The Refutation of Bohmian Mechanics

[camboy]

If I see that I was wrong, I correct myself immediately.

So, as you haven't corrected yourself at all, do I take it you don't accept that anything that you have said is wrong?

If this is not the case, would you mind listing for me the things about which you have changed your opinion as a result of this thread?

You have not the slightest idea about how much literature I have read and how much I am reading
while preparing my contributions to this forum.

As far as deBB is concerned, you appear to be entirely ignorant of everything that has been published since the 1990s, of a great many things published before that, and of absolutely everything that refutes your and Streater's "Bohmian mechanics is demonstrably incorrect" thesis. So I feel free to make certain assumptions.

Scientific dispute takes the free offering of information as a given that doesn't need special thanks.
I also do not expect being thanked for the information I provide on this forum.

That's not my point. No-one is asking for thanks. My complaint is the following. You have made multiple statements on this thread which are demonstrably incorrect. When told they are incorrect and you apparently have no further argument, you simply move onto another point without saying whether you agree with the correction or not. Anyone reading this thread and attempting to make sense of it needs to have that information if they are to draw a conclusion about who is right and who is wrong, otherwise they might simply assume because you are a big clever person and I am a student that you automatically win. Is that your intention? Because it certainly looks like it.

You seem to say a lot without first checking the facts. I am not a professor of quantum physics.

Then I apologize for suggesting that you were.

EDIT: though looking at http://arnold-neumaier.at/im/hs97_16.gif" , you can hardly blame me for my assumption. So you're a professor of mathematics who has the foundations of quantum mechanics as one of his main research interests. Huge difference, I agree. My original point therefore stands that - as a respectable professor at a major university - you have a responsibility not to make sweeping incorrect statements damning entire fields in public forums, since people will believe you merely because of who you are.

from the beginning of this thread, you have made pompous statements implying that everyone who studies de Broglie-Bohm theory is an idiot.

Please take this back. I never said such a thing.

Then what on Earth did you mean by statements such as "The worst thing about Bohmian mechanics is their low standards of quality", "Bohmians are not aware of many things", "Bohmian trickery is inapplicable" and all the rest. Are these supposed to be compliments?

Don't misunderstand me. I am happy to debate you, but not on the understanding that you are so goddamned clever that your so-called disproof of Bohmian mechanics is so obvious it doesn't need to be peer-reviewed, or when you persist in continually using such a sarcastic tone.

 

[akhmeteli]

Your claim that according to forum's rules, truth is dependent on peer reviews.
PF can decide upon what shall be discussed in its space but not upon what is true.

First, you may have noticed an emoticon by my "claim", second, strictly speaking, depending on peer reviews, truth either belongs here or not (so it is indeed "dependent" in this respect on peer reviews). With all due respect, your "truth" of post 7 does not belong here.

We don't need to agree. I won't defend my position here beyond whatt is already in the paper, also because of the PF rules. (However, note that my paper has been cited repeatedly in the published literature, among others in Streater's book on lost causes in physics, where he has a full chapter explaining why he thinks Bohmian mechanics is a lost cause..

No, we don't have to agree. And no, the fact that your paper has been cited does not make its discussion here appropriate. Rules are rules. I am not trying to look "holier than thou". I admit that I also sinned against this rule and got a heads-up from a mentor. Since then I tried to stick to the rules.

I am sure mentors here value your input, as I do, and would give you some slack, as I would do, if I were in their shoes, but you should not abuse our respect.

And again, if indeed the Bohm interpretation is a lost cause, so be it, but I specifically objected to your claim and was not trying to defend the interpretation. To explain my position I may mention that I had a longish discussion with a knowledgeable Bohmian here. Ironically, I also argued in that discussion that there is no clear indication of discrepancy between predictions of the Bohm interpretation and standard quantum mechanics.

I imagine instead that the universe is a hydrogen atom in the ground state - the electron will always stand still and the wrong statistics results.

In your example both the Bohm interpretation and standard quantum mechanics predict the same state forever. It is not at all obvious that the Bohmian interpretation gives wrong statistics in this case (unless you impose your very own theory of measurements on the Bohm interpretation, as you do in your paper). I believe this is just your personal theory.

Bohmians are not aware of many things; they probably never tried to bring quantum computing into their focus. The observables used there do not include a position variable, hence the Bohmian trickery is inapplicable.

If this is meant to be an argument, I fail to see how it is relevant. Maybe I just don't know enough about quantum computing though. However, I did not ask you for arguments, I asked about the status of your claim "no quantum computing in the Bohm interpretation." This is another strong claim, and I just tried to understand if that was common knowledge or just another personal theory of yours. If this is common knowledge, how about a reference? And if there is no peer-reviewed article supporting your claim, then your claim does not belong here. If this is your recent discovery, please publish it first and then discuss it here.

If you don't agree, then please tell me how to do quantum computing in Bohmian mechanics..

With all due respect, this is rich. You made a strong claim, and I just challenged you to support it with valid references. I am under no obligation to prove that your claim is wrong. Furthermore, I have no idea if it is indeed wrong or right.

 

[camboy]

Bohmians are not aware of many things; they probably never tried to bring quantum computing into their focus. The observables used there do not include a position variable, hence the Bohmian trickery is inapplicable.

If this is meant to be an argument, I fail to see how it is relevant. Maybe I just don't know enough about quantum computing though. However, I did not ask you for arguments, I asked about the status of your claim "no quantum computing in the Bohm interpretation." This is another strong claim, and I just tried to understand if that was common knowledge or just another personal theory of yours. If this is common knowledge, how about a reference? And if there is no peer-reviewed article supporting your claim, then your claim does not belong here. If this is your recent discovery, please publish it first and then discuss it here.

If you don't agree, then please tell me how to do quantum computing in Bohmian mechanics..

With all due respect, this is rich. You made a strong claim, and I just challenged you to support it with valid references. I am under no obligation to prove that your claim is wrong. Furthermore, I have no idea if it is indeed wrong or right.

It is wrong. I supplied him with an appropriate reference demonstrating how to do deBB quantum computing in #22 (and again in #27 after he ignored it).

Of course he immediately dismissed it, not because of a coherent 'personal theory' but because "[deBB] can be coerced into accomodating anything - in this case by introducing artificial pointer coordinates that don't exist in the standard description". This simply means "[deBB] is not like standard QM, and I - the great Neumaier - don't like it". It is not an intellectual argument.

 

[A. Neumaier]

And I never before heard that the nerves in the eye move in response to light.

They don't, but the positions of the excited nerves determine the picture you will eventually see.

But in the Bohmian interpretationl, one interprets only changes in the pointer varibles as observables.. Thus the nerves won't serve as pointer variables to observe light.

 

[A. Neumaier]

If the Boltzmann's H-therorem were any evidence for the universe being in global equilibrium then
e would observe this global equilibrium - which means we wouldn't exist, contradiction.[/QUOTE]
Irrespective of physics, this chain of reasoning is logically totally wrong.
Namely, if A is some evidence for B, it does not mean that A implies B.
For example, being in grave is an evidence for being dead, but you can still be in grave without being dead.[/QUOTE]
This means that you have very weak standards for what you regard as evidence for global thermal equilibrium and for quantum equilibrium. Your arguments deon't hold any water, as my example of the hill-climber showed.

Anyway, perhaps we are a statistical fluctuation?

No serious statistician rregards anything as a fluctuation that persists for so long.

 

[A. Neumaier]

I'm not sure what kind of an answer do you expect here. Perhaps the straightest answer is: through the Schrodinger (or Schrodinger-Pauli, or Dirac, or Maxwell ...) equation and the associated equation for the particle trajectories - of the isolated system.

In standard QM, a spin system is given by N spins, basis states that tell which subset of spins is up (the complementary subset is down), their linear compinations as general statres, and a Hamiltonian that is an expression in the su(2) operators J^k_0, J^k_+ and J^k_-, one k for each spin. This determines the quantum dynamics via Schroedinger's equation i hbar psi(t)=H psi(t).

But it doesn't determine the Bohmian dynamics if there is no detector close by to give ontological meaning to the system.

 

[A. Neumaier]

So, as you haven't corrected yourself at all, do I take it you don't accept that anything that you have said is wrong?

Indeed. I believe that my position regarding my paper is correct. Your arguments didn't convince me of a mistake.

If this is not the case, would you mind listing for me the things about which you have changed your opinion as a result of this thread?

For example, I had thought that Bohmian mechanics never considered quantum computing, and I learned that it had. Though the presentation given was not enough to convinve me that BM accounts for qunatum computing - see the still pending dialogue.

As far as deBB is concerned, you appear to be entirely ignorant of everything that has been published since the 1990s,

It may appear s to you,, but it isn't the case.

You have made multiple statements on this thread which are demonstrably incorrect.

more precisely, which seem incorrect to you. I didn't buy your arguments.
In questions of interpretation, there is a lot of room for differing opinions on the same statement.

When told they are incorrect and you apparently have no further argument, you simply move onto another point without saying whether you agree with the correction or not.

The point of a conversation on PF is not to be proved right or wrong but to provide information for readers so that they can make up their own mind. I write to contribute further information, not to justify myself.

Anyone reading this thread and attempting to make sense of it needs to have that information if they are to draw a conclusion about who is right and who is wrong.

They shouldn't take anything on authority if there are conflicting opinions. They should study the arguments of both sides and form their own picture.

looking at http://arnold-neumaier.at/im/hs97_16.gif" , you can hardly blame me for my assumption. So you're a professor of mathematics who has the foundations of quantum mechanics as one of his main research interests.

If you look at my list of research interests http://arnold-neumaier.at/#research , you'll find that quantum mechnaics is a minor part of my research interests. About 4% of my piblications are about quantum mechanics.

My original point therefore stands that - as a respectable professor at a major university - you have a responsibility not to make sweeping incorrect statements damning entire fields in public forums, since people will believe you merely because of who you are.

I don't make sweeping incorrect statements damning entire fields. Saying that Bohmian mechnaics contradicts quantum mechnaics doesn't damn the field. Classical mechnaics also contradicts QM, but nobody thinks that this implies that whoever does rersearch in classical mechanics is an idiot. Far from this!

Then what on Earth did you mean by statements such as "The worst thing about Bohmian mechanics is their low standards of quality", "Bohmians are not aware of many things", "Bohmian trickery is inapplicable" and all the rest. Are these supposed to be compliments?

The first means, for example, that they take things such as the establishment of quantum equilibrium for the universe to be proven although they have extremely little ''evidence'' for it. The second is a truism that holds for everyone, and must be read in context. The third is a statement asserttin that the machinery of Bohmian mechanics is not applicable. Calling it trickery is clearly a subjective statement implying that BM gives an appearance of reality to QM of the same kind as a juggler makes things appear real without being so. This is a nonrefutable statement since BM say often that the motion of the quantum particles is not observable. Thus considering it as trickery is legitimate.

 

[A. Neumaier]

First, you may have noticed an emoticon by my "claim", second, strictly speaking, depending on peer reviews, truth either belongs here or not (so it is indeed "dependent" in this respect on peer reviews). With all due respect, your "truth" of post 7 does not belong here.

If you think giving a reference to an unpublished arXiv paper without discussing it is a serious sin against the rules, you should report it to the PF management, quoting the present post for context.

I am sure mentors here value your input, as I do, and would give you some slack, as I would do, if I were in their shoes, but you should not abuse our respect.

I fully respect the rules as I understand them.

And again, if indeed the Bohm interpretation is a lost cause, so be it, but I specifically objected to your claim

But I cannot discuss my claim further because of the PF rules. So your objection standas like my assertion, and readers must make up their own mind.

I asked about the status of your claim "no quantum computing in the Bohm interpretation." This is another strong claim, and I just tried to understand if that was common knowledge or just another personal theory of yours.

First, I qualified my statement with ''probably'' since I wasn't sure, and indeed, there was a very recent (2010) thesis that tackled it, as was pointed out by others. I immediately acknowledged the article, studied it, and found that it didn't treat spin systems by themselves but only spin systems coupled to an external pointer variable, thus justifying my remark ''The observables used there do not include a position variable, hence the Bohmian trickery is inapplicable.''. However, I learned that the author invented (or got from somewhere else) a new Bohmian trick - namely that one silently changes the system under study to a bigger one, in order to give it the appearance of fitting into the BM philosophy. This lead to a still ongoing discussion.

if there is no peer-reviewed article supporting your claim, then your claim does not belong here.

If everyone were banned who made more than 10 claims that do not appear in a peer-reviewed article, PF would be nearly empty.

 

[Demystifier]

But in the Bohmian interpretationl, one interprets only changes in the pointer varibles as observables.

No, that's not true. I never said that.

 

[Demystifier]

In standard QM, a spin system is given by N spins, basis states that tell which subset of spins is up (the complementary subset is down), their linear compinations as general statres, and a Hamiltonian that is an expression in the su(2) operators J^k_0, J^k_+ and J^k_-, one k for each spin. This determines the quantum dynamics via Schroedinger's equation i hbar psi(t)=H psi(t).

That's correct.

But it doesn't determine the Bohmian dynamics if there is no detector close by to give ontological meaning to the system.

You are wrong. Bohmian dynamics is well defined and gives an ontology even without detectors. But in that case, the statistical predictions may differ from those of ordinary QM. Yet, there is no conflict with experiments because these deviations from ordinary QM cannot be detected (because there are no detectors).

What is true in that case is that there is no any meaningful SPIN ontology. Still, there is some ontology in terms of a wave function and particle positions.

Let me repeat the analogy with classical optics. Colors do not exist, except for the observers. Yet, light waves exist irrespective of the observers.
Similarly, in BM spins do not exist, except for the observers. Yet, wave functions and particle positions exist irrespective of the observers.

 

[Demystifier]

BM say often that the motion of the quantum particles is not observable.

That is an incorrect interpretation of BM. Just the opposite, the motion of the quantum particle is the only observable thing in BM. However, in order to observe it in practice, one must couple it with a macroscopic apparatus containing a large number of the degrees of freedom. Such a large number of degrees of freedom cannot be controlled on a fine level, which means that one cannot know the exact position-dependent phases of the wave functions involved. Without knowing the phases, one cannot predict the exact particle trajectories either. Therefore, one cannot experimentally confirm (or refute) that the measured trajectories coincide with those predicted by the theory.

 

[A. Neumaier]

No, that's not true. I never said that.

You just repeated it:

the motion of the quantum particle is the only observable thing in BM.

 

[A. Neumaier]

Bohmian dynamics is well defined and gives an ontology even without detectors. But in that case, the statistical predictions may differ from those of ordinary QM. Yet, there is no conflict with experiments because these deviations from ordinary QM cannot be detected (because there are no detectors).

Then please give me the dynamics of the unobserved spin system that I described in terms of standard QM in terms of BM.

 

[A. Neumaier]

That is an incorrect interpretation of BM. Just the opposite, the motion of the quantum particle is the only observable thing in BM. However, in order to observe it in practice, one must couple it with a macroscopic apparatus containing a large number of the degrees of freedom. Such a large number of degrees of freedom cannot be controlled on a fine level, which means that one cannot know the exact position-dependent phases of the wave functions involved. Without knowing the phases, one cannot predict the exact particle trajectories either. Therefore, one cannot experimentally confirm (or refute) that the measured trajectories coincide with those predicted by the theory.

But this means (by any meaningful interpretation of the term ''observe'') that one cannot observe the particle position but only the pointer position of the macroscopic apparatus.

 

[Demystifier]

But this means (by any meaningful interpretation of the term ''observe'') that one cannot observe the particle position but only the pointer position of the macroscopic apparatus.

Yes, but this macroscopic apparatus also consists of particles. So one does measure the particle positions, but of the apparatus. Not because the apparatus is fundamentally different, but simply because it is bigger.

 

[Demystifier]

Then please give me the dynamics of the unobserved spin system that I described in terms of standard QM in terms of BM.

That's simple. Standard QM describes it in terms of a wave function for n particles. BM takes the same wave function and says additionally that there are n particles the velocities of which are calculated from this wave function (the exact equation is not important here).

 

[A. Neumaier]

Yes, but this macroscopic apparatus also consists of particles. So one does measure the particle positions, but of the apparatus. Not because the apparatus is fundamentally different, but simply because it is bigger.

One measures a single mean position of the pointer, not the positions of any of the pointer particles.

But this brings me back to my question about the nerves: Where in the nerves is the measured particle whose position indicates whether or not I see a star, and which color it has?

 

[Demystifier]

"No, that's not true. I never said that."

"the motion of the quantum particle is the only observable thing in BM."

OK, I admit, I was not sufficiently precise in the last sentence in quotation marks. By "motion" I meant "particle position as a function of time". Clearly, a particle at rest also has a position as a function of time. OK?

 

[A. Neumaier]

That's simple. Standard QM describes it in terms of a wave function for n particles. BM takes the same wave function and says additionally that there are n particles the velocities of which are calculated from this wave function (the exact equation is not important here).

But in the standard QM picture, the wave function of a spin system (e.g. the Ising ferromagnet) has no position or momentum variables, and hence also no velocities associated with it. Given my specific description of the spin system, what is the BM dynamics? Please be as specific in your formal description, rather than using vague words that leave many things unsaid.

 

[A. Neumaier]

"No, that's not true. I never said that."

"the motion of the quantum particle is the only observable thing in BM."

OK, I admit, I was not sufficiently precise in the last sentence in quotation marks. By "motion" I meant "particle position as a function of time". Clearly, a particle at rest also has a position as a function of time. OK?

OK. But measuring the particle at rest always gives the same measurement result. Thus the positions of the nonmoving nerves in the eye can hardly be used to tell the difference between seeing and not seeing a star.

 

[Demystifier]

One measures a single mean position of the pointer, not the positions of any of the pointer particles.

No, that's not exactly the idea of BM. One observes all these pointer particles collectively, which due to a low resolution appears as a single mean position. But if there was only one pointer particle, due to the low resolution one could not observe it at all.

But this brings me back to my question about the nerves: Where in the nerves is the measured particle whose position indicates whether or not I see a star, and which color it has?

I believe the remark above answers it as well.

 

[A. Neumaier]

No, that's not exactly the idea of BM. One observes all these pointer particles collectively, which due to a low resolution appears as a single mean position. But if there was only one pointer particle, due to the low resolution one could not observe it at all.


I believe the remark above answers it as well.

Not yet. How is the difference between seeing and not seeing the star encoded in the mean position of the nerve particles? Since according to BM the latter is the only thing observable, and we can tell the difference empirically, this difference must be somehow encoded.

 

[Demystifier]

But in the standard QM picture, the wave function of a spin system (e.g. the Ising ferromagnet) has no position or momentum variables, and hence also no velocities associated with it. Given my specific description of the spin system, what is the BM dynamics? Please be as specific in your formal description, rather than using vague words that leave many things unsaid.

Ah, now I see your point. Well, a spin system without position or momentum variables is a toy model that doesn't describe anything in the real world. You are right, for such a system there is no BM dynamics. But BM does not claim to be applicable to every conceivable quantum theory. Instead, it claims to be applicable to the real world.

 

[Demystifier]

OK. But measuring the particle at rest always gives the same measurement result. Thus the positions of the nonmoving nerves in the eye can hardly be used to tell the difference between seeing and not seeing a star.

Not yet. How is the difference between seeing and not seeing the star encoded in the mean position of the nerve particles? Since according to BM the latter is the only thing observable, and we can tell the difference empirically, this difference must be somehow encoded.

What matters is which nerve (with a well-defined position) is excited. But what it means to be excited? It means that there is an electric current in it. Now you will say that the current is nothing but some microscopic ions moving. Sure, but you don't observe one ion. You observe a bunch of them, which makes the current a macroscopic phenomenon. In fact, it seems that all neuro-physics can be well approximated by classical physics:
http://xxx.lanl.gov/abs/quant-ph/9907009 [Phys.Rev.E61:4194-4206,2000]

 

[A. Neumaier]

Ah, now I see your point. Well, a spin system without position or momentum variables is a toy model that doesn't describe anything in the real world. You are right, for such a system there is no BM dynamics. But BM does not claim to be applicable to every conceivable quantum theory. Instead, it claims to be applicable to the real world.

Many real world problems are in fact posed in terms of a Hilbert space which doesn't contain a representation of the Euclidean group and hence has no position and momentum operators.
In particular, all quantum computing is done in such Hilbert spaces. You won't find a position or momentum operator figuring in quantum computation papers.

And precisely this was my point about BM and quantum computing.

BM only adds unnecessary baggage to the standard quantum machinery and has a few tricks to pretend that this gives more reality to QM than the standard view.

Not only that: BM also subtracts a lot from QM, denigrating important features of QM - which to me represent major insights into the nature of physics - to mere calculational tools:

BM sacrifices all important structure in QM - no covariance under canonical transformations, no Heisenberg picture, no natural procedure for forming subsystems, no natural QFT, too many possible variants for the dynamics without any natural means of distinguishing between them. For any serious computation it must resort to the standard QM formulation. The only exceptions are some dynamical simulations, which produce nice pictures and (sometimes) also practically useful results, But the latter can be obtained more efficiently through traditional means, in all cases I know of.

Thus nothing inviting is left.

 

[Demystifier]

Many real world problems are in fact posed in terms of a Hilbert space which doesn't contain a representation of the Euclidean group and hence has no position and momentum operators.
In particular, all quantum computing is done in such Hilbert spaces. You won't find a position or momentum operator figuring in quantum computation papers.

That's all true in a theory, because the particle positions are not essential to understand some aspects of physics, including quantum computations. Yet, an actual quantum computER operating in such a Hilbert space will NEVER be constructed in a laboratory. A true quantum computer can only be made of particles, such as photons, atoms, etc.

 

[Demystifier]

BM sacrifices all important structure in QM - no covariance under canonical transformations,

BM sacrifices the covariance under canonical transformations no more than classical mechanics does. After all, what we really observe in classical mechanics are particle positions, not some bizarre canonical combinations of position and momentum variables.

no Heisenberg picture,

BM can be formulated in the Heisenberg picture as well, but looks more complicated in that picture.

no natural procedure for forming subsystems,

I have no idea why do you think so?

no natural QFT,

I find
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
quite natural.

too many possible variants for the dynamics without any natural means of distinguishing between them.

Even though there are many possible variants, the standard (de Broglie-Bohm) variant is very natural and can be derived in many ways. For a recent derivation based on weak MEASUREMENTS see
http://xxx.lanl.gov/abs/0706.2522
http://xxx.lanl.gov/abs/0808.3324

 

[A. Neumaier]

That's all true in a theory, because the particle positions are not essential to understand some aspects of physics, including quantum computations. Yet, an actual quantum computER operating in such a Hilbert space will NEVER be constructed in a laboratory. A true quantum computer can only be made of particles, such as photons, atoms, etc.

The strength of standard QM is that
-- it can safely ignore all irrelevant variables,
-- it can transform to arbitrary symplectic coordinate systems in phase space,
-- it can work on arbitrary Lie groups adapted to the problem,
without leaving the framework of the theory.

BM has no such option, hence is strictly inferior to the standard view.

Thus it is fully justified that the main stream ignores BM.

The presentation ''Not even wrong. Why does nobody like pilot-wave theory?'' at http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf diagnoses the disease but only has a historical view rather than an answer to that question. The real answer is that the need for BM is marginal compared to the need for QM. BM subtracts from QM too much without giving anything relevant in return.

Though through lip service it encompasses all of QM, in practice it excludes many systems of practical interest because they are not formulated with enough pointer degrees of freedom (and often cannot be
formulated with few enough pointer degrees of freedom to be tractable by BM means). Simulating quantum computing via BM would be a nightmare.

 

[A. Neumaier]

BM sacrifices the covariance under canonical transformations no more than classical mechanics does. After all, what we really observe in classical mechanics are particle positions, not some bizarre canonical combinations of position and momentum variables.

In classical mechanics, a canonical transformation transforms a system in canonical variables into another one in canonical variables. In many systems the observables are not canonical. E.g., distances and angles in molecules - one _cannot_ observe positions, only distances and angles.
(In any Galilei or Poincare invariant theory, positions are unobservable gauge-dependent quantities.)

BM can be formulated in the Heisenberg picture as well, but looks more complicated in that picture.

It looks useless in that formulation.

I have no idea why do you think so?

I wanted to form a subsystem consisting of N spins only, and since the position variables were gone, the BM description was gone.

I find
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]
quite natural.

An author usually finds his own work natural. I find it unnatural that this view doesn't reduce to the standard Bohmian view when you translate in the usual way the field theory back into a multiparticle theory. (There is work by Horwitz and Piron on 4D quantum mechanics along similar lines as yours, it never found much resonance, for very good reasons.)

Even though there are many possible variants, the standard (de Broglie-Bohm) variant is very natural and can be derived in many ways. For a recent derivation based on weak MEASUREMENTS see
http://xxx.lanl.gov/abs/0706.2522
http://xxx.lanl.gov/abs/0808.3324

The quantum field variant and the multiparticle variant, which are equivalent in standard QM, have completely different ontologies in the BM setting. What is natural about that?

 

[Demystifier]

The strength of standard QM is that
-- it can safely ignore all irrelevant variables,
-- it can transform to arbitrary symplectic coordinate systems in phase space,
-- it can work on arbitrary Lie groups adapted to the problem,
without leaving the framework of the theory.

BM has no such option, hence is strictly inferior to the standard view.

Thus it is fully justified that the main stream ignores BM.

The presentation ''Not even wrong. Why does nobody like pilot-wave theory?'' at http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf diagnoses the disease but only has a historical view rather than an answer to that question. The real answer is that the need for BM is marginal compared to the need for QM. BM subtracts from QM too much without giving anything relevant in return.

Though through lip service it encompasses all of QM, in practice it excludes many systems of practical interest because they are not formulated with enough pointer degrees of freedom (and often cannot be
formulated with few enough pointer degrees of freedom to be tractable by BM means). Simulating quantum computing via BM would be a nightmare.

All this points to the conclusion that standard QM is more convenient for PRACTICAL applications, with which I agree. But BM is not developed for practical applications (even though sometimes it has practical applications as well). It is developed with an intention to resolve some FOUNDATIONAL issues. As most physicists are more interested in practical issues than in foundational ones, which is fine and even desirable, it is no surprise that most physicists do not care much about BM and other interpretations of QM. But it does not mean that BM (or some other interpretation) is not right, and that it will not became more useful one day when it becomes better developed.

 

[A. Neumaier]

All this points to the conclusion that standard QM is more convenient for PRACTICAL applications, with which I agree. But BM is not developed for practical applications (even though sometimes it has practical applications as well). It is developed with an intention to resolve some FOUNDATIONAL issues. As most physicists are more interested in practical issues than in foundational ones, which is fine and even desirable, it is no surprise that most physicists do not care much about BM and other interpretations of QM. But it does not mean that BM (or some other interpretation) is not right, and that it will not became more useful one day when it becomes better developed.

In practice, practice decides the interpretation.

 

[Demystifier]

I find it unnatural that this view doesn't reduce to the standard Bohmian view when you translate in the usual way the field theory back into a multiparticle theory. (There is work by Horwitz and Piron on 4D quantum mechanics along similar lines as yours, it never found much resonance, for very good reasons.)

Why do you think that it doesn't reduce to the standard Bohmian view when you translate in the usual way the field theory back into a multiparticle theory? It does. Besides, even though it is partially inspired by the work of Horwitz and Piron, it is different from that, precisely in a manner that avoids the problems of their approach.

The quantum field variant and the multiparticle variant, which are equivalent in standard QM, have completely different ontologies in the BM setting. What is natural about that?

Why do you think that the ontologies are different? Both ontologies are in terms of particle positions. Moreover, for the same states the same particle trajectories appear, except for the fact that QFT contains some additional "dead" particles that exist for an infinitesimally short time.

 

[Demystifier]

In practice, practice decides the interpretation.

In practice, a very small number of people cares about BM, a larger but still relatively small number cares about standard QM, and a much much bigger number of people cares about certain non-scientific religious books. Can we conclude anything relevant from that?

 

[A. Neumaier]

Why do you think that it doesn't reduce to the standard Bohmian view when you translate in the usual way the field theory back into a multiparticle theory? It does. Besides, even though it is partially inspired by the work of Horwitz and Piron, it is different from that, precisely in a manner that avoids the problems of their approach.

Why do you think that the ontologies are different? Both ontologies are in terms of particle positions. Moreover, for the same states the same particle trajectories appear, except for the fact that QFT contains some additional "dead" particles that exist for an infinitesimally short time.

Because the interpretation of the probabilisitic meaning of psi(x,t) is completely different in the two forms.
In the Schroedinger picture and in standard BM, the density of x at fixed t is given by |psi(x,t_0)|^2, while in Horwitz/Piron and in your relativistic BM, it is given by |psi(x,t)|^2delta(t-t_0). You cannot assert both simultaneously.

 

[A. Neumaier]

In practice, a very small number of people cares about BM, a larger but still relatively small number cares about standard QM, and a much much bigger number of people cares about certain non-scientific religious books. Can we conclude anything relevant from that?

Yes: Religion is for everyone, quantum mechanics for the general scientist, and BM for the determinsitic scientist only. I am trying to address the first two groups only, though I know about the practices of the third one.