It is indeed mixing two different things. So what you are saying is that the map is more important in defining the nature of "fundamental", even when we explicitly and intentionally throw away position information to gain a classical ensemble mapping, than is the system the map represents. That is not a question because that is what you said, but you are welcome to take issue with the characterization.
In fact the truth of the system trumps the truth of the map (theory) every time, which is why empirical facts are judge, jury, and executioner of theories. Empirical facts can mean different things in different theories making the claims associated with empirical facts less than factual, but nonetheless contradiction of those facts is a theory killer.
Hence I ALWAYS put the system at a far more fundamental level than ANY theory and/or derivation thereof.
Well of course. The mere fact of QM as an underpinning to classical physics is alone enough to kill the point from a system point of view. Yet if your idealized system is strictly defined by classical theory, much like you put theory ahead of system above to justify a "fundamental" status, then as a matter of fact stochastic behavior is an illusion induced by limited knowledge. Luckily science puts theory in the back seat to the system it describes. In fact many things thought to be fundamental were found to be derivable from something else.
So when you say "We don't actually know that," that must also apply to whatever thing in QM you want to define as "fundamental" in the present theoretical picture. Only the system, not the theory, contains or does not contain the information that specifies these things. Theory can only give a probable best guess based on the level of empirical consistency attained, and even then mutually exclusive interpretations can posses equal empirical consistency.
We need no such empirical test to say what classical theory says, which was all the point I was making. We only need such test to see if nature agrees, which is why I found you claim at the top strange, since you placed theory ahead of nature in defining the quality of what constituted "fundamental".
Only now that nature has spoken and required classical physics to be a limiting case "no way to test your assertion" becomes applicable to the nature of the stochastic behaviors in QM. So your own rebuttal to classical illusion of stochastic phenomena is now turned in the same court to the QM models used to claim the opposite.
Again, in the classical chaos it is indeed unknowable even though the unknown information is by definition there. So the fact of unknowability requires models that treats certainties as though they were random, but the model does not make the system random.
On a personal note I suspect that quantum systems have countlessly many more orders of magnitude of degree of freedom than classical systems, and we merely wrap them in ensembles, call the randomness "fundamental", and wash our hands of the unknowns as though they were merely imaginary. Quantum computers can easily justify this position. How else can a quantum computer do calculations in seconds that a standard computer with as many registers as there are particles in the Universe could not do in the life of the Universe? I even once seen this argument used as evidence for many worlds. Many worlds or not something gives.
Saying "expectation values" mistaken for "deterministic behavior" is woefully inappropriate when as a matter of fact, an independent of ANY real system, define a deterministic TOY model which is by definition entirely and completely deterministic and we can still PROVE that the model has unpredictable behavior.
It is not model dependent. It is NOT dependent on what is or is not real in ANY real system. Hence claiming that determinism in such systems was merely mistaken "expectation values" is DEAD wrong. It was the "expectation values" that proved stochastic behavior when the toy model was explicitly restricted to deterministic mechanics. So your claim is backwards and "expectation values" NEVER amounted to any evidence of determinism.
Again, make up a set of laws, any set of laws. They do not have to represent any real laws of anything, just make sure these laws are strictly deterministic. It can then be proved that based on these fake deterministic laws, and these fake laws alone, that the results of such deterministic laws MUST require stochastic behavior to model reasonably complex systems operating on these laws alone. That is the point. Ignorance of the details of a system do not entail that the system is devoid of deterministic causes behind the unpredictable behavior.
Now I am getting a little more about your perspective so I will articulate my own. It is not the laws that are fundamental. I think there really are symmetries in nature and laws are written to provide a perspective of those symmetries. For instance we could just as easily say the gravitational constant G varies relative to the depth of a gravitational field, but Einstein chose to say the apparent mass varied, which is physically equivalent. Yet regardless of what form or what perspective the laws are written from the symmetries are ALWAYS the same. Then theories are merely provisional specifications of those symmetries and their domains of applicability. So the only category errors that occur is when a symmetry specification is slightly off the mark or the domain of applicability has been misidentified. Symmetries do not require us to specify what nature is "actually" doing, though guessing can help better specify the symmetries.
Now how does this apply to the randomness issue. Well, we know for a fact the the symmetries defined by stochastic behavior is derivable from non-stochastic causal certainties given some unavoidable level of ignorance. This dependence of theory on stochasticity does NOT make it a "fundamental" symmetry even though it remains possible that it is at some level of the system. Because it is derivable from ANY system with "fundamental" stochastic behavior or not. I am perfectly happy with a "replacement" for what nature is actually doing as long as the "replacement" is as complete as we can fundamentally get from within our limitations. I do not think that simply proclaiming that is all we are after, therefore should not search more deeply for what nature might actually be doing, is helpful in getting more accurate and complete "replacements" for predicting what nature is going to do in more detailed circumstances.
True. But the efforts have produced theories which can predict far higher volumes of empirical behavior. These historical breakthrough are often the result of taking some foundational stance at odds with the prevailing stance. So it makes no difference that the foundational stance itself is and will always remain in question, they still play an important role in development. Then to deny the historical importance of the foundational stances in the development of science, and reject their relevance, denies some of the most important elements of theory building in our humanistic tool box.
So no, I will not accept some foundational anti-stance as a substitute for working through the apparent consequences of alternative foundational stances. The foundational stance itself needs no more justification or claims of absolute validity than the contributions to the "replacement" models predictive value.
Yes, the one that gives me nightmares
Yes, This is where I make the distinction between a symmetry and a law, with fundamental stances merely playing a role in morphing perspectives within the symmetries. I do not even thin IMO that fundamental physical constants are fundamental, or not derivable from other models. I do not take foundational stances any more seriously in an absolute sense than a coordinate choice. But coordinate choices can nonetheless be extremely useful.
Yes we are. However, my sympathies for Copenhagen is a twist in my foundational stance no different from a change in perspective as a result of a coordinate transform. There are no such absolutes to this or that stance that makes it fundamentally closer to any actual reality than any other. So, except for the fact of some anti-Copenhagen stances thinking their stance is somehow a better representation of absolute reality, I can also (sometimes) sympathize with their version. I move out of the Copenhagen picture for operational and conceptual reasons having nothing to do with rejecting the validity of the stance itself. Again, it is more like a coordinate transform than a rejection of the stance.
Perhaps I tried too hard above to get the point made. In the sense I was trying to use classical theory to make a point it is identical to chaos theory case. I was not trying to make the point that classical physics had any particular level of validity, only that strictly under the assumption of classical physics without any fundamental randomness you still get stochastic behavior. Just like in chaos theory.
Here the nightmarish part for me. If morphing between foundational stances is no more or less fundamental than a change in coordinate choices as I perceive it to be, then quantum demons should at least principle be possible in some sense irrespective of the absolute validity of their existence. It does not even require them to correspond to any direct measurable, just that they are in principle quantitatively possible under some perspective of what constitutes a measurable. My issues with Bohmian Mechanics run far deeper than any issue I have with CI.