## Book Review: Foundations of Quantum Mechanics by Travis Norsen (Springer, 2017)

I want to start this review with what I liked most and least about Norsen’s new textbook. The premise of this book is to present a story of quantum physics to undergraduate-level students that directly faces up to the conceptual difficulties of the theory and its interpretation, rather than brushing them under the rug with some form of “shut up and calculate.” I find this premise very admirable, since a dismissive attitude towards any attempt to really *understand* quantum theory is quite prevalent in the literature, and especially in undergraduate textbooks. Unlike most of these, this book takes readers on a thorough, if introductory, tour of difficult and controversial topics in the foundations of quantum theory. However, Norsen may have been a little too ambitious, as the level at which some of these ideas are presented, with frequent passages from the original pioneers of the theory, is probably a bit too dense for the average physics undergraduate. Nevertheless, as a companion to a well-organized course about this material, or for that rare undergraduate who already has the itch for a deeper understanding of quantum theory, I think this book is an excellent resource.

That said, let us get into the technical details of the text.

Norsen does a nice job of reviewing quantum theory and the foundations in classical physics and mathematics upon which it rests — with the understanding that students will have already had a solid introduction to the mathematical formalism of quantum mechanics. This style of much of this book is reasonably well-suited to introducing undergraduate students to some of the difficult concepts in the foundations of the theory, however, in some cases, the route taken seems needlessly long — interspersed with passages from original articles and letters, and subsequent analysis of these — making them too dense for most undergraduates. I understand the aversion to spoon-feeding students preconceived conclusions, and the impulse to let the giants of the field speak for the themselves, (to show, for example, just how cryptic Bohr’s own words could be) but unfortunately this style of presentation requires much more patience to digest.

Next, Norsen sets out with very clear discussions of the measurement problem, locality, and ontology, which are used as guideposts throughout the remainder of text. He also reviews an early idea of Schrödinger’s for putting the content of the quantum theory explicitly in space-time (as opposed to configuration space). At this point, the text begins to explore several of more prominent interpretations of quantum mechanics, with some analysis of how the measurement problem is addressed in each, what ontological story (if any) each is telling, and how each handles the locality issues presented by EPR and Bell’s theorem.

These discussions begin with an unpacking of the Copenhagen interpretation of Bohr and Heisenberg, which most quantum physicists claim to believe, and which has led to roughly 80 years of “shut up and calculate,” which is how Mermin once summarized the interpretation. This chapter is organized so as to let Bohr and Heisenberg speak for themselves as much as possible, and it is rightly critical of the conceptual vagueness of their ideas. The theory depends deeply on the principle of complementarity between different physical properties of systems, and on the special role played by an observer, both of which make questions about ontology and locality difficult to address, but Norsen has done a nice job of this by reviewing Einstein’s objections to the theory and putting them in the right context. However, Bohr dodges the ontology question entirely by stating, “There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature *is*. Physics concerns what we can say about nature,” and thus Copenhagen is only an epistemic interpretation of quantum mechanics. In summary, the Copenhagen interpretation led many to believe that any attempt to find an objective ontological description of quantum mechanics (in space-time) was futile. This viewpoint, which is simply wrong, has been the one of largest historical impediments to the conceptual growth of quantum theory, and several chapters of this book are devoted to developing clear-cut counterexamples. Here again, I must express my admiration for Norsen’s direct confrontation with this monolithic and vague belief.

The first of these ontological descriptions in space-time is the De Broglie-Bohm (dBB) pilot wave theory (also called the Bohmian interpretation of quantum mechanics or Bohmian mechanics). Norsen has a confessed affinity for dBB over some other interpretations, and this is apparent throughout the text. In particular, the introductory chapters take several small detours into concepts and material that are not needed for the other interpretations, but this is done in a reasonably organic and unobtrusive way. For example, there is heavy use of configuration space diagrams throughout, which are a perfectly valid tool for analyzing general quantum theory, but which are particularly necessary for understanding dBB. Furthermore, the chapter on the dBB theory is more detailed than those devoted to the other ontological interpretations, which has the subtle effect of presenting it in a more positive light than the others. Thus, while I feel the text in an excellent introduction to the dBB theory, I find its discussion of many-worlds and spontaneous collapse to be slightly brusque by comparison, since many details, and some other modern interpretations, have been left as suggested reading.

The next interpretation Norsen explores is the spontaneous collapse theory of Ghirardi, Rimini, and Weber (GRW), and I think he has done an excellent job giving a clear and concise introduction to the basic workings and merits of this theory. In particular, the rapid collapse of macroscopic objects is discussed, allowing for a space-time ontology that is essentially the same as the one conceived by Schrödinger. Unlike the others, GRW makes predictions that are subject to being falsified by new experiments, which also somewhat elevates it somewhat from an interpretation to a new physical theory, and Norsen explores the situation for experimental data that is presently available.

Lastly, Norsen discusses the many-worlds interpretation of Everett. The core concept of how the measurement problem is avoided by introducing new branches of reality (or worlds) instead of collapses is clearly presented, and several pictures of branching structure and the Born rules are discussed. Norsen also discusses how the many-worlds theory can be understood in space-time, with all of the different branches playing out independently even if they are in the same place, which is an often-overlooked viewpoint among proponents of the theory. However, the theory of decoherence and the selection of a preferred basis, which are essential to the modern understanding of the many-worlds theory, is lacking, with only a few vague allusions made to when we can definitively say that worlds have branched apart. Nevertheless, I think this is an adequate introduction to the theory.

These interpretations, and many others, have been developed well beyond the scope of this book, and Norsen has done a nice job of pointing interested readers at other books and articles that will take them further down any of these roads.

One last comment regards Norsen’s discussion of Bell’s theorem. I think the text gives an excellent review of Bell’s work and introduction to Bell’s theorem, and puts it in a rightly prominent place among the discussion of the different interpretations. However, Norsen seems to have drawn a somewhat dogmatic conclusion from Bell’s theorem that I do not believe is entirely justified, namely that there must exist `causal linkages’ between space-like separated events. This is certainly consistent with both the dBB and GRW interpretations, but the situation in many-worlds is not so cut and dry, as he discusses in that chapter, and the same can be said of other interpretations.

Finally, the issues with the accessibility of the text notwithstanding, I think this is an excellent book in terms of the important issues it addresses and the subject matter it explores — with the bias towards Bohmian mechanics understood. While I think it will be difficult for an unguided undergraduate student, it is an excellent companion for any foundations course, and an excellent guide for any graduate student who wants a starting place to learn about these ideas and references for further reading. As such, I believe that *Foundations of Quantum Mechanics*, by Travis Norsen, would make a good addition to any physics library collection.

Book Review Mordecai Waegell quantum foundations Travis Norsen