Making Sense of QBism: Non-Mathematical Reality & Reforming the Theory

[kith]

But pilot waves (aka Bohmian mechanics) can also be viewed as one such mathematical formulation https://pdfs.semanticscholar.org/2fb0/4475228ff385a44a16e3ba42b432d3bf5b17.pdf so it is not clear why it would be irrelevant from the QBist point of view. But this formulation is explicitly nonlocal.

Thanks for this stimulating paper. I agree that all these mathematical formalisms somehow belong to the theory of QM itself. To me, this raises the interesting question how a mathematical formalism which is usually associated with a certain interpretation is interpreted in other interpretations. So how would a QBist talk about the equations of dBB or the path integral? I think you still dodged my question a bit by writing "But this formulation is explicitl nonlocal" (especially considering that I asked to taboo the word nonlocal ;-)).

 

[Minnesota Joe]

This is why they claim those objects cannot be analyzed or described mathematically. Because of Bell's theorem, you need nonlocality, multiple outcomes, retro-causation, etcetera; they also exclude all those possibilities.

Does claiming a problematic result of a theory is off-limits to analysis make it consistent?

You are saying that QBism evades inconsistency by claiming that objective reality can't be analyzed or described mathematically. If that is a fair characterization, I agree that is a reason for the evasion, but I wasn't asking about that type of inconsistency (tension with Bell's theorem).

Instead I was asking about about an inconsistency between the principle used to evade Bell and with the other beliefs they adopt, if they do, about the existence of objective reality and other minds.

 

[Demystifier]

So how would a QBist talk about the equations of dBB or the path integral? I think you still dodged my question a bit by writing "But this formulation is explicitl nonlocal" (especially considering that I asked to taboo the word nonlocal ;-)).

If I were a QBist who wants to avoid nonlocality at any cost, I would do it this way. Consider two particles in 3 spatial dimensions described by coordinates ${\bf x}_1,{\bf x}_2$. Mathematically it is the same as one particle in 6 spatial dimensions. From this 6 dimensional perspective, all the Bohmian equations are local in the 6-dimensional space. The 6-dimensional space, of course, is not what we experience in experiments, but that's not a problem for QBism. After all, the wave function $\psi$ is also not something that we experience in experiments, and yet nobody complains that it is a problem for QBism. Those mathematical objects are just abstract mathematical tools, they are not reality. In this sense QM is local even in the Bohmian formulation. A similar 6-dimensional perspective can also be taken for two particles in the path-integral formulation. And the generalization to $n$ particles is, of course, obvious.

 

[kith]

This doesn't seem very qbist in spirit to me. I think that they would rather answer along lines which are similar to section 21 in the 2019 FAQBism paper by DeBrota & Stacey which you cited earlier. There, they outline how they interpret unitary time evolution in terms of beliefs.

 

[Demystifier]

This doesn't seem very qbist in spirit to me. I think that they would rather answer along lines which are similar to section 21 in the 2019 FAQBism paper by DeBrota & Stacey which you cited earlier. There, they outline how they interpret unitary time evolution in terms of beliefs.

But in this text they do not deal with the Bohmian formulation of QM. The issue is how would a QBist interpret the Bohmian formulation of QM.

 

[kith]

But in this text they do not deal with the Bohmian formulation of QM. The issue is how would a QBist interpret the Bohmian formulation of QM.

If we treat the Bohmian equations (but not the Bohmian ontology) as part of the theory of QM and look for a QBist interpretation, I expect terms like "experience", "belief", etc. to play a prominent role. For the first part of the Bohmian equations (the Schrödinger equation), DeBrota & Stacey have given such an interpretation in section 21 of their paper, so it seems natural to me, to try to apply a similar scheme to the second part of the equations. I don't know if this can be done and maybe it can't but then I want to understand why. In any case, your account in post #38 doesn't try to go this route.

 

[Demystifier]

For the first part of the Bohmian equations (the Schrödinger equation), DeBrota & Stacey have given such an interpretation in section 21 of their paper, so it seems natural to me, to try to apply a similar scheme to the second part of the equations. I don't know if this can be done and maybe it can't but then I want to understand why. In any case, your account in post #38 doesn't try to go this route.

Perhaps a QBist may think of Bohmian trajectories as something analogous to gauge potentials. They may be useful as an additional computational tool, but they are not "physical" in the QBist sense (e.g. not directly encode beliefs on experiences). The nonlocality associated with Bohmian trajectories is analogous to nonlocality associated with the Coulomb gauge. Moreover, Bohmian velocities obey a kind of "gauge" symmetry, in the sense that the velocities ${\bf v}_{\rm Bohm}$ and ${\bf v}'_{\rm Bohm}$ make the same measurable predictions if they are related as
$${\bf v}'_{\rm Bohm}={\bf v}_{\rm Bohm}+{\bf u}$$
where ${\bf u}$ is an arbitrary solution of
$${\bf \nabla}(|\psi|^2{\bf u})=0$$

 

[kith]

Perhaps a QBist may think of Bohmian trajectories as something analogous to gauge potentials. They may be useful as an additional computational tool, but they are not "physical" in the QBist sense (e.g. not directly encode beliefs on experiences). The nonlocality associated with Bohmian trajectories is analogous to nonlocality associated with the Coulomb gauge.

Yes, that sounds better.

Now even though in electrodynamics, we often use the Coulomb gauge, nobody considers electrodynamics to be nonlocal (or at least does not consider nonlocality in unphysical computational tools a problem).

So if the QBist takes an analogous point of view about the Bohmian formalism of QM, why would she consider QM to be nonlocal (or consider nonlocality in these unphysical computational tools a problem)?

[Also thanks for pointing out the "gauge freedom" in the Bohmian velocities. I wasn't aware of this interesting fact.]

 

[PeterDonis]

why would one consider QM to be nonlocal

Because QM gives experimental results that violate the Bell inequalities. Classical EM does not.

 

[kith]

Because QM gives experimental results that violate the Bell inequalities. Classical EM does not.

The context of what you quoted was the QBist perspective. I edited my post to make this more clear.

I think we shouldn't conflate the specific discussion I have with @Demystifier (about how the Bohmian formulation of QM would be interpreted from a QBist perspective) with the broader question of why QBism is considered to be local by its proponents.

 

[Demystifier]

So if the QBist takes an analogous point of view about the Bohmian formalism of QM, why would she consider QM to be nonlocal (or consider nonlocality in these unphysical computational tools a problem)?

Even though quantum nonlocality cannot be used to send superluminal signals, in http://de.arxiv.org/abs/1006.0338 I argued that it can be used to create an illusion of sending superluminal signals. This illusion is experienced by an agent who does not know that her illusion of free will has been manipulated by an external manipulator. Perhaps a QBist might interpret it as a genuine nonlocality.

 

[kith]

Just a quick comment: I skimmed your paper and didn't understand its main point from this. At the moment, it's unlikely that I give it a more thorough reading. I think that in principle, questions of free will are related to quantum interpretations but I'm more interested in more tangible things.

 

[akvadrako]

In regards to how a subjective theory like QBism could be non-local:

Nominally, a subjective theory is always local because all the information is "in the head" of the observer: it includes everything he needs to know to make the best prediction possible. Let's assume his head is of a finite size and there is a bound on how much information it can contain. Then, if the information needed for a model of his experience with the maximally possible precision exceeds this bound, whatever is generating his experience must be storing and retrieving information non-locally.

Would that make sense to a QBist?

 

[Demystifier]

Then, if the information needed for a model of his experience with the maximally possible precision exceeds this bound, whatever is generating his experience must be storing and retrieving information non-locally.

Interesting! Do you have any example in which the bound could be exceeded?

 

[akvadrako]

Interesting! Do you have any example in which the bound could be exceeded?

Nothing specific. The best I can come up with is imagine an experimenter studying some system. He records lots of data, much more than he can remember even if he's a perfect information storage device. If more of those records are needed to compute the future observations of that system then can be encoded locally, what's physically local must be only an approximation of them. Some non-local information is physically relevant.

I don't know if this really makes sense.

 

[RoelofV]

QBIsm does not, I repeat, does not deny objective reality. What it denies is our ability to fully describe it. The very act of thinking (let alone speaking) about reality implies that we model some aspect of reality. That is we apply some kind of filter or abstraction. Reality exists. There is "stuff" out there but any description of that "stuff" will be incomplete or more accurately will be some kind of abstraction and will - of necessity - leave out details. QBists are by no means solipsists and fully deny solipsism. They fully believe that "stuff" is out there independent of our existence.

QBists accept objective reality and at the same time deny non-locality and believe that this does not lead to a contradiction. This has to do with a fundamentally different interpretation of probability which is Bayesian based rather than frequency based. Put another way QBists associate probability with the observer (as a quantifier of uncertainty/ignorance) about the phenomenon and not inherent to the object itself. This allows different probabilities to be validly associated with the same quantum state for example as different observers can have different degrees of certainty. The Bell theorem assumes a unique probability for a quantum state. This is why QBists state that the Bell theorem is not valid in a QBism interpretation.

QBists agree that objective reality but that it cannot be _fully_ described mathematically. It is certainly possible to describe models (abstractions) of reality mathematically. QBists do not believe that models of reality are misleading or irrelevant nor the mathematics needed to form those models/abstractions.

QBists indeed believe that the map is not the territory.

 

[gentzen]

QBIsm does not, I repeat, does not deny objective reality. What it denies is our ability to fully describe it.

This is an old thread, and this is your first post. Why do you want to "reopen" it? What is your affiliation with QBism? (Because this is your first post, we have no idea "where you are coming from".) Or was this thread simply "so bad" that you just had to correct its misconceptions?