I was reading the thread about wave particle duality linked from the newsletter, and I noticed it said (to use my own words) that the conflict between wave and particle dynamics can be avoided by using operator dynamics instead. Unfortunately, in the case of phonons, I've never seen a description that takes advantage of this. It always sounds to me like essays about phonons start out by talking about atoms vibrating -- apparently using the word "vibrating" in the classical sense -- and the waves of vibration are metaphorically particles, and then presto the metaphor becomes an equation. What would make more sense to me is: 1. What are the ladder operators of a phonon, in terms of those of the electrons and nuclei in the material? (That is, actually using operator algebra, not just handwaving.) 2. Does the canonical relation between the two ladder operators follow from algebra, or is it inferred from experimental evidence? (or both?) 3. What puts these operators on a par with those of actual particles in terms of physical existence, rather than just pulled out of a hat?