Measured Responses to Quantum Bayesianism
Measured Responses to Quantum Bayesianism
David Mermin, in his commentary in the July 2012 issue of Physics Today (page 8), put forth what he calls the QBist (quantum Bayesian) approach to quantum foundations. He claims that replacing a frequentist approach to quantum probabilities with a Bayesian approach solves the quantum measurement problem and fixes the “shifty split” between classical and quantum that John Bell complained about.1 I disagree. Mermin has not addressed the real issue that besets quantum probabilities, he has not solved the measurement problem, and he has put the shifty split in the wrong place.
The quantum measurement problem, understanding an actual physical measurement in fully quantum terms, has two parts. First, unitary time development (Schrödinger’s equation) often results in a quantum superposition of different outcomes—different positions of the apparatus pointer, in the quaint language of quantum foundations. Various equivocations proposed to get rid of that Schrödinger’s cat were among the main targets of Bell’s critique. When this first part is solved the second task is to link the pointer position to the microscopic property the apparatus was designed to measure, at a time before the measurement took place. Experimental physicists talk about detecting a gamma ray emitted by a nucleus, or a neutrino emitted in a supernova explosion, using apparatus that either destroys or violently alters the object under study. They are not fools, though one might think so from reading textbook discussions of measurement that only consider properties of a microscopic system at a time after interacting with the apparatus—best referred to as a preparation, not a measurement.
Mermin seems to think that the measurement problem—presumably the first problem—is solved by using the quantum wavefunction to calculate a probability, in a manner easily taught to undergraduates. However, the main conceptual difficulty with quantum probabilities is not in calculating them but in identifying their referents, what it is they are about. When the weatherman assigns a high probability to a severe thunderstorm on Thursday afternoon, both frequentists and Bayesians will want to seek shelter. They will agree that the probability refers to thunderstorms rather than stock-market prices. The first task in constructing a probabilistic model, for the weather or games of chance or radioactive decay, is to identify a sample space of mutually exclusive possibilities, one and only one of which can be correct or occur in a particular experiment or on a particular occasion. Only when a sample space has been defined is it possible to assign probabilities to suitable subsets, averages to random variables, and so forth.