QBism: The simplest interpretation of quantum physics

This article is part of Adam Frank’s series on Quantum Bayesianism, or QBism. Here are the links to parts 1, 2 and 3.

Quantum mechanics is both our most powerful and strangest scientific theory. It is powerful because it offers exquisite control over the nanoworld of molecular, atomic, and subatomic phenomena. It’s strange because even though we have a complete mathematical formalism, we physicists have been arguing for more than a century about what that formalism means. In other words, unlike other physical theories, the mathematics of quantum mechanics is not clear interpretation. This means that physicists and philosophers have been left arguing about which interpretation makes the most sense. The idea of ​​”simplicity” is sometimes invoked to answer this question.

So today, building on a wonderful discussion that started at X of all places, I want to argue that Quantum Bayesianism, or QBism, offers the “simplest” account of this all-powerful quantum formalism.

The “simplest” explanation.

There are two main parts to the quantum formalism. The first is what is called the dynamic equation. This part gives us a mathematical description of how systems are not disturbed evolve. Physicists love our dynamical equations: things like Newton’s equations for particles or Maxwell’s equations for electromagnetic waves. In classical physics, the dynamical equation was pretty much the end of the story. Nothing more was needed and we came to think that these equations existed “out there”. They were timeless laws of physics that never required any reference to what physicists did.

But this is not the case with quantum mechanics. In non-relativistic quantum mechanics, the Schrödinger equation serves as the fundamental dynamical equation. The Schrodinger equation gives what is called a “wave function,” the mathematical object that describes the state of the system as it evolves in time. But this is where the wrench is thrown into the story. The wave function is strange in many ways. In particular, it tells us that the system (for example, a particle) can have many values ​​of its physical properties (such as position or spin) at the same time. Another way to say it is that the different values ​​overlap. The ambiguity about non-pre-existing properties in a superposition is where all the hilarity about Schrodinger’s famous cats, with their simultaneous “deadness” and “undeadness” originates. “Death” and “not death” could not occur in classical physics, where there is no doubt about the reality of the system’s properties other than experimental uncertainty. So what determines the actual value that a given property takes in quantum physics?

The role of measurement

The answer, interestingly enough, is the measure itself. Along with the dynamic Schrodinger equation, the quantum formalism adds Born’s rule. Born’s rule tells us that when a measurement is made, the dynamics of the Schrodinger equation is interrupted. The superimposed wave function “collapses” to a single value. In particular, Born’s rule tells us to use probabilities drawn from the wave function itself to predict what will be measured.

The dynamical Schrodinger equation: the wave function with its strange superposition of properties and Born’s rule: this is the quantum formalism. The centuries-old debate about quantum interpretation has revolved around how to understand these things in terms of reality But in the long history of this debate, most of the effort has come from trying to work around the Born rule. Since we physicists are very fond of our timeless dynamical laws, Born’s rule was seen as a scar on an otherwise beautiful theory. For many researchers, the task was to preserve this beauty and think how to get out of the constraints of the Born rule. This involved explaining (or explaining) the role of measurement and, by implication, measurers.

It’s an effort that has resulted in some pretty wild extrapolations. For example, the famous Many Worlds Interpretation (MWI) states that every time a measurement is made, a new “world” emerges. In the MWI, there is a world for each part of the wave function. When a measurement is made, these worlds become disconnected from each other, existing side by side like ghosts (which is why I call it the “many ghost interpretation”). In that X conversation I mentioned, my friend and colleague Jason Wright asked, “Isn’t MWI the simplest interpretation because it just takes the wave function as it is?” Within a certain kind of logic, the question makes sense. Those distinct (and possibly infinite) overlapping parts of the wave function just come out of the Schrodinger equation. Why not treat them all as real in some way? (It’s worth noting that Wright says he’s not a proponent of MWI, he’s just asking the question.)

My answer is that there is an even simpler way to see what’s going on, which is exactly what QBism does. Instead of seeing the wave function as the holy of holies, whose reality must be preserved at all costs, focus on what is new in the quantum formalism, namely the rule of born Quantum mechanics has been telling us for 100 years that measurement is important. Feeling it and taking it to heart is exactly what QBism brings to the table.

Focusing on the Born rule

So how does QBism achieve this so simply? It treats the wave function as encoding information our interaction with the world, not the world itself as seen from a perfect vision of God. As my colleague, the eminent quantum physicist Joe Eberly, said, “It’s not the electron’s wave function, it’s yours.” Take this position and you don’t need an infinite number of unobservable ghost worlds or other sci-fi entities. This certainly seems much simpler to me.

The thing about quantum mechanics, though, is that each interpretation pays a price that takes you beyond the easy-to-imagine-in-your-head perspective of classical physics. The price of QBism is to see quantum mechanics revealing fundamental aspects us and the world together, not just the world. The way he pursues this is a relentless focus on the Born rule. Why is there a Born rule? Where does it arise? How does it arise? What is it saying about us as agents who respond to the world as it pushes back against us when we do experiments?

Instead of trying to circumvent Born’s rule and see it as a scar, QBism takes it as the central and very beautiful mystery of quantum mechanics. How it does this and what it might mean for science will be the next installment in my QBism series.

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