dx said:
A situation identical to EPR can be treated as follows: Take a diaprhram with two narrow slits, and let two particles of known momentum pass through them. If the momentum of the diaphragm is known exactly before and after the particles pass through, then A = p1 + p2 and B = q1 - q2 are exactly known, which is compatible with quantum mechanics since [A, B] = 0. Therefore, if we measure p1, then we know that p2 = B - p1. Or, if we measure q1, then we know q2 = q1 - A. So even though we are presented with a free choice of determining either p2 or q2, of the second system by measuring only the first system, q1 - A and B - p1 do not commute.
Ok, q2 and p2 don't commute. Neither do q1 and p1. But we actually measured q1 and p1 in the same trial on the same system. And considering any given trial,, as you noted, we can know (ie., deduce) q2 and p2, and this is compatible with qm -- ie., it isn't a violation of the hup. My thinking as to why it isn't a violation of the hup has been that it's because the hup doesn't apply to single trials where noncommuting measurements are made on spatially separated parts of an entangled system. That is, I've always thought of the deltas as referring to statistical spreads defined by actual measurements, not just the distribution defined by the wavefunction, because that's going to be the same for any trial in a given run, isn't it? And, to bring this home, since EPR is just dealing with the joint measurement in a single trial, then does the hup apply to EPR?
Anyway, to clarify my question regarding the hup and EPR: does the hup apply to single trials of the sort where, say, both the position and the momentum of an entangled system are being measured? If it doesn't, then I'm supposing that the hup simply doesn't apply to EPR. And if it doesn't, then the answer to the OP's first question is that EPR didn't violate or not violate the hup. It just didn't have anything to do with the hup -- for the (possible) reasons given. Or not?? I don't know for sure.
I'll address the rest of your post, sentence by sentence:
dx said:
The point is that the criterion formulated by EPR is revealed to be ambiguous in light of the actual conditions that we are faced with in atomic physics, where concepts such as 'state' and 'behavior' cannot retain their usual meaning due to the existence of the quantum of action.
By "criterion formulated by EPR" I'm supposing that you're referring to their 'elements of reality', ie., that whatever can be predicted with certainty without disturbance must be a consequence of some underlying reality that exists prior to and independent of our probings of it. And yes, of course it has to be ambiguous. It can be reduced to the notion that the fact that detections happen at all is evidence of an underlying reality that exists prior to and independent of our probings of it. What about cloud chamber results? Or the tracks on photographic plates that particle accelerators produce? Isn't this evidence of an underlying reality that exists independent of our measurements of it?
I think that that's basically all that EPR was saying. Ie., that there's an ontological and epistemological realm underlying instrumental behavior, and qm isn't a complete description of it. One might say ... duh! But then, as the formulators of the Copenhagen Interpretation, and others, have pointed out, there's no way to unambiguously, objectively talk about an underlying realm.
So the quantum theory is about instrumental behavior. The quantum of action has to do with instrumental behavior.
And, since the hup has to do with the quantum of action, then the hup can't be interpreted as a statement about the underlying, or fundamental, behavior of our universe. It's only a quantitative statement regarding what we can say about what we know of the universe. And how do we know what we know?
dx said:
The feature of individuality that underlies the comprehension of atomic phenomena is irrational within the scope of classical visualization and mode of explanation.
Not sure what you mean by this, but I'd say that our 'comprehension' of atomic phenomena, insofar as it can be called 'compehension', is entirely within the scope of, and mostly dependent on, classical modes of visualization and explanation.
dx said:
However, any attempt of extrapolation of our causal spacetime description into the atomic domain must ultimately rest on the heavy scales and clocks, whose behavior is and must be accounted for classically. Thus in judging the form that such an extrapolation can take, we are essentially involved in an analysis of the possibilities of definition and observation, with due attention paid to the quantum of action, whose consideration is inevitable in any such analysis.
Ok, so I guess we agree on this.
dx said:
Such an analysis, performed by Bohr, has shown that any situation which permits a causal account of a quantum process excludes a spacetime account of that process, and vice versa.
And this brings us back to the main message of the Copenhagen Interpretation. The formalism of qm doesn't necessarily correspond to what's actually happening in an underlying reality. It does, however, necessarily correspond to what's known about instrumental behavior.
dx said:
Thus, the description of physical reality provided by quantum mechanics cannot be a causal-spacetime description, but a 'complementary' description, where the role of the measuring instruments is central. In fact, the quantum mechanical formalism must be viewed simply as a tool for such a complementarity description, whose well-defined application must always refer to the exact conditions of the experiment.
Well, I'd say that barebones qm doesn't provide, or even pretend to provide, a description of an underlying physical reality. So the fact that it isn't a "causal-spacetime description" of an underlying reality isn't really too surprising or upsetting. The role of measuring instruments and materials isn't just central, it's all there is as far as we can be, objectively, scientifically concerned. So, what you've said makes sense to me, and I agree with it, though I'd like to be able to say it in a briefer, simpler way. Is that possible?