The Refutation of Bohmian Mechanics

[camboy]

Dr. Neumaier,

I wonder - do you ever admit that you are wrong about anything ever? Essentially every statement of fact that you have made in this article has been shown to be due to a misunderstanding on your part seemingly due to your never having read any of the literature. And yet, you never say "Oh, thank you, Demystifer/camboy etc. for pointing that out to me". You just carry on to the next spurious thing "And what about this, what about that?" That's wrong too "So what about the other?".

It is not our responsibility to read the literature for you. And yet, from the beginning of this thread, you have made pompous statements implying that everyone who studies de Broglie-Bohm theory is an idiot. If you were not a respected Professor of Quantum Physics, and a writer of FAQS which are promoted by Physics Forums, this wouldn't matter, but you are and it does. As far as I'm concerned, you seem to be abusing your position to try to destroy a subfield of QM which happens not to accord wih your personal views and research goals. Students and even ordinary physicists who happen not to have read anything about deBB will quite naturally believe every weighty pronouncement that you make. More fool them.

Your ridiculous statements that "it doesn't matter that my opinion of deBB has not been published in the peer-reviewed literature" because "my views are so obviously correct" is not only pompous, but arrogant and self-serving. You are so used to people grovelling at you, that you have forgotten the responsibility that such a position brings. Now if I was a moderator, I would ban you. But of course, they're going to now ban me for being rude to you. Well so be it - someone has to say it.

 

[Demystifier]

Which of the many existing pointer variables is the correct one?

As I said, any and each one which strongly interacts with the measured system.

In particular, what is the correct model if no measurment device is close to the quantum system?

If no macroscopic measurement device is close to the measured quantum system, then no macroscopic measurement device can measure this quantum system (because there is no strong interaction). So in this case none of them is "correct".

Or if one removes one device in favor for another one?

The one (or more) which interacts strongly with the measured system, is the correct one.

Moreover, by this interpretation, spin is not a property of the particles but of the pointer!

That's true.

This is very counterintuitive.

Maybe to you, but to me other interpretations of QM are even more counterintuitive.

Suppose you do a long quantum calculation on a quantum computer, and decide at the very end what you are going to measure and with which device. Then according to the spin ontology, the whole quantum computer becomes an ontological property of the incidentally used measuring device...

Not exactly. Other devices and objects in the universe are also ontological, both before and after the measurement. However, only this particular device is strongly correlated with the microscopic degrees of the quantum computer. That's because, as I said many times above, only this particular device strongly interacted with the microscopic quantum-computer degrees.

 

[Demystifier]

Demystifier - I'm glad to see that you now contributing here. Looking back at the misinformation in this shocking thread it is good to see some posts from someone who knows what he is talking about. I'm only an amateur in deBB, and I thought you and zenith had given up (I know it must be very boring constantly having to refute ignorant arguments).

Thanks, camboy! I see that your understanding of deBB is also very good.

 

[A. Neumaier]

First, one should distinguish quantum equilibrium from the (more familiar) thermodynamic equilibrium.

Of course they are different. But the thesis about BM+quantum computing was using the statistical mechanics analogy.

Second, even though we apparently do not live in the thermodynamic equilibrium, the fact is that we don't know why. It is one of the unsolved questions in statistical physics (and cosmology). Purely statistical arguments lead to the conclusion that we should expect to find nature much closer to the thermodynamic equilibrium than we actually do.

No. There is nothing surprising in that we don't have thermal equilibrium. In statistical mechanics, The proof that equilibrium must be obtained is restricted to the very stringent assumption of ergodicity. Very few real systems are ergodic. Equilibrium is reserved for special systems that are more or less homogeneous.

Actually, the simple maximum-entropy argument is enough.

No. There must also be proof that entropy always increases, and that it increases to its maximum.
This is highly nontrivial in statistical mechanics, and wrong for most complex systems. Nature is full of systems that never reach the maximum entropy state.

It would be very surprising if the situation were different for quantum equilibrium, and that it is achieved without such stringent conditions. Can you point to an online source for the proof?

 

[A. Neumaier]

do you ever admit that you are wrong about anything ever?

If I see that I was wrong, I correct myself immediately. Thus any state of being wrong is very short-lived. If I repeat assertions that seem wrong to you then only because your arguments did not convince me.

to your never having read any of the literature.

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.

And yet, you never say "Oh, thank you, Demystifer/camboy etc. for pointing that out to me".

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.

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.

If you were not a respected Professor of Quantum Physics,

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

Your ridiculous statements that "it doesn't matter that my opinion of deBB has not been published in the peer-reviewed literature" because "my views are so obviously correct"

I didn't say such a thing.

 

[A. Neumaier]

If no macroscopic measurement device is close to the measured quantum system, then no macroscopic measurement device can measure this quantum system (because there is no strong interaction). So in this case none of them is "correct".
.

But the system still has a dynamics. Though apparently not one easily described by BM.

 

[Demystifier]

Of course they are different. But the thesis about BM+quantum computing was using the statistical mechanics analogy.

No. There is nothing surprising in that we don't have thermal equilibrium. In statistical mechanics, The proof that equilibrium must be obtained is restricted to the very stringent assumption of ergodicity. Very few real systems are ergodic. Equilibrium is reserved for special systems that are more or less homogeneous.

No. There must also be proof that entropy always increases, and that it increases to its maximum.
This is highly nontrivial in statistical mechanics, and wrong for most complex systems. Nature is full of systems that never reach the maximum entropy state.

It would be very surprising if the situation were different for quantum equilibrium, and that it is achieved without such stringent conditions. Can you point to an online source for the proof?

OK, now we are at the territory of statistical mechanics. In statistical mechanics there is a Boltzmann H-theorem that provides that entropy never decreases. Perhaps this theorem is not perfectly rigorous (it does not use ergodicity), but in Bohmian mechanics there is an analogous equally (non)rigorous theorem that entropy measuring closeness to the quantum equilibrium also never decreases. So what we have in BM are
1) A theorem, probably not perfectly rigorous, and
2) Many explicit numerical simulations which agree with the theorem
I can agree that more work is needed in order to establish a completely satisfying proof, but the above is certainly a strong evidence (if not the proof).

 

[Demystifier]

But the system still has a dynamics.

Of course.

Though apparently not one easily described by BM.

Why do you think so?

 

[A. Neumaier]

Another, more general, point is at the heart of BM: Any observation eventaually is an observation of a POSITION variable (at the macroscopic level). This is why the Bohmian trickery is applicable in any situation

When we hear something, it can count as an observation, though no position variable is observed.

When we see a star, which position variable do we observe?

 

[A. Neumaier]

Why do you think so?

Because, as you said, none of the pointer variables is ''correct''. How else would you then describe the dynamics of an unobserved system of spins?

 

[Demystifier]

When we hear something, it can count as an observation, though no position variable is observed.

Oh, yes it is. When your ear hears something, the nerves in your ear vibrate. And vibration is nothing but a change of a POSITIONS of parts of an elastic object.

When we see a star, which position variable do we observe?

The position of nerves in the eye.

Of course, it's not that you really "observe" these positions in the psychological sense, but the point is that colors and sounds are ENCODED in the positions of something.

 

[A. Neumaier]

OK, now we are at the territory of statistical mechanics. In statistical mechanics there is a Boltzmann H-theorem that provides that entropy never decreases. Perhaps this theorem is not perfectly rigorous (it does not use ergodicity),

It assumes instead the Stosszahlansatz, which is taken as an unproved assumption.
(For a gas of hard spheres, the Stosszahlansatz can be justified by an ergodic theorem).

Moreover, stating that entropy doesn't decrease is very far from stating that entropy reaches its global maximum (the equilibrium state). For example, one can deduce from the Boltzmann equations in some approximation the Euler equations - there the total entropy is constant, but the dynamics is still highly nontrivial - very far from the equilibrium state. Thus the H-theorem says nothing at all about approach to equilibrium. (In simple terms: if I am climbing a hill and never go downwards, I can still end up anywhere above my current position, no matter how long I wait. No guarantee to reach the hill top.)

Finally, Boltzmann's approach only works for the classical ideal gas.

but in Bohmian mechanics there is an analogous equally (non)rigorous theorem that entropy measuring closeness to the quantum equilibrium also never decreases. So what we have in BM are
1) A theorem, probably not perfectly rigorous, and
2) Many explicit numerical simulations which agree with the theorem
I can agree that more work is needed in order to establish a completely satisfying proof, but the above is certainly a strong evidence (if not the proof).

It is as much evidence for reaching quantum equilibrium as Boltzmann's H-therorem is evidence for the universe being in global equilibrium - nil!

 

[Demystifier]

Because, as you said, none of the pointer variables is ''correct''. How else would you then describe the dynamics of an unobserved system of spins?

Bohmian mechanics describes the dynamics of wave functions and particle positions, period. It does that both for observed and unobserved systems. However, Bohmian mechanics, at the fundamental level, does not describe the dynamics of spins or any other "observables". It is only in the context of specific measurements that certain configurations of particles and wave functions can be INTERPRETED as spins or other "observables".

Just as classical optics is only about electromagnetic waves and not about colors, even though some wavelengths can be interpreted as colors in specific measurement configurations.

 

[Demystifier]

It is as much evidence for reaching quantum equilibrium as Boltzmann's H-therorem is evidence for the universe being in global equilibrium

With that I agree ...

- nil!

... but with that I don't. Anyway, I am glad that now you have a clearer picture what BM, in its current state of development, has achieved and what it has not. Just because some branch of science is not fully developed yet, it is not a reason to abandon it.

 

[A. Neumaier]

Oh, yes it is. When your ear hears something, the nerves in your ear vibrate. And vibration is nothing but a change of a POSITIONS of parts of an elastic object.


The position of nerves in the eye.

Of course, it's not that you really "observe" these positions in the psychological sense, but the point is that colors and sounds are ENCODED in the positions of something.

Ah. So the only pointer variables that count are those in the head of people. For if we observe the pointer of an instrument, all we really observe is also the position of nerves in the eye?

And I never before heard that the nerves in the eye move in response to light. What moves are the electrons inside the eye. But these are not a ''POSITION variable (at the macroscopic level)''.

 

[A. Neumaier]

Bohmian mechanics describes the dynamics of wave functions and particle positions, period. It does that both for observed and unobserved systems.

My question was - how, for an unobserved spin system. Your dogmatic position is of no help in answering that.

 

[A. Neumaier]

With that I agree ...... but with that I don't.

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.

Thus the Boltzmann's H-therorem is no evidence at all evidence for reaching global equilibrium, and because you agreed to the first part of my statement, you have also no evidence for that the state of the universe reached quantum equilibrium in BM.

 

[Demystifier]

Ah. So the only pointer variables that count are those in the head of people.

Not only they, but if you want to understand how something is observed by a human, then you cannot avoid them. They are crucial.

For if we observe the pointer of an instrument, all we really observe is also the position of nerves in the eye?

Irrespective of one's favored interpretation of QM, that is eventually so.

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.

 

[Demystifier]

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.

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.

Anyway, perhaps we are a statistical fluctuation?

 

[Demystifier]

My question was - how, for an unobserved spin system.

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.

 

[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.