Quantum Decoherence and deBroglie-Bohm theory

[ShayanJ]

From time to time I hear that Quantum Decoherence can address the measurement problem only when accompanied by deBroglie-Bohm theory(dBB) (or any hidden variable theory? or MWI?). I want to know why is that?
Also, I saw some papers recently(e.g. this) that prove dBB is incompatible with QM. There is also this paper which suggests an experiment for testing dBB against QM and says that the results support QM and contradict dBB's predictions. So it seems at least dBB is in serious danger, or maybe even ruled out.(Ideas on this?)
Does this mean that Quantum Decoherence is useless now?(Of course if dBB is actually ruled out!)

 

[atyy]

From time to time I hear that Quantum Decoherence can address the measurement problem only when accompanied by deBroglie-Bohm theory(dBB) (or any hidden variable theory? or MWI?). I want to know why is that?

That is not true. The correct statement is that decoherence does not solve the measurement problem, unless accompanied by additional assumptions. One possible set of additional assumptions are those of the de Broglie Bohm theory.

 

[ShayanJ]

That is not true. The correct statement is that decoherence does not solve the measurement problem, unless accompanied by additional assumptions. One possible set of additional assumptions are those of the de Broglie Bohm theory.

Is there a set of additional assumptions that can somehow be called Copenhagen? I mean, can we keep Copenhagen interpretation and solve measurement problem using decoherence? Or maybe use some extended or modified Copenhagen interpretation?

 

[atyy]

Is there a set of additional assumptions that can somehow be called Copenhagen? I mean, can we keep Copenhagen interpretation and solve measurement problem using decoherence? Or maybe use some extended or modified Copenhagen interpretation!

That would be a bit unusual, but names of interpretations are a matter of convention, so you could call de Broglie-Bohm theory "Copenhagen" if you'd like.

My own usage is that Copenhagen is the default interpretation of quantum mechanics, and is the interpretation in which the measurement problem is usually stated. The key point of Copenhagen is that there is a classical/quantum cut (or apparatus/system cut), and the wave function is not necessarily real, and a tool to calculate the probabilities of measurement outcome. The measurement problem enters with the classical/quantum cut.

Decoherence alone cannot solve the measurement problem, because the measurement problem is the lack of definite outcomes when the wave function is extended to the whole universe. Decoherence requires a division of the universe into subsystems, and a restriction of observables to a subsystem. There is no decoherence of the overall wave function of the universe, so if we have a wave function of the universe it seems that nothing happens (or everything does if the many-worlds approach is attempted).

 

[ShayanJ]

That would be a bit unusual, but names of interpretations are a matter of convention, so you could call de Broglie-Bohm theory "Copenhagen" if you'd like.

My own usage is that Copenhagen is the default interpretation of quantum mechanics, and is the interpretation in which the measurement problem is usually stated. The key point of Copenhagen is that there is a classical/quantum cut (or apparatus/system cut), and the wave function is not necessarily real, and a tool to calculate the probabilities of measurement outcome. The measurement problem enters with the classical/quantum cut.

I don't mean that. Of course Copenhagen interpretation is not only about that cut. I mean can we keep all things from Copenhagen interpretation and just replace that cut with Decoherence and have a solution of measurement problem?

 

[atyy]

I don't mean that. Of course Copenhagen interpretation is not only about that cut. I mean can we keep all things from Copenhagen interpretation and just replace that cut with Decoherence and have a solution of measurement problem?

I added a bit to the post above to explain why decoherence alone does not solve the measurement problem. The basic problem is that there is no decoherence of the wave function of the universe. So decoherence doesn't allow the cut to be removed.

 

[bhobba]

From time to time I hear that Quantum Decoherence can address the measurement problem only when accompanied by deBroglie-Bohm theory(dBB) (or any hidden variable theory? or MWI?). I want to know why is that?

Decoherence only explains apparent collapse, by which is meant how a superposition becomes an improper mixed state. If it was a proper one actual collapse would have occurred. Explaining how an improper mixed state becomes a proper one is the modern version of the measurement problem, also sometimes referred to as the problem of why we actually get any outcomes at all. There are a few other issues such as the preferred basis problem and the factorisation problem but its the biggie. In DBB the problem is trivial - you get outcomes because the particle has an actual position and momentum so the improper mixed state is a proper one.

I wouldn't say its the only way though.

I will leave the other questions to those that know DBB better than me.

Thanks
Bill

 

[StevieTNZ]

There is also this paper which suggests an experiment for testing dBB against QM and says that the results support QM and contradict dBB's predictions.

From reading the summary of that paper on the arXiv website, it appears the experiment was performed and the results reported in the paper you link. If this were the case, then dBB would be refuted. However that paper was published in 2002 and we still see discussions on dBB. So maybe there was some challenges to the experiment and the authors conclusion.

 

[ShayanJ]

From reading the summary of that paper on the arXiv website, it appears the experiment was performed and the results reported in the paper you link. If this were the case, then dBB would be refuted. However that paper was published in 2002 and we still see discussions on dBB. So maybe there was some challenges to the experiment and the authors conclusion.

That always bothers me. How can we know how's the situation now?

Thanks all

 

[atyy]

Ghose's paper has been commented on by:

http://arxiv.org/abs/quant-ph/0108038
http://arxiv.org/abs/quant-ph/0101132
http://arxiv.org/abs/quant-ph/0302085
http://arxiv.org/abs/quant-ph/0305131

Edit: There are, however, some holes to be filled to be certain that dBB completely solves the measurement problem, http://arxiv.org/abs/0712.0149: "On the technical side, for DBB to solve the measurement problem we require that the corpuscles track the decohered macroscopic degrees of freedom of large systems. ... Further plausibility arguments have been constructed (e. g. Bell (1981b, section 4), Holland (1993, pp. 336–50), D¨urr, Goldstein, and Zanghi (1996, pp. 39–41), and some simple models have been studied; at present, it seems likely that the corpuscles do track the quasiclassical trajectories sufficiently well for DBB to solve the measurement problem, but there exists no full proof of this."

I edited this post while Shyan was replying to it.

 

[ShayanJ]

Ghose's paper has been commented on by:

http://arxiv.org/abs/quant-ph/0108038
http://arxiv.org/abs/quant-ph/0101132
http://arxiv.org/abs/quant-ph/0302085
http://arxiv.org/abs/quant-ph/0305131

Probably the weakest point of dBB which has not been explicitly checked is that decoherence always works out as our intuition suggests. However, a failure of decoherence would be much more interesting than creating problems for dBB, since it would change our understanding of how the classical/quantum cut can be shifted in Copenhagen.

But these are all for over ten years ago! Its hard to think nothing has changed since then! But if we're forced to think like that, that only makes me disregard dBB even more than before!

 

[atyy]

But these are all for over ten years ago! Its hard to think nothing has changed since then! But if we're forced to think like that, that only makes me disregard dBB even more than before!

Why? If the Ghose paper was in error 10 years ago, why would it now become correct?

 

[vanhees71]

I added a bit to the post above to explain why decoherence alone does not solve the measurement problem. The basic problem is that there is no decoherence of the wave function of the universe. So decoherence doesn't allow the cut to be removed.

How can there be a wave function of the entire universe? There are interacting particles in the universe, and it's clearly relativistic. So how can there exist a wave function as a description of the universe's state, if wave functions aren't suitable for two interacting particles?

If anything as a (pure?) quantum state of the entire universe exists it cannot be described as a single wave function. Despite this technical problem I've also a principle problem with the idea of a quantum state of the entire universe: How can you ever observe the predictions made by associating such a state to the whole universe? You cannot prepare many universes and make experiments with them. So how do you figure out whether the probabilistic physics content of the wave function describes the statistics of an ensemble of universes correctly if there's no possiblity to prepare many universes in this state. I think the notion of a quantum state of the entire universe is a pretty empty idea without any testable consequences and thus unscientific.

 

[ShayanJ]

Why? If the Ghose paper was in error 10 years ago, why would it now become correct?

No, that's not what I mean. I mean why can't we find recently published papers on dBB? I searched but all papers I found are old, not newer than these papers. Of course dBB has many problems to be solved and the fact than there is no(or maybe little) recently published papers on it, means people aren't working on it. It seems that they just wait for someone to criticize it and they answer! It seems like a dead theory.
Also, I should confess I'm looking forward to see dBB ruled out. Of course not because of physical reasons because I'm in no way a physicist. Its just that I like QM as it is. de-Broglie and Bohm just spoil the fun!:D

 

[atyy]

No, that's not what I mean. I mean why can't we find recently published papers on dBB? I searched but all papers I found are old, not newer than these papers. Of course dBB has many problems to be solved and the fact than there is no(or maybe little) recently published papers on it, means people aren't working on it. It seems that they just wait for someone to criticize it and they answer! It seems like a dead theory.
Also, I should confess I'm looking forward to see dBB ruled out. Of course not because of physical reasons because I'm in no way a physicist. Its just that I like QM as it is. de-Broglie and Bohm just spoil the fun!:D

In a sense it is good that dBB is dead, since that means most of its problems are solved. The remaining problems for dBB applied to non-relativistic QM are as difficult as the remaining problems of the foundations of classical statistical mechanics. I confess I did not believe dBB was viable until I found out about Valentini's work. I don't think you can like QM the way it is as a final theory, since there truly is a measurement problem. And it is important to understand that the point of dBB is not that it is the correct theory of nature, but rather that it shows that the measurement problem can be solved. And yes, I too prefer an epistemic understanding of the wave function. Unfortunately, nature doesn't care about what I like. I think there is still hope for an epistemic understanding of the wave function even within dBB.

Anyway, the major problem in dBB is the formulation of the theory for chiral fermions interacting with non-abelian gauge fields. So you can think of all papers about chiral fermions interacting with non-abelian gauge fields as secretly dBB papers (ok, maybe I went too far there, but it is my interpretation of the literature :D). Anyway, that means that these are very recent dBB papers:
http://arxiv.org/abs/0908.0591
http://arxiv.org/abs/0912.2560
http://arxiv.org/abs/1401.6655

 

[vanhees71]

So you can think of all papers about chiral fermions interacting with non-abelian gauge fields as secretly dBB papers (ok, maybe I went too far there, but it is my interpretation of the literature ).

Objection! Approximate chiral symmetry of the light-quark sector in QCD is not secretly on de Broglie Bohm. In my field, I guess there's nobody believing in or even thinking about dBB at all. Why should we? It's just a very important tool to build effective theories of hadrons with some foundation in the standard model. (Untarized) chiral perturbation theory is thus imply a tool to get good phenomenological models for strongly interacting particles/matter at low energies, where (perturbative) QCD is not applicable, and this approximate symmetry pretty much rules the dynamics of hadrons. That's why it's also important for lattice-QCD people to find a good description of chiral fermions. They also don't seem to be thinking about dBB at all.

 

[ShayanJ]

In a sense it is good that dBB is dead, since that means most of its problems are solved. The remaining problems for dBB applied to non-relativistic QM are as difficult as the remaining problems of the foundations of classical statistical mechanics. I confess I did not believe dBB was viable until I found out about Valentini's work. I don't think you can like QM the way it is as a final theory, since there truly is a measurement problem. And it is important to understand that the point of dBB is not that it is the correct theory of nature, but rather that it shows that the measurement problem can be solved. And yes, I too prefer an epistemic understanding of the wave function. Unfortunately, nature doesn't care about what I like. I think there is still hope for an epistemic understanding of the wave function even within dBB.

Anyway, the major problem in dBB is the formulation of the theory for chiral fermions interacting with non-abelian gauge fields. So you can think of all papers about chiral fermions interacting with non-abelian gauge fields as secretly dBB papers (ok, maybe I went too far there, but it is my interpretation of the literature :D). Anyway, that means that these are very recent dBB papers:
http://arxiv.org/abs/0908.0591
http://arxiv.org/abs/0912.2560
http://arxiv.org/abs/1401.6655

Of course I didn't mean I like QM as a final theory. The point is, people mostly like dBB because it preserves(at least partly) the classical nature of physical laws. In fact because of Bell's theorem, it seems that most classical-like interpretation of QM should be something like dBB because non-locality is inescapable. But I just don't see the reason why so many people should be so insistent that nature is as people thought before QM. I think its really more like it that nature behaves as standard QM says, its somehow more like it, that nature doesn't waste "piles and piles of paper" to store information that she actually can do without them. It more beautiful that she actually doesn't. Of course nature doesn't have to look as I prefer, so no one has the right to stop people working on dBB. Its just that I don't like it.
And about those papers. I can't see how those can be related to dBB. Because they can do everything in the context of standard QM and don't bother with dBB. So even if they succeed, they may do it somehow that doesn't do a favuor to dBB.
Also dBB doesn't seem to be able to make a good marriage with SR too. I know people had some attempts but things don't seem to fit nicely.
And quantum fluctuations. How can dBB account for particles coming from nothing when it doesn't accept uncertainty principles as they are in standard QM?

 

[atyy]

Objection! Approximate chiral symmetry of the light-quark sector in QCD is not secretly on de Broglie Bohm. In my field, I guess there's nobody believing in or even thinking about dBB at all. Why should we? It's just a very important tool to build effective theories of hadrons with some foundation in the standard model. (Untarized) chiral perturbation theory is thus imply a tool to get good phenomenological models for strongly interacting particles/matter at low energies, where (perturbative) QCD is not applicable, and this approximate symmetry pretty much rules the dynamics of hadrons. That's why it's also important for lattice-QCD people to find a good description of chiral fermions. They also don't seem to be thinking about dBB at all.

Ha, ha! Yes, I was pretty sure I went too far there. Anyway, the good thing is that if you guys actually solve your problem, you will have also solved the major problem of dBB. (Hmm, do you work on the lattice? I thought you mainly used non-lattice methods?)

 

[atyy]

Of course I didn't mean I like QM as a final theory. The point is, people mostly like dBB because it preserves(at least partly) the classical nature of physical laws. In fact because of Bell's theorem, it seems that most classical-like interpretation of QM should be something like dBB because non-locality is inescapable. But I just don't see the reason why so many people should be so insistent that nature is as people thought before QM. I think its really more like it that nature behaves as standard QM says, its somehow more like it, that nature doesn't waste "piles and piles of paper" to store information that she actually can do without them. It more beautiful that she actually doesn't. Of course nature doesn't have to look as I prefer, so no one has the right to stop people working on dBB. Its just that I don't like it.

The point of dBB is not the classical nature of physical laws. The point is why do we have a difficulty with the notion of the wave function of the universe, unless hidden variables are introduced? Without hidden variables, it seems we cannot have a wave function of the universe, and we always need an observer who is not in the wave function.

Also, dBB is not against the idea that QM is beautiful because it does not waster piles and piles of paper. It is really the possibility of hidden variables (motivated by the measurement problem) that can make the notion of QM as a superb effective theory precise. For example, http://arxiv.org/abs/0711.4770 shows how much simpler QM is compared to a hidden variable theory. The situation is like string theory (let's assume it is correct for the sake of argument) and general relativity - GR is incomplete compared to string theory, but GR doesn't waste the piles and piles of paper that string theory does.

And about those papers. I can't see how those can be related to dBB. Because they can do everything in the context of standard QM and don't bother with dBB. So even if they succeed, they may do it somehow that doesn't do a favuor to dBB.
Also dBB doesn't seem to be able to make a good marriage with SR too. I know people had some attempts but things don't seem to fit nicely.
And quantum fluctuations. How can dBB account for particles coming from nothing when it doesn't accept uncertainty principles as they are in standard QM?

Those papers try to formulate the relativistic standard model of particle physics as non-relativistic quantum mechanics, for which dBB is probably able to solve the measurement problem.

 

[vanhees71]

Ha, ha! Yes, I was pretty sure I went too far there. Anyway, the good thing is that if you guys actually solve your problem, you will have also solved the major problem of dBB. (Hmm, do you work on the lattice? I thought you mainly used non-lattice methods?)

No, I'm not a lattice guy. I'm in the real-time QFT and transport business as well as phenomenological models in heavy-ion physics. Of course, lattice QCD (particularly finite temperature) delivers important input into these models too (e.g., the equation of state of strongly interacting matter).

 

[atyy]

No, I'm not a lattice guy. I'm in the real-time QFT and transport business as well as phenomenological models in heavy-ion physics. Of course, lattice QCD (particularly finite temperature) delivers important input into these models too (e.g., the equation of state of strongly interacting matter).

I see. That's why you are particularly interested in the Keldysh formalism that you mentioned in another thread, whereas I think finite temperature lattice can only efficiently calculate equilibrium quantities?

 

[vanhees71]

Yes, lattice QCD uses the imaginary-time Matsubara method (Euclidean QFT with the approriate (anti-)periodic boundary conditions for fermion and boson fields). Then, at vanishing baryo-chemical potential you have a real-valued exponential in the path-integral which, after discretizing space and imaginary time ("lattice action"), you can evaluate expectation values of field operator products or the partition sum and various other thermal quantities with Monte-Carlo methods.

Lattice has a lot of trouble with (a) finite baryon-chemical potential and (b) generic real-time quantities like transport coefficients, because then you have no more a real valued exponential under the path integral and you cannot use Monte-Carlo methods with importance sampling to evaluate the path integrals for the lattice action anymore. To get real-time quantities you need an analytical continuation of the Matsubara correlation functions to "real time", but that's very difficult since you have given the Matsubara quantities only on a discrete lattice. There are various methods to do this, like the Maximum-entropy Method or fitting spectral functions with a given analytical structure to the lattice data.

To simulate a heavy-ion collision you need to describe the dynamical properties of the corresponding medium. Fortunately, here effective models like relativistic (viscous) hydrodynamics already deliver a good description, showing that at high collision energies a rather collective strongly coupled medium is created. Of course this description is not the full truth, and you also need more sophisticated effective models like transport models leading to the development of transport simulation software (like Ultrarelativistic Quantum Molecular dynamics (UrQMD), Boltzmann Approach of Multi Parton Scatterings (BAMPS), Gießen BUU (GiBUU), (p)HSD ((parton) Hadron String Dynamics)...). All these models are based more or less strongly on real-time quantum field theory, leading to the Kadanoff-Baym equations for propgators. Unfortunately the latter cannot be solved for realistic models because of a high demand on CPU power, although toy models like $\phi^4$ have been numerically solved and compared to transport approximations, which involve a coarse graining procedure (via the socalled gradient expansion), leading to a description where the Wigner functions of the Kadanoff-Baym equations become positive definite phase-space distribution functions. This leads to what's called "off-shell transport models". These are still plagued by some problems but large progress has been made in the recent years. A further simplification is to also invoke the "quasiparticle approximation", i.e., to propagate on-shell "particles" (sometimes with medium modifications and mean-field potentials).

PS: Perhaps we should rather make an own thread about this topic (perhaps in another subforum like the HEP and nuclear physics forum?).

 

[DennisN]

How can there be a wave function of the entire universe? There are interacting particles in the universe, and it's clearly relativistic. So how can there exist a wave function as a description of the universe's state, if wave functions aren't suitable for two interacting particles?

If anything as a (pure?) quantum state of the entire universe exists it cannot be described as a single wave function. Despite this technical problem I've also a principle problem with the idea of a quantum state of the entire universe: How can you ever observe the predictions made by associating such a state to the whole universe? You cannot prepare many universes and make experiments with them. So how do you figure out whether the probabilistic physics content of the wave function describes the statistics of an ensemble of universes correctly if there's no possiblity to prepare many universes in this state. I think the notion of a quantum state of the entire universe is a pretty empty idea without any testable consequences and thus unscientific.

Vanhees71, thanks for this post! I have never thought about QM in this "universal" way - maybe partly because I'm not very much into interpretations/haven't looked at different interpretations in depth. Your post felt like a fresh breeze to my brain :). Now I have something to think about...oo)

EDIT:

How can you ever observe the predictions made by associating such a state to the whole universe?

Furthermore, if our current mainstream cosmological model holds, you can not, and will NEVER be able to. There are cosmological horizons, e.g. particle horizons. There will always be things that are unobservable. Darn!

 

[bohm2]

No, that's not what I mean. I mean why can't we find recently published papers on dBB? I searched but all papers I found are old, not newer than these papers

At least with respect to Bohmian mechanics, the number of citations/references on the Bohmian interpretation has steadily increased not decreased. This is hi-lited in Fig. 1 (page 8) of this paper:

Overview of Bohmian Mechanics
http://arxiv.org/pdf/1206.1084.pdf

Having said that, the same can probably be said of some other non-orthodox interpretations of QM like MWI. With respect to the original papers you linked in your first post, other than the papers that atyy provided there is also this one:

In conclusion, the mentioned article provides an interesting experimental verification of a quantum-optical prediction for photons, but it does not import any consequence to the dBB theory. The conclusion affirmed by the authors of Ref. 4, “The analysis of these data allows a test of standard quantum mechanics against the de Broglie–Bohm theory,” is incorrect.

Comment on “Biphoton double-slit experiment”
http://ddd.uab.cat/pub/artpub/2005/115682/phyreva_a2005m1v71n1p017801.pdf

 

[ShayanJ]

At least with respect to Bohmian mechanics, the number of citations/references on the Bohmian interpretation has steadily increased not decreased. This is hi-lited in Fig. 1 (page 8) of this paper:

Overview of Bohmian Mechanics
http://arxiv.org/pdf/1206.1084.pdf

Having said that, the same can probably be said of some other non-orthodox interpretations of QM like MWI. With respect to the original papers you linked in your first post, other than the papers that atyy provided there is also this one:

Comment on “Biphoton double-slit experiment”
http://ddd.uab.cat/pub/artpub/2005/115682/phyreva_a2005m1v71n1p017801.pdf

Thanks for enlightening us. But I still see it differently.
Now, near a hundred years after the birth of QM, there are a lot of reasons that people move toward a better understanding of its foundations. Of course people were always trying to do that but these recent years seem different to me. Technological and theoretical advances(like the work of Haroche and Wineland in studying individual quantum systems or Bell test experiments,from 2000 till now), made people think that these years are a good time for actually deciding between different interpretations experimentally so I guess this makes people more excited about working on foundations of QM and solving the measurement problem and so it means there is a natural increase in the number of publications about foundations of QM and anything related to it. Now its really natural that some of these guys will work on dBB. But the actual quantity we should consider for having a knowledge of how accepted dBB is, is the ratio of the increase of publications about dBB to the increase of publications about anything related to foundations of QM.
At first, you can see that from 2000 till now, the number of publications is almost constant(which means the excitement weren't much useful to dBB) and second, even taking the increase in the number of publications from 1955 to 2010, its just almost a hundred, which I don't think is much more than the same number for other interpretations. In fact I think that diagram can't be reliable without further information about the annual number of publication about other interpretations and all the advances in technology and experimental methods that are relevant to this area of physics. At the end, I think these years can simply be the maximum point in that digram and I see it probable that there is going to be a free fall in it.

 

[bohm2]

At first, you can see that from 2000 till now, the number of publications is almost constant(which means the excitement weren't much useful to dBB) and second, even taking the increase in the number of publications from 1955 to 2010, its just almost a hundred, which I don't think is much more than the same number for other interpretations. In fact I think that diagram can't be reliable without further information about the annual number of publication about other interpretations and all the advances in technology and experimental methods that are relevant to this area of physics. At the end, I think these years can simply be the maximum point in that digram and I see it probable that there is going to be a free fall in it.

I can't predict the future but I was just pointing out why I disagree with you that "dBB is in serious danger, or maybe even ruled out". There is no evidence for this. Moreover, I don't see BM or any other interpretation as the final picture and either do many researchers sympathetic to dBB interpretation, including Bohm, himself. They just see it as a better means to an end in comparison to the orthodox interpretation, I think.

 

[stevendaryl]

Ghose's paper has been commented on by:

http://arxiv.org/abs/quant-ph/0108038
http://arxiv.org/abs/quant-ph/0101132
http://arxiv.org/abs/quant-ph/0302085
http://arxiv.org/abs/quant-ph/0305131

Edit: There are, however, some holes to be filled to be certain that dBB completely solves the measurement problem, http://arxiv.org/abs/0712.0149: "On the technical side, for DBB to solve the measurement problem we require that the corpuscles track the decohered macroscopic degrees of freedom of large systems. ... Further plausibility arguments have been constructed (e. g. Bell (1981b, section 4), Holland (1993, pp. 336–50), D¨urr, Goldstein, and Zanghi (1996, pp. 39–41), and some simple models have been studied; at present, it seems likely that the corpuscles do track the quasiclassical trajectories sufficiently well for DBB to solve the measurement problem, but there exists no full proof of this."

I edited this post while Shyan was replying to it.

I actually never understood the claim that dBB is equivalent to standard quantum mechanics, precisely because of the "quantum equilibrium hypothesis" mentioned in the first response paper by Struyve and De Baere. I understand the argument that if you have particles distributed in space with an initial distribution given by:

$\rho = |\psi|^2$

then the Bohm quantum equations of motion will preserve this property. However, I don't see how that can be applied to a single particle. If there is only one particle, then its distribution in space must be a delta-function distribution, regardless of the preparation procedure. In general, if you have a finite number of particles, then it's not possible to distribute them according to a continuous distribution (which the square of the wave function always is). Now, maybe the distribution $\rho = |\psi|^2$ is not intended to be the actual distribution of particles, but simply a reflection of our ignorance of the actual location. But if that's the case, then I different problem with it.

If we're talking about a single particle, it might be the case that initially, my ignorance about the particle's position is given by $\rho = |\psi|^2$. But if I later perform observations on the particle, my knowledge about its whereabouts can change. If I detect a particle here, then I would adjust my subjective probability distribution to take that into account. So subjective probability distributions would not simply evolve by the evolution equation derivable from Schrodinger's equation, but would also change due to my acquiring more information. Since according to Bohm, particle velocities are related to the wave function, if the wave function changes discontinuously due to my acquiring new information, that would imply that my subjective information about particle location affects the motions of those particles.

I'm assuming that people have already thought about these things and that there are answers to the questions, but I think that it's a great oversimplification to say, as Struyve and De Baere do, that the quantum equilibrium hypothesis is enough to insure that there are no observational differences between Bohm and standard quantum mechanics.

 

[ShayanJ]

If we're talking about a single particle, it might be the case that initially, my ignorance about the particle's position is given by ρ=|ψ|2\rho = |\psi|^2. But if I later perform observations on the particle, my knowledge about its whereabouts can change. If I detect a particle here, then I would adjust my subjective probability distribution to take that into account. So subjective probability distributions would not simply evolve by the evolution equation derivable from Schrodinger's equation, but would also change due to my acquiring more information. Since according to Bohm, particle velocities are related to the wave function, if the wave function changes discontinuously due to my acquiring new information, that would imply that my subjective information about particle location affects the motions of those particles.

That looks like a measurement problem to me! Because again we should answer the question how the fact that we acquired more information about the system, changed its state.

 

[atyy]

I'm assuming that people have already thought about these things and that there are answers to the questions, but I think that it's a great oversimplification to say, as Struyve and De Baere do, that the quantum equilibrium hypothesis is enough to insure that there are no observational differences between Bohm and standard quantum mechanics.

Yes, the single particle case works, and people have thought about these things. Struyve and De Baere's oversimplification should be considered shorthand that people have thought about these things.

 

[atyy]

That looks like a measurement problem to me! Because again we should answer the question how the fact that we acquired more information about the system, changed its state.

Yes, how does dBB reproduce collapse of the wave function? It does.

 

[stevendaryl]

Yes, the single particle case works, and people have thought about these things. Struyve and De Baere's oversimplification should be considered shorthand that people have thought about these things.

In the context of responding to someone's claim that Bohm is not equivalent to standard quantum mechanics, it seems to me to be extremely misleading to use such a shorthand. Do you know of a link to a more detailed explanation about the equivalence of Bohm and standard QM? Thanks.

 

[stevendaryl]

In the context of responding to someone's claim that Bohm is not equivalent to standard quantum mechanics, it seems to me to be extremely misleading to use such a shorthand. Do you know of a link to a more detailed explanation about the equivalence of Bohm and standard QM? Thanks.

Based on a little Googling, I can't find an online paper explaining how Bohm's theory reproduces standard quantum mechanics when measurement is taken into account, although there is a discussion that mentions Bohm's proof that his theory reproduces the measurement results of quantum mechanics here:
http://publish.uwo.ca/~wmyrvold/Bohm.pdf

The particular issue is a particle in a box. Bohm's model predicts that a particle in an energy eigenstate has velocity zero (because the velocity is related to the imaginary part of the wave function, which can be taken to be zero for an energy eigenstate). But the prediction of quantum mechanics is that a measurement of momentum will yield a nonzero value. Bohm claimed that his theory makes the same prediction, but the paper doesn't reproduce the argument.

 

[atyy]

In the context of responding to someone's claim that Bohm is not equivalent to standard quantum mechanics, it seems to me to be extremely misleading to use such a shorthand. Do you know of a link to a more detailed explanation about the equivalence of Bohm and standard QM? Thanks.

Based on a little Googling, I can't find an online paper explaining how Bohm's theory reproduces standard quantum mechanics when measurement is taken into account, although there is a discussion that mentions Bohm's proof that his theory reproduces the measurement results of quantum mechanics here:
http://publish.uwo.ca/~wmyrvold/Bohm.pdf

The particular issue is a particle in a box. Bohm's model predicts that a particle in an energy eigenstate has velocity zero (because the velocity is related to the imaginary part of the wave function, which can be taken to be zero for an energy eigenstate). But the prediction of quantum mechanics is that a measurement of momentum will yield a nonzero value. Bohm claimed that his theory makes the same prediction, but the paper doesn't reproduce the argument.

I don't know if there is an iron-clad proof that Bohmian Mechanics reproduces exactly all of standard quantum mechanics. The basic heuristic is that Bohmian Mechanics can reproduce any position measurement, provided standard decoherence arguments hold. This is good enough to reproduce measurements of observables other than position, because such observables are measured via position measurements. For example, in the single slit experiment, the transverse momentum just after the slit is measured via a position measurement at infinity, because the far field Fraunhofer limit is essentially a Fourier transform of the wave function just after the slit. This takes care of unitary evolution and measurements of observables, leaving wave function collapse. Wave function collapse is taken care of in Bohmian Mechanics by the definite experimental outcome, allowing us to ignore irrelevant parts of the wave function after measurement. I believe that in principle Bohmian Mechanics allows recoherence, whereas standard quantum mechanics does not, if a measurement has been made, but the recoherence of Bohmian Mechanics is argued to occur on time scales that are irrelevantly large, analogous to the the irrelevance of Poincare recurrences in classical kinetic theory.

Here's my reading list for Bohmian Mechanics.

1. Simple and friendly introduction
http://arxiv.org/abs/quant--ph/0611032
What you always wanted to know about Bohmian mechanics but were afraid to ask
Oliver Passon

2. Comprehensive intermediate level introduction. Section VI is an extensive discussion of measurements.
http://arxiv.org/abs/1206.1084
Overview of Bohmian Mechanics
Xavier Oriols, Jordi Mompart

3. Extensive detailed comparison of Bohmian Mechanics and the quantum formalism, including POVMs
http://arxiv.org/abs/quant-ph/0308038
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
Detlef Dürr, Sheldon Goldstein, Nino Zanghì

There are older checks of most of the famous quantum phenomena, including things like Bell tests, but I don't think those are available free.

Once again I'd like to stress that the point of Bohmian Mechanics is not that it is the correct theory of nature, but rather it demonstrates that solutions to the measurement problem exist.

 

[stevendaryl]

I don't know if there is an iron-clad proof that Bohmian Mechanics reproduces exactly all of standard quantum mechanics. The basic heuristic is that Bohmian Mechanics can reproduce any position measurement, provided standard decoherence arguments hold. This is good enough to reproduce measurements of observables other than position, because such observables are measured via position measurements. For example, in the single slit experiment, the transverse momentum just after the slit is measured via a position measurement at infinity, because the far field Fraunhofer limit is essentially a Fourier transform of the wave function just after the slit. This takes care of unitary evolution and measurements of observables, leaving wave function collapse. Wave function collapse is taken care of in Bohmian Mechanics by the definite experimental outcome, allowing us to ignore irrelevant parts of the wave function after measurement. I believe that in principle Bohmian Mechanics allows recoherence, whereas standard quantum mechanics does not, if a measurement has been made, but the recoherence of Bohmian Mechanics is argued to occur on time scales that are irrelevantly large, analogous to the the irrelevance of Poincare recurrences in classical kinetic theory.

Here's my reading list for Bohmian Mechanics.

1. Simple and friendly introduction
http://arxiv.org/abs/quant--ph/0611032
What you always wanted to know about Bohmian mechanics but were afraid to ask
Oliver Passon

2. Comprehensive intermediate level introduction. Section VI is an extensive discussion of measurements.
http://arxiv.org/abs/1206.1084
Overview of Bohmian Mechanics
Xavier Oriols, Jordi Mompart

Okay, the second reference explains that the equivalence between the two is very indirect. Standard quantum mechanics uses a wave function (or more generally, a density matrix) for the system of interest. In contrast, Bohmian mechanics must always have a composite wavefunction that includes the system of interest, plus measuring devices. In that sense, it's sort of similar to the MWI (Many-World Interpretation) resolution to the measurement problem by treating the observers quantum-mechanically, as well. In a certain sense, maybe, Bohmian mechanics amounts to MWI + a choice of which world is "real".

 

[atyy]

Okay, the second reference explains that the equivalence between the two is very indirect. Standard quantum mechanics uses a wave function (or more generally, a density matrix) for the system of interest. In contrast, Bohmian mechanics must always have a composite wavefunction that includes the system of interest, plus measuring devices. In that sense, it's sort of similar to the MWI (Many-World Interpretation) resolution to the measurement problem by treating the observers quantum-mechanically, as well.

Yes, that's my understanding.

In a certain sense, maybe, Bohmian mechanics amounts to MWI + a choice of which world is "real".

Others have made similar observations. (Technically, Bohmian Mechanics and Many-Worlds are similar in that both have a wave function of the universe and use decoherence.)

Wallace's review http://arxiv.org/abs/0712.0149 mentions this critique of Bohmian Mechanics by Deutsch: "A potentially more serious flaw arises from the so-called “Everett-in-denial” objection to realism (Deutsch 1996; Zeh 1999; Brown and Wallace 2005). ... Advocates of the Everett interpretation claim that, (given functionalism) the decoherence-defined quasiclassical histories in the unitarily evolving physically real wavefunction describe — are — a multiplicity of almost-identical quasiclassical worlds; if that same unitarily-evolving physically real wavefunction is present in DBB (or any other hidden-variable theory) then so is that multiplicity of physically real worlds, and all the hidden variables do is point superfluously at one of them."

Nikolic's "Solipsistic hidden variables" http://arxiv.org/abs/1112.2034 is an amusing variant of Bohmian Mechanics in which, "Finally note that our result that different observers may live in different branches of the wave function is very similar to the many-world interpretation [16, 17], briefly discussed in Sec. 2.2. Yet, there is one crucial difference. In the many-world interpretation, there is a copy of each observer in any of the branches. In our solipsistic interpretation, for each observer there is only one copy living in only one of the branches."