I get asked my opinion of Bohmian mechanics a fair bit, despite the fact that I know very little about it. This came up again recently, so I got some suggested reading from Matt Leifer, on the grounds that I ought to learn something about it if I'm going to keep being asked about it. One of his links led to the Bohmian Mechanics collaboration, where they helpfully provide a page of pre-prints that you can download. Among these was a link to the Bohmian Mechanics entry in the Stanford Encyclopedia of Philosophy, which seemed like a good place to start as it would be a) free, and b) aimed at a non-physics audience, which is a plus, given the cold I have at the moment, which isn't doing much for my clarity of thought.

It turns out I had read some of this before, and my immediate reaction now was the same as my reaction then, namely "It's a miracle you can type while balancing that chip on your shoulder." The introduction is fairly neutral, but as you go down through the article, there are a bunch of little shots at "orthodox quantum theory" which have the cumulative effect of making me start to wonder if the author is actually a crank-- in the previous read (while I was writing How to Teach Physics to Your Dog), I actually gave up after a quick skim for just this reason. As the author is one of the authorities Matt recommended, I read it more carefully this time out, and what follows are some quick impressions based on reading through the article. I would not begin to claim that I have gained any deep understanding, and I'll look at some more physics-oriented resources next (maybe the textbook Matt mentioned, though the freely available front matter had the same shoulder-chip issue noted above), but this is, as the title suggests, the stuff I thought of immediately.

The short version, above the fold to serve as both teaser and attention conservation notice is two items: 1) In many ways, this sounds like an unholy union between Einstein and Heisenberg, and 2) I still don't see the point.

**Quick summary fo the summary article**: Bohmian mechanics is a version of quantum theory which considers two objects of equal importance: A wavefunction, which evolves according to the usual Schrödinger Equation, and a particle with definite position and velocity, which evolve according to a "guiding equation" which depends on the wavefunction. If you prefer something that looks more like classical Hamiltonian mechanics, you can express things in terms of a "quantum potential," and replace the "guiding equation" with a more typical force-type equation.

Every particle considered thus has a definite position and momentum at all times, unlike the situation usually presented in the orthodox quantum theory. If you know the initial position and momentum of a particle with sufficient accuracy, you can thus calculate a perfectly normal classical trajectory for it, with the wavefunction "guiding" the particle along the trajectory. The outcome of many repeated measurements is determined using the "quantum equilibrium hypothesis," which appears to consist of assigning initial positions and momenta that are randomly distributed in much the same way that the positions and momenta of particles in the canonical gas-in-a-box are randomly distributed according to a Maxwell-Boltzmann distribution in statistical mechanics or thermodynamics. The end result is a distribution of final positions that looks exactly like the probability distribution you get from the Born rule in the regular quantum theory, namely the squared norm of the wavefunction at the position of the detectors.

The bulk of the article consists of applying this basic formalism to a variety of quantum examples, and talking about how it a) reproduces all the measured effects of quantum theory while b) maintaining a definite position and velocity for every particle at all times.

**General Comments**:

- The "unholy union between Einstein and Heisenberg" comment above would probably be taken as an insult by everyone involved, but the presentation in the article make it sound like it's combining key features of both of their approaches. The Einstein part is obvious, with the well-defined particle properties at all times. the Heisenberg part comes from the insistence on considering measurement apparatus, for example when they describe the key processes at the end of section 4:

This demonstrates that all claims to the effect that the predictions of quantum theory are incompatible with the existence of hidden variables, with an underlying deterministic model in which quantum randomness arises from averaging over ignorance, are wrong. For Bohmian mechanics provides us with just such a model: For any quantum experiment we merely take as the relevant Bohmian system the combined system that includes the system upon which the experiment is performed as well as all the measuring instruments and other devices used in performing the experiment (together with all other systems with which these have significant interaction over the course of the experiment). The "hidden variables" model is then obtained by regarding the initial configuration of this big system as random in the usual quantum mechanical way, with distribution given by |Ï|2. The initial configuration is then transformed, via the guiding equation for the big system, into the final configuration at the conclusion of the experiment. It then follows that this final configuration of the big system, including in particular the orientation of instrument pointers, will also be distributed in the quantum mechanical way, so that this deterministic Bohmian model yields the usual quantum predictions for the results of the experiment.

This doesn't go to the Heisenbergian extreme of stating that measurement outcomes are the only reality, but it does keep some of the same primacy of measurement, albeit in a hidden way. Rather than having interaction with the measurement apparatus determine a previously indeterminate state, the configuration of the measurement apparatus determines the shape of the wavefunction, which then guides the particles along a particular trajectory.

A lot of time is spent denying the importance of the act of measurement, but it seems to me that this is just pushed back a step. I'm not sure there's as much difference between "measuring the state determines the state" and "the configuration of the measurement apparatus determines the evolution of the definite state" as the author clearly wants me to think.

- There are some claims that strike me as... let's say "inflated in their phrasing." For example, in the paragraph before the one quoted above, the list of virtues of their formulation begins:

First, it makes sense for particles with spin -- and all the apparently paradoxical quantum phenomena associated with spin are, in fact, thereby accounted for by Bohmian mechanics without further ado.

That sounds pretty interesting-- if Bohmian mechanics explains spin, that would be really cool. So I read down to the section on spin, which starts with:

We thus might naturally wonder how Bohmian mechanics manages to cope with spin. But this question has already been answered here. Bohmian mechanics makes sense for particles with spin, i.e., for particles whose wave functions are spinor-valued.

This is anticlimactic, to say the least. Bohmian mechanics makes sense of spin because it works with spinor-valued wavefunctions. Yeah, well, so does orthodox quantum theory-- in fact, I'm teaching an upper-level quantum mechanics course right now that started off with spinor-valued wavefunctions on day one. I'm not seeing the huge gain, here. It's not like the Bohm approach explains the existence of spin, and I can perfectly well formulate the Schrödinger equation in a way that takes spinor-valued functions in a more orthodox theory. Color me unimpressed.

- If I'm not mistaken, every pro-Bohm quote in the article is taken from one book by John Bell. Which makes me wonder why I'm reading this, rather than just reading Bell's book...

- The article tries to walk a weird line between brushing off non-locality/ contextuality as not that big a deal:

However, to understand contextuality from the perspective of Bohmian mechanics is to appreciate that almost nothing needs to be explained. Consider an operator A that commutes with operators B and C (which however don't commute with each other). What is often called the "result for A" in an experiment for "measuring A together with B" usually disagrees with the "result for A" in an experiment for "measuring A together with C" because, even if everything else is the same, these experiments are different and different experiments usually have different results. The misleading reference to measurement, with the associated naive realism about operators, makes contextuality seem more than it is.

(note the shot at "naive" realism, and also the primacy of measurement), while also suggesting that it's a virtue of the theory. This is a little weird.

It's especially weird given the section on Lorentz invariance, where the author admits that "Lorentz invariant nonlocality would remain somewhat enigmatic." That's an understatement.

There's a brief suggestion of an approach that views Lorentz invariance as a statistical property of measurements rather than a fundamental symmetry of space-time, an approach which would seem likely to make a few heads explode (though perhaps fertile ground for SF writers looking to hand-wave FTL), but it's skipped over pretty quickly, which is understandable given the awkwardness of the topic.

- As I said above the fold, I still don't quite see the point. That is, I understand that it's a theory with definite particle properties at all times, but if at the end of the day, you're still going to calculate the probabilities of the outcomes of your measurements using the same old Born rule, I don't see how you've gained anything. Other than a warm sense of philosophical satisfaction at having retained definite particle properties, which combined with a dollar will get you a candy bar.

Which is not to say that there might not be something out there to be gained from this approach. It may be that some future Bohmian version of quantum field theory will produce predictions that differ sharply from the orthodox quantum theory, in ways that will be experimentally testable, or even useful. (Again, the notion of putting Lorentz invariance on the same statistical footing as the Second Law of Thermodynamics seems like an interesting place to look for this sort of thing. And, as a bonus, it would make some heads explode.) Absent that, though, it seems like just another meta-theory, albeit one with more unique mathematical apparatus than Many-Worlds or Copenhagen.

So there's my semi-demi-hemi-informed first thoughts on taking a more serious look at the theory. I may poke through that textbook a little to see if there's anything interesting in the mathematical details, but at the moment, I have a little catching up to do after spending the last couple of days in an illness-induced fog.

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Thanks for looking into Bohmian Mechanics.

But I can't believe that article is giving an accurate description of BM, because it sounds kinda dumb.

It seems like a bunch of hoops to jump through to reform standard theory in a package so you can say "This demonstrates that all claims to the effect that the predictions of quantum theory are incompatible with the existence of hidden variables, with an underlying deterministic model in which quantum randomness arises from averaging over ignorance, are wrong." But that's not a point anyone would argue: the issue to get at is "non-local hidden variables".

Bohmian mechanics seems to me to be one of those things (like Ilya Prigogine, or Hestenes' geometric algebra, or Ron Paul) which has a legion of intensely loyal supporters on the internet who like to oversell its virtues and seem kind of cultish, in a way that's really off-putting.

Here's a couple of links that may be more useful for you, as they use the Bohmian approach for the best reason of all--it makes the calculations more tractable:

http://pubs.acs.org/doi/abs/10.1021/jp055889q

http://k2.chem.uh.edu/preprints/draft-bittner.pdf

(The latter is an invited review chapter for Applied Bohmian Dynamics, Xavier Oriols and Jordi Mompart, Eds.)

One of the problems with science on the internet is demonstrated by the fact that Bohmian mechanics, an extremely old subject whose community of practitioners consists of maybe two dozen people worldwide, is attracting more attention than whole fields which actually have new and interesting things going on all the time. Hey, there are Iron-based superconductors, a fact we did not know about until recently, isnât it more interesting to talk about something new?

(Anything that does not incorporate QFT and all its predictions, many of them follow from combination of Lorentz invariance and QM, will not make heads explode, it will make shoulders shrug).

I dunno. What do you want out of life, man?

An interpretation can do one of two things. Either it can agree with all of the predictions of quantum mechanics (in which case of course you will still use the Born rule et. al.) or it can make a different prediction. If it is the former then people complain that it offers nothing over standard quantum mechanics and if it is the latter then people complain because it disagrees with quantum mechanics, so it must be wrong. The same objection is true of many-worlds, i.e. you still use the Born rule (providing you can make sense of why you should), but you didn't raise that as an objection against it.

In fact, Bohmian mechanics does make predictions that differ from quantum theory if we drop the equilibrium hypothesis -- something it makes sense to do in BM but not in standard QM. If we do that then we have to argue that there is an approach to equilibrium similar to that in statistical mechanics and we have to investigate the possibilities of observing nonequilibrium states. This is what Valentini's work is all about and that's why I suggested you should take a look at it as well.

In some sense BM has the best of both worlds in that we can say it agrees with QM completely if we happen to be in equilibrium, but it does offer the possibility of divergent physics as well.

What I found most surprising in your summary was the lack of mention of the fact that Bohmian mechanics solves the measurement problem, i.e. there is no ambiguity about whether the pointer on a measurement device is actually pointing to a particular outcome or not. This, after all, is the main point of any realist interpretation of quantum theory and nobody would take it even a little bit seriously if it didn't do that. The theory that results does have quite a few quirky features, as you point out, but we know from various no-go theorems that any hidden variable theory HAS to have many of those features, e.g. dependence of the outcome on configuration of the measurement apparatus follows from Kochen-Specker, lack of fundamental Lorentz invariance follows from Bell, etc. Therefore, I don't think these arguments are big drawbacks of the theory, since, if you are a realist, then you still have to solve the measurement problem in some way. (If you are not a realist then I am not quite sure why you would be worrying about interpretations in the first pace). The only semi-coherently-worked-out way of doing this that doesn't fall afoul of no-go results is many worlds, the virtues of which have been discussed already on this blog.

Regarding the chip on the shoulder thing, this is fairly common amongst realist foundations of QM types of a certain age. What you have to remember is that studying foundations from the '60s to the '80s was regarded as a pretty cranky pursuit. Most physicists believed that Bell's theorem had ruled out ALL hidden variable theories, without the crucial qualifier of LOCAL that we would use today. Hell, most physicists still believed that von Neumann had conclusively ruled out hidden variables. Very few people had actually read Bell's papers in any detail. Therefore, if you were working on things like Bohmian mechanics at that time then you had a pretty huge battle on your hands. Tenure, publication in journals and conference invites were not easy to come by for the would be quantum realist (and the situation is only a tiny bit better today). So yes, Goldstein (who wrote the article) probably does have a huge chip on his shoulder, and rightly so considering that through most of his career the physics community has been making it quite clear to him that they think his work is a load of old crap.

Since the combative attitude is so common in the foundations community, I think one needs to tune it out and try to judge the work on its merits. Fortunately, I find that younger foundations researchers don't have this attitude so often (or at least they don't have it yet).

Regarding the preponderance of Bell quotes, this is also fairly common in realist papers of a certain stripe. This is because Bell was one of the clearest thinkers there has ever been in the foundations of quantum theory and was a vociferous supporter of this type of realism. It is really difficult to state the arguments more clearly than he did. Therefore, yes you should be reading "Speakable and Unspeakable..." and so should anyone else who wants to have an informed opinion on foundations. That said, I do agree that the tendency to continuously quote the "gospel according to Bell" can get a bit grating after a while.

The only thing that bugs me as much as it bugs you about the article is the whole "naive realism about operators" shtick. If I were into accusing people of being naive, I could equally accuse the Bohmians of being "naive realists about wavefunctions". There can actually be good reasons for being realist about operators, especially if your realism is tempered by a good dollop of operationalism, which mine is. I'm not saying I completely buy operationalist approaches either, but the phrase "naive realism about operators" does tend to imply that there is no way of being realist about them that is non-naive.

And (as Lubos-Colbert would say) that's the memo.

I was disappointed that my misreading of the title as "Bohemian mechanics" wasn't borne out by the body. Perhaps you could write a followup about the influence of a relaxed scruffiness and gentle irony on 20th-century theories of physics.

Moshe: One of the problems with science on the internet is demonstrated by the fact that Bohmian mechanics, an extremely old subject whose community of practitioners consists of maybe two dozen people worldwide, is attracting more attention than whole fields which actually have new and interesting things going on all the time. Hey, there are Iron-based superconductors, a fact we did not know about until recently, isnât it more interesting to talk about something new?

As I said, people keep asking me about it. If people start asking me about iron-based superconductors, a subject I know even less about than quantum foundations, I will go learn something about iron-based superconductors. Lord knows, I'd be happy to find people who want to talk about something other than quantum interpretations and high-energy theory, but I'm stuck with the Internet we have, not the Internet I would like to have.

Anything that does not incorporate QFT and all its predictions, many of them follow from combination of Lorentz invariance and QM, will not make heads explode, it will make shoulders shrug

I was implicitly assuming that some future Bohmian field theory would match the predictions of QFT that have been experimentally confirmed. Otherwise, it would be pretty pointless.

Matt: In fact, Bohmian mechanics does make predictions that differ from quantum theory if we drop the equilibrium hypothesis -- something it makes sense to do in BM but not in standard QM. If we do that then we have to argue that there is an approach to equilibrium similar to that in statistical mechanics and we have to investigate the possibilities of observing nonequilibrium states. This is what Valentini's work is all about and that's why I suggested you should take a look at it as well.

This is, of course, the obvious weakness in reading about it via the Stanford Encyclopedia of Philosophy rather than more physics-oriented sources-- you get a limited presentation of relatively established stuff. I'll look for Valentini's stuff next.

In some sense BM has the best of both worlds in that we can say it agrees with QM completely if we happen to be in equilibrium, but it does offer the possibility of divergent physics as well.

That is a selling point, I agree. Though the QFT comments above are an important check on anything-- there are some pretty tight experimental constraints imposed by things like the Lamb shift and the electron g-factor, and I think I'd want to see those matched before spending too much time.

What I found most surprising in your summary was the lack of mention of the fact that Bohmian mechanics solves the measurement problem, i.e. there is no ambiguity about whether the pointer on a measurement device is actually pointing to a particular outcome or not. This, after all, is the main point of any realist interpretation of quantum theory and nobody would take it even a little bit seriously if it didn't do that.

I thought that was implicit in the definite particle states business.

Anyway, yes, it solves the solvable bit of the measurement problem, which is to say "Why do we see only one outcome?" The other question-- "Why did this particular realization of this experiment give this exact result?" is sort of pushed back to the equilibrium hypothesis. which, to be fair, is arguably better than any of the other theories.

Regarding the chip on the shoulder thing, this is fairly common amongst realist foundations of QM types of a certain age. What you have to remember is that studying foundations from the '60s to the '80s was regarded as a pretty cranky pursuit.

Oh, absolutely.

It's a vicious cycle-- if you work on something that sounds crank-ish, you get defensive about being seen as a crank, and that defensiveness is also characteristic of cranks. Lather, rinse, repeat.

Still, it's off-putting, especially without an independent way to assess the credibility of the author.

I was disappointed that my misreading of the title as "Bohemian mechanics" wasn't borne out by the body. Perhaps you could write a followup about the influence of a relaxed scruffiness and gentle irony on 20th-century theories of physics.

Well, that's pretty much Einstein in a nutshell, isn't it?

My immediate reaction to "Bohemian Mechanics" is more "Scaramouche, Scaramouche, can you do the fandango?" Which doesn't really lead anywhere good...

Yeah, OK, we agree on the basic point (including BTW the too much HET part, and not always the most solid part of HET either). My short experience with blogging also indicates that once you start talking about the bread and butter of what is going on in your field, people tend to drift off. Still, I feel the need to clarify what is the relative weight of various things, so outsiders donât get this absurdly skewed view. It is hard to do though, at least without being disparaging (as my rant above probably demonstrates).

I tried to teach a graduate course on it, for what it's worth. See here.

If it helps, I don't have a chip on my shoulder. I just think this stuff is quite fun.

Every particle considered thus has a definite position and momentum at all times, unlike the situation usually presented in the orthodox quantum theory. If you know the initial position and momentum of a particle with sufficient accuracy, you can thus calculate a perfectly normal classical trajectory for it, with the wavefunction "guiding" the particle along the trajectory.

If Bohmian QM can calculate a normal trajectory, why not simulate it in the lab with upsized particles and guiding waves? With today's technology, it is possible to guide objects according to any calculated law, with the help of radiofrequency or e-m fields. This would help to settle interpretational issues experimentally.

So... stupid question: Is momentum conserved in Bohmian mechanics?

It seems to me that the Bohm idea is full of problems. Just off top of my head: if every particle has definite position and velocity then why the residual energy of motion "due to the uncertainty principle." How does tunneling of the "real particles" occur? How about decay in general, why that distribution if a real clockworkey mechanism in there? The latter would have a time structure and not be genuine Poisson style decay? Then maybe handling delayed choice experiments, Renninger null, non-interactive redistribution (blockage in an interferometer leg) etc. How does this pilot wave interact with things? And so on.

I'm glad to see Mike Towler weigh in here. Consider him the world's expert on the subject, Chad. Being a modest Englishmen, he will of course deny this. That's fine. Name a better expert then, Mike.

I started a page on Towler, here, in early March, in which I also reference Robert Wyatt's excellent text, Quantum Hydrodynamics. It seems that BM or PWT has many other uses besides Foundational Physics, notably, as a teaching tool in Fluid Dynamics.

Now, if could just tie all of this together with quark-gluon plasma and black hole thermodynamics, hmm, ....

I just wanted to point out that there are several versions of Bohmian theory that reproduce QFT. My favorite is one that uses a particle ontology for fermions and a field ontology for bosonic fields due to Samuel Colin. None of these theories are fundamentally Lorentz invariant -- they can't be due to Bell's theorem -- but they are Lorentz invariant at the operational level provided the equilibrium hypothesis holds. Therefore, you can still use all your favorite Lorentz invariant techniques, just as you can still use the Born rule in nonrelativistic QM. At the fundamental level there is a preferred reference frame, which might admittedly seem distasteful, but the only way you are going to be able to get around that in a hidden variable theory is to make radical changes to the ontology, e.g. relational or retrocausal variables, and no one has made much sense of these to date.

Regarding nonequilibrium, I agree that current experiments provide extremely tight constraints. However, you can say the same thing about almost any proposed modification of QM. In fact, whenever someone proposes an modification of QM, it almost always gets tested fairly quickly in tabletop optical systems. This is fairly pointless because we already know that optical systems obey QM to extremely high precision. If the modifications hold anywhere then it has to be under fairly extreme conditions where current physics has not been tested experimentally. Nonequilibrium has an advantage over other proposed modification schemes in that its effects are expected to wash out very quickly so observing precise QM in the lab does not rule out nonequilibrium in the early universe for example. This is the sort of thing that Valentini is proposing.

Neil B: The answer to your first question is that the mass times the velocity of the Bohmian trajectory is not the same as the momentum you would obtain from measuring the usual momentum operator. Both are also uncertain due to the equilibrium hypothesis, but the measured momentum gets some of its uncertainty from the uncertain position of the measuring device as well. To answer the rest of your questions, you can prove that BM reproduces the predictions of QM exactly, so there is no problem explaining any of these experiments. It is true that in order to do so the Bohmian trajectories have to behave very weirdly compared to our intuitions about how trajectories should behave. For example, the Bohmian trajectory of a stationary state is stationary, so electrons orbiting an atom aren't actually orbiting at all according to Bohm. Trajectories also behave weridly in interferometers, Stern-Gerlach and the like, but basically you're going to have to have weird trajectories in order to reproduce QM rather than classical physics.

Note to self: I need to stop writing so many long comments defending Bohmian mechanics on other peoples' blogs. People will get the wrong idea.

Bottom line: Bohmian mechanics is probably not true as far as I am concerned. However, it is the most coherently worked out realist interpretation of QM and, as such, it is an incredibly useful foil for all sorts of foundational ideas. In particular, it is a first class b*****t detector. Next time you find yourself writing something like "QM implies that a particle can be in two places at once" or "instead of going through one slit or the other, a quantum particle goes through BOTH slits", ask yourself whether this is true in Bohmian mechanics. If not, then it is not really quantum mechanics that implies these things, but quantum mecahnics combined with some unspoken Copenhagenish assumptions that may turn out to be false in the long run.

Matt, if you are still paying attention...typically physical theories have many mathematical formulations, all of which are exactly equivalent, but employ different fiduciary objects (by which I mean those who do not correspond to results of measurements). QM has path integrals and operators on Hilbert spaces, wavefunctions or density operators. In QFT this only gets worse, for example you have bosonization, which means the exact same theory can be formulated in terms of bosons or in terms of Fermions. In other example you see that the dimensionality of spacetime, or the type of fields you have is also description-dependent. So, life is complicated when you look at complicated physical systems, and I am not sure what are the rules to determine the ontological status of those different objects. Is the idea getting a pretty picture, or is there something more systematic involved?

Or, when Clifford (and myself) are struggling to find an answer to a fairly similar question in quantum gravity, in

http://asymptotia.com/2010/05/11/but-is-it-real-part-one/comment-page-1…

is there a set of criteria we can use to reach an intersubjective conclusion?

QM is just weird, period. To agree with what the voltmeter says, the weirdness has to be there. Bohmian stuff to me takes all the weirdness and lops it into a very weird potential. You can do QM as JUST a statistical theory, albeit with negative probabilities. The weirdness has to be there, and it can be smeared around in the math so its harder to notice, or it can be balled up like a dust bunny in the corner of the room, but its got to be there.

See full response at http://www.mythiclogos.com/blog/?p=38. It was a little too long for a comment.

As a realist, basically, I want clearly formulated theories that apply outside physics labs. I like BM, but other alternatives are fine (they do exist) as long as they give a clear ontology, i.e., the contact with reality.

The Dirac equation, hence spin, can be derived from Bohmian notions (http://jostylr.com/thesis.pdf, chapter 3 )

Measurements appear only when discussing experiments. The theory itself is not concerned with measurements. Note that BM allows one to talk about and do experiments that measure the position of the particle incorrectly, but do measure the position observable. Hence the quote about "naive realism about operators"; they do not necessarily correspond to an underlying reality. One needs to prove that they do, when they do. And one needs an underlying theory to do that.

BM forms a very clear starting point for extending theories and can be used to easily extend QM to many places where standard quantization has issues such as general manifolds.

But really, I just want a story that minimizes "ridiculous, but true". And that is BM. It is simple and it is the closest to my sense of reality of all the theories that I have seen.

I think that the simple macroscopic fluid-dynamics related experiments that demonstrated behavior analogous to observations on the quantum level are largely responsible for the resurgence in the popularity of the brogile-bohm theory. But I wouldn't worry about it, since the internet search trends for terms like "bohmian mechanics" are stagnant.

You can say what you will, but many-worlds is as crack pot as it gets. Is it cool, yes. Is it real...not a chance.