Reinterpretation of classical physics in operator/amplitude/e.v.?

[jshrager]

Presumably it's easy to re-formulate non-quantum (i.e., classical) physics entirely in operator -> observable form (perhaps even to the point of using bra/key and amplitude^2 notation, etc -- although since macroscopic objects are supposed to be in a single location, everything would end up being delta functions, or something like that). Can someone point me to someplace that summarizes how this is done? (Maybe this should be a question for classical physics topic, but they might not know what I'm talking about.)

 

[NegativeDept]

I don't think it's easy, but if I understand your question right, it has been done:

Koopman-von Neumann mechanics

As Koopman and von Neumann demonstrated, a Hilbert space of complex, square integrable wavefunctions can be defined in which classical mechanics can be formulated as an operatorial theory similar to quantum mechanics.

This might also be relevant: I saw a talk from some people who worked on smooth transitions between KvN theory and orthodox quantum mechanics. They called it Operational Dynamic Modeling.

 

[jshrager]

Awesome! That *exactly* what I was thinking of. (I'd say something about great minds thinking alike, but it seems way too pretentious to compare my mind to von Neumann's! :-)

Anyway, thanks!

 

[NegativeDept]

I'd say something about great minds thinking alike, but it seems way too pretentious to compare my mind to von Neumann's!

I do that all the time. Whoa, cool, I've just made a big discovery! followed by Oh ****, [famous physicist or mathematician] already figured that out several decades ago and I just didn't know about it.

Von Neumann's name comes up a lot, though I think the all-time champion of I-already-thought-of-that has to be Gauss.