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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.