Although the meaning of the quantum state (“ψ”) seems evident to Michael Nauenberg, among the physicists and philosophers interested in quantum foundations, there continues to be broad and irreconcilable disagreement even after 90 years. Can these 90 years of widespread confusion have something to do with almost all physicists taking for granted the frequentist interpretation of probability? It seems a possibility worth considering.
The subjective view of probability, dating back to Laplace, and eloquently advocated by de Finetti, Savage, Jeffrey, and many others, is introduced on our first page. QBism explores what such an understanding of probability implies for the interpretation of quantum mechanics. Our assertion (“without any justification”) further along the page, beginning “since probabilities are the personal judgments of an agent…,” refers back to the premise of subjective probability, whose implications we are about to examine.
An immediate consequence is that the quantum state an agent assigns to a system depends on what the agent believes about that system. This is not unique to QBism. That different agents can assign different states is the point of Wigner's famous parable about his friend. The probabilities determined by the Born rule are contingent on the state assignment, whether one understands those probabilities from a subjectivist or frequentist perspective. Any experiment that validates or invalidates the standard link between the Born rule and the state assignment for a frequentist does so for a subjectivist too.
QBism is not about the validity of quantum mechanics, but about how to understand the basic concepts that appear in the theory: states, probabilities, measurements, and outcomes. Is the state of a system an objective fact about that system (as Nauenberg seems to believe) or is it a judgment made by a particular agent on the basis of her prior experience of that system (the QBist view)? Is the outcome of a measurement a permanent record of an experiment made “by a macroscopic and time irreversible process,” or is it the personal experience induced in an agent by the response of her external world to any action she takes upon it?
Frequencies are indeed ubiquitous in physics. But the subjective theory of probability distinguishes between frequencies and probabilities. Frequencies are data; probabilities are personal degrees of belief. Frequencies can be assigned probabilities. And probabilities can be refined in the light of subsequently measured frequencies. A famous theorem of de Finetti relates the two.
Nauenberg misses a central point of QBism in his criticism of our discussion of nonlocality. Events are deductions an agent makes to account for her experience. The correlations each agent extracts from quantum mechanics are not between disembodied “events,” but between the experiences (outcomes of her actions on the world) from which she constructs such events.
Nauenberg concludes that “Contrary to Fuchs et al., quantum theory deals with the objective world as directly as does classical mechanics.” Setting aside our doubts about his “essential difference” between classical and quantum mechanics, we only remark that the QBist understanding of science applies to classical as well as quantum physics. Unlike QBism, CBism is not needed to resolve a scandalous incoherence at the foundations of the subject, although it does succeed in clearing up at least one long-standing puzzle.1
QBism is a genuinely novel way of thinking about the function of science. It raises subtle questions about the nature of science, the nature of human experience, and the relation of scientists to each other and to the world they are attempting to understand. We welcome criticism, but urge critics to pay some attention to what we are saying.
