Reply To: On the single-particle Bohmian account


Just briefly, re: the point that an “energy measurement” (of the sort discussed above) doesn’t reveal the true pre-measurement energy of the particle… First, I don’t think it’s even clear what the true pre-measurement energy of the particle would be, according to Bohm’s theory. There is, in some sense, no such dynamically meaningful property according to the theory. (Of course, one could just make something up — as people indeed do — and call that “the energy”… but it wouldn’t, for example, be a conserved quantity… so there’s really no particular reason to define it in any particular way, and hence no particular reason to define it, or talk about it, at all.)

And then the more interesting second point about this: it shouldn’t be surprising that not every measurement can just reveal some pre-existing value of some associated property. We know, from the various no-go theorems (Kochen-Specker, Bell considered in a certain way, etc.) that at least some properties in theories like this will have to be “contextual”. Now often, in discussions of such no-go theorems, the idea of properties being “contextual” is regarded as some very strange kind of thing that would require a lot of obviously-implausible ad hoc put-in-by-hand fix-ups. But one of the really wonderful things about Bohm’s theory is that it shows how exactly the required sort of “contextuality” can come out, trivially, from a kind of brutally obvious dynamics, without anything even remotely resembling “implausible ad hoc put-in-by-hand fix-ups”. The particle is just guided by the wave function in the standard way, and this turns out to imply that, for example, if you “measure the energy” using some “time of flight” type procedure, you’ll get exactly the QM-predicted outcome statistics, and the outcome will be determined (once the completely particle state *and the details of the procedure by which the “measurement” occurs* are specified), even though the “measurement” isn’t really a measurement at all in the sense of revealing some pre-existing value of some dynamically-meaningful quantity.

My paper “The pilot-wave perspective on spin” discusses this point in some depth in the case of spin measurements, where the “contextuality” manifests itself in the fact that two distinct setups, which would both be regarded as valid ways of “measuring the z-component of the particle’s spin”, can give *different* outcomes even for the exact same particle-state input:

And then, yeah, I completely agree with you that there are lots of different potentially promising jumping-off points for our shared goal. Perhaps more on that later… =)

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