A new interpretation of quantum mechanics sees agents as playing an active role in the creation of reality. Blake Stacey outlines the case for QBism and its radical potential.

The pandemic shut down our university when I was in the middle of giving a lecture. We had been anticipating the possibility for a few days, but it was still impeccable timing. I finished my spiel, out came the phones, and suddenly we weren't going to see each other post-spring break after all. For the rest of the term, I did what so many teachers found themselves doing: gamely trying to soldier on. I scrounged and borrowed a whiteboard, easel and webcam, set myself up in the nicest light the house had to offer, and did my best to convey graduate-level physics to an audience of tiny rectangles. And like so many other teachers, I learned there's nothing like a radical change of circumstances for driving one to re-evaluate what the essential ideas of a subject must be. In my case, this was complicated by the minor detail that the course I was teaching involved a lot of quantum mechanics, and the physics profession hasn't yet figured out what exactly the essential ideas of quantum mechanics are.

Oh, we know how to do the calculations. Nobody could have designed a laser or a computer chip if we didn't know that much. But the story that our textbooks tell is implicitly a tale of defeat, in a subtle way. They drop a chapter or three of mathematical arcana upon the poor student, not out of cruelty, but because we can't yet do any better. Complex numbers, matrix algebra, partial differential equations, spectral theory --- not only do the topics grow intimidating rather quickly, they also (if we are scrupulously honest) look rather arbitrary. Out of all the mental contrivances that the Mathematics department can serve up, why does quantum physics rely upon such a particular selection, and why do we employ those tools in the way that we do?

It is difficult to avoid turning philosophical about such matters. Questions like "What is the relation between our mathematical abstractions and physical reality?" feel as though they ought to be followed by a "like, dude". The history of attempts to answer such questions is complicated and contentious and written in no one place. Sometimes, the ideas themselves seem as if they are retreating from clarity. At other times, one wonders if philosophers and physicists wish to write as though clarity were the enemy.

I first started to care about the "interpretation" of quantum physics several years after I began using it. Many physicists don't care about such things at all, or they grow out of it rather than into it. It does indubitably feel strange that we would have to "interpret" a scientific theory; such language seems like it would belong more to critics of free verse or abstract art. ("What I feel the sculptor is trying to say...") But sometimes, when we're trying to develop the theory in new directions, or find the clearest way to teach it to the next generation, or we've just had one too many late nights wondering what it all means, we have to get our fingers philosophical.

Sometimes, the ideas themselves seem as if they are retreating from clarity. At other times, one wonders if philosophers and physicists wish to write as though clarity were the enemy.

After navigating the various viewpoints on offer, I found myself drawn to one that had only recently been articulated, the QBism laid out by Christopher Fuchs and Ruediger Schack. QBism has elements that are radical --- perhaps subversive, even --- while at the same time showing how some things we do as part of "weekday physics" are philosophically respectable after all. And, beyond providing a story to tell about the equations we already have on the books, it points to the tantalizing possibility that we can discover where those equations come from.

The QBist take on quantum mechanics is that, at its core, quantum mechanics is a theory of actions and consequences. A QBist looks for objectivity on a different level than the adherents of many other interpretations do. And the kind of lesson that we think the equations are whispering about reality are, in some quarters, downright scandalous. We resort to jargon like "normative structural realism" and "participatory realism" to give our intuitions shape and form. No existing school of philosophy seems quite right for where the physics wants to go; we'll agree with many predecessors, but often with a caveat or a qualification. Perhaps the best place to start is with that capital B.

The Q in QBism came from Quantum, of course, and the B originated with "Bayes". In the wide spectrum of ways to think about probability, "Bayesianism" encompasses a variety of schools of thought which hold that a probability is a value that an agent asserts, a quantitative expression of a degree of belief. Probabilities encode expectations, and without someone around to do the expecting, there would be no probabilities. Before there were weather forecasters, there were no forecasts, even though the world had plenty of weather. In the proto-QBist days, around the turn of the millennium, the idea was just that the probabilities in quantum physics could be understood in a Bayesian way. But "Bayesian" is a broad label, and those early attempts were not very good at narrowing it down; nor, as further investigation revealed, were they internally self-consistent. That early "Quantum Bayesianism" took several more years to mature into QBism.

QBism regards quantum mechanics as a "user's manual". In this interpretation, quantum mechanics is about what happens at the interface between an agent and the rest of nature. Most of the mathematical entities employed in the theory, like the "wavefunctions" of which so much has been said, boil down to being bundles of expectations. Whose expectations? Yours, or mine, or those of whoever has picked up the user's manual and is trying to benefit from its guidance. Expectations for what? For the consequences of the user's own actions. What kind of actions? Any kind, in principle. Very often, physicists think of a "quantum measurement" as something that requires a laboratory to pull off. But in principle, the act of smelling a rose has every right to be considered a "quantum measurement". It is only that roses are big and we manipulate them clumsily, so one's expectations about a rose will be too fuzzed out for invoking quantum mechanics to be worthwhile in practical terms.

QBism has elements that are radical --- perhaps subversive, even --- while at the same time showing how some things we do as part of "weekday physics" are philosophically respectable after all.

Following the genre conventions of information-theory books, let's name our agent Alice. She has a system of interest before her --- perhaps an atom, perhaps an ion-trap quantum computer or a rose or a loaf of sourdough bread. She contemplates the possible actions she might take upon the system. By using quantum mechanics, she can assign probabilities to the possible consequences of each action, in a self-consistent way. Then she makes a choice and reaches out, taking action and experiencing the result. She can then update her expectations for future experiences in accord with this measurement outcome --- with the new fact that she, in synergy with the system, has brought into being. Prior to the measurement, Alice's uncertainty was not due to ignorance of an outcome already there, waiting to be uncovered, but rather her recognition that the fact of the outcome did not yet physically exist. It is this last realization, the principle that measurement outcomes aren't just waiting to be read off but instead require participation to elicit, that opens up the radical new possibilities of quantum physics.

This is at least an internally coherent narrative about the mathematics, which is the first thing we ask of an interpretation. But what does it say about nature that quantum mechanics is such a good user's manual for you or me or Alice to employ? Why this particular sage advice for swimming in the madness and salt of the world? Here we move into the realm of speculation; it is one thing to provide a narrative and another to successfully extract a lesson from it.

Consider again Alice measuring an atom. Her wavefunction for the atom encodes her personal expectations for future experiences, and her changing her wavefunction for it upon obtaining a novel experience is a transformation within her. But both Alice and the atom participate in the measurement event; both partake in the creation of a new fact for the pair of them. And if the atom can participate in such ongoing acts of creation when the other player is an agent, surely it can do so when the other player is not. That is to say, whatever fundamental capacity for creation the atom brings to an event, it should bring whether or not the other participant is a conscious agent, let alone a trained quantum mechanic. As one of our papers said, "Certainly QBism has creation going on all the time and everywhere; quantum measurement is just about an agent hitching a ride and partaking in that ubiquitous process."

It is this last realization, the principle that measurement outcomes aren't just waiting to be read off but instead require participation to elicit, that opens up the radical new possibilities of quantum physics.

This kind of imagery has predecessors. It's not unlike Karen Barad's notion of "intra-actions", or Alfred North Whitehead's "actual occasions" and "throbs of experience". William James wrote of "new being com[ing] in local spots and patches". And John Archibald Wheeler went all in. For him, the generation of a measurement outcome was the "elementary quantum phenomenon". "Is the entirety of existence," he would ask, "rather than being built on particles or fields of force or multidimensional geometry, built upon billions upon billions of elementary quantum phenomena, those elementary acts of 'observer-participancy,' those most ethereal of all the entities that have been forced upon us by the progress of science?" He would say, "In some strange sense the quantum principle tells us that we are dealing with a participatory universe." But what exactly is that "quantum principle"? There, Wheeler said, physics lacks a good answer: "We understand any other principle of physics in enough completeness to summarize it, beginning with a good name, in a dozen words---but not this."

Now, for all our sympathies with Wheeler, QBism does diverge from his vision and terminology in some ways. For one, "observer" is to us far too passive a word; it carries the connotation of leaning back, not of pounding the pavement and wearing out the shoe-leather. That's why we talk instead of agents, as I did above. So, “agent-participancy”, then.

But Wheeler did have his finger on the right question. We need to nail down that "quantum principle"! The next level of sophistication, the next stage of understanding, is surely to abstract away the "agent-". What can we say of the situations where the "ubiquitous process" has nobody along for the ride, no agent Alice to partake? The first step to answering that, we think, is to quantify just how involved an agent is in eliciting an outcome. If Alice is a good user of quantum theory, then her expectations for one measurement must tie together with her expectations for another, rather than being a wild free-for-all. Exactly how the theory says her beliefs should mesh is an indicator of how her participation matters. Indirectly, it is a clue to what participation means.

So far, this is still only imagery. But by teasing apart the mathematics of quantum theory, unraveling the convenient conventions from the deep enigmas, perhaps the imagery can be made more precise and more evocative than ever before.