Quantum Bayesianism: Reaction to an Interview Part 1

In researching Quantum Bayesianism (or QBism for short) I found a fascinating interview piece online. It is a series put to the Quantum Bayesian (QBian?) Christopher A. Fuchs. While the interview is part of a book which features similar figures being asked the same questions, this interview is offered in whole for free online. I highly recommend you check it out.

Interview with a Quantum Bayesian

The following are some of my thoughts on QBism after reading the interview. ( I should note that since Fuchs is not representative for all QBians everywhere, these should just be considered impressions of QBism and not necessarily correct of all versions of QBism.) This is a continuation of my first post about QBism.

Realism and Anti-Realism

The most basic way to put QBism is that it is anti-realist about quantum states (q-states) but realist about everything else that is uncontroversially considered real in contemporary physics.

One way to explain what it means to be anti-realist about something is to say that it means one believes something is an aspect of mind and not of the world. This is not the best way, however, since delving into the philosophy of science and perception shows that this distinction is not nearly as clear as one hopes. Regardless, it is accurate to say that QBism argues that q-states are expressions of our beliefs about a quantum system and not an expression of any particular part of the system itself.

The most helpful way to think about realism and anti-realism is that it has to do with the meaning of entity-terms. Entity terms are those that we use to refer to things. Typically, an entity-term refers to something which exists. Examples of these from classical physics are "the planet Mars" or "a mass on a low-friction cart". Sometimes, however, we can use an entity term to refer to something that does not exist, however. An example of this from physics both classical and quantum is the "Del operator" (∇), which is considered only functional in use. It is a mathematical and conceptual tool and not a representation of nature (though we use it in multivariate calculus which helps us calculate things that do represent nature).

An anti-realism view of certain entity-terms would try and provide epistemic definitions for those entity-terms. This means that every situation where the offending entity-term is used can be replaced with some sufficiently long sentence describing what it means. For example, since the Del operator is used functionally, one could replace any instance of the use of it as a term with a long explanation of the mathematical role that it plays. This epistemic definition of Del operator would be considered complete because it is not considered real.

Entity-terms which we see as referring to real aspects of the world are not allowed to be constricted in this way. Though it may seem philosophically annoying, if we think of something as referring to an existing thing we must allow the term to be flexible so as to accommodate unforeseen behaviors exhibited by the real object.

Realism and Lack Thereof in QBism

All that to say, QBism considers q-states to not be real things because they can be defined as being functionally defined through the irreducible probabilities associated with them. QBism essentially argues that every q-state can be epistemically defined through the Generalized Born Interpretation. Fuchs says:

"A quantum state just is a probability assignment."

Fuchs says that he attended a conference where it was discussed what kind of linguistic classification q-states should have. In other words, are they nouns, verbs, adjectives, etc.? His answer was they are exclamations (or, more specifically, expletives). This is an absurd answer, but it should illustrate that Fuchs seeks to eliminate any talk which uses q-states.

Q-States cannot be Exclamations

The significance behind saying something is an exclamation should be immediately obvious to anyone who has taken a course in meta-ethics or has researched non-cognitivism. Non-cognitivism holds that moral sentences cannot be true or false, they are only an expression of an attitude, like "Ouch!" or "Hey!" These sentences are not considered true or false.

Sentences which use quantum states cannot possibly be exclamations because they are true or false. When a physicist uses quantum mechanics to describe a physical system he typically begins by assigning it a quantum state, and he can be mistaken or correct about the quantum state he assigns.

It should be noted that saying a q-states are a nouns does not commit one to any metaphysical view about them. Entity-terms that we do not consider actually real are still nouns. For example, one can say metaphorically that "a feeling of dread hung in the air". One can be committed to this dread not literally existing but regardless one will still use the word "dread" as a noun.

Implications of QBism's Anti-Realism

Quick question: why does science work so well? How come these weird concepts science uses can be interpreted by humans and used to manipulate the world so reliably? The easiest answer to this question: the weird concepts of science actually describe the world around us and not simply some aspect of our mind.

Anti-realist views about an aspect of science have the disadvantage of not being able to account for why those concepts are so successful at manipulating the world. Since QBism argues that q-states are not physically real things, then it must admit that it is a huge unexplained mystery as to how quantum mechanics can be used so effectively.

Surprisingly, I found this embraced by Fuchs in the interview. He says that this is the most pressing question of quantum mechanics: "Why the quantum?" (how it is possible that it works so well?). Though this is a solid argument against QBism, this shows that it is obviously no nail in the coffin. For Fuchs, it is not a problem because he sees no other interpretation of quantum mechanics as being sufficient for understanding quantum mechanics in a way that makes sense, therefore "why the quantum?" is just as much a mystery for them as well. (Whether or not he is right in this judgment is another issue entirely, but I will not deal with that here.)

For Fuchs, the ideal resolution of this is when two things are achieved:

1. All discussion of q-states is eliminated or sufficiently accounted for with epistemic definitions of meaning.
2. After reformulating quantum mechanics in this way, scientists discover what it is actually about. That is to say, it comes to light what aspects of the world quantum mechanics truly describes.

This should seem to be obviously a great deal of work to justify something simple: how an extremely useful and well-understood theory is successful in manipulating the world. Instead of simply saying "it describes the world" we must instead shrug our shoulders and then offer the above game plan to understand it. But like I said, this is no death blow to QBism, which suffers no contradiction by agreeing with this picture of quantum mechanics.

(More thoughts to come...)

Correction: In the first draft I referred to the Hilbert space as an example of an entity-term in quantum physics that is not considered "real" (by which I mean "actually existing", and not "number which could be complex but lacks an imaginary value"). Upon reflection, I think that this most likely an incorrect assumption on my part, since it seems to correspond to quantum systems and represents the possible outcomes of measurements on those systems. I'll have to look into it more to figure it out.For now, however, I replaced any mention of "Hilbert space" with mention of the "Del operator", which I am sure is functionally defined. It's kinda cheating since it is a mathematical term, but it gets the point across.