), so right up the alley of our discussion.

Now, where to start? I think your point is that local causality is incompatible with QM's predictions, a result in agreement with LNC. As I follow the argument, you assert that realism is not a factor in this conclusion. Am I close?

 

[Peter McKenna]

I have a question. Is Feynman's diagram for light reflection in glass a proof or example of bell's theorum exhibiting the local causality by the effect of photon spin/polarization and subsequent refraction (assuming spin is effected by; and local polarity is a function of the speed over distance)? Is the curve produced by the percentage of reflection an exhibition of the inequality curve?

 

[Maaneli]

Hi Maaneli, I am ready to discuss. Mostly I follow (i.e. agree with) the argument he is making here. I would not say it is the same as the original paper but certainly very similar.

Also, you have probably already seen this but if not:

M.P. Seevinck, J. Uffink, "Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean' " (2010)

"The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality. "

Nicely references both Norsen and La Nouvelle Cuisine (LNC), so right up the alley of our discussion.

Now, where to start? I think your point is that local causality is incompatible with QM's predictions, a result in agreement with LNC. As I follow the argument, you assert that realism is not a factor in this conclusion. Am I close?

Hey DrC,

Thanks for getting back to me. I haven't seen this paper, so thanks. I'll try to have a closer look at it when I have more time.

Yes, close. To be more precise, the argument is that one cannot conclude from the incompatibility of local causality and standard QM predictions, that standard QM is incompatible with Bell's assumption of realism, but still compatible with Bell's criterion of local causality. Simply because the definition of local causality that Bell uses in his theorem relies on his realism assumption (the existence of beables). What one can conclude however is that standard QM is nonlocal causal.

Is that clear?

 

[DrChinese]

Hey DrC,

Thanks for getting back to me. I haven't seen this paper, so thanks. I'll try to have a closer look at it when I have more time.

1. Yes, close. To be more precise, the argument is that one cannot conclude from the incompatibility of local causality and standard QM predictions, that standard QM is incompatible with Bell's assumption of realism, but still compatible with Bell's criterion of local causality. Simply because the definition of local causality that Bell uses in his theorem relies on his realism assumption (the existence of beables).

2. What one can conclude however is that standard QM is nonlocal causal.

Is that clear?

1. I like this just fine. I think one of the interesting things about Bell is: regardless of the way you choose to marry QM and "common sense" - be it by asserting strict locality, causality, realism, hidden variables, etc. - there is going to be some combination you cannot resolve.

2. I thought the conclusion was a denial of local causality. What you say is almost the same thing, but then I get stuck on the word "causal". What if there is no cause? Not that I would know what that means.

But if I follow your drift, then you are saying that QM can be "completed" by the addition of nonlocal hidden parameters. Which conveniently is supplied by dBB.

 

[Maaneli]

1. I like this just fine. I think one of the interesting things about Bell is: regardless of the way you choose to marry QM and "common sense" - be it by asserting strict locality, causality, realism, hidden variables, etc. - there is going to be some combination you cannot resolve.

2. I thought the conclusion was a denial of local causality. What you say is almost the same thing, but then I get stuck on the word "causal". What if there is no cause? Not that I would know what that means.

But if I follow your drift, then you are saying that QM can be "completed" by the addition of nonlocal hidden parameters. Which conveniently is supplied by dBB.

The conclusion with respect to standard QM is that standard QM (SQM) cannot be embedded within a locally causal theory of hidden variables, because SQM predicts nonlocal correlations between measurement outcomes at spacelike separated detectors. SQM is a causal theory because the time-evolution of the SQM wavefunction is fixed by only an initial condition, and not, for example, by "two-time" boundary conditions. So one can deduce that SQM is incompatible with local causality because SQM is a nonlocal causal theory.

What could it mean to say that there is no "cause"? One (admittedly vague) possibility might be if the wavefunction was defined in terms of Block Time (where there is no objective distinction between past, present, and future instants of time). Then there would be no objective direction of causation, because the wavefunction would be defined throughout an eternal 4-D Block Universe.

Re my drift, essentially yes. The fact that standard QM is a nonlocal causal theory, naturally suggests (just as a logical possibility) that it might be possible to embed it into a nonlocal causal theory of hidden variables. And the deBB theory just happens to be an example of such a logically possible theory (though it is by no means uniquely implied by Bell's theorem).