• The formalism of quantum theory can be viewed as a noncommutative generalization of probability theory. Therefore, it is natural to interpret the states in the same way as probability distributions, which are their commutative special case.
• The measurement problem disappears in the epistemic view because there is no problem with discontinuous changes in an epistemic state, i.e. measurement-update is just like Bayes’ rule in classical probability. Also, there is no problem with having two different states depending on whether you describe the measurement unitarily or use the measurement postulates. The two results just represent the epistemic states of agents with different perspectives, i.e. one who has not seen the outcome and one who has.
• Many phenomena of quantum theory make more sense in the epistemic view. Search the arXiv for Rob Spekkens’ papers on his “toy theory” for lots of examples of this.

Although many people think that interference kills the epistemic view, this is not correct because there are epistemic toy theories, such as the one by Spekkens, that do exhibit interference. The mistake here is to have a too limited view of what the possible ontology underlying quantum theory can be. If you think it has to be particles having definite positions that only go through a single slit then you’ll end up with something like Bohmian mechanics which has ontological wavefunctions. However, there is no reason to believe that there can’t be some sort of wave-like influence that goes through both slits, with the proviso that that influence must contain far less information than the full wavefunction so that it can still be viewed as epistemic and we retain the ability to solve the measurement problem. Spekkens has a version of his theory for photons in an interferometer that demonstrates this, but I don’t think it has been published yet. Still, if you read the main “toy theory” paper you can probably work it out.

Regarding emergence, I would probably phrase things a bit differently if I were writing this post again. You can certainly end up with equations that look classical if you apply decoherence in an appropriate way and look in the Wigner function picture for example. However, as you correctly point out, those are just formal derivations and you need to give them a physical interpretation to understand if you really have an emergence of classicality. To do this, you need to add an ontology, but it turns out that most of the ontologies that have been considered end up relying on precisely these formal derivations to get emergence. Perhaps the best worked out example is in the Everett interpretation where you can look at the long papers by David Wallace to find out how decoherence leads to emergence in that case. There is no new maths in these papers, but it provides the necessary philosophical support that you are looking for in that case. Bohmian mechanics is somewhat similar in that it needs decoherence in order to make the trajectories follow their classical counterparts in a stable manner and again there is no new maths involved in understanding this. Therefore, I guess what I was trying to say is that we seem to understand the broad outline of how classicality emerges, with the proviso that the meaning attached to that understanding is ontology dependent. I do not know if and how this works out in the epistemic picture, since we don’t have a full ontological model of quantum theory that satisfies the epistemic criteria yet. It is more of a work in progress.

Two questions pop into mind.

Firstly, I’ve never met someone who takes an epistemic view of the wavefunction before and am interested in understanding what the motivation for that view is. How does the epistemicist account for interference effects, for example, in the double slit experiment (which I would have thought empirically disconfirms the epistemic view)?

Secondly, given that your interested in the ontological issues, I wonder if your able to describe how decoherence solves the emergence problem in a more ontological manner.
I’ve never seen anyone do that before – every attempt to describe the physical process of decoherence that I’ve seen looks more like a description of a mathematical process being undertaken by mathematical entities up in plato’s heaven!
To be honest, I don’t understand how decoherence solves the emergence problem because I don’t understand what connection the mathematical process has to the purported physical process.
For example, when one speaks of bases, one is speaking of forms of representation (formalism), not things represented (ontology). The position basis, for example, constitutes a way of writing down the physical state of a system. But I could equally write that state down in the momentum basis. Bases are therefore linguistic/mathematical entities and which is basis I choose to use to write down the physical state of a system is of no physical significance.
Now, when someone says something like…

“One of the most impressive achievements is that decoherence can select different types of “basis” depending on the relative strengths of the system-environment and internal system Hamiltonians”

…I don’t entirely know what to make of it. What does it mean to say that a physical process (decoherence) can select different sorts of mathematical/linguistic entities (bases)? At the risk of being uncharitable, it almost looks like some sort of “use-mention confusion”.

I don’t see how the emergence problem is solved, until one can describe, how physical systems undergoing decoherence manifest classical properties, in physical vocabulary. Would be interested in your thoughts on the matter.