This sounds less like metaphysics and more like a math exercise to me, though. Deriving a smaller handful of cleaner axioms that result in quantum mechanics is a valid exercise in mathematical cleanup. And if I'm reading their claims correctly, doing so such that all but one axiom equally applies to classical mechanics, and only the introduction of one specific one yields quantum mechanics, would be legitimately interesting mathematically. It reminds me of Euclid's Fifth axiom, where it turns out that tweaking that one specifically yields multiple different valid geometries.

It probably isn't really progress in the sense the article writer thinks; juggling isomorphic representations is in some sense not "really" progress. But it can still be worth it for the practical improvements and potential didactic improvements. Perhaps if we had better education for QM with a better mathematical model, it would lead to less existential angst in the first place. I've seen Scott Aaronson trying to do some work on that front as well. In fact I'd consider it ironic if QM turns out merely to be slightly difficult and a hundred years of psuedo-philosophical babbling sourced from nothing more than a slanted view of relatively simple principles. I think some people will actually get upset if there is success in taking the mysticism away from QM....

I expressed my distaste of QM marketing.

Axioms of QM are few and clean. Sure, playing around them may be interesting. And if someone found its alternative formulation, more fundamental theory or anything - it would be great.

But (looking at the history of science) I see that the search of mathematical beauty sometimes leads to great discoveries; trying to satiate one's naive intuitions - rarely.

They say that the Born rule can be derived from first principles from their set of axioms. In other formulations, it must be assumed without further explanation. That is progress.

It has already 10 years, at least: http://arxiv.org/pdf/quant-ph/0405161.pdf (a great paper IMHO)

As a layperson, there just seems to be a general discomfort with qm because it's not 'intuitive' or isn't close enough to our subjective experience of everyday reality.

As someone who is bad at math and physics, the complaints don't seem all that different than first-year students scoffing at imaginary numbers, or centrifugal force. You don't "get it" -- so what? Why should the universe be easy to understand? QM just seems like more of the same.

People could handle heliocentricity, then the galaxy, then the universe, but for whatever reason, QM is just a bridge too far. Too weird, I guess.

I guess embarrassment might be the wrong term but it's still an interesting question why quantum mechanics is like it is. And my personal feeling is it's something like people in the past wondering why the sun shines or how life got here - it wasn't that it was a mental trap to ask but just that they hadn't figured out fusion and evolution yet.

As often presented, QM asserts that the system collapses under measurement. But for a fundamental theory, measurement as an external thing doesn't make sense. Thus, when does collapse happen? This is that cat thing.

One can shrug and say, we know what we need for computations. But a fairly fundamental theory should be cleaner. Of course, there is a perfectly simple theory (Bohm's) involving Schrodinger's equation and a guiding equation for particles that has all of this quantum formalism derivable from its dynamics.

A paper by Bell that goes into this point more clearly than I can articulate: http://www.tau.ac.il/~vaidman/IQM/BellAM.pdf

Decoherence-based interpretations (Everett, Żurek, Fuchs...) do not have measurement as anything separate - it's an emergent phenomenon based on the (already present) rules of unitary evolution. So for me its a clear argument why some of the interpretations make more sense that the others.

Decoherence alone doesn't solve the collapse problem.

Could you expand on that? Once you get decoherence, instead of 'measurement' or 'collapse' you get splitting into subspaces, which get practically separated.

Sure, modeling decoherence is not always easy. (And, 'collapse' is often a nice simplification for practical purposes.)

Yes, practical separation occurs. But you still have to explain why our experience is that of a single outcome when the only thing in the theory (the wave function) says nothing of the kind.

Now, this can be rectified by using many worlds, for example. Particularly, integrating out the wave function to get a mass density on 3-space (non-relativistic version) does produce a valid theory which has multiple realities whose evolutions internally would appear to have single outcomes even when that is not actually true. Fuzzy tv reception with multiple overlapping channels is the mental model here.

However, that is not just decoherence. One has to add something. And the question is, why choose a theory that denies the truth of our common experience in such a fundamental way when one does not need to do so?

Pilot-wave theory is, subjectively, very simple and natural. It is not epicycles upon epicycles. In fact, quantum theory practically screams out for it with the existence of the probability current and the many insights that that current drives. There are at least 5 very distinct ways to derive pilot-wave theory from quantum notions.

One last thing to ponder. Wave functions are defined on the configuration space of the particles. The specific space is crucial to defining the evolution operator. Fermions and bosons emerge naturally by considering the configuration space of unlabeled particles.

But if you have no particles, why is a configuration of them useful at all?

That whole 'measurement problem'/Heisenberg cut/wavefunction 'collapse' situation is somewhat iffy from a philosophical point of view.

Which is why a number of interpretations don't feature any such thing.

Name your preferred interpretation, and I'll likely we able to tell you what's 'wrong' with it.