Comments on Bohmian mechanics

This topic contains 2 replies, has 3 voices, and was last updated by  Aurelien Drezet 3 years, 9 months ago.

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    Richard Healey
    Richard Healey

    Where a Bohmian theory exists that is empirically equivalent to a quantum
    theory, the Bohmian theory postulates additional structures while implying
    they are empirically undetectable. Pursuing the Bohmian research program
    today is like pursuing a Lorentzian research program in the light of special
    and general relativity. To do so is both physically and philosophically
    unmotivated. Relativity theory represented a great epistemological advance
    by showing absolute rest and absolute simultaneity to be not merely
    empirically inaccessible but theoretically superfluous structures. Quantum
    theory is epistemologically superior to Bohmian alternatives for the same
    reason that Einsteinian relativity is superior to a Lorentzian “conspiracy
    theory” in which the peculiar behavior of matter blocks all attempts to find
    out the true state of absolute rest.


    Richard, thank you for your stimulating contribution. I think you raise a number of extremely important points (that overlap with the issues raised by Reinhard Werner and Shelly Goldstein and by implication Max Schlosshauer). Of course I don’t really agree with your conclusion (that Bohm’s theory is plagued by a number of pointless/unobservable/metaphysical idle wheels, and is therefore a bad/unpromising/implausible theory) — but I applaud your efforts at raising these important issues in a direct and clear and forceful way!

    There is a lot that could be said in response to, for example, your point about the need (in Bohm’s theory) to posit a dynamically privileged but unobservable foliation of spacetime, and your point about the existence of distinct but empirically equivalent guidance formulas (for particles in a Bohmian version of NRQM and for field configurations or particles in a Bohmian version of QFT). But I want to (perhaps just temporarily) set those issues aside and focus on what I think is the most fundamental of your points, and also certainly the one that causes the most widespread confusion about the theory. I mean the claim that the particle positions/trajectories — the “hidden variables” that are added to the normal quantum wave function — are unobservable in Bohm’s theory.

    To begin with, you are correct that (basically) the exact trajectories — such as the trajectories one always sees plotted in Bohmian discussions of the 2-slit experiment — are not measureable/observable, according to the theory. (I say “basically” because one can quibble with some of your comments about weak measurement. As Einstein pointed out, the theory decides what can be observed. For sure, if one adopts the perspective of some more or less orthodox version of QM, the alleged “weak measurement of velocity” is not at all a genuine measurement of the velocity of a particle… there are no particles according to that theory! But if one adopts the perspective of Bohmian mechanics, actually those same “weak measurements of velocity” *do* count as genuine measurements. But really that’s not what I want to talk about…)

    OK, so the detailed trajectories are basically unobservable. From this, I gather, you basically infer that the particles (whose exact trajectories are basically unobservable) are pointless — we could get the same empirical predictions out by just dropping the particles entirely, and just basing the empirical predictions on the wave function alone, as in ordinary QM. This, I think, is completely wrong. It is based, I think, on a completely wrong way of understanding what Bohmian mechanics is and is trying to do. I mean the idea that Bohmian mechanics is a theory that is basically just orthodox QM, but with some “hidden variables” added. I mean the idea that, for example in the context of the 2-slit experiment, one thinks of the particle source and the slits and the screen and the lab bench on which all this equipment is laid out (and so on) as some kind of given, “classical” stuff which is *not* treated quantum mechanically and hence just unproblematically exists in an unproblematically observable way, while only the particles being shot through the slits are treated quantum mechanically, with that quantum description (for Bohm’s theory) involving *both* a wave function *and* a definite particle position.

    I would agree that, as long as you are thinking of Bohm’s theory in that way, the particles (and hence their exact positions/trajectories) are pointless. But, as I said, that’s just not the right way to think about it.

    Instead, I think, one really has to take seriously the idea that Bohm’s theory is a theory of the whole universe — not just some one tiny little corner of the universe that one segregates off as “the quantum system”. It’s not just the particles being shot toward the slits which one should be thinking of as described by Bohm’s theory, but also the particles composing the shooter, and the barrier with the slits in it, and the detection screen, the lab bench that all this is resting on, the experimenter who put all that stuff there this morning, the entire planet where all of this is occurring, and … *everything*. The whole physical world (of everyday macroscopic experience), that is, is — according to Bohmian mechanics — made of these Bohmian particles. So while it may be true that exact detailed microscopic trajectory of individual particles is (according to the theory) not observable, it is just completely and utterly wrong to suggest that the particles are unobservable, full stop. Literally every time you open your eyes and observe something — a chair, a friend, a distant planet through a telescope, etc. — you are (according to Bohmian mechanics) observing (some macroscopic features of a large collection of) Bohmian particle positions.

    From the perspective of Bohm’s theory, then, the suggestion that one could just get rid of the particles and still have some sort of viable theory, is insane. By getting rid of the particles, you’d be getting rid, not just of some invisible microscopic thing whose detailed properties are unobservable anyway, but of all the furniture in your house, and your house, and your friends, and yourself, and the whole Earth, and indeed the whole observable physical universe! Crazy. (I don’t mean to suggest here that no theory other than Bohmian mechanics — no theory without particles with positions/trajectories — could account for our observation of tables and chairs and planets and whatnot. Maybe after all those things are not made of particles, but are instead made of fields or flashes or strings or some other sort of local beable. The point is rather just that all that stuff has to be made of *something*, and — to count as empirically viable — a theory better posit the existence of some such something and then better make predictions, for how that stuff moves around and interacts in physical space, that corresponds to what we in fact *observe* happening to the tables and chairs and pointers and planets and people… That is, the point is not that you have to have particles specifically, but rather that if you think you can just dispense with the particles, without replacing them with anything else, and maintain the kind of empirical adequacy that Bohmian mechanics enjoys, you have somehow grossly misunderstood — grossly underestimated — the role that the particles play in the theory.)

    Thinking that the particles in Bohmian mechanics are unobservable — and can hence be simply dispensed with — would be like an oceanographer thinking (say, on the grounds that the exact phase space point, of the entire collection of water molecules composing the ocean, is unobservable) that he might as well just dispense with the water molecules in his theory. If he does that, he’s just dispensed with the whole ocean, the whole really-existing (and unquestionably observable) thing he’s trying to study!

    So the point is that one has to be careful. It simply does not follow from “the precise trajectory of an individual particle is, according to the theory, unobservable” that “the particles are unobservable” — let alone “the particles basically play no role at all, they are just idle wheels, and we can get along just as well by simply dropping them”.

    There is of course a lot more to say, and a lot of details that can and should be argued through, but I think that’s enough to steer the discussion toward the “big picture” point that I think is simply being misunderstood when you (and, for example, Reinhard Werner) suggest that the Bohmian particle trajectories (qua “hidden variables”) are just pointless, functionless, dispensable idle-wheels.


    Aurelien Drezet

    Dear Richard, I would like to comment briefly on your suggestion that the so called orthodox interpretation of QM (OIQM) is better than the de Broglie Bohm approach.
    I think that the crucial element which is missing in the OIQM is a clear statement of what is ontology in QM. For Bohr the world must be described by something classical but he is not really able to say what does it really mean. The apparatus is at the end a quantum object and the point of Heisenberg and Bohr is that we must introduce a kind of cut or shifty split. Where does the split occurs this is the big issue in the OIQM and Heisenberg only pointed out that the position of the split is irrelevant. Of course, he was right in the sense that is now given by decoherence theory à la Zurek but still the ontology is not better that it was at the time of Bohr since the environment should be included as an observer in the interpretation. This is even more mysterious since the exact nature of the environment is illusive and also shifty. Do we need to say that the” Universe “ is an observer? For me the OIQM is paradoxical with or without decoherence. Consider the Schrodinger cat or the Wigner friend paradox ; these are examples showing that the border between what is described by the wave function and by the observer has an impact on the ontological nature of the object. The quantum system can’ t at the same time be and not here.! But remember: Following the OIQM the exact nature of an electron before a measurement by an observer is undefined. This is necessary for Bohr otherwise the electron could follow two paths at the same time (I.e. wave particle duality). So if this true for an electron is must also be true for an observer watching a second observer. I can not see how you can exit this circle in the context of OIQM (this was the point of Everett in his thesis). For me the role of the observer is too fragile its definition too mysterious to give a good basis for an interpretation of QM. We need something better something of clear and I think we should accept a realistic view to solve the measurement problem. Bohmian mechanics is the first step. It shows that this is possible. I do not think that the theory will survive in its current form but I believe that OIQM is a dead end for making progress in physics.

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