{"id":4686,"date":"2010-05-13T12:03:27","date_gmt":"2010-05-13T12:03:27","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2010\/05\/13\/quick-impressions-of-bohmian-m\/"},"modified":"2010-05-13T12:03:27","modified_gmt":"2010-05-13T12:03:27","slug":"quick-impressions-of-bohmian-m","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2010\/05\/13\/quick-impressions-of-bohmian-m\/","title":{"rendered":"Quick Impressions of Bohmian Mechanics"},"content":{"rendered":"

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<\/a>, 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<\/a>, 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<\/a>, 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.<\/p>\n

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<\/cite><\/a>), 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<\/a> 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.<\/p>\n

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.<\/p>\n

<\/p>\n

Quick summary fo the summary article<\/strong>: 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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

General Comments<\/strong>:<\/p>\n

– 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:<\/p>\n

\n

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 |\u00cf\u0088|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.<\/p>\n<\/blockquote>\n

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.<\/p>\n

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.<\/p>\n

– 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:<\/p>\n

\n

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.<\/p>\n<\/blockquote>\n

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:<\/p>\n

\n

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. <\/p>\n<\/blockquote>\n

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<\/a> 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.<\/p>\n

– 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…<\/p>\n

– The article tries to walk a weird line between brushing off non-locality\/ contextuality as not that big a deal:<\/p>\n

\n

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.<\/p>\n<\/blockquote>\n

(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.<\/p>\n

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.<\/p>\n

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.<\/p>\n

– 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.<\/p>\n

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.<\/p>\n

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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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.… Continue reading Quick Impressions of Bohmian Mechanics<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,138],"tags":[291,233,292,293,121,92,93,210,88],"class_list":["post-4686","post","type-post","status-publish","format-standard","hentry","category-physics","category-theory","tag-bohm","tag-einstein","tag-heisenberg","tag-interpretation","tag-philosophy","tag-physics-2","tag-quantum","tag-quantum-physics","tag-science-2","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4686","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=4686"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4686\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=4686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=4686"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=4686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}