The Refutation of Bohmian Mechanics

[rogerl]

Bohmian Mechanics conflicts with so many observational facts:

1. Bohmian Mechanics severely violates Lorentz Invariance because the wave function is simultaneously aware of all configuration changes of all matter in all locations in the entire universe at once (instantaneously and nonlocality universe wide). How is the wave function transmitted or conducted (in SpaceTime) where it is in all places of the universe at once?

2. Bohmian Mechanics is all particles. How can it explain quantum tunnelling where particles can literally teleport thru a barrier?

3. In Quantum Field Theories. Particles are created and annihilated. Bohmian Mechanics is all particles. How can it encompass QFT?

4. In particles remain as particles concept in Bohmian Mechanics. How come the electron doesn't radiate in the atom as anything that moves with continuous trajectory can radiate electromagnetically making it lose the energy?

How do the Bohmians handle the above issues?

 

[cgk]

The standard Bohmian mechanics is for non-relativistic non-QFT quantum mechanics. Your points 1 to 3 therefore don't apply, because they are simply not in the domain of the theory's applicability.

On 4: I think you're mixing up something. Just that Bohm mechanics has particles does not mean that they have to behave clasically. They don't -- they still describe standard quantum mechanics, just in a different way. Also note that there are even classical non-stationary charge distributions which don't radiate.

 

[Dmitry67]

I guess there are 2 relativistic 'flavors' of BM, one 'with hidden preferred frame' and 2nd - Demystifier's. I know he had somehow addressed points 1 and 3, even including semiclassical concepts (Unruh radiation, Hawking radiation), even it has not been yet confirmed independently.

There other reasons why I believe BM is wrong, but they are not on a surface.

 

[A. Neumaier]

How come the electron doesn't radiate in the atom as anything that moves with continuous trajectory can radiate electromagnetically making it lose the energy?

How do the Bohmians handle the above issues?

In the ground state of a hydrogen atom, the electron stands still (in an arbitrary position). So there is no cause for radiation. See http://lanl.arxiv.org/pdf/quant-ph/0001011 on p. 6.

 

[unusualname]

I think only 3 is troublesome, but not necessarily fatal.

A big problem with BM is that it is deterministic, and it seems nature is not, but BM can't be entirely dismissed by any experiments yet (Non-locality can be ok if it doesn't allow ftl communication, only certain non-local models are ruled out by the most recent experiments, some discussion with links at physics stackexchange)

 

[alxm]

In the ground state of a hydrogen atom, the electron stands still (in an arbitrary position). So there is no cause for radiation. See http://lanl.arxiv.org/pdf/quant-ph/0001011 on p. 6.

Which is pretty weird. Anyone know how they reconcile that with the fact that the electrons exhibit relativistic-momentum effects?

And in http://www.springerlink.com/content/1u4351g387635r6q/", they do move in closed loop trajectories.

 

[A. Neumaier]

Which is pretty weird. Anyone know how they reconcile that with the fact that the electrons exhibit relativistic-momentum effects?

And in http://www.springerlink.com/content/1u4351g387635r6q/", they do move in closed loop trajectories.

Indeed. As my paper cited before shows, Bohmian mechanics is inconsistent with standard QM once time correlations are taken into account.

 

[akhmeteli]

Indeed. As my paper cited before shows, Bohmian mechanics is inconsistent with standard QM once time correlations are taken into account.

Unfortunately, I did not have much time to study your paper in detail, but the claim is rather strong, so let me ask you something about your paper.

Some formal questions first.

Am I right that your paper has not been published in a peer-reviewed journal?

Have you replied to the critique by Marchildon? (http://arxiv.org/PS_cache/quant-ph/pdf/0007/0007068v1.pdf )(It may well be that I just missed your reply).

Now let me try make some more meaningful remarks (again, they may be completely wrong, as I did not study the issue in detail).

On the face of it, it looks like you may overinterpret the results of your paper in the quoted post. My impression is there are some caveats in the paper related to the measurement mechanism. And this may be a crucial point. My understanding is that standard quantum mechanics contains two major elements: unitary evolution and the theory of measurement. It also seems to me that unitary evolution of quantum mechanics is fully adopted by the Bohm interpretation. If you disagree, please advise. If, however, you agree, then one would expect that discrepancies between standard quantum mechanics and the Bohm interpretation (if any) can only arise from the theory of measurement (and it looks like this is what you may imply in your paper, as you mention that "Bohmian theory discusses measurement only in an approximate way").

It is, however, my understanding that unitary evolution and the theory of measurement of quantum mechanics, strictly speaking, contradict each other (see, e.g., references to the statements to this effect by 1) Albert and 2) Bassi/Ghirardi in my post https://www.physicsforums.com/showpost.php?p=2534219&postcount=31 ) . If this is so, then it may be good for the Bohm interpretation if it fails to faithfully reproduce the theory of measurement of standard quantum mechanics? Furthermore, you yourself describe the measurement mechanism as ill-defined.

The above is not meant as criticism (I sincerely value your posts), but as an attempt to understand the status of this issue.

 

[A. Neumaier]

Am I right that your paper has not been published in a peer-reviewed journal?

No. Truth is not dependent on peer reviews.

Have you replied to the critique by Marchildon? (http://arxiv.org/PS_cache/quant-ph/pdf/0007/0007068v1.pdf )(It may well be that I just missed your reply).

No. I lost interest in Bohmian mechanics once I noticed that all electrons in hydrogen atoms in the ground state stand still at arbitrary positions. I wrote up the report as my farefell address.

Now let me try make some more meaningful remarks (again, they may be completely wrong, as I did not study the issue in detail).

On the face of it, it looks like you may overinterpret the results of your paper in the quoted post. My impression is there are some caveats in the paper related to the measurement mechanism. And this may be a crucial point. My understanding is that standard quantum mechanics contains two major elements: unitary evolution and the theory of measurement. It also seems to me that unitary evolution of quantum mechanics is fully adopted by the Bohm interpretation. If you disagree, please advise. If, however, you agree, then one would expect that discrepancies between standard quantum mechanics and the Bohm interpretation (if any) can only arise from the theory of measurement (and it looks like this is what you may imply in your paper, as you mention that "Bohmian theory discusses measurement only in an approximate way").

The reality is much worse. Bohmian mechnaics achieves agreement with orthodox quantum mechnaics _only_ through measurement considerations. Thus they are able to hide any weakness in their approach by burying it in the fuzzyness of measurement problems.

It is, however, my understanding that unitary evolution and the theory of measurement of quantum mechanics, strictly speaking, contradict each other .

Only because the usual measurement account is an unrealistic idealization of actual measurement.
Maybe read chapter 10 of my new book. Once one acknowledges that the measurement description must be inherently nonideal because the environment can be modeled only approximately, the contradictions disappear.

Furthermore, you yourself describe the measurement mechanism as ill-defined.

In my own interpretation, see https://www.physicsforums.com/showthread.php?t=490492 ,
foundations are independent of measurement, and hence on a much better footing.

 

[akhmeteli]

Dear A. Neumaier,

Thank you very much for your reply.

No. Truth is not dependent on peer reviews.

According to forum's rules, it is:-)

No. I lost interest in Bohmian mechanics once I noticed that all electrons in hydrogen atoms in the ground state stand still at arbitrary positions. I wrote up the report as my farefell address.

I see. Actually, the Bohm interpretation does not look aesthetically appealing to me either. But our personal preferences is one thing, but the claim of your post 7 in this thread is not about preferences.

The reality is much worse. Bohmian mechnaics achieves agreement with orthodox quantum mechnaics _only_ through measurement considerations. Thus they are able to hide any weakness in their approach by burying it in the fuzzyness of measurement problems.

With all due respect, I am afraid you cannot have it both ways. Either "Bohmian mechanics is inconsistent with standard QM...", or "Bohmian mech[anics] achieves agreement with orthodox quantum mech[anics]..."
Furthermore, if there is indeed any inconsistency with standard QM, it is in the realm of measurement, because, as I said (and you don't seem to dispute that), the Bohm interpretation fully adopts the unitary evolution of standard QM. By the way, this fact also suggests that it is not "_only_ through measurement considerations" that "Bohmian mech[anics] achieves agreement with orthodox quantum mech[anics]" (if it does indeed achieves it), it is also because it adopts unitary evolution.

Only because the usual measurement account is an unrealistic idealization of actual measurement.
Maybe read chapter 10 of my new book. Once one acknowledges that the measurement description must be inherently nonideal because the environment can be modeled only approximately, the contradictions disappear.

Again, no offense meant, but this looks very much like double standard to me. Indeed, you told us in post 7 of this thread that "Bohmian mechanics is inconsistent with standard QM...". On the other hand, as I argued above, * if there is indeed any inconsistency, it is between the Bohm interpretation and the theory of measurements of standard QM, as ** unitary evolution is one and the same for the Bohm interpretation and standard QM (if you disagree with statement * and/or statement **, please advise). Whereas when I insist that standard QM is inconsistent with itself, because its unitary evolution, strictly speaking, contradicts its theory of measurement, you are telling me: C'mon, "the measurement description must be inherently nonideal", so actually "the contradictions disappear." I may agree with that statement, or disagree with it, but I cannot reasonably agree with it when talking about inconsistency of the Bohm interpretation with standard QM and in the same breath disagree with it when talking about inconsistency of standard QM with itself.

Based on the above, I very much hope that you will either rephrase your claim of post 7 or agree with me that standard QM is, strictly speaking, inconsistent with itself. In the latter case, the Bohm interpretation's sin (if any) against standard QM won't look so deadly. Again, the Bohm interpretation is no relative of mine, but I think it's valuable, if only as a counter-example to some no-go theorems. Furthermore, it is my understanding that this interpretation was an inspiration for the Bell theorem.

In my own interpretation, see https://www.physicsforums.com/showthread.php?t=490492 ,
foundations are independent of measurement, and hence on a much better footing.

Maybe so, but your claim of post 7 is not about your interpretation. It is specifically about standard QM.

 

[Demystifier]

1. Bohmian Mechanics severely violates Lorentz Invariance because the wave function is simultaneously aware of all configuration changes of all matter in all locations in the entire universe at once (instantaneously and nonlocality universe wide). How is the wave function transmitted or conducted (in SpaceTime) where it is in all places of the universe at once?

BM is indeed nonlocal, but not due to the reason you mention above. In fact, the wave function in BM is exactly the same as in standard QM. So, if the above meant that BM is nonlocal, then it would imply that standard QM is nonlocal as well.

2. Bohmian Mechanics is all particles. How can it explain quantum tunnelling where particles can literally teleport thru a barrier?

BM is NOT all particles. BM is particles AND wave function. It is the wave function that causes the particle to move through the barrier. It does not teleport through it, but simply gets more energy to "jump" over it.

3. In Quantum Field Theories. Particles are created and annihilated. Bohmian Mechanics is all particles. How can it encompass QFT?

Here is how:
http://xxx.lanl.gov/abs/0904.2287 [Int. J. Mod. Phys. A25:1477-1505, 2010]

4. In particles remain as particles concept in Bohmian Mechanics. How come the electron doesn't radiate in the atom as anything that moves with continuous trajectory can radiate electromagnetically making it lose the energy?

When a charged particle obeying classical laws accelerates, then it radiates. However, in BM a charged particle does NOT obey classical laws. These nonclassical laws are such that a charged particle may accelerate without producing radiation.

 

[JesseM]

BM is indeed nonlocal, but not due to the reason you mention above. In fact, the wave function in BM is exactly the same as in standard QM. So, if the above meant that BM is nonlocal, then it would imply that standard QM is nonlocal as well.

Doesn't the Bohmian wave function include information about the precise position of all particles at all times, while the QM wave function in general doesn't?

 

[Demystifier]

... Bohmian mechanics is inconsistent with standard QM once time correlations are taken into account.

Bohmian mechnaics achieves agreement with orthodox quantum mechnaics _only_ through measurement considerations.

I don't see how these two statements are mutually consistent. Are you saying that

1) BM achieves agreement with orthodox QM WHENEVER measurement considerations are taken into account,

or that

2) Even with measurement-considerations-taken-into-account BM does not agree with standard QM when time correlation are considered?

 

[Demystifier]

Doesn't the Bohmian wave function include information about the precise position of all particles at all times, while the QM wave function in general doesn't?

The Bohmian wave function ITSELF does NOT include information about the precise positions of particles. Just as standard wave function doesn't.

BM is similar to a classical motion of a test particle in a fixed gravitational field. The fixed gravitational field itself knows nothing about the actual position of the test particle.

 

[JesseM]

The Bohmian wave function ITSELF does NOT include information about the precise positions of particles. Just as standard wave function doesn't.

BM is similar to a classical motion of a test particle in a fixed gravitational field. The fixed gravitational field itself knows nothing about the actual position of the test particle.

Ah, I was thinking of the particles more like gravitational sources which do influence the gravitational field, but you're saying the particle positions have no influence on the field at all? So if at some time T we start with some initial state of the wave function, there are an infinite number of possible initial particle configurations that would be consistent with that initial wave function state, and the future evolution of the wave function is exactly the same regardless of which particle configuration we choose, with the particles just passively "puppeted" by the dynamics of the wavefunction?

 

[Demystifier]

Ah, I was thinking of the particles more like gravitational sources which do influence the gravitational field, but you're saying the particle positions have no influence on the field at all? So if at some time T we start with some initial state of the wave function, there are an infinite number of possible initial particle configurations that would be consistent with that initial wave function state, and the future evolution of the wave function is exactly the same regardless of which particle configuration we choose, with the particles just passively "puppeted" by the dynamics of the wavefunction?

Exactly. More precisely, this is so with the fundamental wave function.

But in BM there are also more subtle concepts of effective and conditional wave functions, which explain how the motion of particles makes the illusion that the wave function collapses when a particle is detected. If you want, I can explain it as well.

 

[Dmitry67]

Particle positions, as I understand, are calculated 'backwards' from a wave evolution. If you replace QM equations with some other equations QM2, you will be able to redefine the non-local currents to satisfy these new equations. In fact, you can do it for ANY evolution of a wave (when of course, the total probability is 100% and is conserved over the time).

If BM was true, then there would be some kind of magic coincidence, like, the QM equations would be the only case consistent with the 'currents'. It would be an indication that there is some kind of deep underlying truth.

 

[A. Neumaier]

According to forum's rules, it is:-)

Nonsense.

Actually, the Bohm interpretation does not look aesthetically appealing to me either. But our personal preferences is one thing, but the claim of your post 7 in this thread is not about preferences.

Yes, and I believe it to be true, and gave the reasons in my paper.

With all due respect, I am afraid you cannot have it both ways. Either "Bohmian mechanics is inconsistent with standard QM...", or "Bohmian mech[anics] achieves agreement with orthodox quantum mech[anics]..."

It achieves it precisely for single-time statements of quantum mechanics written in terms of canonical coordinates, and not beyond. For example, you cannot do quantum computing in Bohmian mechanics.
Even worse, the quantum field ontologies proposed are incompatible with the original Bohmian ontology when specialized to single-particle states.. Thus there are as many inequivalent ontologies as there are ways to represent a given quantum system.

The worst thing about Bohmian mechanics is their low standards of quality...

the measurement description must be inherently nonideal", so actually "the contradictions disappear."

They only disappear under the carpet of fuzzy arguments.
[

 

[A. Neumaier]

I don't see how these two statements are mutually consistent. Are you saying that

1) BM achieves agreement with orthodox QM WHENEVER measurement considerations are taken into account,

or that

2) Even with measurement-considerations-taken-into-account BM does not agree with standard QM when time correlation are considered?

Bohmian mechanics agrees (for time correlation statements) with quantum mechanics only superficially, because it relies on a fuzzy notion of measuremnt to make many of their arguments.
In the simple case I gave in the paper, it predicts time correlations of opposite sign as standard quantum mechanics. And if I rmember correctly the refutation of my argument consisted not in pointing out a mistake in my calculations but by referring to a vague measurement argument that should tell why actual observation gives the right results in spite of the wrong sign.

But I don't care anymore about BM, and therefore won't defend my statement in the paper further.

 

[yoda jedi]

Exactly. More precisely, this is so with the fundamental wave function.

But in BM there are also more subtle concepts of effective and conditional wave functions, which explain how the motion of particles makes the illusion that the wave function collapses when a particle is detected. If you want, I can explain it as well.

..."After a measurement, the particle is trapped within one particular wave packet with the usual quantum-mechanical probability. Because the other wave packets are spatially separated from it after the measurement, they can no longer influence the particle. This represents an apparent collapse of the wave function and the occurrence of a definite measurement result. In principle, however, the remaining packets, although empty, can interfere again with the packet containing the particle, but the probability for this is tiny in macroscopic situations"...

 

[yoda jedi]

http://lanl.arxiv.org/pdf/quant-ph/0001011.

..."Due to the complicated form of the Bohmian dynamics, it seems difficult to compute time correlations for realistic scenarios where a comparison with linear response theory and hence with experiment would become possible. But perhaps numerical simulations are feasible. On the other hand, it is unlikely that, if the predictions of quantum mechanics and Bohmian mechanics differ in such a simple case, they would agree in more realistic situations"...





Chemical Physics Letters 332 (2000) 145-153
http://www-ucc-old.ch.cam.ac.uk/research/dn232/pub/Bohm.pdf

..."Only recently have workers begun to employ the theory to simulate the dynamics of systems of chemical interest [4-7]. These recent efforts indicate that the de Broglie-Bohm approach is both intuitively attractive in its `causal interpretation' of quantum events [8] and computationally promising"...


.

 

[camboy]

Nonsense.
For example, you cannot do quantum computing in Bohmian mechanics.

Except, of course, that you can:

"Quantum computing in the de Broglie-Bohm pilot-wave picture" by P. Roser [http://arxiv.org/abs/1012.4843" ]

 

[akhmeteli]

Dear A. Neumaier,

Thank you for your reply.

Am I right that your paper has not been published in a peer-reviewed journal?

No. Truth is not dependent on peer reviews.

According to forum's rules, it is:-)

Nonsense.

So what exactly is nonsense - my words or the forum's rules banning discussions of "new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals..."?:-)

...our personal preferences is one thing, but the claim of your post 7 in this thread is not about preferences.

Yes, and I believe it to be true, and gave the reasons in my paper.

You mention in your paper, among other things, that in “discussions with proponents of Bohmian mechanics, it is claimed that my interpretation of the Bohmian formalism is erroneous, in that I am not making the proper distinction between the ontological ”beable” and the epistemological ”observable”, and compare the statistics of unobserved Bohm trajectories with those for quantum observations.”

And I tend to agree with these “proponents of Bohmian mechanics”. In your arguments against their opinion you actually demand that Bohmians do not dare to resort to discussions of the measurement procedure. So this procedure can be used by standard quantum mechanics, but not in the Bohm interpretation? Sorry, with all due respect, I don’t buy that. You are trying to compare the predictions of the Bohm interpretation and the standard quantum mechanics, remember? Should not the measurement procedure be the same, as far as possible?

With all due respect, I am afraid you cannot have it both ways. Either "Bohmian mechanics is inconsistent with standard QM...", or "Bohmian mech[anics] achieves agreement with orthodox quantum mech[anics]..."

It achieves it precisely for single-time statements of quantum mechanics written in terms of canonical coordinates, and not beyond.

Beyond that it has the same unitary evolution as orthodox quantum mechanics, and that is an awful lot, if you ask me. Imagine for a moment that the Universe starts in the same state in the Bohm interpretation and in the orthodox quantum mechanics. As the unitary evolution is the same, the evolved state ten billion years thereafter will be the same in both interpretations, unless you believe that unitary evolution is not universal.

For example, you cannot do quantum computing in Bohmian mechanics.

What is the status of this statement? Any references? Looks like Bohmians are not aware of that: http://plato.stanford.edu/entries/qm-bohm/ (you may wish to look for “quantum computing” there).

Even worse, the quantum field ontologies proposed are incompatible with the original Bohmian ontology when specialized to single-particle states.. Thus there are as many inequivalent ontologies as there are ways to represent a given quantum system.

The worst thing about Bohmian mechanics is their low standards of quality...

They only disappear under the carpet of fuzzy arguments.

Again, we may like or dislike the Bohm interpretation, but this has nothing to do with your claim in post 7. Let me just repeat that there can be only one source, if any, of inconsistency between the Bohm interpretation and standard quantum mechanics – the theory of measurements, and the theory of measurements of standard quantum mechanics is, strictly speaking, inconsistent with standard quantum mechanics anyway. So why blame Bohmians for any inconsistency?

To conclude, I respectfully disagree with the arguments of your article and believe that your claim of post 7 is just your personal theory. For reasons outlined in this thread I believe the claim is misleading in the best case. I respect you as a very knowledgeable person, but that does not mean I have to agree with everything you say.

 

[A. Neumaier]

So what exactly is nonsense - my words or the forum's rules banning discussions of "new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals..."?:-)

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.

And I tend to agree with these “proponents of Bohmian mechanics”.

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.

Imagine for a moment that the Universe starts in the same state in the Bohm interpretation and in the orthodox quantum mechanics. As the unitary evolution is the same, the evolved state ten billion years thereafter will be the same in both interpretations, unless you believe that unitary evolution is not universal.

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.

What is the status of this statement? Any references? Looks like Bohmians are not aware of that: http://plato.stanford.edu/entries/qm-bohm/ (you may wish to look for “quantum computing” there).
.

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

 

[Demystifier]

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

See post #22 above.

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, including quantum computing and time correlations. Of course, to understand that, one needs to understand the theory of quantum measurements, which you find vague.

 

[Dmitry67]

As there are more proponents of BM here, it would be interesting to ask again a question I asked Demystifier (Demystifier - please don't reply - I wonder if different proponents of BM share the same point of view).

So, in BM evolution of wavefunction is the same as in MWI. Only particles make the difference. So, like in MWI there are 2 'branches' - dead cat and alive cat. We see the alive cat.

Question: does (empty) wavefunction of the dead cat (observer) feel pain when dying and why?

 

[camboy]

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.

You do need to agree. Not least, because your paper was never published in the peer-reviewed literature, and justified refutations of it and other similar claims have been. If you had tried to get it published, it would have been rejected (maybe it was?) because it is demonstrably incorrect.

Streater is also incorrect, as has been pointed out many times. For a discussion not behind a pay wall, see Ilja Schmelzer's page http://www.ilja-schmelzer.de/realism/BMarguments.php" . Both your and Streater's argument stem from a basic misunderstanding off deBB theory, as I believe has already been pointed out here. See in particular Schmelzer's discussion of 'measurements at different times'.

When people disagree with you, they always preface their remarks with "You're a clever man, Arnold, but..". And I'll do the same, but you have to remember that both you and Streater suffer from an extremely serious case of confirmation bias - you refuse to contemplate anything that is in conflict with your particular viewpoint of physics. Go on admit it, you haven't read a deBB paper since the last century have you? If you think the whole thing is wrong, then write a (correct) paper on it and get it published in a peer-reviewed journal. People will thank you for it - after all, a lot of people from many disciplines work on this now and they don't want to be wasting their time, do they? Remember, nobody's managed to refute it in the last 84 years, so somebody will probably give you a prize of some sort.

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.

The statistics refer to an ensemble of hydrogen atoms, each member of which will have the electron standing still at a different position (depending on how it was prepared). Over the ensemble, the statistics will be correct. I don't know how you can misunderstand this.

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

I've already told you in post #22, but because you seem never to read things that contradict your worldview, you just ignore me. Let me repeat:

"Quantum computing in the de Broglie-Bohm pilot-wave picture" by P. Roser [http://arxiv.org/abs/1012.4843" ]

 

[A. Neumaier]

Except, of course, that you can:

"Quantum computing in the de Broglie-Bohm pilot-wave picture" by P. Roser [http://arxiv.org/abs/1012.4843" ]

Thanks for the reference. I didn't know this. But the presentation only confirms my view that bohmian mechnaics is an artificial add on to standard QM, and that it can be coerced into accomodating anything - in this case by introducing artificial pointer coordinates that don't exist in the standard description.

Whereas a N-particle system is represented by a wave psi(x_1,...,x_N,t) without reference to measurement, the spin wave functions all depend on a pointer variable y related not to the spin but to the measuring instrument. Thus spins cannot be described independent of a measuring apparatus. And if there are two devices with which a spin casn be measured, one would presumably need two pointer variables, and a larger space of wave functions. Now which of these description has a true ontological status?

The problem with Bohmian mechanics is that one can make it work in too many ad hoc ways, so that none of the resulting models can claim to have any preferred ontological status. But this defeats its main virtue.

 

[A. Neumaier]

If you think the whole thing is wrong, then write a (correct) paper on it and get it published in a peer-reviewed journal.

I have more important things to do than to kill an already dead cat.

The statistics refer to an ensemble of hydrogen atoms, each member of which will have the electron standing still at a different position (depending on how it was prepared). Over the ensemble, the statistics will be correct. I don't know how you can misunderstand this.

In a universe consisting only of a proton and an electron, there is no way to do such a preparation.

A single counterexample is enough to discredit a general claim.

 

[camboy]

I have more important things to do than to kill an already dead cat.

Course you do, love.

In a universe consisting only of a proton and an electron, there is no way to do such a preparation.

A single counterexample is enough to discredit a general claim.

What an unbelievably content-free objection. Don't you get embarrassed by this? I would.

 

[dextercioby]

In a universe consisting only of a proton and an electron, there is no way to do such a preparation.

I sense a conflict here between the meanings of concept of <statistics> which eventually lead to the different interpretations of the (possibly the same) theory.

In the Copenhagen interpretation, one could describe a universe made up of only one electron and one proton and purely from theory compute the probability of measuring the electron's position within a finite spatial volume.

The statiscal/ensemble interpretation however claims that quantum mechanics is a theory of infinitely many indentically prepared systems (in particular H-atoms), so that the universe is never made up of an electron & a proton, but from an infinity of such particles.

By reading the thread I sense that the Bohmian Mechanics (seen as a different interpretation, or even a different formulation of the same theory) uses the same meaning of statistics as the ensemble one, or ?

 

[Demystifier]

By reading the thread I sense that the Bohmian Mechanics (seen as a different interpretation, or even a different formulation of the same theory) uses the same meaning of statistics as the ensemble one, or ?

Yes. In fact, the Bohmian interpretation can be viewed as a specific realization of the general idea of ensemble interpretation.

 

[A. Neumaier]

I sense a conflict here between the meanings of concept of <statistics> which eventually lead to the different interpretations of the (possibly the same) theory.

In the Copenhagen interpretation, one could describe a universe made up of only one electron and one proton and purely from theory compute the probability of measuring the electron's position within a finite spatial volume.

The statistical/ensemble interpretation however claims that quantum mechanics is a theory of infinitely many identically prepared systems (in particular H-atoms), so that the universe is never made up of an electron & a proton, but from an infinity of such particles.

By reading the thread I sense that the Bohmian Mechanics (seen as a different interpretation, or even a different formulation of the same theory) uses the same meaning of statistics as the ensemble one, or ?

Unlike QM and its ensemble interpretation (which is valid only for small subsystems of the universe that can be identically prepared many times), Bohmian mechanics is heralded by its champions as a deterministic theory.

Deterministic foundations make sense only if they can describe the whole universe as a big deterministic system. This universe is at any time in a well-determined, unique state, and cannot be replicated many times. Thus any statistics (collected by an observer inside this single universe) must be the result of this deterministic dynamics in this particular state. Statistics in a deterministic theory is therefore the result of chaotic motion, not of a replication of the dynamics under different initial conditions.

As my example shows, Bohmian mechanics models systems where the postulated statistics does not follow from the dynamics but must be put in by hand as an assumption on multiply prepared systems. Only if the initial distribution matches exactly the required statistics, the outcomes are correct.

Thus Bohmian mechanics is no deterministic theory in the usual sense, since for its interpretation it needs to make assumptions of a stochastic nature that cannot be derived from the dynamics.

 

[Demystifier]

And if there are two devices with which a spin casn be measured, one would presumably need two pointer variables, and a larger space of wave functions. Now which of these description has a true ontological status?

If both devices exist in the laboratory (or elsewhere in the real world), then both are "preferred" and ontological. If only one exists, then this one is the preferred and ontological one. Simple, isn't it?

 

[A. Neumaier]

If both devices exist in the laboratory (or elsewhere in the real world), then both are "preferred" and ontological. If only one exists, then this one is the preferred and ontological one. Simple, isn't it?

And if none is in the laboratory?

Wouldn't you have to treat all the possible devices anywhere in the world as pointer variables parameterizing the spin wave function?