A skeptic's view on Bohmian Mechanics

[A. Neumaier]

[49] J. Fröhlich, B. Schubnel: “Quantum Probability Theory and the Foundations of Quantum mechanics”, arXiv:1310.1484v1 [quant-ph].

Reading this paper, I found their reference to a blog article by Reinhard Werner, one of the leaders in quantum information theory, on Bohmian mechanics, with sharp comments and questions such as the following:

Bohmian trajectories have no connection to empirical fact, and even the Bohmian theory itself claims no connection. So they are just a piece of fantasy. You may call the trajectories the reality givers (I even heard “realizors”) of the theory, and base an “ontology” on them. But they are still but a figment of your imagination. [...]

Why take wave functions as the description of single systems rather than density operators? I could give some arguments for that. You can drive Bohmian trajectories with density operators just as well, and they would tend to be less singular. [...]

Is it really worth saving Physical Reality at the expense of real physics? [...]

To me the “fapp fixed outcomes” problem is a target on which even partial progress is highly welcome. It would require an increase of our understanding of complex systems and an improvement of our mathematical technique. Assuming that to be solved, there would be virtually nothing left of the measurement problem, except maybe a two line historical comment in a paper. The Bohmian perspective seems to be the opposite. You don’t care about the hard problem, but only about that last, utterly trivial bit. [...]

[Bohmian mechanics and quantum mechanics] supposedly make the same predictions about positions, the two are “empirically equivalent”. Note how this argument grants that quantum mechanics had no measurement problem in the first place, since it apparently takes it as unproblematic that there will be agreement. The empirical content of Bohmian Mechanics entirely rests on this bridge. Again, it is left entirely to the quantum physicists to work out how stable pointer positions come about. Bohmian Mechanics will then extend a blessing of Reality. That’s all it does. [...]

If there is no direct connection between observable and Bohmian positions at the microscopic level, how am I justified to assume it at the macroscopic level? Should we invoke prestabilized harmony? Is this not rather like the measurement problem itself? [...]

What kind of physics would Bohm’s Demon see, by which I mean that hypothetical entity with direct access to the Reality of Bohmian trajectories, but to nothing else?

At the end he poses http://www.itp.uni-hannover.de/~werner/Bohm.html , for which one can earn a bottle of good wine. I don't know whether @Demystifier likes wine, but perhaps he likes to decide the question with a mathematical proof.

And then follows on the blog a lively debate ...

 

[Demystifier]

At the end he poses http://www.itp.uni-hannover.de/~werner/Bohm.html , for which one can earn a bottle of good wine. I don't know whether @Demystifier likes wine, but perhaps he likes to decide the question with a mathematical proof.

I don't like wine, but I think that the only hard part of the problem is to solve the Schrodinger equation for that case, which does not depend on whether you use or not use Bohmian mechanics. Once you have the solution of the Schrodinger equation (which may be a task for any quantum physicist), the questions specific to the Bohmian interpretation should be easy to answer.

 

[A. Neumaier]

(which may be a task for any quantum physicist)

But any quantum physicist is unlikely to be interested in it, since it is a question about the behavior of Bohmian particles.

That you (and anyone else in the Bohmian camp) take so little interest in actually discussing and solving these kind of problems reinforces the observation by Werner that Bohmian mechanics did not generate interesting results from a technical point of view but understands itself just as a commentary on quantum mechanics, without which most physicists can happily live.

 

[ShayanJ]

without which most physicists can happily live

This is confusing! Most physicists are already living happily with quantum mechanics, without MWI, or your thermal interpretation or decoherence or even without thinking what interpretation they're using or whether the interpretation they're using is consistent or not. So how is it that the same thing is interpreted as the shortcoming of BM?

P.S.
I don't like BM, but people are obviously being unfair to it!

 

[A. Neumaier]

This is confusing! Most physicists are already living happily with quantum mechanics, without MWI, or your thermal interpretation or decoherence or even without thinking what interpretation they're using or whether the interpretation they're using is consistent or not.!

I agree. There is no need for an interpretation beyond what everyone happily lives with, unless one can answer questions that need a lot of math of the kind needed for solving the Bohmian Detector Problem. Someone happy to live without an answer to this within the Bohmian interpretation will also be happy without the Bohmian interpretation itself. I don't understand why you find this confusing!

Note that I spent myself a lot of time with the Bohmian interpretation before I rejected it as superficial, essentially for the reasons given by Werner. It didn't add any understanding but wasted a lot of my time.

My thermal interpretation is nothing new, it just gives explicit words for what people happy with QM are using anyway when interpreting their theories and results. Not a single additional feature is present. And it poses some highly nontrivial mathematical problems involving many-body problems related to measurement, whose solution I am working on. Having not solved them is one of the reasons I delay publication of a formal account of the interpretation.

 

[Demystifier]

Bohmian mechanics did not generate interesting results from a technical point of view but understands itself just as a commentary on quantum mechanics, without which most physicists can happily live.

As I stressed several times, there are some technical physical practical results of BM:
https://www.amazon.com/dp/9814316393/?tag=pfamazon01-20

Nevertheless, I agree that most of the work on BM (or any other interpretation beyond the minimal pragmatic one) is just a commentary on quantum mechanics, without which most physicists can happily live. But some people need more to reach happiness, and BM (just as all other interpretations beyond the minimal pragmatic one) is devised for them.

 

[Demystifier]

But any qunatum physicist is unlikely to be interested in it, since it is a question about the behavior of Bohmian particles.

Just because it is a question about BM doesn't make it relevant for BM.

 

[ShayanJ]

There is no need for an interpretation beyond what everyone happily lives with

I didn't say that. Interpretations are not there to make such people happy. They're there to make other people happy. I can't stop myself from comparing it to quantum gravity. Why do we feel the need to quantize gravity? Because general relativity predicts singularities and we're not happy with it? So just be happy with it, problem solved! Because black holes don't seem to conserve information and we're not happy with it? So just be happy with it, problem solved! Because gravity seems so much different from other interactions and we're not happy with it? So just be happy with it, problem solved! Is this the kind of physics you like?

 

[A. Neumaier]

I didn't say that.

I know. But I said that. All researchers choose what they like to do research on and what they are prepared to believe on hearsay, or defer judgement. This is about happiness, not about physics.

Those problems will eventually be solved where enough people are unhappy with them that one of them finds the energy and creativity to actually do the work.

 

[Demystifier]

There is no need for an interpretation beyond what everyone happily lives with

There is no such interpretation with which everyone is happy.

 

[A. Neumaier]

There is no such interpretation with which everyone is happy.

You seem not to be familiar with figures of speech.

 

[Demystifier]

You seem not to be familiar with figures of speech.

Maybe I could learn it by writing a paper entitled "Why everyone needs Bohmian mechanics".

 

[ShayanJ]

I know. But I said that. All researchers choose what they like to do research on and what they are prepared to believe on hearsay, or defer judgement. This is about happiness, not about physics.

Those problems will eventually be solved where enough people are unhappy with them that one of them finds the energy and creativity to actually do the work.

Well, you said "I agree", so I thought that's what you got from what I said!
Anyway, that's exactly what I wanted to say. The physics community now is divided. The majority of physicists are happy with quantum mechanics and see no problem in it and just want to use it. There are some people who see some problems and want to solve them. These are not only Bohmians. Everyone who does some research on foundational issues is in this camp. So its not that there are problems that only Bohmians see, its just that Bohmians have their own way of looking at these problems. And I really don't see anything different here and that's what confusing me. Why everyone treats Bohmian mechanics so much different than other interpretations? Its not better than others but its not worse too!

 

[A. Neumaier]

Why everyone treats Bohmian mechanics so much different than other interpretations? Its not better than others but its not worse too!

The minimal interpretation is the common intersection between all and hence a necessary part of every interpretation - even of the Bohmian, which reduces itself to it when measurement is taken into account. Therefore it deserves a special place. The Copenhagen interpretation is the oldest, and hence also has a special place. Among the other interpretations, the Bohmian gets special attention on this forum because one of the active members, demystifier, has a strong position about it and another one (myself) has a diametrically opposite point of view.

I don't like many worlds or consistent histories, but for lack of a highly interested opponent they don't get the share of critical remarks from me that they would deserve. I don't like Copenhagen either, but since it has in atyy a strong defender on this forum, I had enough motivation to be at times very critical of it.

 

[A. Neumaier]

There are some people who see some problems and want to solve them.

The problem is that there are very different ideas of what it means to have solved them. For me, there are unsolved problems in measurement theory but solving them means attacking difficult many-body problems., For others, the only unsolved problems can be handled in a paper of 10 pages or less, something done already by Bohm or Everett. In my opinion, they scratch the surface only, and leave the real work undone - as Werner also complained.

 

[ShayanJ]

The problem is that there are very different ideas of what it means to have solved them. For me, there are unsolved problems in measurement theory but solving them means attacking difficult many-body problems., For others, the only unsolved problems can be handled in a paper of 10 pages or less, something done already by Bohm or Everett. In my opinion, they scratch the surface only, and leave the real work undone - as Werner also complained.

That's right. And I'm sure you, as an experience researcher, know better that me that its important than all these people try to solve the problems they see, the way they see fit. That's because basic research is like that, we don't know what we're doing! its not always clear what is a problem and what is not. And its not always clear what is a solution and what is not. So you try to solve the problems you see the way you see fit, the same with Demystifier.

 

[stevendaryl]

Reading this paper, I found their reference to a blog article by Reinhard Werner, one of the leaders in quantum information theory, on Bohmian mechanics, with sharp comments and questions such as the following:At the end he poses http://www.itp.uni-hannover.de/~werner/Bohm.html , for which one can earn a bottle of good wine. I don't know whether @Demystifier likes wine, but perhaps he likes to decide the question with a mathematical proof.

And then follows on the blog a lively debate ...

Werner wrote:

Bohmian mechanics and quantum mechanics] supposedly make the same predictions about positions, the two are “empirically equivalent”. Note how this argument grants that quantum mechanics had no measurement problem in the first place, since it apparently takes it as unproblematic that there will be agreement.

I'm quoting it because it is something that I had noticed about Bohmian mechanics. The rough argument that Bohmian mechanics is observationally equivalent to standard quantum mechanics involves just showing that Bohmian trajectories lead to the same probability current as standard quantum mechanics. But that's not the end of the story, because the quantum recipe goes beyond probability currents. There is also the update of the wave function: Von Neumann's collapse hypothesis. After you measure a composite system to have eigenvalue $\lambda$ of some operator $O$, then from that moment on, you use, not the original wave function, but the projection of the wave function onto the subspace of wave functions with eigenvalue $\lambda$. The measurement problem is the question of whether and how to understand this apparent collapse with the smooth evolution of the wave function. Decoherence and Many-Worlds and so forth are different ways to understand what's going on during measurement.

The benefit of Bohmian dynamics is supposed to be that there is no collapse, and the only updating is ordinary updating of a probability distribution to reflect new information, plus the change of the quantum potential due to changes in system setup. To show that Bohmian mechanics really agrees with observation, though, requires showing that the apparent collapse is explainable using pure quantum mechanics (via decoherence or whatever). I'm just repeating what Werner said at this point, but it does seem to me that a rigorous proof that Bohmian mechanics is consistent with our observations requires essentially solving the measurement problem for standard quantum mechanics first.

 

[stevendaryl]

The problem is that there are very different ideas of what it means to have solved them. For me, there are unsolved problems in measurement theory but solving them means attacking difficult many-body problems., For others, the only unsolved problems can be handled in a paper of 10 pages or less, something done already by Bohm or Everett. In my opinion, they scratch the surface only, and leave the real work undone - as Werner also complained.

I appreciate this comment very much. In a certain sense, the disagreements among the various interpretations of quantum mechanics, and the feeling that there is no completely satisfying interpretation involve the question of whether and how quantum mechanics explains the behavior of measurement devices involving an astronomical number of particles. That's not likely to ever be done except in some approximation, and there is a danger that the nature of the approximation already assumes something of what is to be proved. (For example, if you treat measurement devices using classical mechanics.)

 

[Demystifier]

but it does seem to me that a rigorous proof that Bohmian mechanics is consistent with our observations requires essentially solving the measurement problem for standard quantum mechanics first.

It's illusory to search for a rigorous proof, simply because the measurement problem necessarily involves a very large number of degrees of freedom ($10^{23}$ or so). This is like searching for a rigorous derivation of classical statistical mechanics from classical mechanics, and it is known that a rigorous derivation of classical statistical mechanics does not yet exist.

 

[stevendaryl]

It's illusory to search for a rigorous proof, simply because the measurement problem necessarily involves a very large number of degrees of freedom ($10^{23}$ or so). This is like searching for a rigorous derivation of classical statistical mechanics from classical mechanics, and it is known that a rigorous derivation of classical statistical mechanics does not yet exist.

That's true. My point is this:

A lot of the appeal of Bohmian mechanics is that it doesn't have a measurement problem. It doesn't give a special role for measurement interactions. In contrast, the standard "recipe" for quantum mechanics does treat measurement as something different. By the standard recipe, I mean the practical rules of thumb for applying quantum mechanics, which are basically:

• Treat measuring devices classically.
• Treat microscopic systems quantum mechanically (that is, they evolve smoothly according to Schrodinger's equation) between observations.
• Apply the Born rule for measurement results.
• If there are multiple measurements performed on the same system (or on different components of a composite system), then use the "collapsed" wave function after a measurement.

The standard recipe is what empirical tests of quantum mechanics are really testing. The "measurement problem" to me is the problem of explaining why the standard recipe works without treating measurement and measurement devices as something special. (Or alternatively, spelling out why they are special.) Showing that Bohmian mechanics (or any other no-collapse interpretation of quantum mechanics) is empirically equivalent to the standard recipe requires solving the measurement problem.

 

[A. Neumaier]

It's illusory to search for a rigorous proof, simply because the measurement problem necessarily involves a very large number of degrees of freedom ($10^{23}$ or so).

There is a lot of rigorous statistical mechanics done in mathematical physics. See, e.g., the nice book by Ruelle. The only approximation made there is the thermodynamic limit, replacing numbers like $N=10^{23}$ by infinity. One can then even estimate the relative error made by this replacement, and it is of the order $N^{-1/2}$, hence very tiny. Thus there is no barrier of the kind you seem to suggest. At least rigorously proving the validity of QM to 11 decimal places is in principle feasible.

 

[Demystifier]

There is a lot of rigorous statistical mechanics done in mathematical physics. See, e.g., the nice book by Ruelle.

Does this book explain why a priori probability density in the phase space is uniform? Or is it just an axiom?

 

[Demystifier]

Showing that Bohmian mechanics (or any other no-collapse interpretation of quantum mechanics) is empirically equivalent to the standard recipe requires solving the measurement problem.

That's how I present Bohmian mechanics in Sec. 2 of
https://arxiv.org/abs/1112.2034
I first explain the aspects of quantum theory of measurement that do not depend on interpretation, then I explain why do we need particle positions, and finally I explain what is the role of particle trajectories. The traditional presentation of BM, which has the reverse order, leads to frequent misunderstandings of BM. My ordering, I hope, should help to avoid such misunderstandings.

 

[A. Neumaier]

Does this book explain why a priori probability density in the phase space is uniform? Or is it just an axiom?

It is a book about mathematical physics, so it spells out all assumptions made like in a math book.

 

[DrChinese]

Maybe I could learn it by writing a paper entitled "Why everyone needs Bohmian mechanics".

We already have something pretty close, and I bet you've seen it:

Why isn't every physicist a Bohmian? (Passon, 2004)
https://arxiv.org/abs/quant-ph/0412119

----------------------

That link is not intended to be a an endorsement, as I am not a Bohmian. Call me a local non-realist: - non-commuting observables do not have simultaneous reality (there is observer dependence as rejected by EPR) and no cause/effect propagates faster than +/-c (respecting locality).

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c. You never see 2 entangled particles unless they were in contact (limited by c) with some other system that gave rise to the entanglement. I would think that non-local mechanism would give rise to entanglement of all kinds of other things where c is not a limiting factor, if it is also the "out" that explains quantum non-locality. (And yes I know BM is supposed to be equivalent to QM, but this question still seems open to me.)

My point is thus that quantum non-locality always has very special spatial limits, and those limits are exactly defined by factors of c. That can't be a coincidence, and I don't think that should be a limit in a theory postulating non-local interactions without any upper limit.

 

[zonde]

And then follows on the blog a lively debate ...

I found debate quite interesting. One thing that was rather clear, Werner does not understand Bell argument. And he won't listen to explanations how is that.
While I don't believe that BM is the final word in interpretation debate of QM it has couple of very nice features that other interpretations do not have.

• BM provides ontology without adding some new philosophy that is not quite consistent with scientific approach.
• BM particle positions provide answer to problem of certain outcomes.

Werner was apparently more concentrating on things that BM can't say.

 

[zonde]

Why everyone treats Bohmian mechanics so much different than other interpretations? Its not better than others but its not worse too!

Because it's better (not good, just better). It does what it does without new philosophy. And for the same reason it is of course much more boring.

 

[A. Neumaier]

One thing that was rather clear, Werner does not understand Bell argument.

You judge too easily.

Please show me where he errs in his widely cited survey article about Bell inequalities and entanglement. Even when one is not interested in mathematical details about all possible Bell inequalities, the first 9 pages make interesting reading. They contribute new aspects even for those familiar with Bell's work!

Though he understands the matter differently than you and the participants of the debate, you shouldn't think that he is naive or blind. He published extensively on the subject!

Some of his related papers were cited over 3000 times. (Bell's famous 1966 paper On the problem of hidden variables in quantum mechanics has fewer citations, according to Google Scholar!)

 

[DrChinese]

You judge too easily.

Please show me where he errs in his widely cited survey article about Bell inequalities and entanglement. Even when one is not interested in mathematical details about all possible Bell inequalities, the first 9 pages make interesting reading. They contribute new aspects even for those familiar with Bell's work!

From your nice reference, section 2, page 3:

However, in all derivations two types of elements can be identified:

locality: no-signalling, non-contextuality
classicality: hidden variables, classical logic, joint distributions, counterfactual definiteness, “realism”

Since Bell’s inequalities are found to be violated in Nature, one of these two assumptions needs to be dropped. Quantum mechanics (in statistical interpretation) chooses locality, whereas hidden variable theories drop locality in order to retain a description by classical parameters. In either case, however, fundamental features of the pre-quantum way of describing the world are lost.

 

[RockyMarciano]

From your nice reference, section 2, page 3:

However, in all derivations two types of elements can be identified:

locality: no-signalling, non-contextuality
classicality: hidden variables, classical logic, joint distributions, counterfactual definiteness, “realism”

Since Bell’s inequalities are found to be violated in Nature, one of these two assumptions needs to be dropped. Quantum mechanics (in statistical interpretation) chooses locality, whereas hidden variable theories drop locality in order to retain a description by classical parameters. In either case, however, fundamental features of the pre-quantum way of describing the world are lost.

In either case fundamental features are lost, but dropping locality (when done seriously, i.e. actually predicting information propagating FTL) is simply incompatible with science as we know it, that pressuposes causality and as a matter of fact nonlocality is only found as an interpretation without observable consequences in the models that claim it. So in practical terms only one assumption of the two is viable.
It would be perhaps interesting to discuss what dropping classicality actually implies, for instance in relation with the structure of the mathamatical spaces used in physics.

 

[Demystifier]

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c.

That's because wave functions, described by relativistic wave equations (such as Dirac or Klein-Gordon equation), do not propagate faster than c. If you ask me why wave/field equations have such a relativistic form, I have to disappoint you that BM (or any other fundamental theory currently known) does not have an answer to this question.

 

[Demystifier]

It is a book about mathematical physics, so it spells out all assumptions made like in a math book.

Take a look at the paragraph after Eq. (1.4). As you can see, the justification for Eq. (1.4) is very far from being rigorous.

That's not because Ruelle was sloppy at that point. That's because some fundamental aspects of statistical mechanics still don't have a rigorous foundation.

 

[A. Neumaier]

Take a look at the paragraph after Eq. (1.4). As you can see, the justification for Eq. (1.4) is very far from being rigorous.

In mathematical physics one doesn't need to justify the assumptions, only the conclusions.

 

[dextercioby]

Can one point to the exact title of the book by David Ruelle?

 

[ShayanJ]

Can one point to the exact title of the book by David Ruelle?

https://books.google.com.au/books?id=mNtWfcj_xhwC&printsec=frontcover#v=onepage&q&f=false