Originally posted by DeepThought
In classical physics theory the observation is identical to the property. Rather than say: "We observe the particle to be at position x." we say: "The particle is at position x." - the theory allows us to make [b]continuous observations which don't alter the experimental outcome so there is no particular epistemological problem with ignoring the obs ...[text shortened]... ishes entirely if the basic quantities are matrix elements and the derived quantities positions.[/b]

In some sense, the notion that "observation" changes the state of a particle is really trivial - if you hit a balloon with a sledgehammer, you will change its state too.

In classical physics, "observation" doesn't do anything because classical physics is obtained from quantum physics by replacing all the observables by their expectation values. Thus, one can interpret classical physics as the quantum physics where all wavefunctions have already collapsed.

Originally posted by KazetNagorra
In some sense, the notion that "observation" changes the state of a particle is really trivial - if you hit a balloon with a sledgehammer, you will change its state too.

In classical physics, "observation" doesn't do anything because classical physics is obtained from quantum physics by replacing all the observables by their expectation values. Thus, ...[text shortened]... terpret classical physics as the quantum physics where all wavefunctions have already collapsed.

One could track a cannon ball using two co-moving radar emitters so that the field momentum transferred to the ball from each radar was equal and opposite, leaving the ball unaffected (at least as far as its trajectory is concerned). Classical physics assumes the light source (in the case of visual tracking) can be made arbitrarily dim so that for any given subject one can justify the existence of a limit where the subject is unaffected by an observation. In quantum theory this is not possible simply because one must use photons. With an individual photon one could reduce the frequency to try to take the same limit, but if the wavelength significantly exceeds the size of the subject of the measurement it will simply not be detected. Which means that one cannot take the limit that the observer leaves the subject undisturbed while observing it, because the basic units of quantum theory are quanta.

I don't think that classical physics should be seen simply as a limit of quantum theory. Clearly it is no longer regarded as rigorously true, but it has its own world view and assumptions. That one can obtain the Hamilton-Jacobi equation from the Schroedinger equation in the limit that Planck's constant goes to zero is more of a necessary condition for quantum theory to be a valid theory than anything else - it basically has to predict classical mechanics to be empirically reasonable.

I'm a little wary of your expectation value approach to finding classical physics. That may well lead to the correct macroscopic physics, but could easily differ in its predictions from those of classical mechanics. For example, superconductivity is essentially incomprehensible in classical mechanics as it is impossible to express the concept of a Bose-Einstein condensate in the formal language of classical mechanics.

Originally posted by DeepThought
One could track a cannon ball using two co-moving radar emitters so that the field momentum transferred to the ball from each radar was equal and opposite, leaving the ball unaffected (at least as far as its trajectory is concerned). Classical physics assumes the light source (in the case of visual tracking) can be made arbitrarily dim so that for any g ...[text shortened]... the concept of a Bose-Einstein condensate in the formal language of classical mechanics.

Superconductivity is a macroscopic quantum phenomenon. Obviously classical physics doesn't describe it in any limit.