Bohm Questions: What are Test Particles Good For?

[Vanknee]

Maaneli,

First, let's point out the parts of the discussion we agree about. I do not think that the Hamiltonian refers to anything physical. It refers to 'reality' by the potential (even if you'd say that the forces are necessary, but that's not part of what we agree on). Then, if DGZ do think of a wave function as a Hamiltonian as you describe it, I agree to dismiss it with you¹. But I understand your worry as concerning the fact that DGZ is a guidance view, not a monistic ontology. And I understand monistic as saying that there is only the corpuscles and the potential V. It is not dualistic because I do not give any kind of reality to the wave function, it refers to the potential, as the Hamiltonian refers to the external potential.
Note that I disagree that "potential energy itself is not physically real because its magnitude is entirely conventional". The fact that the magnitude of the potential is conventional does not imply anything about the reality of the potential. It is possible to understand the notion of potential as a relational property of space time points. This point has a potential higher than this other. If you use this formulation you make the convention disappear. I agree that it rests on a controversial hypothese (space time points), but I think you choose forces over potential a bit too fast. Anyway, as I said before, the debate monistic/dualistic ontology does not concern this part of the theory, I only want to deny that there is a quantum potential/force. If someone could bring a convincing interpretation which does not introduce a special quantum force but implies that we have to understand potentials primary to forces, would you accept it?

The second part of your objection concerns the necessity of a causal explanation. And I don't know why an explanation should be causal. The examples you give rest on the fact that the corpuscle "has some knowledge". It is obviously an analogy. But what does the analogy stands for? What is for a corpuscle to know where it should go? You could anwer as the necessity to have a force "telling" it where it should go. But your argument is circular, you ask for something you presuppose. Someone who does not agree that the corpuscle must have some knowledge (someone who doesn't agree that there is a need of forces) will not agree with you conclusion either we need something to make the knowledge transit: forces. My point of view would be, there is nothing telling the corpuscle where to go, but the geometry of the system (represented by V) determines the motion of the particle. We have the exact same debate than for the first part. What should we choose, potential or force?

remember that potential energy itself is not physically real because its magnitude is entirely conventional
[...]
the quantum potential force on a particle [...] is independent of the magnitude of the wavefunction, instead only depending on the form of the wavefunction.

As you can see here you are not completely consistent. Either potentials are real or they are not. So according to you point of view, I suppose you would take quantum forces as the real thing, this is Belousek strategy. Unfortunately (for you, not for me ;) ), if you do so these forces correspond to a non local action at distance. There is nothing transporting the information, Belousek acknowledges this as a weakness of his theory...

I still need to answer your objection about the stationary states, I'll do it another time...

By the way, what is exactly the interpretation you support?


¹I must admit I didn't catch this part of this interpretation, I always had the impression they were just vague about it. Do you have a quote where it is clear, or does this come from your discussions with them?

 

[Maaneli]

Maaneli,

First, let's point out the parts of the discussion we agree about. I do not think that the Hamiltonian refers to anything physical. It refers to 'reality' by the potential (even if you'd say that the forces are necessary, but that's not part of what we agree on). Then, if DGZ do think of a wave function as a Hamiltonian as you describe it, I agree to dismiss it with you¹. But I understand your worry as concerning the fact that DGZ is a guidance view, not a monistic ontology. And I understand monistic as saying that there is only the corpuscles and the potential V. It is not dualistic because I do not give any kind of reality to the wave function, it refers to the potential, as the Hamiltonian refers to the external potential.
Note that I disagree that "potential energy itself is not physically real because its magnitude is entirely conventional". The fact that the magnitude of the potential is conventional does not imply anything about the reality of the potential. It is possible to understand the notion of potential as a relational property of space time points. This point has a potential higher than this other. If you use this formulation you make the convention disappear. I agree that it rests on a controversial hypothese (space time points), but I think you choose forces over potential a bit too fast. Anyway, as I said before, the debate monistic/dualistic ontology does not concern this part of the theory, I only want to deny that there is a quantum potential/force. If someone could bring a convincing interpretation which does not introduce a special quantum force but implies that we have to understand potentials primary to forces, would you accept it?

The second part of your objection concerns the necessity of a causal explanation. And I don't know why an explanation should be causal. The examples you give rest on the fact that the corpuscle "has some knowledge". It is obviously an analogy. But what does the analogy stands for? What is for a corpuscle to know where it should go? You could anwer as the necessity to have a force "telling" it where it should go. But your argument is circular, you ask for something you presuppose. Someone who does not agree that the corpuscle must have some knowledge (someone who doesn't agree that there is a need of forces) will not agree with you conclusion either we need something to make the knowledge transit: forces. My point of view would be, there is nothing telling the corpuscle where to go, but the geometry of the system (represented by V) determines the motion of the particle. We have the exact same debate than for the first part. What should we choose, potential or force?


.As you can see here you are not completely consistent. Either potentials are real or they are not. So according to you point of view, I suppose you would take quantum forces as the real thing, this is Belousek strategy Unfortunately (for you, not for me ;) ), if you do so these forces correspond to a non local action at distance. There is nothing transporting the information, Belousek acknowledges this as a weakness of his theory...

I still need to answer your objection about the stationary states, I'll do it another time...

By the way, what is exactly the interpretation you support?


¹I must admit I didn't catch this part of this interpretation, I always had the impression they were just vague about it. Do you have a quote where it is clear, or does this come from your discussions with them?

Vanknee,

But I understand your worry as concerning the fact that DGZ is a guidance view, not a monistic ontology.

No, the other way around. I thought I was pretty clear about that in many instances. I have no problem with the guidance view as fundamental. In fact I did say "it could be a force (causal view) or an impulse (guidance view)".

And I understand monistic as saying that there is only the corpuscles and the potential V.

If there is an external potential, then yes. Otherwise, there are only corpuscles.

It is not dualistic because I do not give any kind of reality to the wave function, it refers to the potential, as the Hamiltonian refers to the external potential.

More or less. Remember they want to claim the wavefunction is a physical law though. Not just some conventional object. So it's not exactly like the external potential.

I must admit I didn't catch this part of this interpretation, I always had the impression they were just vague about it. Do you have a quote where it is clear, or does this come from your discussions with them?

Well I think they were quite clear about this comparison. Go to section 12 on page 10 and look at equations 17 - 19 of their paper:

Bohmian Mechanics and the Meaning of the Wave Function
Authors: Detlef Dürr, Sheldon Goldstein, Nino Zanghì
contribution to ``Experimental Metaphysics---Quantum Mechanical Studies in Honor of Abner Shimony,'' edited by R.S.Cohen, M. Horne, and J. Stachel, Boston Studies in the Philosophy of Science (Kluwer, 1996)
http://arxiv.org/PS_cache/quant-ph/pdf/9512/9512031v1.pdf

Note that I disagree that "potential energy itself is not physically real because its magnitude is entirely conventional". The fact that the magnitude of the potential is conventional does not imply anything about the reality of the potential.

I guess you would say that the potential energy could be a physically real relational property? I was saying it is not physically real because many different potential energies give rise to the same field and force magnitude and direction, after taking the gradient. Just like the gauge fields in classical electrodynamics. Physicists call something physically real if it is gauge invariant. The potential energy is not gauge invariant however.

Anyway, as I said before, the debate monistic/dualistic ontology does not concern this part of the theory, I only want to deny that there is a quantum potential/force.

You mean eliminate the quantum potential/force from the mathematics of the theory or deny the quantum potential/force as something physically real? In the former case, it would lead to an inconsistent deBB theory. In the latter case, all you have to do then is show that the wavefunction itself is not physically real, since the quantum potential is ultimately constructed out of the magnitude of the wavefunction. Although, I don't see how you could claim that the quantum potential force is not physically real, and yet the guidance velocity is physically real. That would amount to saying that there is a physically real particle velocity, whose time-derivative is not physically real. That makes no sense to me.

If someone could bring a convincing interpretation which does not introduce a special quantum force but implies that we have to understand potentials primary to forces, would you accept it?

Honestly I don't think this idea makes logical sense. Perhaps a more elaborate version would make more logical sense, and then I could tell you whether I accept it.

And I don't know why an explanation should be causal. The examples you give rest on the fact that the corpuscle "has some knowledge". It is obviously an analogy. But what does the analogy stands for? What is for a corpuscle to know where it should go?

No, you misunderstood again. The examples I gave were logical consequences of the nomological wavefunction interpretation of DGZ. I presented those examples to show the absurdity of it.

You could anwer as the necessity to have a force "telling" it where it should go. But your argument is circular, you ask for something you presuppose. Someone who does not agree that the corpuscle must have some knowledge (someone who doesn't agree that there is a need of forces)

My examples apply to the guidance view just as well as the causal view.

My point of view would be, there is nothing telling the corpuscle where to go, but the geometry of the system (represented by V) determines the motion of the particle. What should we choose, potential or force?

Wait a second, are you referring to classical mechanics or deBB theory? If the former, I can understand that viewpoint. If the latter, then I completely disagree. The external potential V has nothing fundamental at all to do with the Bohmian particle trajectories.

As you can see here you are not completely consistent. Either potentials are real or they are not. So according to you point of view, I suppose you would take quantum forces as the real thing, this is Belousek strategy.

Um, I think you're reading into my words something I never said or talked about. Again, I am also talking about the implications of the nomological wavefunction interpretation for the deBB guidance view.

<< Unfortunately (for you, not for me ;) ), if you do so these forces correspond to a non local action at distance. There is nothing transporting the information, Belousek acknowledges this as a weakness of his theory... >>

There would be nonlocal action at a distance even in an ontological view of the wavefunction. The question I am interested in is whether we should take this nonlocality as a property of a physically real wavefunction and configuration space, or an epistemological wavefunction and configuration space. I think the DGZ nomological interpretation of the wavefunction implies that two Bohmian particles interact instantaneously with no mediating physically real field (this is not the case in an ontological interpretation of the wavefunction; in an ontological interpretation of the wavefunction, the wavefunction in configurations space is the physically real field that mediates the interactions between the particles). And I think the DGZ view makes no physical sense.

By the way, what is exactly the interpretation you support?

Once again I think the wavefunction and configuration space are epistemological, mathematical devices, as implied by the stochastic mechanical (Nelson, Nagasawa, Fenyes, Cavalleri) derivations of the wavefunction and Schroedinger equation. So the wavefunction is epistemological very much like the transition probability density solution (which also evolves in configuration space) to the diffusion equation in classical statistical mechanics, and the Schroedinger equation is very much like the diffusion equation, being an phenomenological approximation to an underlying, microphysical stochastic particle dynamics described by some kind of Langevin equation of motion.

 

[Maaneli]

Vanknee,

<< If someone could bring a convincing interpretation which does not introduce a special quantum force but implies that we have to understand potentials primary to forces, would you accept it? >>

Ok, I think I understand now what you have in mind. Yes, I could be inclined to accept it.

 

[DrChinese]

...The term "Bohmian mechanics" is a relatively more recent usage started in the early 1990's by Duerr, Goldstein, and Zanghi, (DGZ) to refer to their own specific interpretation and approach to the theory (as well as their own interpretation of what Bohm thought about his own theory, Bohm's own actual interpretation nothwithstanding), which they, naturally, think is the universally correct one. Since then they have done a PR campaign to make sure there is dominant use of the term "Bohmian mechanics" throughout the literature.

What I personally think is problematic about the use of the term "Bohmian mechanics", and the intentions of DGZ in using the term "Bohmian mechanics", and which is why I have decided to stop using it in public discussions, is that ...

Thanks for this information. I was not aware that usage of "Bohmian Mechanics" carried an added significance for many of you, including yourself and ttn.

So you prefer the term "de Broglie-Bohm Theory"?

 

[Maaneli]

Thanks for this information. I was not aware that usage of "Bohmian Mechanics" carried an added significance for many of you, including yourself and ttn.

So you prefer the term "de Broglie-Bohm Theory"?

You are welcome. Yes, I prefer the term "de Broglie-Bohm theory" because it gives due credit to Louis de Broglie's contributions. I think DGZ, who invented the term "Bohmian mechanics", should have instead invented terms like "Bellian mechanics" or "de Broglie-Bell theory/mechanics" or "de Broglie-Bohm-Bell theory", because Bell and de Broglie were the ones who advocated the first order guidance view, and deemphasized the quantum potential causal view, as DGZ have done. Bohm was never an advocate of the guidance view or the interpretations of DGZ, and personally was insulted (or so I was told) by the way his name was associated with the DGZ approach.

 

[DrChinese]

You are welcome. Yes, I prefer the term "de Broglie-Bohm theory" because it gives due credit to Louis de Broglie's contributions. I think DGZ, who invented the term "Bohmian mechanics", should have instead invented terms like "Bellian mechanics" or "de Broglie-Bell theory/mechanics" or "de Broglie-Bohm-Bell theory", because Bell and de Broglie were the ones who advocated the first order guidance view, and deemphasized the quantum potential causal view, as DGZ have done. Bohm was never an advocate of the guidance view or the interpretations of DGZ, and personally was insulted (or so I was told) by the way his name was associated with the DGZ approach.

So if I have it right:

de Broglie-Bohm theory: the quantum potential is key; this is the version you support and is consistent with Bohm's views. Is ttn a follower of this as well? I assume that Passon is too?

DGZ version ("Bohmian mechanics"): the guidance condition is fundamental and the quantum potential is de-emphasized. Bell preferred this version, as I understand it. Is Demystifier in this camp (not asking you to speak for him, just wonder if you happen to know)?

 

[DrChinese]

Given the title of this thread, I have a question:

How does the dBB explain entangled photons a la PDC? OK, I see that the non-local character of the theory means that there is in principle a way to connect happenings at Alice with happenings at Bob, regardless of distance. But I would guess that for the Bell test answers to be properly correlated, that the quantum potential would need to be the same for both photons as long as they are entangled. Am I close? :)

 

[Maaneli]

So if I have it right:

de Broglie-Bohm theory: the quantum potential is key; this is the version you support and is consistent with Bohm's views. Is ttn a follower of this as well? I assume that Passon is too?

Correction: In de Broglie-Bohm theory the quantum potential is not necessarily key - in other words, it does not represent Bohm's particular view of the equations of the theory. The term deBB theory is intended just to agnostically refer to all the properties of the theory (wavefunction, particles, quantum potential), and to the original contributions of both de Broglie and Bohm. In fact, de Broglie, who actually emphasized the guidance view, was the first to also coin the term "pilot wave theory". Bell was actually the first to use the term "de Broglie-Bohm" to refer to the theory originally discovered by both de Broglie and Bohm. Bohm used the term "causal interpretation" or the "ontological interpretation" to refer to his particular interpretation of the theory. Nowadays, researchers who want to stay out of this terminological disagreement typically just use the term "de Broglie-Bohm theory" or "pilot wave theory".

Travis is a staunch subscriber to the DGZ view and always uses the term Bohmian mechanics, as you may have noticed. I don't know though how aware he is of this terminological disagreement. Passon doesn't state his preference, as he uses all the terms in his papers.

DGZ version ("Bohmian mechanics"): the guidance condition is fundamental and the quantum potential is de-emphasized. Bell preferred this version, as I understand it. Is Demystifier in this camp (not asking you to speak for him, just wonder if you happen to know)?

Right. I don't know if Demystifier is in the DGZ camp, but in all his papers I have seen him use the term Bohmian mechanics almost exclusively. I suppose we could just ask him.


Demystifier, what do you think of this terminological disagreement?

 

[DrChinese]

Travis is a staunch subscriber to the DGZ view and always uses the term Bohmian mechanics, as you may have noticed. I don't know though how aware he is of this terminological disagreement. Passon doesn't state his preference, as he uses all the terms in his papers.

Right. I don't know if Demystifier is in the DGZ camp, but in all his papers I have seen him use the term Bohmian mechanics almost exclusively. I suppose we could just ask him.

Demystifier, what do you think of this terminological disagreement?

The issue for me is that I am still learning about dBB/BM. Travis had never objected to me about the terminology, so what you say makes sense. He also talks about Bell's later writings a lot, so that makes sense too.

As I look into the issues around the theory, some of the arguments are tied to one version or another. For example, there was an experiment run a few years back that was billed as a "Experimental realization of a first test of de Broglie–Bohm theory". This based on Ghose's formulation, which has been denounced by other proponents of dBB. So some of the debate has my head spinning. :D

 

[Maaneli]

The issue for me is that I am still learning about dBB/BM. Travis had never objected to me about the terminology, so what you say makes sense. He also talks about Bell's later writings a lot, so that makes sense too.

May I recommend then the most objective and diverse account of deBB theory in the literature:

What you always wanted to know about Bohmian mechanics but were afraid to ask
Authors: Oliver Passon
http://aps.arxiv.org/abs/quant-ph/0611032

Why isn't every physicist a Bohmian?
Authors: Oliver Passon
http://aps.arxiv.org/abs/quant-ph/0412119

As I look into the issues around the theory, some of the arguments are tied to one version or another. For example, there was an experiment run a few years back that was billed as a "Experimental realization of a first test of de Broglie–Bohm theory". This based on Ghose's formulation, which has been denounced by other proponents of dBB. So some of the debate has my head spinning. :D

Yes, Ghose's formulation is objected to for good reason. I recommend also this paper:

Comments on some recently proposed experiments that should distinguish Bohmian mechanics from quantum mechanics
Authors: W. Struyve, W. De Baere
http://arxiv.org/abs/quant-ph/0108038

 

[Demystifier]

DGZ version ("Bohmian mechanics"): the guidance condition is fundamental and the quantum potential is de-emphasized. Bell preferred this version, as I understand it. Is Demystifier in this camp (not asking you to speak for him, just wonder if you happen to know)?

I'm in nobody's camp, but I prefer to think that the guidance law, and not the quantum potential, is the fundamental concept. I use the expression "Bohmian mechanics" not because it is the best name for it, but simply because most people use this term. Otherwise, I think that the expression "pilot-wave" is the best name, but I don't use it frequently for the reason explained above.

 

[DrChinese]

May I recommend then the most objective and diverse account of deBB theory in the literature:

What you always wanted to know about Bohmian mechanics but were afraid to ask
Authors: Oliver Passon
http://aps.arxiv.org/abs/quant-ph/0611032

Why isn't every physicist a Bohmian?
Authors: Oliver Passon
http://aps.arxiv.org/abs/quant-ph/0412119

Yes, Ghose's formulation is objected to for good reason. I recommend also this paper:

Comments on some recently proposed experiments that should distinguish Bohmian mechanics from quantum mechanics
Authors: W. Struyve, W. De Baere
http://arxiv.org/abs/quant-ph/0108038

I read the second Passon paper (which was very good), and it definitely had my head spinning trying to follow the arguments and counter-arguments. Of course, there is no easy way out on it, so I'll have to continue to study.

Ditto for the Struyve-Baere comment, which Ghose answered: http://arxiv.org/abs/quant-ph/0208192

The difficulty is that each person has a point of view (as we all do), and it is not fully convincing for an author to try to counter arguments from the "other" side. The other side seems to remain unconvinced throughout much of the debate, and both sides end up declaring "victory". That makes it hard for me to see where there is a modicum of agreement between the sides. For example: after Ghose's paper and the Struyve-Baere comment (and the other) and Ghose's answer to the comment, the experiment was later performed. So I presume that those performing the experiment ultimately thought Ghose was right (else their time was wasted): http://arxiv.org/abs/quant-ph?papernum=0206196

This is one area in which the PhysicsForums threads is very beneficial, because the various positions can be better discussed in a back and forth manner. So my thanks to all of you for continuing to help me better understand the best that dBB/BM has to offer.

 

[DrChinese]

I'm in nobody's camp, but I prefer to think that the guidance law, and not the quantum potential, is the fundamental concept. I use the expression "Bohmian mechanics" not because it is the best name for it, but simply because most people use this term. Otherwise, I think that the expression "pilot-wave" is the best name, but I don't use it frequently for the reason explained above.

Thanks! I am not trying to pigeon hole anyone, but it is definitely helpful to know a little about where folks stand.

 

[DrChinese]

So what about this: can anyone point me to a reference that explains how entanglement works in dBB/BM?

I presume there must be something like the following:

f(Alice)=f(Bob) while Alice and Bob are entangled so that the "answer" to any observation of Alice and Bob will be suitably correlated. And I am imagining that f(Alice) is the Guidance equation or the Quantum potential, depending on your perspective. As I understand it, the correlation would not be due to a signal directly moving from Alice to Bob (or vice versa) instantaneously so much as the fact that conditions in the universe were applied identically on each. I see that Alice and Bob sprang from identical conditions (al least in PDC) but I understand that the rest of the universe exerts an impact on Alice and Bob as well.

I know I am wandering in the park on this, can anyone point me in the right direction?

 

[DrChinese]

After doing a little searching, I am beginning to think my question is a bit more complex than I had realized. I found a couple of references:

EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory
Authors: K. Berndl (Munich), D. Duerr (Munich), S. Goldstein (Rutgers), N. Zanghi (Genova) (Submitted on 26 Oct 1995)[/url]

and

Bohmian trajectories for photons
Authors: P. Ghose (S.N.Bose Natl. Centr.), A. S. Majumdar (S.N.Bose Natl. Centr.), S. Guha (IIT Kanpur), J. Sau (IIT Kanpur) (Submitted on 14 Feb 2001[/url]

Now I see that reference 1 states: "Within this framework an EPR experiment can be described—the subsystems, while not explicitly interacting, are coupled by their common wave function (ta, tb)...Despite the presence of EPR-correlations, these do not permit the transmission of “signals”: From the results of measurements on system a alone, one can draw no inference about the possible interventions on system b—the kinds of experiments performed on system b..." which makes sense to me.

On the other hand, reference 2 says that some Bohmians question whether bosons have Bohmian trajectories as Fermions do: "Bohm and his coworkers have all along emphasized a fundamental difference between fermions and bosons in that fermions, in their view, are particles, whereas bosons are fields. This asymmetry in the Bohmian picture of fermions and bosons arose due to the absence, in their view, of a consistent relativistic quantum mechanics of bosons with a conserved four-vector current which is time-like and whose time component is positive."

They proceed to compute the Bohmian trajectories for a pair of PDC photons, developed from the Kemmer equation (like I have any idea what that is). One of the authors is Ghose, whose credibility is questioned by some on this board. He sometimes writes no-go type papers on various Bohmian hypotheses, but seems to be pretty familiar with the field.

So do either of these papers work as a starting point to understanding the constraints that must exist on a pair of entangled particles? It seems clear that for entangled Alice and Bob, their trajectories must evolve with a manner of symmetry.

 

[Maaneli]

After doing a little searching, I am beginning to think my question is a bit more complex than I had realized. I found a couple of references:

EPR-Bell Nonlocality, Lorentz Invariance, and Bohmian Quantum Theory
Authors: K. Berndl (Munich), D. Duerr (Munich), S. Goldstein (Rutgers), N. Zanghi (Genova) (Submitted on 26 Oct 1995)[/url]

and

Bohmian trajectories for photons
Authors: P. Ghose (S.N.Bose Natl. Centr.), A. S. Majumdar (S.N.Bose Natl. Centr.), S. Guha (IIT Kanpur), J. Sau (IIT Kanpur) (Submitted on 14 Feb 2001[/url]

Now I see that reference 1 states: "Within this framework an EPR experiment can be described—the subsystems, while not explicitly interacting, are coupled by their common wave function (ta, tb)...Despite the presence of EPR-correlations, these do not permit the transmission of “signals”: From the results of measurements on system a alone, one can draw no inference about the possible interventions on system b—the kinds of experiments performed on system b..." which makes sense to me.

On the other hand, reference 2 says that some Bohmians question whether bosons have Bohmian trajectories as Fermions do: "Bohm and his coworkers have all along emphasized a fundamental difference between fermions and bosons in that fermions, in their view, are particles, whereas bosons are fields. This asymmetry in the Bohmian picture of fermions and bosons arose due to the absence, in their view, of a consistent relativistic quantum mechanics of bosons with a conserved four-vector current which is time-like and whose time component is positive."

They proceed to compute the Bohmian trajectories for a pair of PDC photons, developed from the Kemmer equation (like I have any idea what that is). One of the authors is Ghose, whose credibility is questioned by some on this board. He sometimes writes no-go type papers on various Bohmian hypotheses, but seems to be pretty familiar with the field.

So do either of these papers work as a starting point to understanding the constraints that must exist on a pair of entangled particles? It seems clear that for entangled Alice and Bob, their trajectories must evolve with a manner of symmetry.

The first paper by Berndl et al. is a decent starting point, though they are more interested in pin-pointing the nature of the "conflict" between pilot-wave theory and Lorentz invariance. In terms of the critiques of reference 2, those issues about a positive, timelike 4-current for bosons are widely accepted to have been resolved in pilot-wave QFT generalizations of Struyve et al.:

A minimalist pilot-wave model for quantum electrodynamics
Authors: W. Struyve, H. Westman
Journal reference: Proc. R. Soc. A 463, 3115-3129 (2007)
http://arxiv.org/abs/0707.3487

Also have a look at:

On the uniqueness of paths for spin-0 and spin-1 quantum mechanics
Authors: W. Struyve, W. De Baere, J. De Neve, S. De Weirdt
Journal reference: Phys. Lett. A 322, 84-95 (2004)
http://arxiv.org/abs/quant-ph/0311098

If you would like to better understand how deBB theory accounts of EPRB correlations for electrons and other fermions, I recommend looking at Peter Holland's textbook, "The Quantum Theory of Motion", and Bohm and Hiley's "The Undivided Universe". They both have explicit discussions of EPRB for electrons from a pilot-wave point of view. Also have a look at page 74 of Genovese's review paper where he generally describes how deBB describes the Stern-Gerlach experiment:

Research on Hidden Variable Theories: a review of recent progresses
Authors: Marco Genovese
Journal reference: Physics Reports 413 (2005) 319
http://arxiv.org/PS_cache/quant-ph/pdf/0701/0701071v1.pdf

 

[DrChinese]

The first paper by Berndl et al. is a decent starting point, though they are more interested in pin-pointing the nature of the "conflict" between pilot-wave theory and Lorentz invariance. In terms of the critiques of reference 2, those issues about a positive, timelike 4-current for bosons are widely accepted to have been resolved in pilot-wave QFT generalizations of Struyve et al.:

A minimalist pilot-wave model for quantum electrodynamics
Authors: W. Struyve, H. Westman
Journal reference: Proc. R. Soc. A 463, 3115-3129 (2007)
http://arxiv.org/abs/0707.3487

Also have a look at:

On the uniqueness of paths for spin-0 and spin-1 quantum mechanics
Authors: W. Struyve, W. De Baere, J. De Neve, S. De Weirdt
Journal reference: Phys. Lett. A 322, 84-95 (2004)
http://arxiv.org/abs/quant-ph/0311098

If you would like to better understand how deBB theory accounts of EPRB correlations for electrons and other fermions, I recommend looking at Peter Holland's textbook, "The Quantum Theory of Motion", and Bohm and Hiley's "The Undivided Universe". They both have explicit discussions of EPRB for electrons from a pilot-wave point of view. Also have a look at page 74 of Genovese's review paper where he generally describes how deBB describes the Stern-Gerlach experiment:

Research on Hidden Variable Theories: a review of recent progresses
Authors: Marco Genovese
Journal reference: Physics Reports 413 (2005) 319
http://arxiv.org/PS_cache/quant-ph/pdf/0701/0701071v1.pdf

Thanks, I'll review these and come back with any questions.

-DrC