I enjoyed the February 2019 issue of Physics Today on Reviews of Modern Physics at 90 but was disappointed with the article “Quantum foundations” by David DiVincenzo and Christopher Fuchs (page 50). The most useful part of that article was the reference list, which shows RMP’s diversity of papers on the subject. My 1970 article on the statistical-ensemble interpretation of quantum mechanics (QM),1 which people tell me has encouraged them to continue research on quantum foundations (QF), was omitted from the list.
Unfortunately, DiVincenzo and Fuchs continue to mystify measurement in QM, as if it were some deep philosophical concept that must be treated before QM has even been fully formulated. They assert that “physicists and philosophers are still debating what a ‘measurement’ really means.” What is important for QF is not the meaning of the word but an understanding of the physical process. The authors do not cite any of the published papers that provide such an understanding. And they give too much attention to two marginal interpretations: the many-worlds interpretation (MWI) and quantum Bayesianism (QBism).
In QM, a measurement of an observable should yield an eigenvalue of the observable. If the initial state of the measured object is a superposition of eigenstates corresponding to different eigenvalues, then the interaction of the measurement apparatus with the object will lead to a final state of the whole system—measured object plus apparatus—that is a superposition of different measurement results. The squared amplitude of each term yields the probability of obtaining that result in an individual measurement. That statistical prediction, the Born rule, is common to the Copenhagen and statistical-ensemble interpretations. But the MWI takes a radically different turn. It postulates that the universe branches into several parallel worlds, with each term of the superposition corresponding to the unique result of the measurement in one branch world.
The usual role of an interpretation of QM is to begin with the established mathematical formalism and provide an intuitively comprehensible idea of the physical process that the math describes. The MWI does not do that. Instead, it adds a mysterious process of world-splitting, a strange new cosmology that is alien to the mathematics of QM and not really an interpretation of QM at all. A typical QM measurement, such as that of a spin component in the Stern–Gerlach experiment, is a local and very low energy event. It is not credible that the measurement could have the huge cosmological effect of bifurcating the universe.
When I first heard of the world-splitting assumed in the MWI, I went back to Hugh Everett’s paper2 to see if he had really said anything so absurd. I found that he had not said so explicitly, but he sometimes used words that could be interpreted in more than one way. The MWI is a possible interpretation of them, but not the most natural one, so I thought. And Everett’s framework still has value even without resorting to the MWI’s world-splitting. His concept of a “relative state” is useful, for instance, and he is correct in rejecting the notion of the quantum state “collapsing” after a measurement.
QBism begins with the assumption that all kinds of probability can be regarded as subjective Bayesian probabilities. That assumption can be maintained only by ignoring the literature on interpretations of probability, from which it is clear that several different kinds—or interpretations—of probability exist. DiVincenzo and Fuchs may have ignored the classic philosophical writings on the subject because they were written by philosophers for philosophers and so do not address the needs of physicists.
I have published a paper on the foundations of probability theory, written from the point of view of a quantum physicist.3 I classify the main kinds or interpretations of probability into three groups: inferential probability, of which Bayesian theory is an example; frequency or ensemble probability, commonly used in Gibbsian statistical mechanics and in QM; and propensity theory. Propensity, a degree of causality that is weaker than determinism, is not merely another interpretation of probability. Its mathematical theory must also differ from that of probability theory, as Paul Humphreys showed4 in 1985. Although the axioms of propensity3 differ from those of probability, the two axiom sets overlap. Both support the law of large numbers, so propensity theory is compatible with the most useful part of the frequency interpretation of probability.
In general, QM states do not determine the results of a measurement, only the probabilities of the possible results. That a state’s influence on the results is not deterministic suggests strongly that the quantum probabilities given by the Born rule should be interpreted as propensities. They refer objectively to the physical system and its environment, not to any agent’s knowledge, so they are not naturally interpreted as subjective Bayesian probabilities.
Interpretations of probability may differ not only in philosophy but also in substance. As I discuss in reference 3, John Bell’s theorem illustrates how local hidden-variable theories are incompatible with QM. E. T. Jaynes was a well-known supporter of the Bayesian theory of probability. In 1989 he repeated Bell’s derivation of inequality but carefully treated all instances of probability as Bayesian. He found that the derivation could not be completed without invoking an extra assumption that was not justifiable in the Bayesian theory. Bell’s theorem involves questions about causality, so it is natural to use propensity theory to treat it. That method is successful in deriving Bell’s inequality.3
Not all probabilities occurring in QM can be treated as subjective Bayesian probabilities. That limitation disqualifies QBism, a Bayesian-based theory, as an interpretation of QM that can succeed in quantum foundations. The initial assumption of QBism is not valid.
