nnope said:
Yep you've completely lost me...
I'll try one more time, which you are welcome to ignore.
* Classical Mechanics uses an ontological (state of reality) based description of phenomena. A particle is defined by a set of variables that always have specified (though possibly unknown) values we observe and which dynamically evolve over time according to dynamic laws.
* Quantum Mechanics (if you don't take the phrase "state vector" too literally) uses a praxic (same root as pragmatic and practical) based description of phenomena. A quantum is a correlation between an emission event and detection event, which we represent with the "bra" and "ket" of the Hilbert space/dual space pair. The "state" vector is better named a "mode" vector as in "mode of production" or dually "mode of registration".
The language of QM is more active and as such more general. We can always actively describe objective states but when you get into the details of QM and look at such peculiar implications as Bell's inequality violation, you find that there's actively describable phenomena that defy moderate objective description. It's like owning a helicopter instead of an automobile. There's just more places to see off-road.
A final note. We are very strongly predisposed to think in an object based way. This is because we evolved doing such things as throwing rocks at rabbits for food and fur rather that tossing individual electrons or photons through diffraction gratings. Quantum descriptions are counter intuitive for much the same reason as relativistic descriptions are, we likewise don't run around very often at appreciable percentages of the speed of light relative to each other with very accurate watches. We all stay pretty much the same speed as our planet. It takes study of the mathematics to internalize implications and get a "feel for" or intuition of relativistic behavior. It is doubly hard for QM since there's no analogies to help us. The underlying paradigm of description is different in an essential way.
There is one domain of daily experience where we (hopefully) do forsake objective descriptions for more praxic active ones. That is in human relations. I hesitate to start here as one may confuse my comments as advocating the mystics "quantum consciousness" BS. But taking this as an analog of using distinct types of description note that...
When we attempt to observe the "state of mind" of other people we must interact, and in so doing the very act of asking questions, or putting them through tests will alter them in a way that defies objective descriptions. Even if the observer is carefully hidden, the nature of a specific observation requires the individual be placed in a specific scenario. The individual is changed by that experience. A study of social phenomena has many of the same issues as QM with regard to observation of the phenomena each studies, acts of observation do not commute. Although we will use objective labels on individuals we mostly all acknowledge that these are fuzzy categories and what defines us is how we behave.