[kgwgk]

> In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future".

Those “beliefs about the future” may or may not be correct. If you describe a system with a wave function you claim that you know the quantum state perfectly and there is no margin for error.

How do you think QBism helps in the following scenario?

We have spins prepared in some state, say |up>. We agree that the wave function |up> gives a complete description of the quantum states. That’s our shared belief, if you will.

While you are not looking, I do perform some operations and the corresponding mental readjustments change my beliefs: now I describe the spins with the wave function |down>. You keep your original beliefs.

Now we measure the spins along that axis. I predict a negative outcome with 100% probability, you predict a positive outcome with 100% probability. I get it right every time, you get it wrong every time.

If the |down> quantum state is not "really objectively out there", how do you explain these results?

[n4r9]

I imagine a QBist would say that when you performed your additional secret operations you gained more information and therefore you were able to develop more accurate beliefs.

Is your issue that a belief can be completely wrong, or rather that two people can hold diametrically opposing beliefs?

[kgwgk]

I quoted above Fuchs, the main proponent of QBism, saying that in that example "We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance." So it is not about refining our knowledge of the physical state as it was, it is about changing the physical state and learning what the new state happens to be.

Different people can have different beliefs (different descriptions of the physical state) but not all the beliefs are equally valid. We can in principle check how well they fit with the (shared, objective) reality. In general this is possible only statistically (comparing realized frequencies with calculated probabilities) but in the example above it can be done from a single event: if something impossible according to your beliefs does happen, your beliefs were incompatible with reality and therefore untenable.

[n4r9]

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.

[kgwgk]

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".

[n4r9]

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.

http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/PTO00007...

> 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.

https://www.wired.com/2015/06/private-view-quantum-reality/

> QUANTUM STATES DO NOT EXIST

> 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

https://arxiv.org/pdf/1003.5209.pdf

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

[kgwgk]

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.