> in general we just can't [describe a system in the limiting regime using the fundamental theory] without hand-waving, period...It's sort of true, but not in a useful way.
And I am saying that it in fact can be done, and has been done, in physics and math in a very non-hand-waving way. One can show rigorously when a certain abstractions is accurate.
Well... sure, but I think you're still almost purposely missing the point. Take this example - can we prove that a system of differential equations emerges in a meaningful way from discrete systems? Yes, obviously. That's a far cry from the OP's "if you think about it, all things are quantum", which is where this thread started and what I'm talking about.
It also illustrates the actual point pretty well - when you have a good set of differential equations that describe observed phenomena, that higher level of abstraction gives MORE insight into the processes at play, even when we know that it emerges from something more fundamental. Only when that model is a poor approximation do we need to appeal to the more fundamental regime (or when that fundamental regime is what we're studying).
If you think that fact that levels of abstraction give insight is a rebuttal to the OP, you don't under what he's doing. Understanding how the fundamental theory reduces to the abstraction (1) allows you to precisely know the limits of the abstraction and (2) allows you to port knowledge you have about one side to the other.
Like, this comment of your is a great example of the sort of confusion that arises when you don't understand the non-relativistic limit:
> Lol, so you've got a working theory to bridge the quantum and classical worlds? That is, you've figured out how to make general relativity and quantum mechanics emerge from a more fundamental theory?
> in general we just can't [describe a system in the limiting regime using the fundamental theory] without hand-waving, period...It's sort of true, but not in a useful way.
And I am saying that it in fact can be done, and has been done, in physics and math in a very non-hand-waving way. One can show rigorously when a certain abstractions is accurate.