# QBism

### It's as big a break with 20th century ways of thinking about science as Cubism was with 19th century ways of thinking about art.

Last week my paper “A QBist Ontology” was published in *Foundations of Science*. For those who are interested, here is the **official link**, here is a freely accessible** author-shared copy**, and here is a downloadable **post-peer-review, pre-copy edit version**.

The paper has a curious history. When I tried to post the original manuscript to arxiv.org (the pre-print server used by physicists all over the world), the moderators questioned my qualifications — this after having posted a total of 38 papers including 22 which had been published in peer-reviewed academic journals. I copied my reply to David Mermin (see **here**), who sent an email to the moderators, in which he made some flattering remarks about the importance of my work and his interest in it. This did not change their decision. Apparently they could not take the predominantly idealistic ontology advanced in the paper. I forwarded their final decision letter to Mermin, who then wrote to a friend of his who is currently on arxiv.org’s Scientific Advisory Board. The paper was subsequently accepted.

The original manuscript was also rejected by *Foundations of Physics*. For this I am grateful, as it gave me the opportunity to improve it. After a couple of further revisions it was accepted and published in *Foundations of Science*. Several parts of the paper — or rather, several ideas put forward in it — have already been introduced in this newsletter. The focus of today’s mailing is QBism, a refreshingly new interpretation of quantum mechanics.

Let’s begin by talking about probability. Probability is a measure of likelihood ranging from 0 to 1. If I assign to an event a probability equal to 1, I am certain that it will happen; if I assign to it a probability equal to 0, I am certain that it will not happen. Tossing a fair coin yields heads with probability 1/2; casting a fair die yields any particular natural number between 1 and 6 with probability 1/6. These are examples of the Principle of Indifference, which says: if there are *n* mutually exclusive and jointly exhaustive possible events, and if I have no reason to consider any one of them more likely than any other, then I should assign to each a probability equal to 1/*n*. (Saying that events are mutually exclusive is the same as saying that at most one of them happens. Saying that events are jointly exhaustive is the same as saying that at least one of them happens.)

There are two kinds of situation in which we may have no reason to consider one possibility more likely than another. In situations of the first kind, there are objective matters of fact that would make it certain, if we knew them, which particular event will happen. The probabilities we assign whenever we know some but not all relevant facts are in an obvious sense subjective. They are testaments to an insufficient knowledge of relevant facts.

In situations of the second kind, there are no objective matters of fact that would make it certain which particular event will happen. The probabilities we assign in this case are not attributable to a lack of knowledge. Quantum-mechanical probabilities are of this novel kind. Since they have nothing to do with anyone’s ignorance of something relevant, they are often considered objective. One of the strong points of QBism is its unwavering insistence that “objective probability” is a contradiction in terms.

There are, broadly speaking, three ways to understand probability: (i) as objective chance (a physical propensity, disposition, or tendency); (ii) as relative frequency, and (iii) as a degree of confidence or belief. While the first two senses are ubiquitous in the quantum-theoretical literature, the third is a rarity and, in the radical version floated by QBism, a novelty.

The first prominent champion of objective probability was Werner Heisenberg, to whom the quantum-mechanical wave function represents “something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality”.1 It “contains statements about possibilities or better tendencies (*potentia* in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer”.2

The tenability of the potentiality interpretation hinges on the status of an interpretive principle according to which the following conclusion is warranted: if a quantum state assigns probability 1 to the possible value *q* of an observable quantity *Q* then *Q* is in actual possession of the value *q*. (Technically this interpretive principle is known as the “eigenvalue-eigenstate link.”) Though often regarded as an essential ingredient of standard quantum mechanics, the principle is actually wrong, for an observable *Q* has a particular value *q *only if *Q* is actually measured and *q* is the result. If a quantum state assigns probability 1 to a possible value *q* of *Q*, this only means that *q* is certain to be the outcome of a successful measurement of *Q*. But if probability 1 by itself is not sufficient for the *actual* existence of a value, then a probability less than 1 is certainly not sufficient for the *potential* existence of a value.

The relative-frequency definition of likelihood, for its part, suffers from an incurable circularity. Frequentists claim that if one repeats a random experiment (such as tossing a coin) over and over, the fraction of trials that result in a given outcome (say, heads) converges to the “true” probability of the outcome (1/2) as the number of trials grows without bound. While they admit that “anomalous” frequencies (greater or less than 1/2) are likely to be obtained as long as the number of trials is finite, they insist that these frequencies will be less and less likely. In short, what they mean by “likely” depends on what they mean by “likely.”

This leaves us with the Bayesian interpretation of probability as a subjective degree of confidence. According to the Bayesian, the probability I assign to a possible event is the degree of confidence with which I expect it to occur.

QBism (short for “Quantum Bayesianism”) takes the Bayesian interpretation of probability to the next level. According to Mermin,3 QBism is “as big a break with 20th century ways of thinking about science as Cubism was with 19th century ways of thinking about art.” The big break lies not in its interpretation of quantum mechanics as a generalized Bayesian theory of probability but in this *plus* a radically subjective interpretation of the events to which, and on the basis of which, probabilities are assigned. To the QBist, a measurement is an action taken to elicit one of a set of possible experiences, and the measurement outcome is the experience elicited thereby.

While QBism — acknowledged by its founders to be a work in progress — is still rough at the edges philosophically, it has much to commend it. The fact that the mathematical apparatus of quantum mechanics only makes sense as a probability calculus tends to be obscured by the axiomatic manner in which quantum mechanics is usually taught. In standard axiomatizations of the theory, probability is introduced almost as an afterthought, as are the events to which it is assigned. *The Ashgate Companion to Contemporary Philosophy of Physics*4 bears this out by drawing a distinction between the “bare quantum formalism,” which it declares to be “an elegant piece of mathematics ... prior to any notion of probability, measurement etc.,” and the “quantum algorithm,” which it runs down as “an ill-defined and unattractive mess.” In truth, there is no such thing as a *bare* quantum formalism. Every single axiom of every axiomatization of the theory only makes sense as a feature of a probability calculus.5 Chris Fuchs — arguable the most ardent advocate of QBism — once asked: “If quantum theory is so closely allied with probability theory, why is it not written in a language that *starts* with probability, rather than a language that ends with it?”6 QBism has come tantalizingly close to writing it in just such a language.

Another strong point of QBism is the way in which it cuts the Gordian knot presented by the “disaster of objectification”.7 What is meant here by “objectification” is the occurrence of a measurement outcome. The disaster is that quantum mechanics cannot explain how it is that measurements have outcomes. It seems perfectly reasonable to assume that a measurement involves an interaction between a measurement apparatus and a system on which the measurement is performed. Yet if this interaction is modeled as a physical process, and if this process is described in quantum-mechanical terms, what follows is that there are no measurement outcomes; if the observable that is being measured lacks a definite value prior to the measurement, then the pointer that is supposed to indicate the outcome will also lack a definite value. This means that another apparatus is needed to measure the position of this pointer, and so on *ad infinitum*. Hence the disaster of objectification is also known as “von Neumann’s catastrophe of infinite regression.”

The QBist way of cutting that Gordian knot is to insist that there is no difference between observations qua measurement outcomes and observations qua (private, subjective) experiences. Instrumentalism — a doctrine often falsely attributed to Niels Bohr — makes this distinction. The distinction is, to say the least, suspect, inasmuch the reason a measurement outcome is a measurement outcome is that it indicates the value of an observable, and no value can be indicated in the absence of a sentient observer to whom it is indicated. By emphasizing that measurement outcomes are (subjective, private) experiences, QBists ascribe the obvious definiteness of measurement outcomes to the incontestable definiteness of human sensory experience.

One problematic aspect of the current state of QBism is the ambiguous use made by its proponents of the expression “external world.” Consider the following statement by Mermin8: “The world acts on me, inducing the private experiences out of which I build my understanding of my own world.” There is (i) the external world that we construct on the basis of our experiences, and there is (ii) the external world that induces private experiences in us. How these two external worlds are related to each other has been a central issue throughout the history of philosophy. They certainly cannot be uncritically identified (see **this mailing**).

Related to this is the question regarding the extent to which experiences can be objectivized.9 Because up to now QBists have largely accepted the instrumentalist misconstrual of Bohr’s views, they also have so far failed to consistently address this issue.

What we have learned from Kant is that our experiences can be objectivized if we can consistently think of them as a system of objects (property-carrying substances that interact and change in accordance with causal laws). Kant would have considered it secondary that in order to qualify as objective, our experiences must also be communicable in a language that everyone can understand. **Bohr** realized that quantum mechanics presents us with experiences that cannot be organized into a system of objects, but that can nevertheless be consistently objectivized, *provided* that they can be communicated in a language that everyone can understand. Experiments performed on quantum systems fall into this category.

When Fuchs and Schack10 state that QBism must treat “all physical systems in the same way, including atoms, beam splitters, Stern-Gerlach magnets, preparation devices, measurement apparatuses, all the way to living beings and other agents,” they overlook that, in order to be communicable in a language that everyone can understand, experiments must be capable of being described in terms of property-carrying substances that interact and change in accordance with causal laws. This includes beam splitters, Stern-Gerlach magnets, and the rest, which therefore cannot be treated in the same way as atoms and subatomic particles.

The crucial difference between quantum systems on the one hand and beam splitters, Stern-Gerlach magnets, and the rest on the other, is that the latter are directly accessible to sensory experience, while the former are accessible to sensory experience only indirectly, via experimental arrangements which *are* directly accessible to sensory experience. What QBists overlook (or are as yet unwilling to accept) is that not only the outcome-indicating positions of apparatus pointers but the properties of every object, insofar as they are directly accessible to sensory experience, are necessarily definite.

The following scenario, invented by Eugene Wigner11 and known as “Wigner’s friend,” will be instructive here. In this scenario, Wigner’s friend Frida measures the spin of an electron with respect to a certain axis. After the measurement but before Frida becomes aware of the outcome, the system consisting of the electron’s spin and the measurement apparatus is (by widespread consent) in an indeterminate state in which neither the spin nor the position of the apparatus pointer has a definite value. Once Frida takes cognizance of the outcome, both the spin and the position of the apparatus pointer have the values that Frida observes, directly (by looking at the pointer) and indirectly (by inferring the spin from the position of the pointer). Enter Wigner. He knows that Frida has measured the spin of an electron with respect to a certain axis but is as yet unaware of the outcome. So he assigns to the system consisting of the electron’s spin, the measurement apparatus, *and* Frida an indeterminate state in which neither the spin nor the position of the apparatus pointer has a definite value *nor* is Frida aware of a definite outcome. How can we make sense of this mess?

Originally Wigner took his scenario to imply that the quantum theory of measurement was logically consistent only “so long as I maintain my privileged position as ultimate observer”: the “true” state is the one assigned by him. As a way out of this solipsism, Wigner suggested that the equations of quantum mechanics may be radically different “if conscious beings enter the picture.” A decade and a half later, retracting his earlier claims, he declared consciousness to be outside the scope of quantum mechanics.

According to QBism, there is no “true” state. Quantum states, like the probabilities they serve to assign, are subjective and dependent on the assigner’s prior information. It is therefore wrong to assign a state without mentioning who assigns it and on the basis of which prior information, as I did when I wrote, “after the measurement but before Frida becomes aware of the outcome ... the system ... is in an indeterminate state.” Before Frida becomes aware of the outcome, she is right (according to QBism) to base her predictions on an indeterminate state in which the position of the apparatus pointer lacks a definite value. And before Wigner learns from Frida which outcome she has obtained, he is right (according to QBism) to base his predictions on an indeterminate state in which Frida’s state of mind is indeterminate with respect to the outcome experienced by her.

Bohr would have agreed with QBism that the objective world is what we collectively believe to exist. An implicit assumption underlying this collective belief is that experiences are definite. Bohr might not have agreed with QBism that measurement outcomes *are* experiences, but he made it clear enough that measurement outcomes owe their definiteness to *being experienced*. And he would have insisted that the properties of any object, insofar as they are directly accessible to sensory experience, cannot be indeterminate. The outcome-indicating positions of apparatus pointers are by definition accessible to direct sensory experience, so they cannot be indeterminate. Hence Frida would be wrong to base her predictions on a state in which the position of the apparatus pointer lacks a definite value. Wigner, for his part, would be wrong to base his predictions on a state that is indeterminate with respect to the outcome experienced by her. Technically speaking, Wigner must assign to Frida an incoherent mixture reflecting his ignorance of the outcome experience by her, rather than a coherent superposition reflecting an objective indeterminacy of her state of mind, just as Frida must assign to the pointer position an incoherent mixture reflecting her ignorance of the outcome indicated by it, rather than a coherent superposition reflecting an objective indeterminacy.

In a word, QBists still have a lot to learn from Bohr, even as the rest of the physics community can profit by paying attention to QBism.

W. Heisenberg, *Physics and Philosophy, *p. 41 (Harper and Brothers, 1958).

*Op. cit.* p. 53.

N.D. Mermin, (2017). Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it, in R. Bertlmann and A. Zeilinger (Eds.), *Quantum [Un]Speakables II: 50 Years of Bell’s Theorem*, pp. 83‒93 (Springer, 2017).

D. Wallace, Philosophy of Quantum Mechanics, in D. Rickles (Ed.), *The Ashgate Companion to Contemporary Philosophy of Physics*, pp. 16‒98 (Ashgate, 2008).

See for instance U. Mohrhoff, *The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All*, 2nd Edition, Sec. 20.2. (World Scientific, 2018); U. Mohrhoff, Quantum mechanics explained, *International Journal of Quantum Information* 7, 435‒458 (2009).

C.A. Fuchs, Quantum Bayesianism at the Perimeter, *Physics in Canada* 66 (2), 77‒81 (2010).

B.C. van Fraassen, The problem of measurement in quantum mechanics, in P. Lahti and P. Mittelstaedt (Eds.), *Symposium on the Foundations of Modern Physics*, pp. 497‒503 (World Scientific, 1990).

N.D. Mermin, Making better sense of quantum mechanics, *Reports on Progress in Physics* 82, 012002 (2019).

Here it is necessary to distinguish between objectification (as in “disaster of objectification”) and what Schrödinger called objectivation — the construction of a common external world from subjective experiences. Since the verb “to objectify” goes with “objectification,” I use the verb “to objectivize” to go with “objectivation.”

C.A. Fuchs and R. Schack, QBism and the Greeks: Why a quantum state does not represent an element of physical reality, *Physica Scripta* 90 (1), 015104 (2015).

E.P. Wigner, Remarks on the mind-body question, in I.J. Good (Ed.), *The Scientist Speculates*, pp. 284–302 (Heinemann, 1961).