God knows where all the particles are!

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    A reason to appreciate Bohmian mechanics is that it makes the trivial point that nonlocal hidden variables are possible, and at the same time shows in all desirable detail why it is a bad scientific project to follow that route. For in the end it achieves precisely the explanatory power of the exclamation “God knows where all the particles are!”. It does, of course, help to scratch that philosophical itch of Realism. In this regard it may be a perfect “Beruhigungsphilosophie”. But, by lack of empirical input, when it comes to any details about the trajectories, the only argument for doing the theory one way or another is lack of imagination, perhaps with a heavy dose of “naive realism about the position operator”.

    That, in a Bohmian universe, the trajectories are unobservable in principle was to put to me in a very strong form by Shelly Goldstein. For a recent talk (http://carnap.umd.edu/philphysics/wernerslides.pptx) I had introduced the “Bohmian Demon” a hypothetical entity able to see the trajectories. Somehow I felt perhaps that the whole show should be for the benefit of at least one, if imaginary, being. Shelly explained to me that, precisely in a Bohmian Universe, there could be no such entity. So I guess Shelly is an agnostic about trajectories and I am more of an atheist, but apart from matters of faith we do agree.

    Dustin Lazarovici

    That the Bohmian trajectories are (in principle) unobservable is, of course, a very common objection against Bohmian mechanics. This objection is usually based on two things: 1. a positivist dogma and 2. a misunderstanding of the logical relationship between Bohmian mechanics and Quantum mechanics.

    You also seem to misunderstand the spirit and content of Bohmian mechanics when you think that it is based on or motivated by a “naive realism about the position operator”, but I guess that’s not the main point.

    In any case, your argument is based on the assumption that BM is essentially standard quantum mechanics plus an (adhoc) addition of particle trajectories. If that was the case, one could make an occam’s razor argument to the effect that the trajectories add no predictive power or empirical content and thus should be despensed with. In fact, even this statement wouldn’t be correct since (the constituents of) macroscopic objects also move on Bohmian trajectories. Indeed, the whole empirical content of the theory is in the particle positions, i.e. the distribution of matter in space. But let’s grant that the trajectories of subatomic particles per se have no empirical content.

    However, Bohmian mechanics is NOT Quantum mechanics plus trajectories. In fact, the Bohmian has quite a bit of work to do in order to derive the usual quantum formalism from the two dynamic equations defining Bohmian mechanics.

    Indeed, Bohmian mechanics is the microscopic theory and QM is the measurement formalism derived by statistical analysis. BM is not an extension of QM, but a REDUCTION of QM. The quantum formalism is derived from and explained by BM.

    BM is logically prior to and conceptually simpler than textbook QM. Everything follows from two precise mathematical equations rather than a set of fuzzy axioms involving “measurement” or “observers” or “operators” or whatever. For both reasons, the occam’s razor argument doesn’t actually hit BM.

    If you forget about the microscopic theory, i.e. about particles and their trajectories, you don’t necessarily lose empirical content. After all, the Bohmian agrees that the standard quantum formalism is – for all practical purposes – correct. However, you lose the physical content of the theory, i.e. the way in which the qauntum formalism actually relates or refers to stuff in the physical world. You literally don’t know what you’re talking about when you do your operator business or solve Schrödinger’s equation or compute transition amplitudes.

    Now, you may say that for you, the physical content of a theory is only in observable (macroscopic) quantities. You may say, for instance, that the trace in a cloud chamber is physical – because that’s what you can see – but a microscopic particle that a theory posits as the “cause” of this trace is unphysical, because that you cannot see.

    I guess this position is defendable, to some degree. It certainly agrees well with the old Copenhagen school of thouht. But then you are the one who’s being dogmatic, adhering to a very particular positivist philosophy, and who displays a lack of imagination. There’s nothing sophisticated about not believing in atoms.


    Thanks, Werner, for your contribution — and thanks, Dustin, for your comments (which I agree with completely). I wrote some comments in response to Richard Healey’s contribution over on this other thread:

    Comments on Bohmian mechanics

    Basically I was there echoing/elaborating what Dustin expressed by noting above that “the whole empirical content of [Bohm’s theory] is in the particle positions, i.e. the distribution of matter in space.” So people interested in this thread might want to check out that other one as well.


    Dear Dustin,
    so you do agree also that Bohmian trajectories are unobservable as a matter of principle. I think that does have some bearing on the issue of “empirical content”. In fact, I would say that this directly shows that Bohmian Mechanics has zero empirical content.

    That is, if you take “empirical” as referring to some kind of experience. Your vague reference to “matter distribution” (I guess you mean distribution of Bohmian particles) does not help if whatever is distributed there cannot be detected by any kind of interaction with the system. You probably think that at the macroscopic level it all does not matter so much. If you throw in enough decoherence assumptions, wave your hands sufficiently and suggest that after all particles are probably roughly where the bump in the wave function is, you can maybe talk yourself into thinking of matter distribution (which you have somehow come to think of as Bohmian particle distribution) as an interpretational primitive.

    But if we talk logical analysis, you will just have to admit that Bohmian Mechanics declares its own “emprical content” (matter distribution) to be unaccessible to experience, i.e., zero.

    The question which comes first, BM or QM is maybe a matter of taste. To me the Bohnmian “derivation” of QM looks very much like adding spooky trajectories and rederiving QM by forgetting them. But I admit that this may just be my training in QM getting in the way. I can see that if you are a philosopher or a mathematician (i.e., not interested in applying the theory) you may find BM more palatable.

    Miroljub Dugic

    Dear Reinhard: it cannot be wrong to have e.g. electrodynamics [read: an interpretation] as a theoretical background for electric machines [read: operational QM], can it?

    Dear Dustin: theoretical explanations offered by Bohm’s theory, as yet, require a huge leap of faith and only modest benefit–do you agree?


    Dear Miroljub, I don’t quite get your point. Of course, as a theoretical physicist I am all for explanations. That is my line of work. I just do not see BM providing any. The Bohmian line that QM does not explain anything, because it is not operating in terms of some “real factual situation of the universe” is based on a different idea of explanation. The whole disagreement is about that.

    Bohmians claim that by inventing this objective description they make the theory more “clear” or “exact”. I claim that the scientific value of such inventions is on the same level as the mystical explanation that Reality is what is in the mind of God (and in either case: carry on with science as usual, because this doesn’t teach you anything new). If that makes you happy or soothes you, fine by me. I don’t find it worth too much paper.

    Dustin Lazarovici

    Dear Reinhard (if I may call you Reinhard),

    there seems to be a misunderstanding. Of Course, according to Bohmian mechanics, macroscopic objects are composed of microscopic (Bohmian) particles. And indeed, as Travis explains, the empirical content of the theory is in the position/configuration of macroscopic objects, including measurement devices, records and so on.

    Now you seem to suggest that the fact that you cannot observe the trajectory of a Bohmian particles implies that you couldn’t observe the trajectory of a macroscopic object composed of Bohmian particles. But this is not correct.

    “Absolute uncertainty” – which is a Theorem in BM – implies that you cannot know more about a system than its psi^2-distribution, psi being its effective wave-function. Applied to a single particle, this means that you cannot know/measure/observe its precise trajectory. Applied to a macroscopic object, composed of a great number of particles, this means that you cannot know its exact microscopic configuration, i.e. the position of every single constituent particle. However, a huge number of different microstates coarse grain to one and the same macrostate.

    In other words: you don’t have to know/measure/observe the exact position of 10^24 microscopic particles composing a table to know/see the position of the table in your office.

    Of course, if you were to spell out the Bohmian account in more Detail, it would involve decoherence and the fact that macroscopic wave-function can be sufficiently well localized on sufficiently large time-scales and it would involve the fact that typically, the microscopic configuration is roughly where the bump in the wave-function is. But these are all theorems in BM, i.e. they can be proven.

    To summerize: that, according to BM, you cannot observe the trajectory of microscopic particles is true, but not really a problem. That, according to BM, you cannot observe the macro-trajectory of macroscopic objects would be a problem, but it’s not true.

    @Miroljub No, I don’t agree that Bohmian explanations require a huge leap of faith and yield only modest benefit. I’m not sure why I should.


    Dustin wrote: “there seems to be a misunderstanding”.

    That is my sense as well. Reinhard, it seems like you have a number of simple factual misconceptions about how Bohm’s theory works and what it says. Did you read the long comment on the other thread that I linked to above? If you have questions about how/why/whether the sorts of things I was saying there are true, it would probably be quite helpful to hash them out here. On the other hand, to me it seems rather pointless to just ignore the claims of the people who understand the theory well, and continue with the straw man type rhetoric against the theory. If you think we’re wrong about something, by all means call us on it. We can argue about it and at least maybe somebody else reading the exchange will learn something. But what’s the point of saying things like “Bohmian trajectories are unobservable as a matter of principle” when you know Bohmians don’t accept that as an accurate characterization of the theory?

    Miroljub Dugic

    Dear Reinhard,

    I am not a Bohmian. My scientific preferences can be found elsewhere, e.g. in ‘Other topics’ of this forum, which i enjoy and use to learn some new things. My point was just that [like some other theories] Bohm’s theory points out a really important issues which are far from being resolved–as i asked Dustin about. Personally, i do not have any problem with God’s view to physics. It may sound silly to you, but there is a pragmatic reason for this: Good questions often lead to a discovery; even finding a dead end is something worth pursuit. Of course, i cannot tell if this will turn out to be the destiny of the Bohm’s theory.


    Dear Dustin and Travis,

    so, according to Travis, I “have a number of simple factual misconceptions about how Bohm’s theory works and what it says.” I feel that I do understand fairly well how the theory works, but that is somehow at variance with what Bohmians like to say about it. Of course, the root for the whole disagreement is further down in the views of what a scientific theory should be. This forum is no place to work that all out. But let me indicate a few points related to the issues raised.

    One key element of a physical theory to me is the point where the connection between the mathematical framework and the real world is made. Somehow Bohmians seem to try to avoid that by directly claiming reality for the particles and their trajectories and that’s that. (“It’s all in two simple equations”…) This kind of reality is entirely in a lofty Platonic world, and we are merely invited to imagine that we live in such a world. No messy questions of interpretation there, and, of course, everything has to work out with respect to experience, because the standing assumption is that the universe, including any potential observer, is already in that harmonious set of equations. All is clear and exact. Peace be with you.

    This is very poetic and simple (to the extent that PDEs in zillions of variables are) but how would you convince me that we live in such a world? I know you would probably not try (because of the serious non-uniqueness), and instead try to convince me that that Platonic thing at least is a possible world. That would not be saying much, however, and would put the reality claims of the Bohmian Universe on a par with Middle Earth. Of course, you have distributed Reality tags in your fantasy, e.g., for the “matter distribution”. But those are just words, as long you don’t give a rule of how to make the connection to the real world.

    I suppose the idea here is that “matter distribution in the real world” is such an immediately obvious thing that it suffices to say that a suitable averaging of the mathematical point distribution should be the real world matter distribution. But there is nothing obvious about that in BM. How do we actually determine the matter distribution? I know no other way than to somehow interact with it. But since the interaction is always with the wave function, and the BM particles themselves are gravitationally and electrodynamically invisible, the trajectories are not related a priori to anything one might observe via an actual interaction. There seems to be agreement on this for small systems. So why should the Bohmian particle distribution be of any relevance to ascertaining “matter distribution” in the large?

    Of course, we expect that for a macroscopic system you can get away with a lot of coarse graining and fuzziness, so probably you can get away with a lot of conceptual fuzziness as well and that identification is probably sort of ok. Not that you have a proof of that which does not assume a solution of the FAP measurement problem, and a counterfactual assumption about disjoint wave function supports. Maybe if you leave your mathematical hat in the closet, you can just make the assumption that things work out as you expect they should. This is all quite fuzzy, and is plagued by a theory of measurement that requires you to solve a many-particle problem, which means that you can never get concrete (I heard the term “unprofessionally vague” in this context).

    This is precisely the virtue of the Heisenberg/von Neumann/whoever cut: It allows you to come to a theory that actually allows predictions. You could now say: but this is anyhow included by nostrification (i.e., via the implication BM==>QM). Then the message amounts to this: If you want to solve a problem, like describing an experiment, scrap BM, go QM. On Sundays, when you want to live in that Platonic world, you can still be a Bohmian.

    All the best, Reinhard

    PS: Travis, you warned me of the dramatic consequences of removing the Bohmian trajectories from the furniture in my house. But I just did that (by forgetting some variables from the guiding ODE), and it looks pretty much the same. So I decided to leave it in its new Bohmian-free state. I hasten to add, I left your furniture nice and real, but frankly, I am not sure how you would ever notice the difference.

    Aurelien Drezet

    Dear Reinhard, I was not apparently allowed by my computer to write you a comment directly (probably the bohmian demon in my Windowsystem). I Copy and paste a reply in the Max section on Bohmian concerning the value of Bohmian mechanics for physics: I changed a bit the structure.

    First of all, BM offers a much better perspective than Copenhagen concerning describing what is reality. More precisely, if you focus your attention on the empirical contents of Bohm’s theory and say that it looks like the view of a god (: ‘only god knows where the particle is ‘ ) then you could conclude that BM is indeed metaphysical. However, I ask now what do you exactly mean by empirical contents? I think that when you try to answer a question like this one you should be quite prudent and modest. Like Heisenberg discussing with Einstein we should never forget: Theories always come before the experiments (I am both a theoretician and an experimentalist and I accept that very well). Now, BM is a theory it has a clear dynamical framework and it reproduces all data (at least in the non relativistic domain). What you want more?
    Like you we could say that the paths predicted by BM are surrealistic (actually it was Scully after Heisenberg who used this language but it fits here as well) and not observable. Well, that’s a bit provocative but this is not true. Trajectories given by BM agree with facts and can be tested in that reduced sense (Weak measurements or Protective measurements even allow more see below). Indeed, BM will predicts the good probability which are associated with the trajectories and there is nowhere contradiction between BM and QM (by the way what is QM without a clear ontonlogy a set of rules for technicians ?). Of course, you can not measure a path like you could do it in classical mechanics because Heisenberg principle prohibits that but this is the price to pay here: If you want to reproduce QM predictions you must accept this limitation. You must abandon some aspects of Classical mechanics. If you reject that: no chance for you to explain QM. Heisenberg refused even to listen Bohm for that reason : BM for him was classical physics so it should be wrong. But Heisenberg was mistaken : We dont try to save the classical realm but its goal which is to give an interpretation of the world independently of the observer.
    I want to say a bit more about that: If you anyway reject Bohm or Stochastic QM à la Nelson what should you propose instead? If you go back to Copenhagen then you are only hiding yourself under the quantum carpet since you dont have a definition of what is the reality anymore: you need an observer but you cant define it precisely. Do you need a PhD, like Bell suggested provocatively, an environment, an infinite number of Wigner’s friends (with cats)? This is wavy and the choice of Bohm is not. If you want to observe a path anyway I suggest to use protective measurements [Aharonov Vaidman, Phys Lett. A 178, 38 (1993).]. Indeed, the protective measurement protocol can be used to ‘detect’ the particle at points that the Bohmian particle never comes near. This is because the wave function is an active element in BM. This allows to record a velocity without disturbing the position. There is no paradox because you didn’t use a ‘destructive’ von Neumann protocol for velocity. You are still free to define the position of the particle after that so you will get both the velocity and the position. This is not yet a path but you are getting closer from it. Clearly, Of course the Bohmian program has some limitations. If you remember Popper and his falsificationism you realize that BM is not completely testable (This is necessary, I repeat it, for reproducing QM). This is a problem I agree but nowhere It has been written that Popper was right for ever. Additionally, the sciences do it in the same way like BM and nobody seems to be offended by that. Consider cosmology and Black holes ? Would you say that these objects are not for science? what about quarks if we can not separate them ? These theoretical objects have some consequences which can be tested but we can not observe all and some part will stay for ever may be outside the experimental deomain. Anyway, I agree with you on a another point BM is not unfortunately unique. I don’t speak here about Nelson theory which is no yet in the maturity of BM (despite years of efforts) but more about the problem of relativistic BM. Since for BM we need a privileged observable (like position in the non relativistic theory) we should define the same for quantum field and an univocal answer is not yet existing. Personally, I believe that BM is only a temporary expedient. One day we will get a much better theory which will explain why particles have such and such properties like mass and charge. BM is the best candidate for helping us if we can give a better foundation to the theory. Still, I think that Bohr view on reality is a dead end since it will only offer you the sleeping property of opium and will not allow you to, may be, discover something new (or not).


    Dear Reinhard, I don’t understand what you find “Platonic” about “claiming reality for the particles and their trajectories”. How is this, in principle, any different from the claims that people made in the 19th century about matter being made of atoms?

    You ask: “how would you convince me that we live in such a world?” I guess I would start by pointing out that the story told by the theory about how big, directly-observable, macroscopic collections of particles move, is consistent with what we see in fact happening. That of course doesn’t prove that the theory is right. But surely it counts for something — it’s enough that it should make one take the theory very seriously as a real possibility. You say Bohmians “don’t give a rule of how to make the connection to the real world”. But the connection is crystal clear: what the theory says about how (macroscopic collections of) particles (like pointers, etc.) should move, matches how we in fact observe them to move. If that isn’t what you’re looking for, what in the world are you looking for? What kind of connection between a physical theory, and the real world of direct perception, would satisfy you??

    Your paragraph starting “I suppose…” contains several confusions/misconceptions about the theory. 1. There is no “averaging” of the “point distribution” involved. The particles have actual positions. There’s a definite configuration. That (not some average of anything) is the “real world matter distribution” according to the theory. 2. You say “the interaction is always with the wave function”. I think you mean that, according to Bohm’s theory, you (who are, of course, according to that theory, made of particles) cannot interact with the other particles (also posited to exist by the theory); you can only interact with the wave function. That’s just not right. I suppose you could say that in some sense the interactions between particles are mediated by the wave function. But it’s just ridiculous to understand the theory as saying that particles can’t interact with each other. 3. You suggest in particular that “the BM particles themselves are gravitationally and electrodynamically invisible”. That’s simply wrong. Maybe what you mean here is that the particles do not move (and do not influence other particles) according to the laws of Newtonian mechanics (with gravitational/electromagnetic interactions). That’s true. But just because something has a new, quantum dynamics doesn’t make it invisible. If there are gravitational/electromagnetic interactions in the Hamiltonian, then the particles interact gravitationally/electromagnetically, and are simply not “invisible” in the sense you mean.

    I’ll stop there (although there are more confusions/misconceptions). But I’ll just highlight this comment, which I think is quite revealing: “This is precisely the virtue of the Heisenberg/von Neumann/whoever cut: It allows you to come to a theory that actually allows predictions.” I think it is clear that you are continuing to think about Bohm’s theory in exactly the (wrong) way I outlined in my previously-linked-to comment on the thread started by Richard Healey.


    Hi Travis,
    what I meant by “gravitationally and electrodynamically invisible” is just the undisputed fact that you should not take these particles as a source for the respective fields. In my statement that the “interaction is always with the wave function” replace “with” by “via”. Again I just meant the form of the equations. I admit that a positive reference to the cut was a bit of a provocation. I am also guilty of the “misconception” about Bohmian Mechanics that I don’t see it as solving any problem (except formally restoring some fake Reality). Naturally, this is not what BM experts like you say. That is called disagreement, and it remains to be seen where the misconception is, or to what extent these camps can agree to disagree.

    So long, Reinhard

    Dustin Lazarovici

    Dear Reinhard,

    thank you very much for your very nicely written responses. I’m still not sure that your hostility towards BM isn’t fueled by some factual misunderstandings (the things that Travis keeps pointing out), but I think I’ve got a better sense for where your objections come from.

    Please allow me to add a few remarks. I don’t try to change your mind, I just try locate the core of the disagreement a bit better.

    1) BM does not presuppose realism (whatever you mean by that, exactly). Accepting BM, you can take any philosophical attitutude you look like towards the particles and their trajectory. You can, for instance, take the anti-realist stance that they’re mere theoretical entities but still endorse BM as the most conceptually clear way of doing QM.

    Of course, you CAN take BM seriously as a “realist” description of the physical world. At least it makes sense to ask: what would the world look like if BM were true (and how well does this agree with our actual physical world). It doesn’t make sense to ask: what would the world look like if textbook QM were true, because textbook QM does not provide a clear, coherent picture of the microscopic regime.

    2) Micro-to macro transition is indeed a very subtle business. It’s probably not a coincidence that so many Bohmian have their background in this particular field of mathematical physics. I understand, on some level, why you would like to avoid this business, that you describe as “fuzzy”.

    I just don’t think that it’s a good idea to embrace instead a set of “rules” that are fuzzy and vague to begin with and that don’t even try to achieve constiency between the microscopic and the macroscopic level. And I refuse to believe that your problems go so far that you literally don’t understand atomism, i.e. how a prediction about the distribution of particles in 3-dimensional space amounts to a prediction about the actual, observable world.

    3) I don’t think anyone could convince you that BM solves any problems, because you’re obviously an expert in quantum phyiscs and you probably feel that, on the level on which you care, there are no problems with the theory. So let’s assume for the sake of argument that BM doesn’t solve any practical problems.

    Still, as a quantum theory, it comes with a lot of virtues: mathematical precision (everything is defined by equations), observer-independence, consistency between the micro- and the macro level, just to name a few.

    Until not so long ago, these features were considered as highly desirable by almost all scientists. I think they are still considered as highly desirable by most. However, at the advent of QM, many physicists gave them up, because they – mistakingly! – thought they had to.

    Still, you are free to believe that these features are not only not desirable but actually very bad. That’s fine, I guess, it’s ok to have different preferences about what a physical theory should do. Just don’t pretend then that Bohmians have some naive philosophical prejudices, while you don’t. At the very least, we are all just as prejudiced, only in opposite directions.

    Best, Dustin


    Hi Reinhard, Re: “gravitationally and electrodynamically invisible”, I think I understand what you meant, but I still think you are misunderstanding (or maybe it would be better to say misapplying) Bohm’s theory here. It really is, I remain convinced, just what I said in my comments in response to Richard: you insist on thinking of Bohm’s theory as a replacement for just the quantum part of the Frankenstein picture of the world you’re accustomed to from ordinary QM (I mean with the quantum part and the classical part gruesomely stitched together); I agree that if you think of it that way, it will seem pointless and stupid; but you should really try to appreciate that that is not the right way to think of it (not, at any rate, if you want to give it a fair hearing and try to understand what people who like it like about it).

    Let me try to elaborate this just to make it as clear as I can (and so you can point out any mistakes I’m making in understanding your point of view). You wrote that, according to Bohm’s theory, “you should not take these particles as a source for the respective fields”. By which I think you mean the following: if I have some particle (or, say, a planet) here in the classical world, and I want to know how it will move, I figure out what the gravitational/electric fields are in its vicinity and then solve F=ma; to figure out what the fields are like, I add up the contributions from all of the sources; but if I treat the Bohmian particles (over on the quantum side of the shifty split) as sources, there will be cases where I get completely wrong predictions for the motion of the particle/planet; so obviously I shouldn’t treat the hypothetical Bohmian particles as sources in this way; which then means that the hypothetical Bohmian particles have no effects at all on me and the particles and planets over here on this side of the shifty split; which means I might as well simplify my quantum theory by just eliminating them. Is that a fair summary of your thinking?

    The reason I think it’s wrong is that Bohm’s theory should be understood not just as a theory about “the quantum part” of some hybrid Frankenstein world, but instead as a theory about the whole world, full stop. And so if you want to know how some one particle affects some other particle or planet (or instrument pointer or your brain or whatever) you need to at least start by treating everything involved in a uniformly quantum (here, Bohmian) way. I think at this stage you just give up and dismiss the whole thing on the grounds that any such treatment (of, say, two planets colliding) in a “uniformly quantum way” will necessarily involve lots of idealizations and approximations and will therefore be, in your opinion, so “fuzzy” as to be completely meaningless. The Bohmian people see it differently, though, maybe because they are more comfortable with fuzzy things, or maybe because they are more able to appreciate that the details that are fuzzed over will not change the crucial points of principle. But in any case, to me at least, and I think to a lot of other people (but not to you, or at least not yet!), it is completely clear and obvious that a uniformly Bohmian-quantum treatment of two planets colliding, or whatever, will make perfect sense and will perfectly correspond to what we see in the real world: if there is some long-range gravitational attraction, but, say, something like a short range electrostatic repulsion, and the initial state (of the relevant particle positions and the wave function) is the sort that would give rise, for each planet in the absence of the other, to some more or less classical motion (nice wide gaussian wave packets or whatever), then what Bohm’s theory says is that the planets will speed up as they get closer together but then bounce off each other… just exactly the kind of thing we in fact observe happening. As I said before, I think it would be crazy to say that, according to the theory, the planets don’t affect each other (even if their interaction is “via” the wave function). And they are predicted to behave in just the way we observe such things to behave in such situations. So it is simply false to say either that the particles are pointless (in the sense that they don’t affect other things, other particles) or that if you do what you need to do to have the particles not be pointless, then you get wrong predictions. The wrong predictions you have in mind are simply *not* what Bohmian mechanics actually predicts. They are instead what some crazy Frankenstein theory that you have in mind, and that you mistake for Bohmian mechanics, predicts.

    Dustin Lazarovici

    Hi Travis, thank’s for clarifying! I’m not sure that Reinhard was thinking about planets and the “classical limit” of BM, though. I thought he was referring to the (indeed undisputed) fact that, on the microscopic level, particles interact via the wave-function, so that the interactions are strikingly nonlocal and need not depend on the actual positions in the way classical intuition would dictate.

    For instance, if you take a beam splitter and you wiggle the mirror on the left and you see that the point on the screen is wiggling as well, you cannot conclude that any Bohmian trajectory was actually passing by the left mirror.

    At least, that’s the kind of argument that I always hear from Lev Vaidman or Nicolas Gisin. And it’s not a bad argument, I think. It’s were for me, the debate usually hits a dead end. Because either you’re willing to take BM seriously and except these things as (correct) predictions of the theory and maybe unavoidable consequences of nonlocality. Or you insist that you can’t take the (microscopic) trajectories seriously, unless they are somehow operationally accessible. And indeed, that’s not quite what the Bohmian has to offer.

    I’m sorry to interfere in your exchange. Of course, Reinhard doesn’t need me to come to his defense. 🙂 I’m just eager to see how you (Travis) will respond to this particular argument.


    Hi Dustin — First, I don’t think you’re “interfering” at all. I’ve found all of your comments to be extremely illuminating and on-point! Second, I know the kind of Vaidman/Gisin argument you’re referring to, and (not surprisingly) I agree with you that it’s really no argument at all if you’re willing to just take BM seriously. And I do see why you interpret Reinhard as thinking along these same lines — clearly the occasionally “surrealistic” character of the trajectories is part of, or at least related to, what’s on Reinhard’s mind. But I’m not sure that’s really the main point. I’ve said what I think the essence of his, uh, mis-application is, and as of right now, I still continue to think that. But… only Reinhard can know for sure whether the problem, really, is that he’s thinking of BM in the Frankenstein way I described above, or if he’s instead worrying about the trajectories being surrealistic. Maybe he’ll elaborate and we can make some progress towards mutual understanding…

    Robert Griffiths

    Dear Travis,

    Early in this thread you made reference to your contribution to Healey’s “Comments on Bohmian mechanics”. I took a look at it, and maybe these remarks should go there, but they also seem to fit very well in this discussion.

    I once heard the story, no doubt apocryphal, that when one of Wigner’s students would go to him claiming some new and profound result about Hilbert space, the master would reply: What does it say in the case of 2 x 2 matrices? In somewhat the same spirit I suggest that before claiming that Bohm’s interpretation allows us to understand tables and chairs and planets, we first try it out in a very simple case: the motion of one particle. Does it give us the right answer?

    Not every reader of this column will be familiar with the claims of Englert et al. that Bohmian trajectories are “surrealistic”. Perhaps the best reference is not their original paper (see the bibliography in [3]), but instead one by Dewdney, Hardy, and Squires [1], three physicists who at least at that time, were very sympathetic to the Bohmian perspective. (If my memory does not fail me, Dewdney was a student of Hiley, who was Bohm’s close associate.) What they showed was that a Bohmian particle can in certain circumstances trigger a detector (containing its own Bohmian particle interpreted in proper Bohmian fashion) while coming no place near it. The fundamental idea is the same as what you find in Vaidman’s “Counterfactual communication protocol” in this forum: an empty wave can do various things even when the corresponding particle is far away. And given the nonlocality that Bohmian experts readily admit is present in the theory, that should come as no surprise.

    But for experimental physicists a theory like this is, indeed, a nasty surprise, for they design their experiments and interpret the results assuming that interactions are local. (As my authority on this matter may be questioned, let me say that as an undergraduate many years ago I myself carried out an experiment of this sort, and in more recent years have attended talks by competent experimentalists in which it was clear that they interpreted their experiments in this way.) Indeed, justifying the experimentalists’ perspective that the observed outcomes (‘pointer positions’) reveal properties of the (microscopic) measured system before it interacted with their apparatus, is what I call the ‘second measurement problem’, and I am about to claim in print [2] that Bohmian mechanics does not provide an adequate solution: it sometimes gives the right answer, and sometimes the wrong answer. This is a serious issue if one wants to claim that Bohmian mechanics is in agreement with experiment.

    In the Dewdney et al situation [1] the consistent histories (CH) approach [3] gives an answer in agreement with the way an experimentalist would view the situation; i.e., it solves the second measurement problem discussed in [2]. And since CH provides an explanation, via quasiclassical frameworks (Gell-Mann and Hartle), of how classical physics as a good approximation to quantum physics under the proper circumstances, it is as good as anything else in on offer when it comes to a quantum understanding of chairs and tables and planets. So why should I believe your claim that the Bohmian approach is giving the right answer for 10^23 particles when it gives the wrong answer for 1 or 2?

    Bob Griffiths

    [1] C. Dewdney, L. Hardy, E. J. Squires, “How late measurements of quantum trajectories can fool a detector”, Phys. Lett. A 184, pp. 6-11.

    [2] R. B. Griffiths, “Consistent Quantum Measurements”, arXiv:1501.04813; it should appear before too long in Studies in the History and Philosophy of Modern Physics.

    [3] R. B. Griffiths, “Bohmian mechanics and consistent histories”, Phys. Lett. A 261, pp. 227-234. arXiv:quant-ph/9902059.


    Dear Bob,

    I completely agree with the advice you give via the Wigner anecdote. If you want to understand a theory, start with the minimal examples. However, my impression is that Bohmians have given up on getting any physical sense out of few-particle examples.

    I spent a good part of last summer on an exchange with Shelly Goldstein on a simple detector problem: Take two detectors of the kind you describe and ask for the correlations between the passage of a projectile’s Bohmian path near one of them with that particular detector firing. I had a bet going on this with Nicolas Gisin, so I was looking for an informed answer. Shelly was only happy to look at the case where the projectile’s wave function has two terms which have disjoint suports for all times up to ionization (a case which plays a prominent role in the BM theory of measurement), but I could not bring any one to even look at the generic case of a projectile with wave function spanning both detectors. In the end (after about 50 printed pages) I was told by both Shelly and Detlef Dürr that mathematical rigor is overrated, but didn’t get close to an answer.

    It also seems (from a pamphlet written as a BSc thesis) that Bohmian students are discouraged from looking at few-particle examples. Instead they should look at Bohmian measurement theory where the supposed empirical equivalence with QM resides. But for those many-particle systems control is very poor, and you have to rely on assuming that all is as expected (wave function splits into branches with disjoint support, so the relative wave functions actually satisfy Schrödinger eqs., and no further interaction (like some reading the results) destroys that property, etc). Of course, two solutions of the non-relativistic Schrödinger eq. never have disjoint supports, and you would need some estimate on the transitions of trajectories between the branches. These will not be trivial, because BM dynamics is chaotic and fast around zeros of the wave function (so very likely in the region between branches). But all this is just ignored.

    Anyway, your point was the few-particle part, and I wish you good luck for getting any sensible answer.

    Best, Reinhard


    Dear Dustin, Aurelien and Travis,
    I guess this workshop is coming to a close, so let me try to wrap up some.

    Dustin: My “hostility” to BM is only that I am totally underwhelmed by it. Given that, I did put way too much energy into discussions like this in the last year or so (on this particular occasion on the explicit invitation by Travis), during which I have clearly not succeeded to help any Bohmian think a new thought. So I have made the resolution to not divert that much energy from my scientific work anymore, so whatever “hostility” you sensed is over with this workshop.

    Concerning your points:
    1) It may be that you can adopt BM without being a believing realist. But there would be no point in that really. Why adopt a theory that in every situation asks you to solve additional (but irrelevant) equations?

    2) Indeed, the micro to macro transition, the emergence of a classical world, and all that are complex issues. I agree that some of the Bohmians have done reasonable work in mathematical statistical mechanics. But they go all hazy when it comes to BM, and write pamphlets with fairly low mathematical content, discussing complex situations on the _assumption_ that things work out as they would like to have it. The “clarity” of BM is in just sticking with the equations and never ever solving them. The “simplicity” comes from not getting your hands dirty. So I am not at all impressed by the status of BM as a mathematical theory, although, as a mathematical physicist I would have enjoyed these discussions much more if Bohmians had done a better job and there was at least some mathematical substance to discuss (even though the physics would still be shaky).

    For your final sentence in that post: I agree that we are all prejudiced (and in this case in opposite directions). I thought this exchange was about sorting some of that out, but maybe it wasn’t.

    Hiding under a quantum carpet? Indeed I don’t have a definition of Reality, which I think is better than having a “definition” that sucks. This is because I am a realist in the broad sense of aiming at a kind of empirical science that wants learn from Nature, thereby getting closer and closer to whatever reality is. Just inventing a reality by identifying it with some objects in a mathematical framework concocted for that purpose is not a helpful step in that direction. So I am criticizing BM for not being realistic in the broad sense, and instead jumping to premature procalmations of “reality”.

    Combine your reference to Popper with the Einstein quote. BM actually does decide what can be measured, and there is a Bohmian Theory of measurement, which is a rehash of the formal theory of measurement by von Neumann, with the twist that the pointer is assumed to be identified by its Bohmian positions. According to that theory, what is measurable is exactly what is measurable in QM, definitely excluding all trajectory features beyond equal time position configuration. Since nothing can be learned about the trajectories, Popper would indeed tell you to scrap the stuff that can never be falsified empirically. But Popper was not just known for formalized methodology, brilliantly ridiculed by Feyerabend. He was also very much concerned with enlightenment, the “enemies of open society”, and their immunized truths. Even within just science the falsification idea still has some value as a good practice rule (not as a rigid principle). BM is pretty well immunized, and that does make it less convincing for me, although I am not a strict Popperian.

    Just a brief remark on weak measurement as supporting BM trajectories (as in that recent experiment by the Steinberg group). That is complete bullshit. Of course, you can make measurements of the probability current. It is just another QM operator, and I don’t want to discuss here to what extent it is actually determined by the weak measurement, so let us assume it does. But this is a point by point statistical measurement, and only when those data are all in you can play connect-the-dots, and draw those trajectories. Nothing whatsoever in that experiment suggests that anything moves on those lines. Embarrassingly, both Detlef Dürr and Shelley Goldstein have cited these experiments as providing empirical support for BM (I just checked the reference of Detlef’s paper, and realized it is actually a joint one with Dustin). That is just dishonest.

    On the final sentence of your post: Whether BM will inspire any new ideas is anybody’s guess. Past experience shows that while the QM community has produced quantum information theory and many new results on statistical mechanics of large quantum systems (to mention just the corners I know best), the BM community has utterly missed these developments and has not come up with a single idea pointing to a hitherto unexplored phenomenon.

    So Frankenstein it is? This stitching together of different theories is not just very common in physics, there is no way without, if you actually want to come to conclusions that have some bearing on the real world. You may not like that, and completely opt out of the enterprise of connecting to real experiments. That is why called the cozy Bohmian world of just two equations Platonic. Often the stitching is quite loose, and I would see my job in many cases in improving it, i.e., strengthening the logical connections between different branches (preferably by a theorem). But at the micro-macro divide the distinction is quite clear, including the movability of the cut. In an image I got from Berge Englert: I your are standing at the beach with your feet in the water the exact border between sea and land may be impossible to define. Nevertheless the distinction between sea and land is perfectly clear in the bigger picture. Nothing is “gruesomely stitched together” here.

    Supposedly it is a virtue of BM to treat micro and macro on the same basis. I don’t think that is quite true when it comes to the theory of measurement, because all of that depends on assumptions of classicality (also made on the quantum/stat mech treatment of the theory) plus some extra ones on disjoint wave function supports for macroscopically distinct pointer positions, which are strictly speaking false (but Bohmians seem happy anytime to replace error estimates by hand waving, so no problem). Still the supposed virtue is that everything in the universe is treated by the same set of equations. But at the same time it is a problem, because you lose touch with reality.

    I get your point about the electromagnetic invisibility: If there are no charged particles around, only Bohmian ones, you don’t have to worry about fields anyway. The physics of electrodynamics is supposedly all in the traced out quantum electrodynamical field. But actually this is just what I meant: Bohmian particles are not so important agents in the game (indicated partly by them not even producing a field) so they can easily be eliminated. Let me just dwell on this a bit and on the question of Bohmian furniture.

    The standard picture of BM is that the positions of massive particles are real, spin isn’t and the quantum electrodynamical field isn’t either, since photons are not included with their trajectories. So the subalgebra of Real Things that you select is NOT maximally abelian, and you are happy to trace out some bits (like spin,…). So in order to see how the theory works, let us just play with that parameter a bit. Now I happen to be of the opinion (for the sake of this discussion) that Leptons are of secondary importance, since it is only their way of making Baryons move about which justifies even talking of them. Clearly, in good lowest order Born-Oppenheimer spirit, what defines the position of a pointer is its distribution of nuclei, which the electrons just help keeping together. So I think Leptons should be traced out along with the photons and the spins, i.e., should be De-Bohmified and stripped of their unearned Reality status. I think it is clear that all the things you usually say remains true in this simplified BM, in which only Baryons have trajectories and are Real. The joint distribution of Baryons will still be in BM equilibrium, but that distribution is now computed from the wave function (like formerly for spin), by tracing out the non-Real degrees of freedom. Good theory then, philosophically equivalent to BM.

    Now let us carry this process a bit further. I started after my last post with the furniture of my house, which is now no longer real. It still looks the same, because seeing involves photons, and they were not real in the first place (only their wave functions needed to tickle some molecules in my Retina). But even to touch it is still the same, because my finger’s Baryons still have trajectories (i.e., are Real). They move much the same way, only now it is the average position of the table’s individual particles rather than the individual positions entering the equations of motion. Not much can go wrong here, because the wave functions are anyhow the same, and at the macroscopic level, according to the Bohmian handwaving principle, they will behave as expected.

    You can see where this goes. I would next De-Bohmify Outer Space, then the rest of the world, including myself, but not you, Travis, because it would be impolite to take Reality away from a Bohmian. Imagine yourself to live in such a world (as you often asked me for BM). How would you like that? I think it should make you equally happy. Much happier than a solipsist, actually, who thinks he is alone in the world but isn’t, whereas your case would be the other way round.

    All the best, Reinhard

    Dustin Lazarovici

    Dear Reinhard,

    I really appreciate you sharing your point of view and I have thought (and will continue to think) about some of your arguments. If you don’t mind me saying: I believe that the discussion could have been even more productive, though, if you hadn’t been so polemic, at times. E.g. Bohmians don’t write papers or theses, they write “pamphlets”. I think that’s really unnecessary and disrespectful.

    My comment regarding the philosophical prejudices was just to challenge your claim that BM has to rely on naive philosophical ideas, while your (operationalist?) view doesn’t.

    In any case, what I take away as a criticism of BM is that it relies on a lot of “in principle” statements. Like: “In principle it’s possible to describe the measurement aparatus in a Bohmian way an receive the correct results.” I admit that the arguments we have to offer in support of these claims are a bit hand-waving. They rely on approximations and idealization.

    The Bohmian believes that he’s hand-waving about the “right” part of the theory. QM tells us that the measurement aparatus has to play a crucial role in “bringing about” the measurement outcomes and a measurement aparatus just is an extremly complex system from a microscopic point of view. Moreover, we believe that deriving the entire quantum formalism under reasonable approximations and idealizations is good enough to validate/corroborate the microscopic theory. The situation is, again, similar to classical statistical mechanics where kinetic gas theory is corroborated/valiadted by the fact that you can derive the laws of thermodynamics under reasonable approximations and idealizations.

    However, I understand and respect your position when you don’t see much value in such “in principle” statements and the “handy-waving” arguments we have to offer in support.

    Nevertheless, concerning also your exchange with Detlef and Shelly, I believe that the reason why we don’t have more rigorous results to offer are mostly pragmatic. The Bohmian community is small, our time is limited and many-body problems are very very hard. Most of us just don’t see much value in spending too much time and effort to proof a result that we understand / accept anyway and that – to be honest – still wouldn’t convince you or any other critic.

    Best, Dustin

    Miroljub Dugic

    Dear Dustin,

    I find your final words disappointing [“Most of us just don’t see much value in spending too much time and effort to proof a result that we understand / accept anyway and that – to be honest – still wouldn’t convince you or any other critic.”]. I am almost sure that what Reinhard reproaches to BM is manly about the attitude described by your words. In an interpretation, what might be more useful/important than the “proof a result that we understand” and how could you possibly know that nobody would be “convinced”? Such a motto fuels criticism towards BM.

    Best regards,


    Dustin Lazarovici

    Dear Miroljub,

    I believe the attitude I described has nothing to do with BM, in particular. Every mathematical physicist has to be very selective with the kind of problems he or she choses to work on. (Of course, this applies to every scientist, but to mathematical physics in particular, because the average time you have to invest in one publication is quite long).

    You could spend a lifetime on mathematically rigorous treatments of more and more realistic detector models in Bohmian mechanics. Ok, I must admit: the problem is actually somewhat interesting. Maybe someone will pick it up, eventually. There are just more interesting problems out there. (Not to speak of the sociological fact that it sounds like a real career killer for young scientists.)

    Anyway, I honestly doubt that Reinhard (or anyone else) would have seriously changed his attitude towards BM if Shelly or Detlef had invested a considerable amount of time to provide a satisfiying answer to his problem. Nevertheless, to the degree that Reinhard’s issues with BM are mathematical, we should be self-critical enough to say: ok, point taken, maybe we could do more and better work in this respect. I just don’t believe that, at its core, the controversy is really about mathematics or the alleged lack thereof.

    On a related note: Detlef and Shelly and Travis and others have spent many many years adressing all sorts of questions and objections about Bohmian mechanics. When another paper comes out, claiming to prove that BM is wrong, more often than not someone from the Bohmian community will make the effort to reply and completely eviscerate that argument.

    Unfortunately, it’s an empirical fact that no one who is fundamentally opposed to the theory (for whatever reasons) ever changes his mind when you resolve any concrete issue that he claims to have with Bohmian mechanics. This doesn’t mean that one should stop debating or answering serious questions, of course. It just means that there’s no point in jumping on every challenge that someone throws at you.

    Best, Dustin


    Dear Dustin,
    on the note of your pre-previous post: I take back the word “pamphlet”. What I meant is the kind of paper that starts with declaring mainstream QM to be deluded, in contrast to “exact” and “clear” BM. What is the point of this self-congratulatory note? Shouldn’t clarity be the result of an investigation and left to the reader to judge? And exactness should be obvious from the work, especially for a mathematical physicist. But it is just used as a code in reference to that unprofessioally silly quote from Bell calling QM “unprofessionally vague”. Anyhow, I agree we should value the bits of rational argumentation that may nevertheless be present in spite of appearences.
    As to theses: I find it a pretty bad topic for a thesis to prove the superiority of BM against some alleged opponent. What comes out might well look like a pamphlet. But that is not the student’s fault who is just being deprived of a chance to learn how science should work.

    To your last post. Again, my fault. If you find it not worth the while of Shelly and Detlef to discuss BM in detail, I clearly shouldn’t have bothered.

    So long, Reinhard


    I just wanted to highlight two ironies that I found in catching up with this thread.

    1. Re: the “surreal trajectories”, I find it somewhat amusing that people who basically think it’s impossible to say anything coherent about what’s really going on physically at the microscale, are nevertheless quite certain that (in certain cases) what BM says is going on is clearly wrong. By what standard, exactly, is it being decided that what BM says in these cases can’t be right? I’m happy to agree with Dustin and others that the story is somewhat surprising or unexpected based on some naive classical intuition or whatever. But isn’t it completely obvious to everybody that there are more options open to us than just (1) our naive classical intuition turns out to be exactly right in every detail, and (2) we have to completely give up and say nothing about physical reality at the microscale? BM provides a clear picture/story of what happens, which is occasionally surprising or counter-intuitive in its details, but which nevertheless gives exactly the right statistical predictions for things that are directly observable. I don’t claim to know whether BM is right or not, but I think it’s a near-certainty that whatever turns out to be right will have this exact character (rather than (1) or (2) above).

    2. Re: Reinhard’s criticism of Bohmian mechanics and/or Bohmians for using assumptions / approximations / hand-waving, when analyzing measurement and the emergence of macroscopic behavior, I guess (as Dustin already said) there is some truth there and maybe the Bohmians should accept it as a good challenge that our position would be stronger if we could make these sorts of analyses more rigorous. OK. But still, come on. However hand-wavy and approximate and unrigorous one thinks the (extant) Bohmian analysis of measurement is, isn’t it 100% crystal clear that the orthodox/operationalist treatment favored (e.g.) by Reinhard — in which literally new ad hoc rules are just made up out of whole cloth and postulated on no grounds whatever except that they seem to be needed because the basic micro-dynamical axioms started to output nonsense — is far far worse? The truth is that Bohm’s theory provides a theory in which it seems possible in principle to give a rigorous *analysis* of measurement. That is, compared to orthodox/operationalist perspectives, an incredible advance and achievement, and I think it is quite hypocritical for anybody who endorses the orthodox/operationalist perspective (which is just obviously much much worse in *exactly* this same respect) to criticize BM for the allegedly approximate/hand-wavy character of its analysis.


    Ok Travis, maybe we are getting somewhere.

    For (1) I would just ask you to avoid terms like “directly observable”. Not even position is in BM, as you well know.

    Does BM ever make “exactly” the right predictions? Surely not, because this depends on the additional assumptions. Actually, no theory ever makes “exact” predictions. You will realize this when you actually, finally, maybe, do analyze concrete situations. What you will need is the combination of whatever “exact” mathematical framework with a lot of dirty stuff, rough estimates, approximate models and all that. I will be the last person to hold that against BM. What I do object to is your pretending that you don’t need that.

    Of course, I am aware that none of you guys is actually interested in concrete physics, and that that is not the aim of BM anyway. But even when you want to just do in-principle physics, you should be more explicit about what kinds of assumptions will be needed. That is part of the theory. The simplicity of “just two equations” simply is a lie.

    What I expect will turn out is this: You will need the same kind of assumptions that QM needs (maybe suitably translated to BM language) PLUS some additional ones about orthogonality of macroscopic wave functions if you actually try to bring in effective wave functions and want them to satisfy Schrödinger’s eq. (See Rainer Plaga’s thread). The plausibility of these will need to be analyzed. Maybe someone even comes up with some theoretical arguments.

    It may be that BM “provides a theory in which it seems possible in principle” to analyze a measurement. It just hasn’t been done except by blanket nostrification of QM. So before you call anyone a hypocrite, clean up your own act. And please, please, drop those silly claims of “exactness”, which only show that you have no idea of how physics works.

    On that note, your desciption of operational QM as a theory “in which literally new ad hoc rules are just made up out of whole cloth and postulated on no grounds whatever except that they seem to be needed because the basic micro-dynamical axioms started to output nonsense” is very interesting. Where did you get that? Do you have a random generastor in the basement? It certainly does not relate to anything I ever did in the field or have seen done.

    Best, Reinhard

    Dustin Lazarovici

    Dear Reinhard,

    If a may add a word regarding the “hand-waving” objection (i.e. Travis’ point 2):

    The parts of BM that you describe as “fuzzy” concern the treatment of very complex, macroscopic system. This is the stuff that physicists always get somewhat pragmatic about. At least, I’ve never seen a mathematically rigorous treatment of a realistic detector (or measurement apparatus) in ANY theory.

    More importantly, the problems you want to challenge BM with, are all on the level of the wave-function and their Schrödinger evolution. These are problems that everybody has to face if he is willing to take quantum mechanics seriously and apply it to anything more than highly idealized microsocpic systems.

    Of course, if “standard QM” produces results that are relevant in this context (“decoherence”, “dephasing” etc.) it’s absolutely legitimate for the Bohmian to use them. But again, rigorous, quantitative results are very difficult to come by.

    If, on the other hand, you try to avoid these problems by simply denying the “universality” of quantum mechanics, by denying, for instance, that a measurement apparatus has a wave-function in the first place, then you have to face the criticism that your theory is vague and/or inconsistent because there just is no sharp divide between the microscopic and the macroscopic level.




    Reinhard, Could you elaborate on your statement that (even) position is not “directly observable” in BM? I don’t think you’re right, but then I’m not entirely sure what you mean. I would say that position is directly observable in BM in the sense that it is possible, according to the theory, to find out the actual position of some particle at some time. I’m guessing you wouldn’t dispute that (but I’m really not sure, because your ideas/criticisms tend to be obscured by a frothy layer of polemical rhetoric), but would consider it insufficient. That is, I think you assume that genuinely “directly observing” particle positions somehow has to mean monitoring them over time, with perfect accuracy, but without changing the trajectory from what it would have been in the absence of such monitoring. I would of course agree that if *that’s* what you mean by “directly observing” a Bohmian particle position, then you are right, you cannot do that. But I wouldn’t consider that an appropriate definition/standard for “genuinely observing particle positions”.

    (And then similarly, vis a vis the “surreal trajectories” business, I think the situation there is just that, some experimental setup which you might have naively expected to constitute a “genuine observation of the particle position”, according to BM, actually turns out, according to BM, *not* to be that. I again wouldn’t consider that as refuting the claim that it is possible to genuinely observe particle positions in BM: “anything that seems to me, naively, without really considering in detail what the theory says, like it should constitute a valid position measuring device, must actually be a valid position measuring device” is not the appropriate standard. What’s relevant is just that it is in fact possible, according to the theory, to observe particle positions — and you cannot ignore what the theory itself says about exactly under what conditions, and with what accuracy, and for which kinds of setups, etc., this is possible.)

    But all of this seems like the kind of stuff that you’ll just pounce on and denounce as worthless loose talk. So maybe it would be helpful to instead try to argue in the context of some simple but concrete example. Let’s take the “Einstein’s Boxes” setup, where there’s some particle that can either be on the left (psi_L) or on the right (psi_R), or perhaps a superposition of the two. Now imagine a position measuring apparatus with a pointer (initially in state phi_0) that is intended to swing to the left/right (phi_L/phi_R) to indicate the presence of the particle on the left/right. Let’s assume that the detector is ideal/perfect in the sense that, if the particle is prepared in the initial state psi_L, then the Schroedinger evolution of the combined particle/pointer system goes like this:

    psi_L(x) phi_0(y) –> psi_L(x) phi_L(y)

    and then similarly for the other case where the outcome should be certain:

    psi_R(x) phi_0(y) –> psi_R(x) phi_R(y).

    Now of course according to BM there is, in addition to the wave function, the actual particle positions X and Y. If we assume that the initial configuration X(0), Y(0) is random and |Psi|^2 distributed (where Psi = psi phi is the “Universal” wave function), then it is a theorem that this remains true over time. OK, so in the case that the particle is prepared in state psi_L(x), the final position of the pointer Y(t_f) ends up in the support of phi_L(y) with certainty. That is, the pointer definitely ends up veering left if the particle definitely started out on the left. And similarly for the other possibility.

    Now what about the case where the initial quantum state has the particle in a superposition of psi_L and psi_R? Well in this case, the actual position X(0) of the particle will be either in the support of psi_L or in the support of psi_R. (I assume that these supports don’t overlap.) Then the Schroedinger evolution of the universal wf is as follows:

    [ psi_L(x) + psi_R(x) ] phi_0(y) –> psi_L(x) phi_L(y) + psi_R(x) phi_R(y)

    which can be understood as two disjoint lumps in configuration space. The actual particle/pointer positions at the end, X(t_f) and Y(t_f), will end up in the support of one lump or the other, just depending on whether X(0) was initially in the support of psi_L or psi_R. So the pointer indeed registers the actual pre-measurement (“Bohmian”) position of the particle, and with perfect faithfulness/fidelity.

    That’s the kind of thing I have in mind when I say that “the position of a particle can be genuinely measured in BM”. I would be very interested to understand better exactly which parts of this you find wrong and/or so fraught with dubious handwaving as to be worthless. Is it for example that the measuring device is treated so schematically (as basically just a single particle, the pointer, with all the real details of the physical structure and operation of the device mocked up with some special interaction Hamiltonian between the “particle” and “pointer” which, to annoy you maximally, I didn’t even bother to write down)? Or is it the assumption that the two wave packets under consideration don’t overlap at all? So that, in a more realistic treatment in which there is some small overlap, it could occasionally happen that the pointer moves Right when the particle actually starts out on the Left, and vice versa, so the measurement is less than 100% faithful? Or is the problem that you think there’s some infinite regress, since the pointer position will be just as observable/unobservable as the original particle, so that this kind of schematic analysis just moves the problem back one level without really solving it? Or what? I’d really like to understand better exactly what you see as problematic.

    And then let me also clarify (again in the context of this simple example) what I meant to be saying about ordinary/operationalist/orthodox QM, when I accused it of just making up ad hoc rules on the fly. I meant, specifically, the need to apply “measurement postulates” (such as the collapse rule). That is, instead of treating the particle+pointer in a fully quantum way, which would obviously produce the entangled post-measurement state I wrote above, in which there is no particular fact about which direction the pointer is pointing (which I would say contradicts, or at least appears to contradict, what we see with our eyes in actual labs in this kind of situation), we treat the particle-pointer interaction as a “measurement” in which the normal dynamical rules (namely Schroedinger’s equation) momentarily fail to apply. And so we just say — in flat contradiction to what the unitary Schroedinger dynamics would apply — that the pointer, being classical rather than quantum, just magically ends up pointing Left or Right, with 50/50 probability, as a result of its interaction with the particle, which interaction also results in the wave function of the particle collapsing to either psi_L (if the particle magically points Left) or psi_R (if instead the particle magically points Right). Now maybe you will disavow this kind of “orthodox” treatment as not capturing what you, Reinhard, think is going on. If so, I’d love to understand better what you think is going on. But what I just described really is the orthodoxy — it’s what all the textbooks say, for example. And I don’t think anybody could dispute the claim that, compared to this orthodox treatment, the Bohmian analysis really adds something. It explains how the pointer ends up pointing in a definite direction, which (under the admittedly idealized setup assumed) correlates perfectly with the pre-measurement position of the particle, purely as a result of the two basic dynamical postulates, without any need for additional ad hoc “measurement postulates”. So let me re-assert my point from before this way: anybody who accepts this orthodox account, but who also criticizes BM for the allegedly hand-wavy and un-rigorous and unconvincing and ad hoc character of its analysis of this kind of measurement, is a hypocrite. Hopefully you can clarify exactly why this does not apply to you. =)


    indeed I have no problem with fuzzy assumptions, if you are honest about them. I would also clearly not object to Bohmians using arguments from QM. It is a different thing though, when the claim is that from “exact” BM you can derive QM, when that derivation is full of decoherence assumptions about the measuring devices. You could say that the claim of BM=>QM, and with it the claim that BM has non-zero empirical content, logically requires a solution of the FAPP measurement problem. You guys consider that a triviality (Bell coined the FAPP phrase to belittle all practical purposes), to me it is a pretty tall order. But without spelling these things out (at least a bit better) you can hardly speak of a “derivation”.

    Maybe I should remind you that operational QM does not have a measurement problem. The theory works just fine without setting up wave functions for the measuring apparatus (Nobody gets anywhere with that anyhow). If you ever came to analyze a concrete experiment you would be well-advised to the same, even as a Bohmian. In fact, you wouldn’t do your job right if you didn’t work from a macroscopic description of the devices. You would need to show that the particular choice of wave functions for the devices is irrelevant (like the device trajectories), because that stability is part of the definition of an experiment. So to answer your question: I do not assume a wave function for the apparatus. It may have one (whatever that means), and at some meta-level describing the apparatus in many body quantum terms (i.e., by statistical mechanics) may be an interesting problem. But that is not part of quantum mechanics as I know it.

    Best, Reinhard

    Miroljub Dugic

    Dear Reinhard,

    may i ask you for a clarification of: (A) “Maybe I should remind you that operational QM does not have a measurement problem.“, in conjunction with (B) “It may have one (whatever that means), and at some meta-level describing the apparatus in many body quantum terms (i.e., by statistical mechanics) may be an interesting problem.”?

    Why there is not a need for something like the (B) or FAPP in solving the classical Newton’s equations?

    Bets regards,



    I just meant that any observation in BM requires the description of the whole measuring apparatus in BM terms. As I was told recently (arXiv:1408.1651), it is morally wrong to think otherwise, even if position is meaasured. Of course, BM seems to have a special relationship to position and I have seen the agreement of the particle/system density with the QM configuration probability density cited as an argument for the “empirical equivalence” with QM. That may suggest a more direct link to some casual readers, but as I showed in the paper criticized in the above arXiv paper, you also get wrong results. Of course, on the other hand it is apparently not only morally right, but mandatory to consider the observation of a pointer’s position to be obviously given by Bohmian positions (In an earlier post you wouldn’t even grant a slight smearing, which I only put in to make the agreement a bit less demanding). I find this switch from “morally wrong in the small” to “obvious in the large” in need of better explanation.

    (Don’t get me started on surreal. On the one hand, since you don’t see the trajectories anyway, I don’t care too much. On the other, one can discuss whether they can be connected to other things we know, and physical intuitions of various sorts, for example those based on locality of interactions, which also do make sense experimentally. Bob Griffith’s examples go in that direction. )

    For your Einstein box example, I have to limit myself to a few comments. After all we are already two days overtime (relative to the workshop announcement). (1) It may surprise you, but the projection postulate is not part of operational quantum mechanics, for the simple reason that it is often not true. (2) A measurement of the right/left dichotomy can be described for many practical purposes by just assuming the rule for the probabilities. That this leads to a macroscopically fixed record is an assumption made before the theory even starts. Justifying that is not part of the theory. (3) If you do bring in the counter, making this an example of indirect measurement, then what you say about linearity and entanglement is undisputed. (4) If you think that what you call a pointer here leads to macroscopically fixed records, think again. You can easily reverse this “measurement” coherently (routine lab practice these days), which is certainly not prevented by assigning any “real” Y, which is every bit as elusive as the “real X”. So the Bohmian positions may be a justification for saying that things are always really somewhere, if that soothes you. But that is not the kind of certainty we demand of pointers. If your decoherence assumptions are sufficiently strong, i.e., if you establish that records remain fixed no matter how many people or machines look at them or interact with them in any of the typical ways macroscopic systems interact according to statistical mechanics (which is very special in comparison to full many-body quantum mechanics), then you would have a justification for calling your second thingy a pointer. Since the many body language is the only one you allow for the measurement device this is not an unreasonable request from me. For QM that kind of measurement theory is a nice-to-have, but quite unnecessary for either theory or applications. (5) The overlap of supports condition is an artifact of the position dogma, and quite often not satisfied. For me the fact that momentum eigenfunctions (or the projections for positive/negative momenta, to stay close to your example) is secondary. But I am too tired to sort that out for you. (6) Getting some notion of orthodoxy from the textbooks is an easy way to set up an effigy. I completely agree that there are many bad textbooks and confused texts by Bohr, and almost all are weak on foundational questions. But the theory is not just in textbooks, and it might be a more interesting target to get some best practice examples and test your theory on those (Or shoot at my textbook, when it comes out). What would it add? Do the trajectories actually give you an insight? Or is their only role, on honest inspection, to just be there and soothe your ontological pains? Would De-Bohmified furniture really look different to you?

    So long, Reinhard


    OK, yes, let’s wrap up. I appreciate your comments and they actually help me understand your view better. But I guess I would have to summarize by saying two things. One, you’re making a big fuss (as Dustin already pointed out) about the kinds of things (like schematic treatments of pointers and associated implied decoherence assumptions) that any quantum mechanical treatment of these issues will have to involve, at least for the forseeable future. Sure, we can all agree that it would be nice to have more realistic quantum mechanical treatments of macroscopic objects, with certain qualitative (but strongly motivated) assumptions about decoherence, etc., replaced by hard theorems. But it seems silly to me to think that there is going to be any kind of fundamental surprise here, and also silly to act as if these sorts of things are somehow uniquely or especially problematic for Bohm’s theory. And then two: it seems that the things that, in my opinion, Bohm’s theory does genuinely add to more orthodox treatments, you basically just dismiss with a shrug, on the grounds that, for you, the alleged problems that these alleged advances allegedly address, were never actually problems in the first place. I’m thinking here in particular of your remark that “operational QM does not have a measurement problem”. In so far as that’s true, it can only be true because what you mean by “operational QM” literally involves no attempt whatsoever to say what is actually going on physically in the quantum world. And to me it is just an expression of a very boring and stale and unscientific philosophy (think Osiander here), rather than some kind of insightful criticism of Bohm’s theory, to say that you elude all the problems that supposedly plague Bohmian mechanics simply by refusing to even try to aim at providing a realistic description. That’s not deep and it’s not insightful… it’s just a “betray[al of] the great enterprise”.

    Anyway, that’s how I see things after this interesting exchange. Thanks again for your participation and, it being your thread, I think you should get the last word if you want it.


    Looking back, I find my initial statement not so bad as a summary. In this exchange I did not see any argument suggesting that Bohmian trajectories should be taken more seriously than a fairy tale. Inventing some idle wheels for a theory and claiming that these now make the theory more realistic is diametrically opposed to what I would call realistic. The main differences are hence in the views about what science should be. These differences
    were indeed further clarified in our exchange, and that is what I will be taking home.

    Here are some items that came up in the exchange that may be worth thinking about for a Bohmian.
    (1) From Rainer Plaga’s question: What happens in a Bohmian mixed state preparation, when none of the apparatus basis states have “forever disjoint” position supports? Then even if the particle is dynamically decoupled, none of its effective wave functions will satisfy the Schrödinger eq. So this idea of making a wave function for a subsystem by plugging in the real value Y for the apparatus may cause more problems than it solves.

    (2) About fuzzy assumptions: I think it is not correct to say that everything is in two simple equations, which essentially need no further interpretation. When it comes to analyzing anything concrete experiments much more has to be brought in. If you want, you can think of operational QM as a pragmatic way of organizing this additional information, including standing assumptions about fixed measurement results. BM needs these too, but has to express them, much less transparently, in terms of many-body apparatus wave functions. This is the place where everything becomes hazy, very much in-principle, and a little bit dishonest.

    (3) The idea of De-Bohmification: This is a simple substitution test. Use the current treatment of “unreal” variables like spin and apply it to some of the positions. This new theory, except for the slightly artificial real/unreal distinction, has exactly the same arguments going for it as BM. Try to honestly answer the question whether you would notice the difference. Travis found the idea of doing without the trajectories “crazy”. But is it any more crazy than just forgetting about the ether?

    Anyway, thanks for participating.
    So long, Reinhard

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