QBism is not a homophonic quantization of an early 20th century art movement but an increasingly influential set of ideas on how to understand quantum theory and its implications for science. This engaging book may serve as its popular manifesto.

What came to be known as quantum Bayesianism and later QBism began at the turn of the 21st century as a point of view on states and probabilities in quantum theory developed by physicists working in quantum information theory. More recently, the QBist vision of science has extended beyond quantum theory.

Applied to radioactive decay, the Born Rule of quantum theory successfully predicts such things as the half-life of the first excited state of the hydrogen atom. Most physicists regard this and other probabilities predicted by quantum theory as objective physical features of the world, typically identifying the probability of decay with the relative frequency of decay as measured in an experiment. But any probability between 0 and 1 inclusive is *logically* consistent with any actual relative frequency, however improbable, and appealing to the low probability of a radically deviant frequency renders a frequency account of probability circular.

QBists agree with De Finetti and some (though not all) statisticians who hold that there is no such thing as objective probability—there are only the various degrees of belief each of us has regarding matters of which he or she is currently ignorant. The quantum state yields probabilities of measurement outcomes, and QBists also adopt a subjectivist or personalist interpretation of quantum states. For them, a quantum state assignment does not represent the state of the physical world but the state of mind of the one who assigns it, and the Schrödinger equation does not describe the evolution of the system to which she assigns this state but tells her how to modify her beliefs about what she will find when measuring it (if she learns nothing new in the interim).

After a brief introduction, von Baeyer's book is in three parts. The first and longest part offers a general reader an almost equation-free historical introduction to quantum theory. Part II is a brief overview of probability, emphasizing its applications in daily life as well as quantum theory. The author presents criticisms of classical and frequentist interpretations of probability; he illustrates an application of Bayes' theorem to determine one's probability of having cancer given a positive test result; and he argues that its versatility, generality, and logical consistency recommend a subjective Bayesian interpretation as the primary interpretation of probability. While the medical example illustrates Bayes' theorem, it does nothing to bolster this argument since a frequentist will identify the prior probability of cancer with the base rate in the population.

We finally meet QBism in the six short chapters of Part III. von Baeyer anticipates the shocked reaction against its subjectivity he expects from those (like him) for whom physics represented an ideal of objective scientific inquiry into the nature of reality. His prior defense of subjective Bayesianism may have softened the blow, but many will still be reluctant to abandon the view that a system's wave-function represents its objective physical state. To convince them to do so, he argues that QBism's subjective view of quantum states and probabilities naturally resolves “paradoxes” of wave-collapse, Wigner's friend, and Schrödinger's cat, while doing away with “spooky” action at a distance.

If a system's wave-function represents its objective physical state, then wave-collapse (von Neumann's projection postulate, Dirac's quantum jump) is a physical process whose occurrence is difficult or impossible to reconcile with Schrödinger evolution, relativistic spacetime structure, and local action. But for a QBist there is no problem since there is no such process. Any user of quantum theory should merely reassign her wave-function to update her personal degrees of belief on learning the outcome of a measurement. Wigner and his friend may assign different wave-functions, reflecting their different experiences about what happens inside the friend's isolated laboratory. The superposed entangled quantum state assigned to Schrödinger's cat represents not its physical state but the assigner's state of belief about what he will find when opening the box with the cat in it. There is no Einstein–Podolsky–Rosen paradox because their criterion of reality is false: no element of reality is required to ground a prediction with probability unity—merely the subjective certainty of the one who makes the prediction. Bell's theorem does not demonstrate instantaneous action at a distance because quantum correlations violating Bell inequalities concern not the outcomes of spatially separated measurements but a *localized* agent's expectations about such outcomes.

I believe such undoubted benefits of QBism may be purchased more cheaply, as I explain elsewhere.^{1} Sometimes two agents should assign to a system different quantum states because their physical (not mental) situations give them access to different information. But physical conditions determine an objectively correct state assignment for each situation. The resulting Born probabilities represent neither frequencies nor any agent's actual degrees of belief, but the objectively correct degrees of belief for anyone who happened to be in that situation. They exemplify an *objective* Bayesian account of probability. In favorable circumstances, their correctness may be experimentally manifested by relative frequencies.

Just over a century ago, a reviewer of the cubist manifesto wrote “their theory of painting is founded upon a philosophic idealism. It is impossible to paint things ‘as they are,’ because it is impossible to know how and what they ‘really’ are;” and that the manifesto's whole object is “to defend cubism as the liberator from systems, the means of expression of the one truth, which is the truth in the artist's mind.” That's all very well for art, you may say, but not for a hard science like physics, which aims to say how the objective world really is and what laws govern it.

Von Baeyer defends his QBist manifesto against such skepticism in the final, more philosophical, part of his book, which matches its subtitle *The Future of Quantum Physics*. He foresees not only the general acceptance of a QBist interpretation of quantum theory but also the extension of the QBist vision of science to the rest of physics and beyond. He views laws of nature as created by us to economically summarize what we have experienced and takes QBism to honor Wheeler's vision of a participatory universe in which “particles” and agents jointly create a universe whose external reality is manifested by the unpredictable experiences that result from each agent's interactions with it. According to QBists Chris Fuchs and David Mermin, each agent uses quantum theory not so much to predict the outcomes of experiments as to better anticipate his or her individual experiences of them as well as other people's reports of their experiences. Von Baeyer seeks to secure the objectivity of QBist science by appeal to a large common core of shared experiences, but it is not clear what this comes to if all I know of your experiences is what I hear from your lips.

Von Baeyer's understanding of QBism is reliably based not only on familiarity with QBist writings but also on many conversations with its proponents, whose views he quotes, especially in the last part of his book. Many physicists, including Einstein and Bell, aspired to create a perfect map or model of ultimate physical reality. QBism scotches that aspiration: for a QBist “science is not about ultimate reality but about what we can reasonably expect” (p. 221). Is this an admission of defeat? Not according to Marcus Appleby, for whom a world we could perfectly map would be too confining—as limited as ourselves.

Today, QBism offers just one of a wide variety of radically different takes on quantum theory, each with its supporters. Converts like von Baeyer make especially enthusiastic advocates, and this book is a simply and attractively written manifesto that fairly and concisely represents the view its author favors. Any physicist who skips or ploughs through its first part will then be rewarded by an elementary introduction to the main QBist ideas, which may or may not encourage a deeper study. A general reader should be warned that QBism is today a radical minority view among physicists. As a philosopher of physics, I found the treatment of probability overly brisk and remain unpersuaded by von Baeyer's defense of the objectivity of QBist science.

## References

*Richard Healey is Professor of Philosophy at the University of Arizona. As a philosopher of physics, he has been trying to understand quantum theory for over 40 years while seeking to convince physicists and philosophers how much they stand to learn from each other by cooperating in this undertaking. His forthcoming book* The Quantum Revolution in Philosophy *represents his latest attempt to do both.*