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

[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).

 

[DrChinese]

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).

Very well said! As you are meaning these terms, I agree with everything you are saying. I think it is interesting that nonlocal can properly be used in several contexts here.

 

[Maaneli]

Very well said! As you are meaning these terms, I agree with everything you are saying. I think it is interesting that nonlocal can properly be used in several contexts here.

Cool, so ... would I be right to conclude that you now agree that realism and locality are not independent assumptions in Bell's theorem?

 

[DrChinese]

Cool, so ... would I be right to conclude that you now agree that realism and locality are not independent assumptions in Bell's theorem?

As said, it comes down to the words. You said: "...standard QM (SQM) cannot be embedded within a locally causal theory of hidden variables..." To me, that is essentially the same as saying "standard QM cannot be embedded within a local realistic theory."

I also like the way you say that QM makes predictions which are nonlocal causal. Yet that kind of nonlocality is quite different that the nonlocal connections in Bohmian type theories. In entanglement situations, the nonlocal connection relates to spin conservation. The nonlocal connection is associated with the entangled particles and apparently none other. And there is no apparent cause to the spin value.

In BM, there are nonlocal influences between all particle positions, and these are sufficient to explain the appearance of spin values. So in my book, these are very different uses of the term nonlocal (not that you were saying otherwise).

I believe the Heisenberg Uncertainty Principle is essentially something which implies both nonlocality and contextuality. So that could be construed as to imply nonlocal nonrealism. So yes, you could say that those are not separate independent assumptions from that side. But either way, the question is: could a local contextual theory be feasible? I still don't see why not.

 

[Maaneli]

DrC,

Thanks for your comments. Unfortunately, I'm very busy at the moment and may not be able to give a thoughtful reply any time soon. But I do intend to reply eventually.Maaneli

 

[Eye_in_the_Sky]

... the definition of local causality that Bell uses in his theorem relies on his realism assumption (the existence of beables).

The part in the parentheses can be made more precise so as to read:

... (that (certain relevant) beables exist as local beables).
_________________________
_________________________

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

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 one concludes is that, according to standard QM, the "Alice-and-Bob scenario" involves a phenomenon which is either:

(i) causally nonlocal ,

or

(ii) nonseparable – (i.e. "state" nonseparability) across a spacelike region of spacetime .
___________

Or, equivalently in Ruta's words:

(at least) one of the following applies:

(i) causal nonlocality ,

or

(ii) constitutive nonlocality .
___________

Or, equivalently in Bell's language:

(at least) one of the following is the case:

(i) violation of "local causality" ,

or

(ii) existence of "nonlocal beables" .
___________

And finally, equivalently, in DrC's words:

(i) "causal locality" does not hold ,

or

(ii) "reality" is dependent upon "observation" (i.e. Alice's reality is dependent upon Bob's choice of measurement, and/or vice versa – but not necessarily causally so) .
_____

e.g. from two posts from another thread:

... either [causal] locality does not hold, or reality is dependent on observation.

... Bob's reality is determined by a choice of measurement by Alice [along with the associated outcome].

_________________________
_________________________

... Okay, now going back:

... but then I get stuck on the word "causal". What if there is no cause? Not that I would know what that means.

This sounds like one of the places I have been stuck at for some time now, namely:

What does it (really) mean to say the following?

Alice's reality is dependent upon Bob's choice of measurement (and/or vice versa) – but not causally so.

(... Or is that not even (really) how to say it?)

 

[DrChinese]

And finally, equivalently, in DrC's words:

(i) "causal locality" does not hold ,

or

(ii) "reality" is dependent upon "observation" (i.e. Alice's reality is dependent upon Bob's choice of measurement, and/or vice versa – but not necessarily causally so) .
_____

e.g. from two posts from another thread:


... Okay, now going back:


This sounds like one of the places I have been stuck at for some time now, namely:

What does it (really) mean to say the following?

Alice's reality is dependent upon Bob's choice of measurement (and/or vice versa) – but not causally so.

(... Or is that not even (really) how to say it?)

See, it turns into a bit of a sticky wicket.

All I ever end up with is realizing that one classical notion - at a minimum - must go. If you juggle around enough, you can pick it yourself. Determinism, causality, observer independence, locality, separability, ...