Reinhard Werner

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  • #2946

    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

    #2942

    Travis,
    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

    #2938

    Dustin,
    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

    #2921

    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

    #2893

    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

    #2871

    Dear Rainer (if I may),

    it is not completely clear to me what SQM is. In the operational account of the theory (let’s call that OQM) the only requirement on a preparation process is that the preparing system is dynamically decoupled from the ES and from whatever measuring device you plan to use. Entanglement between preparing system and ES is fine, in which case, of course, the prepared state would be mixed. That is not a conceptual issue. If the artful experimenter has achieved a pure state then, of course, the initial state was a product.

    If you insist that every system (including your ES) ought to be in an ontologically interpreted pure state (some people, but not OQM, consider that part of SQM), then you would perhaps demand some particular choice of basis on the preparing system, and the outgoing pure states would be conditional on that. The prepared density matrix would thereby represented as a particular ensemble of pure states. But any choice of basis will do (This is one of the ways to discuss the statistics of a CHSH-type correlation experiment). In particular, each of the outgoing pure states of the ensemble will satisfy the Schrödinger equation for that subsystem (which makes sense, because we assumed dynamical decoupling).

    Now in the Bohmian case you need more, as this theory rarely restricts to subsystems gracefully. In fact, they will probably sell this bug to you as a feature (the discovery of nonlocality) and say that anyhow the theory is not meant to work for any ES, but only for the whole Universe. If you want BM to hold effectively for the subsystem, you should take the “effective wave function” as described by Roderich. In an entangled situation the prepared system’s trajectory usually depends on the Y of the preparing device, and thus, for example on the dynamics of the preparing system, even long after, in SQM or OQM you have traced out the preparing system. That is, in BM you can usually not “trace out”. In particular, your conditional wave functions have no inclination to satisfy the Schrödinger equation of the ES. This is why you need an extra condition on the position space supports of the wave functions, as Roderich explained, which effectively puts you in a product situation, basically the only case where it works. There is no general physical reason I can see why that support condition should hold, and it is probably easy to come up with quite ordinary preparing processes where it does not.

    Bohmians usually argue that it “obviously” holds when the selection criterion on the preparing device is macroscopic. I have no idea what they would say if what is selected on such a pointer criterion is still mixed. Maybe call in an exorcist. Or do some more hand waving and wishful thinking. Or denounce such cases as artificial. Maybe somebody will even answer here.

    With best regards, Reinhard

    #2866

    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.

    Aurelien:
    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.

    Travis:
    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

    #2864

    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

    #2863

    Dear Jean,

    so BM is “a real theory”? As opposed to what? I also find your use of the attribute “rational” pretty strange. I suppose you would describe yourself as a rationalist, and I do like your book with Sokal on his hoax. But I think you are just mistaken that rationality is tied to some kind of ontology (as in that silly slogan that quantum mechanics must be about “something”). Rational thought is as much about relations as it is about things. So a scientific theory like quantum mechanics strives to build relations between contingent facts, and to understand special instances from overarching principles. None of this needs hypothetical mass points to be “realistic” or “rational”.

    In contrast, Bohmian mechanics contains a lot of stuff which is highly arbitrary, because unrelatable to experience. No rational argument about these aspects of the theory seems possible, and surely these features cannot be called realistic (in the broad sense) either.

    I was also puzzled by your description of BM as “deterministic”. You have that massive source of randomness stuck into the initial conditions by the Maker of the Unverse. That is a construction you can make in any probabilistic theory so in that way every probabilistic theory is deterministic. So even if you can argue that our universe just sits on one trajectory and still displays quantum randomness almost surely, the “almost” is with respect to God’s measure. So your randomness assumption can be rephrased as a “typicality” condition. Again you can do this in any probabilistic theory. So a more accurate statement would be that in BM randomness is shifted to -\infty.

    The “perfect clarity” is another puzzle to me. Every concrete question I ever followed up on in this theory ended in a heap of evasions. So I suppose you mean the sort of clarity you derive from scripture, in this case maybe the gospel “Unspeakables” by St. John, from which you offer readings in your long text.

    With best my regards,
    Reinhard

    #2861

    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

    #2796

    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

    #2766

    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.

    #2661

    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.

    #2660

    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

    #2637

    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.

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