Book Reviews 539 Quantum Mechanics, by Bas C. van Fraassen. Oxford: Clarendon Press, 1991. Pp. xvi +541. £50.00. Bas van Fraassen's Quantum Mechanics represents the culmination of years of work, by one of the leading philosophers of science, on the foundational issues of nonrelativistic quantum mechanics; as such, it should be expected to be a big, Downloaded from https://academic.oup.com/mind/article/102/407/539/953696 by guest on 29 September 2021 rich, and challenging book. Quantum Mechanics is all of these and more. The subtitle of the book is "An Empiricist View", and could not be more appropriate. When van Fraassen leaves off exposition and takes up interpretation and philo- sophical analysis, he does so with the exclusive goal of showing how a construc- tive empiricist should (and often more importantly, should not) deal with interpretive and ontological issues in quantum mechanics ("QM" hereafter). After describing Quantum Mechanics in general terms, I will briefly discuss van Fraassen's "modal interpretation" of QM, and his views on EPR correlations and so-called "identical particles." The book is organized into four main sections. The first lays out van Fraassen's views about (in)determinism, symmetries, and probability. The second section, "The Empirical Basis of Q. ntum Theory", is incongruously titled, because in it van Fraassen discusses only one type of experiment, out of the vast range of phe- nomena supporting QM: the EPR correlation experiments. This section describes phenomena that violate Bell's inequalities, and what kinds of probability models can and cannot be compatible with such violations; one major conclusion of this section is that non-classical logic and/or probability theory are not demanded by such phenomena, though the study of quantum logics is valuable in its own right. The third section, "Mathematical Foundations", gives an extremely abstract and rigorous presentation of the basic elements of quantum theory, and how they fit together to yield the models of QM; half of this section is devoted to the difficult issues of composite systems and measurement interactions, grist for the philo- sophical problems of measurement and non-locality. The fourth and largest sec- tion has the philosophical meat of the book: discussions of some prominent "interpretations" of QM, and extensive treatment of the issues of the EPR corre- lations and the puzzles of identical particles. It is here that van Fraassen gives his views, in detail, of how an empiricist should approach the alleged philosophical problems of QM. I have mentioned that van Fraassen's presentation of QM and its interpretive issues is both abstract and rigorous; this is one of the book's great strengths, but also perhaps its greatest liability. Van Fraassen chose to present QM in terms of his own notational conventions, and his notation is both idiosyncratic and diffi- cult to master. In reading Quantum Mechanics, readers familiar with quantum mechanics from typical university physics courses will be at no significant advan- tage over readers with no physics background at all. Instead, readers with sub- stantial background in logic, probability theory, and formal mathematics, will have an easier time reading the book in detail. This raises the question of what the appropriate audience is for this book. It is written in a way that presupposes no prior knowledge of quantum mechanics, and so is in principle accessible to 540 Book Reviews any philosophers who can master the notational formalism. But in practice, phi- losophers not already working on the philosophy of QM will find the difficulty of Quantum Mechanics too great for the payoff in understanding of foundational issues. This is especially so since, given its abstractness of approach and unusual notation, Quantum Mechanics does not leave one prepared to move on to most Downloaded from https://academic.oup.com/mind/article/102/407/539/953696 by guest on 29 September 2021 other works in the philosophy of QM. For the professional philosopher of phys- ics, van Fraassen's book on the one hand offers much: penetrating and lucid crit- icism of the "standard interpretation(s)" of QM, a revised and thorough presentation of van Fraassen's own modal interpretation, and a trenchantly anti- metaphysical analysis of the central philosophical issues. On the other hand, the book omits some topics that are of increasing interest in the profession, such as Bohm-type hidden variable theories and foundational issues in relativistic quan- tum mechanics. The first section of Quantum Mechanics largely repeats material from his ear- lier book Laws and Symmetry, but is worth reading carefully, even for readers familiar with Laws and Symmetry, because it begins to introduce much of the notation used throughout the book. A word about the relation between these books is in order. Laws and Symmetry was intended to advocate the semantic approach to the structure of theories, using the concept of symmetry as a partial replacement for the concept of law (while jettisoning the latter concept in its met- aphysical guises); and Quantum Mechanics was to illustrate the implementation of this approach, in a detailed way, in the interpretation of a central scientific the- ory. The two books do complement each other (and the earlier Scientific Image), but they have no trouble standing alone, and readers need not fear that they will need to read the earlier Laws and Symmetry in order to understand Quantum Mechanics. The interpretation that van Fraassen has developed over the last 20 years is the modal interpretation; it is a view that solves some of the puzzles of measurement, while introducing a curious kind of dualism into the description of nature. While van Fraassen claims to advocate the modal interpretation (specifically, the Copenhagen variant of it), it would be more accurate to say that he displays it. For in the end, van Fraassen makes no claim about the truth or probable truth of his interpretation. Instead, he describes his interpretation with clarity and preci- sion,- and says "here is one way that the world might be, if QM is true", and claims only the virtue of having increased our understanding of QM by giving us another consistent interpretation. Van Fraassen makes no claim that his interpretation is more likely to be true than the standard interpretation, or the Everitt interpreta- tion, ...; nor can he do so, given his own empiricism. The dualism introduced by the modal interpretation is a dualism of dynamic states of systems on the one hand, and the possession of values of observables by these systems (van Fraassen calls such possessions "events") on the other. Dynamic states are the traditional mixed and pure states in Hibert spaces of quan- tum mechanics; they evolve according to the Schrodinger equation in a determin- istic way, and undergo no "collapse of the wave packet" or "state-vector Book Reviews 541 reduction". But in addition to the dynamic state (and consistent with it), systems also often possess values of various observables, e.g., an electron may have spin up in a certain direction. Measurement interactions do not reveal anything new about dynamic states, but do reveal possessed values of the measured observ- ables. In times when no measurement is being performed, what values of observ- Downloaded from https://academic.oup.com/mind/article/102/407/539/953696 by guest on 29 September 2021 ables are actually possessed by a system is something that may change randomly, or chaotically, or not at all; QM tells us very little about this. What QM does do is tell us the probabilities for finding a given value for a measured observable, after a measurement; and no more. On this picture, QM is a complete description of one aspect of reality—dynamic states of systems—and a very incomplete description of another aspect, namely the actual values of observables possessed by systems. Van Fraassen describes the strange features of his modal interpreta- tion just as thoroughly as its more intuitive features; and even readers who come away from it with no feeling that it might be true cannot but agree with van Fraas- sen's claim that, by creating the modal interpretation, he has increased our under- standing of QM in an important way. The two most distinctive features of Quantum Mechanics, already seen above, are its anti-metaphysical approach to all issues, and its claim that engagement in the interpretive work in QM is valuable for the insights it can give into what the world may be like, if the theory is true. These features are also prominent in the discussions of the last three chapters, on the EPR correlations and on identical particles. On the issue of identical (or indistinguishable) particles, van Fraassen advocates resisting the metaphysical urge to explain the Bose-Einstein or Fermi- Dirac statistical behaviours of particles as arising from their non-existence or their "lack of identity". Instead, van Fraassen begins the work of carefully explor- ing the extent to which QM itself has the resources for individuating fundamental particles. He argues in the end that fermions can be individuated in the framework of QM, while bosons cannot; but this gives us no metaphysical truths about the existence or non-existence of fermions and bosons as individual entities. Both kinds of particles may lack individual identity, as field-theoretic models suggest; and both kinds may have identity, even bosons—though if the latter is to be the case, bosons must have properties outside the scope of QM that serve to individ- uate them without being empirically significant. On the issue of EPR correlations, van Fraassen argues, very simply, that the spooky "action at a distance" correlations do not need to be explained; they must simply be accepted.