I am intrigued by the current debate in physics concerning the significance of the wave function in quantum theory. The nature of the debate opens the door to a host of philosophical issues surrounding both physics and mathematics. In an article appearing in the June issue of Scientific American, I was introduced to a relatively new, alternative view of the nature of the wave function (known now as QBism by its proponents). Theoretical particle physicist, and author, Hans Christian von Baeyer, describes something of the history of interpretations of quantum strangeness, and outlines the way the issues are dealt with in QBism.

QBism, which combines quantum theory with probability theory, maintains that the wave function has no objective reality. Instead QBism portrays the wave function as a user’s manual, a mathematical tool that an observer uses to make wiser decisions about the surrounding world—the quantum world. Specifically, the observer employs the wave function to assign his or her personal belief that a quantum system will have a specific property, realizing that the individual’s own choices and actions affect the system in an inherently uncertain way. Another observer, using a wave function that describes the world as the person sees it, may come to a completely different conclusion about the same quantum system. One system—one event—can have as many different wave functions as there are observers. After observers have communicated with one another and modified their private wave functions to account for the newly acquired knowledge, a coherent worldview emerges.

Seen this way, the wave function “may well be the most powerful abstraction we have ever found,” says theoretical physicist N. David Mermin of Cornell University, a recent convert to QBism.

The most immediate allure of not attributing a physical reality to the wave function is that it rids the quantum realm of disturbing paradoxes, like a particle occupying two locations at the same time, or information traveling faster than the speed of light. In the 1930s Niels Bohr emphasized the formalism that gave the wave function its power as *a computational tool*. But this view of the wave function is strengthened considerably in QBism which incorporates the use of Bayesian statistics. Bayesian statistics was established by Thomas Bayes in the 18th century, and then independently rediscovered and developed further by Laplace in the early 19th century. The Bayesian paradigm employs probability as a conditional measure of uncertainty much like the ordinary use of the word. Statistical inference, then, is the modification of the uncertainty about a quantity in the light of new evidence. Bayes’ Theorem specifies how this modification is made. These probabilities contrast with the probablities defined by observed frequencies – how many times something actually happens. In simple cases like coin tosses, the two kinds of probablities agree. But, von Baeyer explains,

For the prediction of the weather or of the outcome of a military action, the Bayesian, unlike the frequentist, is at liberty to combine quantitative statistical information with intuitive estimates based on previous experience.

I find it worth noting that Bayesian statistics are also being used widely to model perception, cognitive development and learning in general.

Christopher A. Fuchs, now at the Perimeter Institute in Ontario, is a prominent spokesperson for QBism. Von Baever reports in his article that Fuchs recently made an important mathematical discovery that provides QBism even greater strength. He has shown that experimental results can be predicted without using wave functions at all, and using probabilities alone.

There is an illustration in the Scientific American article that I believe allows a mistaken oversimplification of the issue. In the illustration, the wave function is placed either in the box that has Schrodinger’s famous cat, or inside the head of the person looking at the box. The wave equation may be an instrument, but the complexity of its development, and its use, should serve to amplify the complexity of our relationship to the world we perceive.

In a paper collecting answers to interview questions, Fuchs takes note of the fact that QBism makes Wheeler’s question, “why the quantum,” even more pressing.

In other words, even if quantum theory is purely a theory for apportioning and structuring degrees of belief, the question of “Why the quantum?” is nonetheless a question of what it is about the actual, real, objective character of the world that compels us to use this framework for reasoning rather than another. We observers are floating in the world, making decisions on all that we experience around us: Why are we well-advised to use the formalism of quantum theory for that purpose and not some other formalism? Surely it connotes something about the general character of the world—something that is contingent, something that might have been otherwise, something that goes deeper than our decision-making itself.

Then later,

What has been lost sight of is that physics as a subject of thought is a dynamic interplay between storytelling and equation writing. Neither one stands alone, not even at the end of the day.

No doubt the difficulty with QBism is the manner in which notions of objectivity and subjectivity are being handled. But this is an intriguing problem, and one which the content of mathematics always poses. I’ll end with Fuch’s take on the problem of allowing ‘subjectivity’ into science.

“Subjective” is such a frightening word. All our lives we are taught that science strives for objectivity. Science is not a game of opinions, we are told. That diamond is harder than calcite is no one’s opinion! Mr. Mohs identified such a fact once, and it has been on the books ever since. In much the same way, quantum theory has been on the books since 1925,

and it doesn’t appear that it will be leaving any time soon. That isn’t lessened in any way by being honest of quantum theory’s subject matter: That, on the QBist view, it is purely a calculus for checking the consistency of one’s personal probabilities. If by subjective probabilities one means probabilities that find their only source in the agent who has assigned them, then, yes, quantum probabilities are subjective probabilities. They represent an agent’s attempt to quantify his beliefs to the extent he can articulate them. Why should this role for quantum theory—that it is a calculus in the service of improving subjective degrees of belief—be a frightening one? I don’t know, but a revulsion or fear does seem to be the reaction of many if not most upon hearing it. It is as if it is a demotion or a slap in the face of this once grand and majestic theory. Of course QBism thinks just the opposite: For the QBist, the lesson that the structure of quantum theory calls out to be interpreted in only this way is that the world is an unimaginably rich one in comparison to the reductionist dream. It says that the world has excitement, risk, and adventure at its very core.

And it says that we are made of stuff belonging to that world that possesses an inexhaustible talent for building structure from sensation.

I don’t understand this theory but I’m pretty sure it’s not even wrong. Beauty is in the eye of the beholder but facts are not.

Why would anyone be surprized that the wave function isn’t real? No scientific equation of physics is real. Is someone actually expecting that one day we’ll flip over a rock and find E=MC2 under it, and we’ll all shout Eureka?

– Greg

Thank you. This is very nice encouragement.

To encourage you, I quote myself from a book review of a Poincare biography:

“There is even a short section on Poincaré’s minor contribution to the early quantum theory (p. 378), which he encountered a year before his death at the celebrated 1911 Solvay conference. The ever quotable Max Planck later offered this magnificent compliment: “An old man will be inclined to ignore the hypothesis, the enthusiast will welcome it uncritically, the skeptic will seek grounds to deny it, the productive man will test it and fructify it. Poincaré, in the profound paper which he dedicated to the quantum theory, proved himself youthful, critical, and productive” (p. 150).

HvB

Yes. I will try to do more with this myself.

been toying with bayes for years…

i personally have found it tricky to match it to human engagement in a neat way

sounds like these guys have managed something

your final commentary matches the title

and indeed QBists may have found a route to ‘subjective science’