Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation, disagreement about the meaning of the theory is stronger than ever. New interpretations appear every year. None ever disappear.

Probability theory is considerably older than quantum mechanics and has also been plagued from the beginning by questions about its meaning. And quantum mechanics is inherently and famously probabilistic.

For the past decade, Carl Caves, Chris Fuchs, and Ruediger Schack have been arguing that the confusion at the foundations of quantum mechanics arises out of a confusion, prevalent among physicists, about the nature of probability.1 They maintain that if probability is properly understood, the notorious quantum paradoxes either vanish or assume less vexing forms.

Most physicists have a frequentist view of probability: Probabilities describe objective properties of ensembles of “identically prepared” systems. Caves, Fuchs, and Schack take a personalist Bayesian view: An agent assigns a probability p to a single event as a measure of her belief that the event will take place.2 

Such an agent is willing to pay less than $p for a coupon that will pay her $1 if the event happens, and she is willing to underwrite and sell such a coupon for more than $p. Surprisingly, the standard rules for probability follow from the requirement that an agent should never face certain loss in a single event. (For example, if p exceeded 1, she would pay more than $1 for a coupon that returned at most $1; if p were negative, she would pay somebody to take a coupon from her that might cost her another $1.) Avoiding certain loss is the only constraint on an agent’s probability assignments.

The probability of an event is not inherent in that event. Different agents, with different beliefs, will in general assign different probabilities to the same event.

The personalist Bayesian view of probability is widely held,3 though not by many physicists. It has profound implications for the meaning of quantum mechanics, which Fuchs and Schack call quantum Bayesianism—QBism for short. Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.

QBism immediately disposes of the paradox of “Wigner’s friend.” The friend makes a measurement in a closed laboratory, notes the outcome, and assigns a state corresponding to that outcome. Wigner, outside the door, doesn’t know the outcome and assigns the friend, the apparatus, and the system an entangled state that superposes all possible outcomes. Who is right?

For the QBist, both are right: The friend assigns a state incorporating her experience; Wigner assigns a state incorporating his. Quantum state assignments, like probability assignments, are relative to the agent who makes them.

QBism also eliminates the notorious “measurement problem.” Classical probability theory has no measurement problem: An agent unproblematically changes her probability assignments discontinuously when new experiences lead her to change her beliefs. It is just the same for her quantum state assignments. The change, in either case, is not in the physical system the agent is considering. Rather, it is in the probability or quantum state the agent chooses to encapsulate her expectations.

From the beginning, Werner Heisenberg and then Rudolf Peierls maintained that quantum states were not objective features of the world, but expressions of our knowledge. John Bell tellingly asked, “Whose knowledge? Knowledge about what?” The QBist makes a small but profound correction: Replace “knowledge” with “belief.” Whose belief? The belief of the agent who makes the state assignment, informed by her past experience. Belief about what? About the content of her subsequent experience.

Bell also deplored a “shifty split” that haunts quantum mechanics. The shiftiness applies both to the nature of the split and to where it resides. The split can be between the quantum and the classical, the microscopic and the macroscopic, the reversible and the irreversible, the unspeakable (which requires the quantum formalism for its expression) and the speakable (which can be said in ordinary language). In all cases the boundary is moveable in either direction, up to an ill-defined point. Regardless of what is split from what, all versions of the shifty split are vague and ambiguous.

For the QBist, there is also a split. It is between the world in which an agent lives and her experience of that world. Shiftiness, vagueness, and ambiguity all arise from a failure to realize that like probabilities, like quantum states, like experience itself, the split belongs to an agent. All of them have their own split. What is macroscopic (classical, irreversible, speakable) for Alice can be microscopic (quantum, reversible, unspeakable) for Bob, whenever it is part of her experience but not his. Each split is between an object (the world) and a subject (an agent’s irreducible awareness of her or his own experience). Setting aside dreams or hallucinations, I, as agent, have no trouble making such a distinction, and I assume that you don’t either. Vagueness and ambiguity only arise if one fails to acknowledge that the splits reside not in the objective world, but at the boundaries between that world and the experiences of the various agents who use quantum mechanics.

Albert Einstein famously asked whether a wavefunction could be collapsed by the observations of a mouse. Bell expanded on that, asking whether the wavefunction of the world awaited the appearance of a physicist with a PhD before collapsing. The QBist answers both questions with “no.” A mouse lacks the mental facility to use quantum mechanics to update its state assignments on the basis of its subsequent experience, but these days even an undergraduate can easily learn enough quantum mechanics to do just that.

QBism explains the persistence of the disreputable notion that “consciousness collapses the wavepacket.” That is true, but in a banal way. The conscious experience of an agent guides her actions in any number of familiar ways. If she has at least an undergraduate degree in physics, these may include revising, on the basis of new experience, her expectations of future experience embodied in her prior quantum state assignments.

There are glimmerings of QBism in the writings of some of the founders of quantum mechanics. Niels Bohr wrote, “In our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience.”4 (Once I thought the crucial word here was “relations”; now I realize it is “experience.”) Erwin Schrödinger, often philosophically at odds with Bohr, noted, “The scientist subconsciously, almost inadvertently simplifies his problem of understanding Nature by disregarding or cutting out of the picture to be constructed, himself, his own personality, the subject of cognizance.”5 (Here the crucial word is “subject.”)

I find QBism by far the most interesting game in town. It has not, however, been enthusiastically received by the contemporary quantum-foundations community. Fuchs, in his role as QBism’s most fervent advocate, is admired as a provocateur, his more technical work is highly regarded, and he was elected to the leadership of the American Physical Society’s topical group on quantum information. But I would say that, with some important exceptions, the general response to QBism has been to shrug it off. I attribute that, in my uncharitable moments, to people having too much fun working on the puzzles that QBism has eliminated.

I write this Commentary not to persuade such experts, but to bring QBism to the attention of the much larger community of physicists who have no professional interest in quantum foundations. The message from QBism is this: You needn’t feel guilty about never getting nervous about this stuff. You were right not to be bothered. But for the sake of intellectual coherence, you had better reexamine what you wrongly may have thought you understood perfectly well about the nature of probability.

1.
See, for example,
C. A.
Fuchs
, http://arxiv.org/abs/1003.5209, secs. 1–3.
2.
For a short, readable introduction, see
R.
Jeffrey
,
Subjective Probability: The Real Thing
,
Cambridge U. Press
,
New York
(
2004
).
3.
J. M.
Bernardo
,
A. F. M.
Smith
,
Bayesian Theory
,
Wiley
,
New York
(
1994
), and the 65 pages of references therein.
4.
N.
Bohr
,
Collected Works
, vol.
6
,
J.
Kalkar
, ed.,
North-Holland
,
Amsterdam
(
1985
), p.
296
.
5.
E.
Schrödinger
,
Nature and the Greeks, and Science and Humanism
,
Cambridge U. Press
,
New York
(
1996
), p.
92
.