In what specific ways is Bohmian mechanics helpful?

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    I would like to know in what specific ways you have found Bohmian mechanics helpful (or unhelpful) in (1) thinking about a specific phenomenon or experiment (Gedanken, or real) in quantum mechanics, and in (2) working out the theory of this phenomenon or experiment. Examples, off the top of my head: quantum teleportation, quantum cryptography, decoherence, delayed-choice quantum eraser, no-cloning, quantum computation, quantum algorithms, weak measurement. Let’s exclude the double-slit experiment, since it has already been used so many times to illustrate Bohmian mechanics.


    Roderich Tumulka

    Hi Maximilian, I have a few examples. I am not sure whether they are of the kind you are interested in, but I thought I mention them nevertheless.

    Bell has a paper [Intl.J.Quant.Chem. 14 (1980) 155; reprinted in “Speakable and unspeakable in quantum mechanics” p. 111] on how Bohmian mechanics answers the question of whether a delayed-choice experiment involves retrocausation.

    There is quite some literature on how Bohmian mechanics helps for scattering theory; here is a selection of references:
    M. Daumer et al., J. Stat. Phys. 88 (1997) 967, arXiv:quant-ph/9512016.
    D. Durr et al., Lett. Math. Phys. 93 (2010) 253, arXiv:1002.0984.
    T. Norsen, Am. J. Phys. 82 (2014) 337, arXiv:1305.1280.

    People have also used Bohmian mechanics to consider the questions of how long a tunneling particle remains inside the barrier and whether it moves there faster than light. Two references:
    C.R. Leavens, in: J.T. Cushing, A. Fine, S. Goldstein (eds.), Bohmian Mechanics and Quantum Theory: An Appraisal (Kluwer, Dordrecht, 1996).
    And, again, T. Norsen, Am. J. Phys. 82 (2014) 337, arXiv:1305.1280.

    I personally found the Bohmian picture useful for studying the probability distribution of the time at which a detector clicks. I hope to write a paper about it one day.

    I have used Bohmian mechanics in the analysis of systems in thermal equilibrium, which has led to the use of the so-called GAP measure, a probability distribution over wave functions appropriate in thermal equilibrium [S. Goldstein et al., J. Stat. Phys. 125 (2006) 1193, arXiv:quant-ph/0309021]. The GAP measure was introduced without Bohmian mechanics (and termed “scrooge measure”) by R. Jozsa et al., Phys. Rev. A 49 (1994) 668, but no connection to thermal equilibrium was made.

    I am presently working on a paper with S. Goldstein and W. Struyve using Bohmian mechanics to evaluate the question whether Boltzmann brains will appear numerously in the late universe, assuming the late universe will be in the Bunch-Davies state on a de Sitter space-time.

    Best, Rodi


    Roderich Tumulka

    Here are some general remarks on the practical usefulness of Bohmian mechanics (in a rather random order). They don’t address Maximilian’s specific question but contribute to the overall theme of ways in which Bohmian mechanics is helpful.

    * Consider two theories making the same predictions: one clear, precise, and simple, the other unclear, vague, and complicated. Which one is better? There is no doubt that Bohmian mechanics is clear, precise, and simple (a complete definition fits on a single slide). Copenhagen QM is not completely clear (Feynman: “Nobody understands quantum mechanics”), and it is vague and complicated because of the measurement axiom that refers to observers and measurements (vague concepts, as nobody has a precise definition of which physical objects count as “observers”).

    * It is one of the goals of physics to find out how the world works; it would seem odd to say, now that Bohmian mechanics provides a coherent answer that standard QM could not provide, that we are no longer interested in this goal.

    * In the same vein, it is one of the goals of physics to find explanations of the observed phenomena. Again, it would seem strange to say we are no longer interested in explanations of, say, the double slit experiment–even more so in view of the idea, introduced by Bohr and eloquently elucidated for the double slit in Feynman’s lectures, that such an explanation be impossible. Let me add, I agree that it is one of the goals of physics to make predictions (and another to develop better technology), but there are also the goals to find out how the world works, and to find the explanations of the phenomena that call for explanation.

    * Bohmian mechanics has inspired some discoveries, e.g., Bell’s nonlocality theorem. (My own recent work on multi-time wave functions and interior-boundary conditions was inspired by Bohmian mechanics.) It may also be useful in the search for, e.g., a theory of quantum gravity.

    * Bohmian mechanics is easier to learn for students than standard quantum mechanics.

    * Bohmian mechanics has applications to numerical methods for solving the Schrodinger equation. (Experts find a higher efficiency if grid points are not evenly spaced but |psi|^2 distributed, and a higher efficiency if the grid points “move with the flow,” which is what Bohmian trajectories do.)

    * Let me draw some parallels with the following questions: Do we need mathematicians? Should students learn proofs (say, of the Gauss integral theorem)? Well, for practical physics computations it is usually not relevant to know the proof of the Gauss theorem, while it is very relevant to know the theorem itself. That is, a limited level of rigor is often sufficient for getting the right answer and efficient for getting it quickly. Nevertheless, sometimes math can get very confusing, and then it is useful to know the details of math facts. (E.g., how exactly is the delta function defined? And what exactly does it mean to say that the Laplacian of 1/r is -4 pi delta?) So, it is good that there are mathematicians who are very careful when formulating statements and proofs. (And, after all, what they do is correct.) The situation is a bit similar with Bohmian mechanics: Even if it is usually not necessary for finding the correct predictions, it can be useful to have a precise version of QM, particularly when QM gets confusing.

    * Bohmian mechanics provides some useful approximations for the computation of predictions, e.g., concerning the statistics of arrival times (when will the detector click?) and semi-classical approximations. While the predictions are the same in Bohmian mechanics and standard QM, and can be computed also without Bohmian mechanics, certain approximations are suggested by the Bohmian approach. To be sure, the approximation can equally be used if Bohmian mechanics is wrong (say, if collapse theories are right).

    * Bohmian mechanics permits an analysis of quantum measurements, while they are taken as primitive and/or unanalyzable in standard QM. In Bohmian mechanics, one can prove theorems about measurement. E.g., positive-operator-valued measures (POVMs, also known as “generalized observables”) arise from Bohmian mechanics through an analysis but have to be postulated in QM as an extension of the theory. As another example, I once used Bohmian mechanics to give a simple, clean, and clear-cut proof of a superselection rule (i.e., that certain superpositions are indistinguishable from mixtures), while standard QM could offer only hand-waving talk in support of this rule.

    * Bohmian mechanics also permits an analysis of issues with philosophical subtleties, e.g., (i) limitations to knowledge, (ii) quantum non-locality, (iii) tunneling times. (i) This is the phenomenon that some facts in the world cannot be completely revealed by any experiment; e.g., wave functions cannot be measured. (ii) Bell’s theorem says that entangled particles must undergo some action-at-a-distance (which cannot, however, be used for sending messages). (iii) Bohmian trajectories provide an obvious definition for how long a particle stayed inside the barrier during tunneling and a deconstruction of the allegation of faster-than-light motion inside the barrier. All of these examples have aspects that go beyond mere operational statements (“if we set up an experiment like this …, then the outcome will be x=… with probability p(x)=…”). And in all of these examples, the clear picture provided by Bohmian mechanics allows us to understand and deal with these aspects.

    * Bohmian mechanics takes away the need for philosophical contortions when explaining QM or talking about what happens in certain experiments or what happens out there in the world. (As an example of such a contortion, Bell mentions: “Was the world wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared?”)


    Hi Max, Thanks for your submission, which I think is an excellent one for stimulating some discussion about what people who like Bohmian mechanics find valuable about it. I have actually found Bohmian mechanics very illuminating in thinking about several of the things you mentioned, and when I first read your submission I thought “It would be good to write up a little note explaining, for example, how Bohmian mechanics helped me stop losing sleep over the delayed choice quantum eraser.” As it happens, I then went looking around some of the other discussion threads and found a nice post by Daniel Rohrlich, in the “time-symmetric theories” forum, where he claims that “retro-causality is intrinsic to quantum mechanics”. The example turns out to be closely related to the quantum eraser (and some other things) so I figured I’d kill two birds with one stone and talk about Rohrlich’s specific example instead.

    But first, I wanted to say something more general about why I like Bohmian mechanics. It’s true that it provides, I think, a very illuminating concrete model against which to judge claims of the form “Quantum mechanics conclusively establishes X!” (where X is, for example, the failure of determinism, or the existence of parallel worlds, or the metaphysically creative role of observation or consciousness, or …). That is, Bohmian mechanics provides a very convenient way of seeing that many, many claims that one hears about what QM proves/establishes/requires, are actually just wrong. The available data simply do not require those things. This sort of debunking is the purpose to which I’ll put the theory in my comments about Rohrlich’s example below. But to me that’s kind of a polemical side benefit, rather than the central reason that one should actually like the theory. That central reason is: it might be true. And what I mean by that is: Bohmian mechanics is the kind of theory that might actually be “the final word” about how things really work (at least, to the extent that you pretend that non-relativistic QM is empirically adequate). Orthodox QM, by contrast, has no chance (in my opinion) of being that final word — it is to me just unbelievable that there are really two different worlds (one “quantum” and one “classical”) with distinct ontologies and dynamics and then only vaguely-defined ad hoc rules for how those two worlds interact when they meet. That just can’t be right. It’s instead clear that orthodox QM is some kind of phenomenological makeshift that, virtuous and accurate though it may be in terms of its predictions, simply can’t be the final description of what’s happening in the world.

    Of course, Bohmian mechanics is not the only such viable candidate “description of what’s happening in the world”. There are a couple of different flavors of GRW type theories that are viable candidates; maybe (I’m skeptical, but maybe) Everett’s many worlds picture is such a candidate; and of course there are presumably many such viable candidate theories that we just haven’t thought of yet.

    I’m not sure if Bohmian mechanics is (again leaving aside issues about extensions to QFT, etc.) true. But it *might* be true. And that mere possibility is a remarkable achievement — something that many/most extant “interpretations of QM” cannot match. This is, in a sense, the same point that people have in mind when they claim that Bohm’s theory solves the measurement problem. But that, to me, is too negative a way to put it, so I’m trying to rephrase that point in more positive terms. Anyway, that’s what I regard as the central virtue of the theory. It might actually be true.

    Since this preamble got long, I’ll comment about Rohrlich’s example in a separate post…


    So… Rohrlich’s argument that “retro-causality is intrinsic to QM”. For some details, see Section II of Rohrlich’s paper “A reasonable thing that just might work”, which is here:

    The basic idea is as follows. Consider three people, Alice, Bob, and Jim, who share a bunch of GHZ-state particle trios:

    |GHZ> = ( |+z>|+z>|+z> – |-z>|-z>|-z> ) / sqrt(2).

    Rohrlich points out that if Jerry measures the spin of his particle along the z-axis, the remaining two particles (held by Alice and Bob) will be left in a product state (one of two possible product states, really, depending on the outcome of Jerry’s measurement). Whereas if instead Jerry chooses to measure the spin of his particle along (say) the x-axis, the remaining two particles will be left in an entangled state. So the idea is that Jerry can *control* whether Alice’s and Bob’s particles are entangled, or not. And this of course has observable consequences: Jerry can control whether (at least once the data are later appropriately binned according to Jerry’s outcomes) Alice’s and Bob’s measurements are, on the one hand, totally uncorrelated — or, on the other hand, so strongly correlated that they violate a Bell inequality.

    So far so good.

    But then Rohrlich goes on to point out that the above remains true even if Jerry’s measurement on his particle happens *after* Alice and Bob have already made their measurements and recorded their data. So it seems that Jerry can control whether or not Alice’s and Bob’s particles were entangled (at the earlier time of Alice’s and Bob’s measurements) — i.e., Jerry can control whether or not Alice’s and Bob’s outcomes violate a Bell inequality — by his free and *later* choice about whether to *later* measure his particle in the z- or instead the x- direction.

    Here is Rohrlich: “[All this] nicely illustrates the fact that quantum mechanics is retrocausal…. On the one hand, there is no reason to doubt that Alice, Bob, and Jim have free will. Indeed the results of Alice and Bob’s measurements are consistent with whatever Jim chooses right up to the moment when he decides to measure [spin along z] or [spin along x] on each of his particles and record the results. On the other hand, there is no doubt about the effect (in Jim’s past light cone) of Jim’s choice. After Alice and Bob obtain the results of Jim’s measurements (within his forward light cone) they can reconstruct from their data whether their particles were entangled or not at the time they measured them. Thus quantum mechanics is retrocausal….”

    It’s maybe not clear whether Rohrlich means to claim that the particular candidate theory “orthodox quantum mechanics” is inherently retro-causal, or instead the more general claim that *any* empirically viable quantum theory will have to be retro-causal. If the latter claim is intended, though, it is definitely false, and we can see that it is false by considering what is going on in this experiment according to Bohmian mechanics.

    I don’t want to write out all the technical details (which are trivial anyway), so here’s the gist of it. The important thing to consider is the “effective [or here, equivalently, conditional] wave function” of Jerry’s particle at the time he ends up making his measurement. This is the “one-particle wave function” that, in Bohmian mechanics, can be understood as guiding the particle in question along its deterministic trajectory through the Stern-Gerlach apparatus (or whatever). See, e.g., my paper on “The pilot-wave perspective on spin” if these concepts are unfamiliar:

    Anyway, in the case that Jerry is the first to make a measurement, the conditional wave function of his particle is such that (for the standardly-assumed statistical distribution of possible Bohmian particle positions within the wave) his outcome is 50/50 random, no matter what axis he measures the spin along. As a result of his measurement, though, the conditional wave function(s) associated with the other two particles change (non-locally, to be sure) and hence the subsequent trajectories of Alice’s and Bob’s particles are different from what they would have been had Jerry instead made a different (or no) measurement.

    In the other case, though, where Alice and Bob perform their measurements first, Jerry’s outcome turns out *not* to be 50/50 random for all measurement directions. For example: suppose Alice measures her particle along the x-axis and Bob measures his particle along the n-axis (60 degrees toward the y-axis from the x-axis… just the kind of measurements we’d expect them to be making if they planned on seeing later if a Bell inequality was violated) and suppose that Alice and Bob both find their particles to be “spin up” along the measured direction (this will happen, according to Bohmian mechanics, some of the time, depending on the exact initial positions of the various particles). Then it turns out that the conditional wave function of Jerry’s particle is such that, if Jerry measures along the z-direction, his outcome is 50/50 random… *but*… if Jerry measures along the x-direction, there is a 25% probability that his particle will be “spin up along x” and a 75% probability that his particle will be “spin down along x”. It’s not 50/50 random at all.

    To be sure, there is nonlocality here: Alice’s and Bob’s measurements change the state (meaning, here, the conditional wave function) of Jerry’s particle and hence (sometimes, maybe) cause it to emerge in a different direction from the Stern-Gerlach device than it would have (even for the same initial position of Jerry’s particle!) had Alice’s and Bob’s measurements been different (or not been done at all or had they come out differently). So there is non-local (faster than light) causation, but no retrocausality. So the claim that the phenomena in question require retrocausality is simply wrong. The feeling that there is somehow something retro-causal going on, is in fact just a result of the false assumption that Jerry’s measurement outcome is “really 50/50 random” when, in fact, in the relevant cases, it’s not. What maybe vaguely looks like retro-causation from some perspective is instead, from the perspective of Bohm’s theory, just a matter of biased post-selection.

    Some random notes about all this:

    * Ordinary QM, with nonlocal collapse, also provides a (rather parallel) way of understanding why retrocausality isn’t required in this kind of situation. I say it’s “rather parallel” because what I said about the Bohmian conditional wave function of Jerry’s particle above is just exactly the same as what ordinary QM would say happens to “Jerry’s particle’s wave function” after Alice’s and Bob’s measurements collapse the overall 3-particle state. Of course, I prefer the Bohmian account, even for this polemical purpose, because, well, Bohmian mechanics might actually be true.

    * The same exact ideas apply (in almost exactly the same exact way) to the delayed choice quantum eraser. There too, there is (at least according to Bohm’s theory) no backwards-in-time causation. There may be faster-than-light causation (depending on exactly what quantum eraser setup one is talking about) but really the appearance of retrocausation is fully explained in terms of biased post-selection.

    * And finally note that the basic idea here is really quite simple. Roderich Tumulka linked above to Bell’s nice article about Wheeler’s delayed choice (thought) experiments, explaining how there’s really nothing retrocausal (or, frankly, nothing the least bit weird *at all*) going on, according to Bohm’s theory. That’s definitely worth reading/reviewing. And here’s another simple example that I think brings out (what is, from the Bohmian point of view) the error in Rohrlich’s reasoning quite simply. Consider the EPRB situation — a pair of spin-1/2 particles in the singlet state. Suppose Alice and Bob are just both measuring their particles spins along the z-axis. The outcomes are of course perfectly (anti-) correlated. Well, you might argue as follows: “suppose Alice measures first and Bob measures second; Bob’s measurement outcome is 50/50 random (because QM); but the results are perfectly (anti-) correlated; so it must be that Bob’s result retro-causally affects the state of Alice’s particle, prior to her measurement, and hence affects the outcome of Alice’s earlier measurement!!” But of course that is silly. I mean, that’s one logically possible story, I suppose, but it’s hardly required. It’s perfectly possible to explain everything without retrocausality — by just allowing that Alice’s measurement (which happens first!) non-locally influences Bob’s particle (and hence the outcome of his subsequent measurement). See my paper on spin, linked above, for details about this case. I think, when the dust clears, it really is equivalent to Rohrlich’s more complicated case — the error in both arguments comes down to assuming (unjustifiably and wrongly, from the Bohmian point of view) that some later measurement is “really 50/50 random”.


    Dear Roderich and Travis,

    Thanks a lot for your insightful replies. I’ll dig up some of the references you listed. And I certainly agree with Travis that no retrocausality is required to explain the delayed-choice experiments.



    Miroljub Dugic

    Dear Roderich,

    while trying to learn more about Bohm’s theory, i cannot detect Bohmian mechanics in quant-ph/0309021. Could you please help me by pointing out the essential points (conceptual or technical)?

    Best regards,



    Dear Max,

    don’t expect too much. There will be nothing for teleportation, computation, no-cloning etc except a blanket “nostrification”, i.e., the claim that if QM can do it so can BM (because, allegedly, BM==>QM). But the analysis of trajectories will add nothing at all to the understanding of these structures, because, to begin with, it is all in variables which are not position, so not on the radar of the theory (except by reading the position of some pointer at the very end).

    In fact, do not expect anything for arrival times or even the double slit either. Why do find people the double slit paradoxical? Because they wonder how it can make a difference to a particle going through slit A whether or not slit B is open. The Bohmian answer here is exactly the “shut up and calculate” answer: You just have a different boundary condition, so you have to recompute the wave function, stupid. (Only in the Bohmian case you should compute a bit more fore the guiding eq.) Basically, you are merely told “this is just a manifestation of quantum non-locality”. Drawing a bunch of trajectories on top of the wave functions adds nothing you could call an “explanation” for anyone who found the slits paradoxical in the first place.

    About arrival times, Roderich seems to think that this is a good project. It is not, because there are two very distinct issues. One is the first hitting time of the Bohmian or Nelsonian position process. Whatever you will find is not quadratic in the wave function, so (as Bohmians are fully aware) will NOT be what you read on your measuring device. So if Roderich is interested in “studying the probability distribution of the time at which a detector clicks” (as opposed to “the time at which a Bohmian particle hits a surface”) his best option is to scrap the Bohmian approach and do some honest QM. I worked on that in the 80s, and I can tell you that there are several ways of doing that, in varying degree of detail, even though most of the standard textbooks do not cover this.

    Best, Reinhard


    Aurelien Drezet

    Dear Max, Here is my reply to your question and to the provocative comments by Reinhard Werner .
    First of all, BM offers a much better perspective than Copenhagen concerning describing what is reality. Reinhard Werner gives strong criticisms about the Bohm program but I think that his view is somehow misleading because he is unable to clearly understand that point. 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 you could conclude with him that it is metaphysical. However, I ask him now what does he means 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 forger: Theories always come before the experiments (I am both a theoretician and an experimentalizing 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 Reinhard Werner we could say that the paths predicted by BM are surrealistic (actually it was Scully which 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). 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. 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 an environment an infinite number of Wigner’s friends? 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 ? Anyway, I agree with Reinhard Werner 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 masse 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.


    Miroljub Dugic

    As a layman in Bohm’s theory, may i ask for a brief explanation of how is it possible for the particles having ontologically definite trajectories not to radiate EM waves?


    Aurelien Drezet

    It is a bit late sorry, the server is making strange things like posts disscuned in mail but not appearing on this web page. I wrote you this answer a couple of days ago but it got lost :

    Dear Miroljub Dugic, I have presently no idea how to give a clear answer to that question (Bohmian Mechanics is a program of research in this domain). What I can tell you for now is that the non relativistic version of BM exists with external potentials. This works very well. Then you have the model proposed by Bohm for quantum EM fields where bosons are described in a different ways as electrons. In principle so your answer is in that work (even if I dont like it too much because it is strange for me that photon are not playing the same role as electrons as particles). However, I dont think that anyone has developped a good model of QED in the context of bohmian mechanics so that your question has no good answer even if the maths will tell that indeed the electron do not always radiate in agreemeent with QM . In my view BM is sill waiting for something deeper in the relativistic domain and the answer to your question will come in this context. Probably BM is not the only guiltyguy and relativistic BM shares the complete responsability as well. This is one of my topic work but I have unfortunatelly not so much time devoted to Bohmian mechanics currently (students are demanding).

    with best regards



    Dear Miroljub,
    you might also ask in the same way why, if a hydrogen atom in the ground state is a static configuration (as in BM), a gas of such things does not behave like a gas of permanent (though random) dipoles but like a gas of neutral particles. The difference would indeed be massive, and I heard Berge Englert raising this question.

    Travis’s answer on the other thread is the standard Bohmian one: All interaction between particles must be via the guiding equation, so they are stripped of all physical characteristics except position. As Aurelien points out this would suggest that you either stick with Coulomb potentials only (hence deny transitions to the ground state), or you include an electromagnetic quantum field in your Hilbert space part, but leave the photons without trajectories.

    It is maybe unfair to ask Bohmians about how to incorporate the radiation field. This is not easy for QM either. Certainly no one today can just drop the Coulomb interactions and replace them by a non-perturbatively treated QED field. There has been some good progress in terms of the Pauli-Fierz Hamiltonian, like showing tat the ground state of field+atom is really what we think it is, and excited states do decay sending out photons with the right frequency etc. So this might be a reasonable level.

    By definition the Bohmians have it all covered, no matter what physicists come up with. In this case: Trace out the photons. They are not real and do not have or need any trajectories.

    Best regards, Reinhard


    Miroljub Dugic

    Dear Aurelien and Reinhard,

    to me, your answers indicate the possible foundational incompleteness of BM.

    When i teach my students why such a strange theory like QM has ever appeared, i have to prove nonstability of the Rutehrford’s model of the hydrogen atom. Like every mastery, physics requires different tools — classical mechanics and electrodynamics in this case.

    Now, if the analogous analysis in the context of BM leads to nowhere… I don’t understand how could we ever believe in ontic reality of quantum particles.

    On the other hand, the standard open systems theory clearly accounts for all the constituent ‘systems’ and fields and clearly says what’s been known from the outset, that all [nonrelativistic] quantum systems are open, including all the atomic species.

    Finally, Reinhard, thank you very much for mentioning different partitions of the hydrogen atom. As much as i can see [and have seen in the last 15 years with my collaborators] quantum mechanics equally, and equally successfully, regards arbitrary decompositions into subsystems (including ‘virtual particles’). Just to be fair, here i note the following link: .

    Best regards,


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