Quantum mechanics out of the cradle
May. 2nd, 2004 09:37 amAnother comment on Afshar's optical experiment: I suppose that the real point of this (which may well have been Afshar's actual point, as opposed to Cramer's—I suppose we'll know when he publishes) is that people who talk about the interpretation of quantum mechanics are often too hung up on buzzwords from the early days of the theory, such as "wave/particle complementarity". That whole business about quanta being particles sometimes and waves sometimes turns out to be just a limited special case of a whole family of statements about the measurement of non-commuting operators. By moving the operators away from the ones used in the simplest and most famous examples, you can get results that don't really fit the slogans of the 1920s. I don't think that Afshar's result really invalidates the most popular interpretations of quantum mechanics, but it probably does invalidate a pat analysis in terms of things being either particles or waves all the time. There are all sorts of possible in-between situations.
In fact, one of the things that makes me somewhat uncomfortable about interpretations like Cramer's is that they seem more committed to an old-fashioned waves-and-particles analysis than the more popular modern interpretations are. This also makes me leery of Bohm-type pilot-wave hidden variable theories. The advocates of such interpretations usually have means of extending them beyond single-particle QM, but they tend to seem excessively elaborate to the uninitiated, or at least to me.
All that said, there is something special about the basis of states in which particles have strongly localized positions. Namely, position tends to be easy to measure (to some limited precision) because the interactions in known physical laws are local in the position basis, but not in other bases. (This is a point that Sidney Coleman particularly likes to make.) Most of the puzzlement you sometimes see about the privileged nature of the position basis can be resolved by thinking about that. The picture of a particle as a tiny hard object that hits things like a BB comes, not out of the operator formalism of QM, but from a property of dynamics that, from the perspective of QM itself, is a contingent fact (and that breaks down in such extensions to the standard model as string theory). This contingent fact, though, is probably why interpretations that lean heavily on waves and particles do as well as they do (this is particularly amusing for Bohm's theory, which itself is extravagantly nonlocal on the sub-quantum level).
In fact, one of the things that makes me somewhat uncomfortable about interpretations like Cramer's is that they seem more committed to an old-fashioned waves-and-particles analysis than the more popular modern interpretations are. This also makes me leery of Bohm-type pilot-wave hidden variable theories. The advocates of such interpretations usually have means of extending them beyond single-particle QM, but they tend to seem excessively elaborate to the uninitiated, or at least to me.
All that said, there is something special about the basis of states in which particles have strongly localized positions. Namely, position tends to be easy to measure (to some limited precision) because the interactions in known physical laws are local in the position basis, but not in other bases. (This is a point that Sidney Coleman particularly likes to make.) Most of the puzzlement you sometimes see about the privileged nature of the position basis can be resolved by thinking about that. The picture of a particle as a tiny hard object that hits things like a BB comes, not out of the operator formalism of QM, but from a property of dynamics that, from the perspective of QM itself, is a contingent fact (and that breaks down in such extensions to the standard model as string theory). This contingent fact, though, is probably why interpretations that lean heavily on waves and particles do as well as they do (this is particularly amusing for Bohm's theory, which itself is extravagantly nonlocal on the sub-quantum level).