I've never found epistemic interpretations compelling (like QBism, which is what the article is about). I'll try to explain why.
First, the stuff we do with quantum mechanics just seems sort of... really obviously objective? It's not like Bell tests work for me but not for you, or quantum computers factor numbers for me but not for you. If I sell you a machine to produce a specific superposition, and it produces the wrong one, you can tell. Yes you need to run it multiple times and do statistics, but ultimately anyone can check that the machine is doing the wrong thing.
Second, two agents can't actually disagree on what the superposition of a state is, to any appreciable degree, without one of them being provably irrational (modulo some weak-sauce assumptions we take for absolute granted in classical mechanics). [1]
Third, note that (w.l.o.g) diagonally polarized photons are superpositions of horizontally and vertically polarized photons. This suggests that, in an interpretation where superpositions are less real than classical states, slightly rotating a polarizing filter radically changes the conceptual machinery used to understand a photon passing through the filter. That seems... silly? There is a rotational symmetry in the system that should be natural in the model (e.g. see how special relativity reifies Lorentz boosts).
Fourth, although this is ironically subjective, I've never read an epistemic explanation of some quantum phenomenon and thought "Ah, that makes it clearer!". But that has happened with collapse interpretations, with path integral interpretations, and with many-worlds.
Superpositions are statistical distributions. Only statistics are wholly predictable. Individual events are wholly unpredictable.
You can have two statistical views of the same experiment in which each individual event is different but the statistics agree.
You can have a distribution of views in which events are somewhat different to varying degrees and the statistics still agree.
Each view will experience itself as unique in specifics while agreeing that the distribution of events is identical.
That doesn't solve the problem.
It's hard to get random processes to define an identical distribution without having classical mechanics as a foundation.
Basic QM hand-waves this away with "Here's some math that defines the distribution and..." But that's like "Starting with this universe we can..."
It so happens that the statistics correlate spatially with various field potentials. Which is interesting, but... Why is there a distribution at all? Why are there creation/destruction operators? Where does the "code" that defines this mechanism live? How do particles know they should follow it?
Do particles even exist, or are they just something random and constrained a field does every so often? How do fields know the physical configuration of an experiment has changed and sometimes that information appears to travel FTL? (Even though it can't be used for signalling.)
How does a particle keep track of how many other entities it's entangled with and in what ways? Where does that information live? (Bell suggests it's not inside the particle itself. So where is it?)
Is all of this shaped by some kind of hidden causal propagation mechanism which also defines how relativity works?
And so on. A complete explanation would answer all of these questions - and others - with ease. Clearly we're nowhere near that.
> How does a particle keep track of how many other entities it's entangled with and in what ways? Where does that information live? [...] A complete explanation would answer all of these questions - and others - with ease.
I disagree with this framing. Fundamental laws of physics are always going to have unanswered questions of this type. Given any set of rules you can ask "But what explains those rules? What are they built out of? How are they enforced?". Sometimes those questions will have answers and lead you deeper, but for truly foundational laws you'll be wasting your time. It'd be like asking "Where is the true platonic number 2 located? Is it in Canada?".
You can ask the same questions of classical mechanics, of course. We tend not to because it agrees with our intuitions, but you can. For example, where would a classical particle store its velocity? For that matter, where would it store its position? It's circular to say it stores its position where it is! Clearly a "true" theory of classical mechanics would answer these very important questions.
Concretely, there are a variety of ways of writing programs that act like quantum mechanics, that differ wildly on how the state is represented. This detail is simply not pinned down by the postulates of QM. That being said, what all these programs do have in common is that they are actually tracking information related the state; that the state is ontic.
So pick your favorite state representation: state vector, density matrices, Feynman paths, whatever, they all work! That doesn't mean they're describing things that aren't real, it just means there's many ways of correctly describing reality; such convenience!
I should probably add that I know everything I've said isn't convincing to a skeptic. Ultimately it comes down to: I know I can think of the quantum state as being really real, and that will work totally fine. I find that style of thinking is effective for me, and intuitively compelling, so I do it.
Every once in awhile I'll run into someone pointing out the philosophically fraught underpinnings of assuming reality is real or whatever, and I basically won't care because my goal is to be effective; not to be Descartes-level-certain about everything.
An example of something that would make me care is if QBism contained some key conceptual trick that made problems easier, and gradually many papers started using it because of this advantage. Or, of course, if there was an experiment distinguishing between interpretations.
I think Strilanc’s second point is that apparently according to QBism two agents may have different quantum descriptions for a system and we cannot say that one is more correct than the other because the theory rejects that there is a “correct” description.
(pro QBist physicist here). Just some clarifications on the interesting points you raise.
1. In practice, experimental physicists can and do disagree all the time about what their apparatuses are doing, what the results mean, and so on -- at least, they do at the beginning of the experiment. By the end, they have gone through a process that results in agreement, which allows them to write a paper together declaring things in an objective manner. So it is important to distinguish between the "inputs" to scientific practice (our individual, subjective initial guesses about what is going on) from the products of that practice (effectively objective statements). QBism interprets wavefunctions not as products but as inputs: we need to start with a prior "best guess" about the probabilities, and it its the interactive process of updating our subjective priors in light of data that leads us to converge on a single wavefunction, which then attains an objective status in the sense of being the same for everyone. QBism's point is that this whole process of "objectification" is itself a process to be analyzed, not taken for granted as if the objectivity were there from the beginning.
2. The PBR theorem (which you cite) doesn't bite QBism, and PBR themselves admit as much in their paper. See point 8 in [https://arxiv.org/abs/1810.13401].
3. What you say would be silly, if QBism treated classical states as "more real" than quantum states. But they don't.
QBism treats quantum and classical states on the same footing: both are sets of subjective probabilities about the outcomes of possible measurements you could do. So classical states are probability distributions, and probabilities in QBism always represent subjective degrees of belief of an agent (following the de Finetti/ Ramsey school of probability theory). The difference between classical and quantum states in QBism does not lie in what the states ARE, it lies in the rules that tell you how to compute one state given your subjective beliefs about another state. And those rules are objective in QBism; as objective as the rule that says probabilities have to add up to one.
4. Doubly ironically then, this is probably the one point raised by critics that hits the QBists hardest. QBism can bring clarity to many issues (I find it handily resolves the measurement problem and non-locality of "collapse" - see eg.[https://arxiv.org/abs/1311.5253]) but there are still plenty of physical phenomena that don't yet have a neat QBist explanation.
> in an interpretation where superpositions are less real than classical states
What do you mean by “classical states”?
In your example diagonally polarized photons are not more “a superposition” than any other photon. For a pure state like that one being or not “a superposition” depends on the basis, it’s not a property of the state.
In this case the "classical state" would just be a preferred basis for the polarization. And basically what I'm saying is "If superpositions of polarizations aren't real, why is there such a natural way to change the basis so that any given polarization isn't in superposition?".
Analogy: if simultaneity is absolute, why is it so easy to confuse people about what happened at the same time by changing my speed?
I don’t see how does it relate with the interpretations of QM and QBism in particular.
Superpositions are not “less real” than basis states (if such a distinction makes sense) within a theory (psi-epistemic or psi-ontological) as far as I understand.
First, the stuff we do with quantum mechanics just seems sort of... really obviously objective? It's not like Bell tests work for me but not for you, or quantum computers factor numbers for me but not for you. If I sell you a machine to produce a specific superposition, and it produces the wrong one, you can tell. Yes you need to run it multiple times and do statistics, but ultimately anyone can check that the machine is doing the wrong thing.
Second, two agents can't actually disagree on what the superposition of a state is, to any appreciable degree, without one of them being provably irrational (modulo some weak-sauce assumptions we take for absolute granted in classical mechanics). [1]
Third, note that (w.l.o.g) diagonally polarized photons are superpositions of horizontally and vertically polarized photons. This suggests that, in an interpretation where superpositions are less real than classical states, slightly rotating a polarizing filter radically changes the conceptual machinery used to understand a photon passing through the filter. That seems... silly? There is a rotational symmetry in the system that should be natural in the model (e.g. see how special relativity reifies Lorentz boosts).
Fourth, although this is ironically subjective, I've never read an epistemic explanation of some quantum phenomenon and thought "Ah, that makes it clearer!". But that has happened with collapse interpretations, with path integral interpretations, and with many-worlds.
[1]: https://en.wikipedia.org/wiki/PBR_theorem