Decoherence doesn't really solve these issues. It gives you an approximately diagonal density matrix for the macroscopic degrees of freedom, but: (a) Not exactly diagonal (b) There isn't a unique decomposition of the macroscopic density matrix even after decoherence thus it cannot be taken as simply ignorance of some set of macrostates.

You need something stronger, namely superselection or irreversibility.

That's correct, But there are numerous good methods to propogate irreversible dynamics in qm. Many of these are exact in the limit of a noninteracting bath of bilinearly coupled oscillators which is sufficient to describe a measurement collapse. There's no mystery or inexact proscription to such a simulation of a collapse process. It's just complicated.

> There's no mystery or inexact proscription to such a simulation of a collapse process. It's just complicated.

Then there are a lot of Nobel prize winning physicists who would love to be enlightened about how simple the mystery actually is.

You are really missing the point - the details of how a measurement happens with specific instruments is not what the measurement problem is about.

The issue is linear evolution means the measurement of a superposition leads to a superposition of measurement devices. If the quantum state is real that gives you many worlds.

If you are suggesting there is nonlinear evolution, well a) it must be non-local and b) the theoretical research suggests it would be inconsistent. QM is a very rigid theory - “an island in theory space”. It isn’t easy to slightly modify.

> The issue is linear evolution means the measurement of a superposition leads to a superposition of measurement devices. If the quantum state is real that gives you many worlds.

And that's problematic because? Because it explains away the whole measurement problem, there is nothing to explain, it's an artifact of a macroscopic observer's point of view?

It's like saying that SR/GR with their space-time continuum being real is problematic, so let's keep to the (post)-Newtonian point of view, but oh no, it now has all this weird amendments and additional terms, and when you try to extend it to the whole of the Universe, it breaks down/gives really weird stuff. Well, duh, of course it does, if one tries to pull an owl on a globe, it simply won't fit.

Well you don't need to have nonlinear evolution to get what alpineidyll3 is saying. It's sufficient for the observable algebra of macroobservables to be commutative. This allows the evolution to be linear and have no interferences.

The QM is "an island in theoryspace" idea isn't strictly true either. QM is one among an entire family of probability theories. It's only rigid when considered purely from the point of view of Probability theories based around vectors in Hilbert space. However considered as part of OPTs in general there's nothing that makes it difficult to modify.

It's not unitary evolution breaking down, just that the Born rule isn't a consequence of unitary evolution. They're separate independent hypotheses. In most derivations of QM from an axiomatic basis they're consequences of separate combinations of axioms.

Thanks. Do you by chance have a good source for a gentle introduction into axiomatic QM? Like undergrad level is fine, I've taken basic QM and worked through Griffith's intro book on my own, and I've had a lot of math.

I'd love to read more but my google results aren't turning up a good definitive introduction.

No it can't. There have been many attempts and they don't work. The Born rule is independent of unitary evolution. The closest one can get is to declare that the quantum state is fundamentally a statistical object (i.e. the only information in it is observation probabilities) and then with certain assumptions about the size of the state space you can show that the Born rule is the only possible rule for connecting the state to statistics consistent with the unitary dynamics.

So under the assumption that the state encodes probabilities, state space assumptions and consistency with unitary evolution you get the Born rule. However this is not the same as the Born rule arising dynamically from unitary evolution alone.

Well in the most common family of interpretations "collapse" isn't an actual physical process, just Bayesian updating. So you wouldn't expect to find physical evidence of it in that sense.

It's true that from the perspective of an external superobserver the quantum state evolves to contain terms for each observer observation state. However since all interference observables turn out to be non-physical for macroscopic systems we get a superselection rule and so the probabilities for different macrostates are classical probabilities and thus reflect simple ignorance of the observer's post measurement state.

There's very little motivation for reading the quantum state "ontically" in the way you are doing.