DevilsAvocado said:
- Gödel’s incompleteness theorems show that there are inherent limitations in all axiomatic systems.
No, they don't. They make very specific claims about specific axiomatic systems—those that describe the properties of the natural numbers. To naively carry this over into axiomatized physics models is to assume, with no justification, that every statement about the natural numbers has an analogous physical statement (i.e. a statement about a physically realizable state in terms of elementary processes). What physical process is a reflection of, e.g., the Goldbach conjecture? Fermat's Last Theorem? If you look at the Gödel statements used in the theorems, the suggestion that
they have physical analogues is even sillier. Plus, there's a fundamental difference between choosing axioms for the natural numbers and choosing axioms for physics: the latter have empirical consequences. This wishy-washy pop sci idea that Gödel's incomplete theorems have anything to do with scientific models is just as unfounded (and annoying) as New Agers saying, "Quantum mechanics says anything you can imagine is possible!" Mathematical theorems are precisely worded for a reason: if you start running off with vague assertions based on out-of-context generalizations, you're going to say a lot of very incorrect things.
Now, when it comes to the extremely well working model of quantum mechanics; it all works like a dream – mathematically. But when you start talking about QM and try to provide “natural explanations”, it doesn’t always work that great...
And this is supposed to count against the theory somehow? Our brains evolved in environments completely dominated by classical behaviour. Quantum theory is weird because it's unfamiliar, and likely always will be to some extent. The inability to describe QM with 'natural explanations' just demonstrates the shortcomings of intuition—since a natural explanation is just something that makes sense intuitively to us. That is precisely why we use the mathematical models: they take us where our intuition can't. The difficulty of making intuitive sense of QM has no relevance to whether or not the theory is complete.
Because, for one thing; the theory does not say anything about what happens at (macroscopic) measurements, and often it’s right there the ‘weirdness’ starts. Where exact is the border between microscopic QM fields/particles and classical macroscopic objects (if any)?
This, and nearly everything else in this paragraph, is wrong. QM has no restrictions about length scales. There is no postulate saying, "By the way, all this stuff only applies to microscopic objects (whatever that means)." The emergence of classical behaviour from quantum phenomena is well understood through mechanisms like quantum decoherence, Ehrenfest's theorem (and other specific instances of the correspondence principle), the path integral formulation of QM (in which the ratio of the classical action to ##\hbar## determines how dominant quantum effects are), and many other
derived properties of QM. There is no arbitrary cut-off point at which we say, "Well, let's stop using QM here." There is no mystery as to how the equations of classical mechanics emerge from various limiting cases of quantum mechanics; disagreements about the nature of quantum states has absolutely no bearing on that fact.
Hello! Where’s the ‘completeness’ in all that?
Nothing you've said has anything to do with the 'completeness' of QM, by any standard definition of the word. You're apparently confusing 'incomplete' with 'makes me uncomfortable'.
As you see, it’s a weird world out there
And it's plenty weird enough as it is without people pointing to well-understood phenomena while waving their hands about and saying, "Ooh, isn't that mysterious?"
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