Scott: Thanks, that clarifies it. (As far as the, what now I look up and find to be the partial trace thing)
Scott and Eliezer: As far as what density matricies “really physically are”… well, this isn’t an answer so much as a notion of what form the answer might take: Since the laws of probability and rationality are LAWS rather than “just good ideas”, it isn’t entirely shocking that there’d be some mathematical object th that would seem to act like the place where the territory and map meet. More to the point, the some mathematical object related to the physics that says “this is the most accurate your map can possibly be given the information of whatever is going on with this part/factor of reality.”
Alternately, since our map has to be encoded physically. ie, the map isn’t the teritory, but the territory contains the map, then not too shocking that there’s something about reality that could tell us something semidirectly about maps.
I may just be reshuffling my confusion here. In fact, I pretty sure I am, but it does seem to me that something like what I said above is possibly “what a density matrix ‘really’ is”
Scott: Thanks, that clarifies it. (As far as the, what now I look up and find to be the partial trace thing)
Scott and Eliezer: As far as what density matricies “really physically are”… well, this isn’t an answer so much as a notion of what form the answer might take: Since the laws of probability and rationality are LAWS rather than “just good ideas”, it isn’t entirely shocking that there’d be some mathematical object th that would seem to act like the place where the territory and map meet. More to the point, the some mathematical object related to the physics that says “this is the most accurate your map can possibly be given the information of whatever is going on with this part/factor of reality.”
Alternately, since our map has to be encoded physically. ie, the map isn’t the teritory, but the territory contains the map, then not too shocking that there’s something about reality that could tell us something semidirectly about maps.
I may just be reshuffling my confusion here. In fact, I pretty sure I am, but it does seem to me that something like what I said above is possibly “what a density matrix ‘really’ is”