I think I'm with you but I don't understand how this is a criticism of QBism (if that's indeed what it is). It's possible for one's beliefs to turn out to be completely wrong because of some secret actions which you were not aware of. This is just as true classically as in the quantum regime. I don't see that this requires more of an explanation than we've already given it.
This is not a criticism of QBism. It's an explanation of what QBism says, as far as I understand, and how (at least in this case) it's no different from the standard QM description: the system of interest is initially in a known quantum state described by one wave function, we perform a measurement, the quantum state is now the eigenstate corresponding to the outcome of the measurement and described by a different wave function. In standard quantum mechanics the change in the quantum state is called "collapse of the wave function", in QBism it may be called "mental readjustment" but I fail to see any substantial difference if that "mental readjustment" comes together with an actual physical change in the system ("the measurement is solely disturbance").
I just find that it's misleading to say that
> in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.
or
> in some interpretations the wave function is "really objectively out there", but in others [presumably including QBism] the wave function is "just a good way to store my beliefs about the future".
Ah, I think I have a clearer understanding of what you're getting at now.
I think your first objection is to the idea that nothing physical is actually happening during the collapse of the wave function. On this I completely agree and I apologise for having used very poor phrasing. When I said "merely a reflection" I didn't intend to mean that nothing physical is occurring. I meant that (according to QBism) there is not a real objective quantum system whose real objective quantum state irreversibly collapses into a single real objective pure state. Rather, an agent has a physical interaction (a "kick") with the real world, which incurs a particular outcome, after which the agent updates their beliefs about the outcomes of future interactions in a manner analogous to Bayesian updating. The fact that this update process happens to be conveniently described by a mathematical operation we call "collapse" is neither here nor there to a QBist.
I think your second objection is something like this: some beliefs are better than others. In many situations there appears to be one belief which is "the best". Therefore whichever belief is "the best" is essentially an objective description of the world. Therefore the quantum state of a system is real and objective.
Is that a fair assessment?
Whether or not this objection holds water, I must retain the claim that in QBism the wave function is not "really objectively out there". It is clear that in QBism a quantum state represents an agent's beliefs (or in weaker interpretations, an agent's information) regarding a system, not something objective about the system. Fuchs, Schack, Caves and others have said this again and again. For example:
> Contrary to those desires, quantum theory does not
describe physical reality. What it does
is provide an algorithm for computing
probabilities for the macroscopic
events (“detector clicks”) that are the
consequences of our experimental
interventions.
> In other words, Fuchs argued, the wave function does not describe the world—it describes the observer. “Quantum mechanics,” he says, “is a law of thought.” Quantum Bayesianism, or QBism as Fuchs now calls it, solves many of quantum theory’s deepest mysteries. Take, for instance, the infamous “collapse of the wave function,” wherein the quantum system inexplicably transitions from multiple simultaneous states to a single actuality. According to QBism, the wave function’s “collapse” is simply the observer updating his or her beliefs after making a measurement.
> The world may be full of stuff and things
of all kinds, but among all the stuff and all the things,
there is no unique, observer-independent, quantum-state
kind of stuff
> Specifically, there can be no such thing as a
right and true quantum state, if such is thought of as defined by criteria external to the agent making the assignment: Quantum states must instead be like personalist,
Bayesian probabilities
BTW, have you heard of the PBR theorem? It made me do a lot of thinking about what it could possibly mean for the quantum state to be a physical fact vs simply information about an underlying state. If these sorts of ideas are interesting to you, you might enjoy a write-up of the theorem by Matt Leifer: https://arxiv.org/pdf/1409.1570.pdf
I am aware of PBR and I find it quite convincing. Regarding QBism it's not clear to me what's the point.
There is the "information processing" aspect. You have a model of physical system based on the available information (in the form of probabilities over a space of states). If you acquire more information (without changing the state of system!) you can refine your description. That's "Bayesian updating" part. If you change the system, you also get a new description. But that is not merely an update of your beliefs about the unchanged state of the system based on new information, and Fuchs distinguishes this "readjustment" from the Bayesian conditionalization.
I don't think the mechanism discussed in the previous paragraph is controversial. In standard QM you can also have imperfect information about a quantum state. Then you do not have a wave function at all. You may have a density matrix, which can be used to compute the probabilities of potential measurements, but you don't know what is the underlying state. And the underlying state exists only if you have a proper mixture, but if you're looking at a subsystem of a larger system in a non-separable state you have an improper mixture and even if you had perfect information about the composite system there is no wave function describing the subsystem.
Then there is the "quantum state is not a description of physical reality" aspect [1]. But you can have the Bayesian description of our knowledge of quantum states without breaking the link between quantum states and physical states (and I'd say that according to PBR if you have perfect knowledge of the quantum state, i.e. you have a wave function, then it does correspond to a physical state).
We could also apply the same treatment to Classical Mechanics:
The states of the system correspond to points in a phase space. The "information processing" aspect looks reasonable: we can describe our knowledge about the state as a probability distribution over the phase space, refining our knowledge means getting a more concentrated distribution as we incorporate additional information. We can also interact with the system, so we get a new description that is not simply a refinement of the previous distribution but incorporates the physical change effected. In the case when we have perfect knowledge (our description is a point in the phase space) we know how this point will evolve and no information can be gained at all. But we still can perturb the system to a different point in the phase space (this is what Fuchs would call a "readjustment").
The "state is not description of physical reality" aspect do not look so reasonable. We can say that states do not exist. Those points in phase space do not describe physical reality, they describe only the observer. There is not such a thing as a right and true state of the system, if such is thought of as defined by criteria external to the agent making the assignment. States must instead be like personalist, Bayesian probabilities. We can say all that, but what is the point?
I don't say that there are not issues with QM, but I don't see how QBism does solve them. Whatever the problems may be with the "quantum-states-are-physical-states" approach, the "quantum-states-are-not-physical-states/physical-states-are-something-else" approach may get rid of some of them but that's not exactly solving them and introduces new issues in defining what is the relation between "quantum states" and "physical states" (hopefully there is some, if we're doing physics).
[1]: which is controversial, here QBism is closest to the “hardcore” Copenhagen view (the wave funciton is a mathematical device used to calculate in the context of an experimetal setting) than to the "standard" QM theory which is based on the state of a physical system being described by its wave function.
So... quantum interpretations can broadly be categorised thus.
1) Psi-ontic: the wave function is a real objective property of a system. This splits further depending on what is said to happen during collapse:
1a) Collapse is real (I don't know if this interpretation has a name but I think a lot of practising physicists think in these terms): this leads to the measurement and Wigner's friends problems I alluded to above
1b) Collapse is apparent (many worlds, de broglie-bohm): this is somewhat more satisfactory but usually raises other issues (e.g. the emergence of the Born rule).
2) Psi-epistemic: the wave function is a representation of some subjective state regarding a system and an agent. This splits further depending on how subjective you're prepared to go.
2a) Weakly psi-epistemic: the wave function represents an agent's state of information/ignorance regarding some true underlying objective ontic state of the system. This type of interpretation is (more or less) demolished by PBR.
2b) Strongly psi-epistemic (QBism): denies the existence of an underlying objective ontic state of a system. The wave function merely represents an agent's beliefs regarding the outcome of future interactions with the system.
I agree QBism is pretty controversial and that it lacks a certain satisfying explanatory mechanism. However I don't think you can deny that it is more than simply "standard QM", or that there are some good reasons for preferring it.
QBism doesn't seem "more" than standard QM to me, it seems "less" because it's just standard QM without pretending that the quantum state describes the physical state. There may be some reasons to throw the towel on realism and just shut up and calculate, but it's not like that's a new idea.
The operations done to establish from the available information what is the quantum state of a system and to calculate predictions are exactly the same in QBism and standard QM. All the positive-operator-valued-measures stuff works just the same, as far as I can tell, when quantum states are considered representations of reality. If our knowledge is sharp we have a wave function which describes the physical state, otherwise we have a density matrix and we ignore the precise state but we can make predictions about physics. In QBism we have the same predictions (and the same wave function / density matrix but devoid of meaning).
I don't completely understand the split 2a/2b and how 2b is more tenable. What does "the outcome of future interactions with the system" mean if there is no "true underlying objective ontic state of the system"? I understand that according to QBism quantum states do not represent reality. But does physical reality exist at all or not? Is there a "physical state of the system", even though it cannot be described using QM? If there is no state of the system, what does "system" mean? How is the "outcome of the interactions with the system" determined?
This thread is getting a lot longer and more involved than I anticipated. Apologies but for the sake of my own free time and sanity I may have to slow down and make more use of citations. The main point I was trying to get across was that QBism does say these things about quantum theory, regardless of whether or not you find it tenable.
As I say the mathematics is invariant across interpretations, therefore the Born rule and POVMs have a use to an Everettian just as they do a QBist. The difference is what they think of the physical meaning of such a thing. [0][1]
Interpreting quantum theory with a radical, personalist Bayesian perspective of the quantum state is novel, although it has historical precedents starting with Bohr and continuing with Jaynes, Wheeler. [2]
QBists broadly speaking tend to assume a pragmatist view of realism, at least in relation to quantum theory. Fuchs describes it as "participatory realism". There is a physical reality but we are ourselves entwined with it and cannot assume that the models we construct are objective and observer-independent. I think Fuchs has argued that the measurement problem, Wigner's friend, Bell's theorem and Kochen-Specker all point us irrevocably towards a radical Bayesian perspective of the quantum state. The task remaining is to disentangle the subjective from the objective:
> The professed goal is to strip away all those elements of quantum theory that can be interpreted in subjective, agent-dependent terms. The hope is that whatever remains will hint at something essential and objective about nature. [3]
I don't deny that QBism says things, but they don't seem so interesting to me. At least not as much as I expected when I approached the subject some time ago. I'm a fan of Jaynes and his work on information theory and statistical mechanics and I very much like the Bayesian angle here but it can be applied exactly the same (even better, I'd say) in a "realist" setting.
I think the problems in QM may not be problems after all if we could understand the physics better. Standard QM also consists in doing "as if" the quantum state represented physical reality: we (should) know that QM cannot be right and it's just an approximation to something else (QFT or whatever unification with GR) and even the way we apply QM cannot be right because it's also full of approximations (isolated systems do not exist, etc.). The "problems" that QBism "solves" may be artifacts due to those approximations and not fundamental problems. I find that all the (highly-speculative) physical theories trying to explain why things are "as if" QM was true are more promising than the metaphysical proposals of QBism or MWI (and as much as the MWI is metaphysical at least it seems better defined!).
I lack the time and patience to read the thousands of pages that Fuchs has written on the subject and I don't expect you to explain them to me either. So long, and thanks for all the fish^H^H^H^H discussion.
