I am afraid you are misunderstanding on this point, err, "probability locus". ;-)
Correspondence says that the new theory should boil down to the results of the old theory under the conditions the old theory is known to hold (On cases where the new supplants the old, then of course the new takes precedence, otherwise, why bother?)
And of course probabilistic dynamics is one of the hallmarks of quantum mechanics.
Sorry for the late, terse reply. Just came back from hiking in Flagstaff and I'm all stiff and sore, with all the weekend's work yet to do.
No wonder I'm FReeping.
Of course grey_whiskers my earlier reply left out a whole lot of details regarding the correspondence principle. My general understanding of it is as you describe, above. The operative word there is should, and the qualification is "under the conditions the old theory is known to hold." The point is the conditions (and expectations) of the old theory, though eminently valuable and indispensable for accurate prediction of macro-level phenomena, apparently generally do not hold at quantum levels. Atoms are not solid bodies, or composites of solid bodies; they aren't structured like miniature solar systems; events occur within them that appear to be spontaneous (uncaused); the behavior we observe is disturbed by the very fact of our observing it; etc., etc. Where Newtonian mechanics is all about precise observations (measurements) leading to precise predictions -- where there is a direct one-to-one correspondance between a phenomenon and the physical laws that pertain to it, which seem to operate more or less autonomously -- there is none of this to be found at the quantum level.
There seems something almost completely arbitrary about the imposition of the correspondance requirement, "from the outside" as it were. If I am understanding Bohr correctly, the classical (Newtonian) language must be used to describe quantum events because that language has evolved over a very long period of time based on normal modes of human perception; i.e., based on the way that humans have been organizing their experience from time immemorial. Thus the classical language is based on visual perception. Quantum events are totally non-visualizeable. There is no suitable language in which to speak of them. So you use the language you have.
Bohr seems to have thought there might be some smooth interface between events occuring at quantum levels and the world of classical experience. But if so, he couldn't say exactly what or where that interface is; he proposed atoms with very large outer orbits as candidates. But I think it's fair to say that nobody knows this for a certain fact.
What is most striking to me is the utter break at quantum levels with classical physics on the matter of causation. Classical mechanics requires that in order for something to happen, something must have caused it. There is also the supposition that bodies are "real" and their interactions "certain" independently of the observer, and that their properties are given, completely intrinsic to them. All of this is undermined by what we know about quantum physics. It is difficult to see a smooth interface between these two realms. But if people want to look for it, I certainly wish them every success.
In any case, I can understand why science would seek to find such a smooth interface; for both realms obviously exist, and so on grounds of the complementarity principle, they together ought to express "unity" at some level....
Einstein evidently thought that quantum mechanics could not be "the last word" about the fundamental structure of reality, that there must be some deeper principle at work yet to be discovered that would supply the requisite unity.
Bohr evidently didn't share this view, thinking perhaps we shall never know whether there is a deeper principle at work. But that's okay, because according to him science is not about finding out how nature "is," but only about "what we can say" about nature: He's pointing to language here. Since the Newtonian language is really the only scientific language we have (and as already mentioned is visually based), it must serve in explications of the unvisualizeable realm of quantum events.
Einstein's desire -- it seems to me -- is metaphysical at its root. Bohr tried to keep philosophical thinking -- other than epistemology -- out of his science altogether. [I can't express how deeply I admire both these great men.]
I hope you enjoyed your hiking expedition, grey_whiskers -- though I'm sorry you're feeling a little sore today! Me, too. Yesterday I conducted a marching band down the street in two Memorial Day parades/observations. My "mace arm" is killing me.... But I'm sure I'll be fine tomorrow. :^)
Thanks so much for writing!