glengarry said:
When you talk about "interpretation," you are talking about the attempt to correlate a pure mathematical formalism with some kind "happening" that is occurring "out there."
Not quite. A theory is defined by a set of statements that tells us how to interpret the mathematics as predictions about possible results of measurements. In other words, we need to interpret the mathematics to turn it into a theory of physics. But I would define QM as a
theory of physics, not as some piece of mathematics. So at least by my definition of "QM", it already includes an interpretation of this kind. This means that an "interpretation of QM" must be something else entirely (as long as we use my definition of QM).
An "interpretation of QM" should be an attempt to interpret QM as a description of what's
actually happening to the physical system at all times, even at times between state preparation and measurement.
By the way, I have explained this several times before, and I don't think anyone has ever understood what I meant. At least not the first time. Maybe I'm not explaining it well, I don't know. (Hm, now that I think about it, I think Demystifier understood it). I probably won't try to elaborate on this, because discussions about interpretations take absurd amounts of time, and I don't want to get sucked into another one.
Most of the ideas that people call "interpretations of QM" don't satisfy this simple definition of an interpretation of QM. Some of them (like Everett's MWI) are interpretations of the first kind, i.e. attempts to use a different set of axioms to turn the underlying mathematics into a theory of physics. Many other "interpretations" aren't even that. They're just loosely stated ideas about what reality might be like.
glengarry said:
But I do not think of QM as anything other than a purely non-realistic statistical theory.
I do too, most of the time. But I used to think that this was the only possibility, so I was quite frustrated when I realized (a couple of years ago, during one of these discussions) that QM might actually describe a physical system. Now I'm torn between those two options (a kind of MWI and the possibility that QM is just a set of rules that tells us how to calculate probabilities of possibilities). One of the reasons why I think the realist interpretation is worth investigating is that I think it might be capable of explaining some things that the anti-realist interpretation isn't.
glengarry said:
That is, the very idea of calling a Hermitian operator an "observable" is the first step into interpretive "hell." All we should really be saying is that an operator merely operates on a field of possible values by way of probabilistically choosing one of these values, with the statistical effect (i.e. averaged over infinite "operations") being that the expected value has born fruit.
I like the approach that you can find in some advanced books: "Observables" are defined as equivalence classes of measuring devices (which are defined operationally). Then we take one of the axioms QM to be that observables are represented mathematically by members of some C*-algebra (like the algebra of bounded self-adjoint operators on a complex separable Hilbert space).
glengarry said:
It is for this reason that I propose the banishment of the following terms from all quantum mechanics textbooks:
-particle
-wave
-position
-velocity
-spin
-collapse
-observer/observation
-experiment
-apparatus
-mass
-energy
I don't see how we could dispose of any of those, except "collapse".
glengarry said:
So, if we can only get the "powers that be" to categorize QM as a mathematical art, as opposed to a physical one, then we can finally end all the silliness as far as what QM is "really" supposed to mean.
Uh...uh...

Uh...wh...You want people to think of the best theory in all of science as...mathematics!? If we throw out the
best theory, shouldn't we throw out all the others too?
glengarry said:
And finally, instead of calling it "quantum mechanics" (after all, what does the word "mechanics" imply?), let's just call it: the statistical theory of measurement! Ta-da... no more interpretation!
"Statistical" implies things too, and so does "theory"...and even "measurement". I guess we're just going to have to find some weird symbol that no one uses and say that it's the new name of the theory formerly known as QM.