We are certainly not accustomed to experiments coming from Steven Weinberg. After all, he is the pre-eminent theoretical physicist of today (and perhaps of the last half-century), a Nobel laureate for his crucial work on the electroweak unification, and contributor to dozens of key issues in fundamental physics and cosmology. Perhaps more than any other living physicist, he embodies the triumphs of theoretical science and huge explanatory strides it has made in the course of the last 75 years or so. And yet, lo and behold!, the ultracompact Lectures on Astrophysics represent a bold and radical experiment in science teaching.

It is a pleasure to report that the experiment is an unblemished success.

First, we need to put things in context. At 226 pages of not-too-small type, Weinberg's booklet is less than 1/4 the page count of a topically comparable classic like Frank Shu's The Physics of Astrophysics (in two volumes, published 1991–1992). It is about 1/5 of Astrophysical Formulae, the massive compendium by Kenneth Lang originally published in 1974, with its many improved and expanded subsequent editions. It is incomparably slimmer than Weinberg's own previous major textbooks, notably Gravitation and Cosmology (1972) and Cosmology (2008). Yet, the scope of Lectures on Astrophysics is arguably wider. How is the trick achieved?

Weinberg is entirely candid about it from the very beginning:1 

It would be most logical to begin this chapter with an introduction to the physics required to understand modern stellar theory, including calculations of nuclear energy production and opacity, and only then go on to the stars themselves. Logical, but perhaps a bit boring. It is not always possible to maintain one's interest in the details of nuclear and atomic physics without knowing how these results are to be used. So, in this chapter, we start with the stars.

Thus, we have it: foundations of astrophysical theory strongly focused on four areas, which are also self-explanatory titles of the four chapters: (1) stars, (2) binaries, (3) the interstellar medium, and (4) galaxies. Several specific topics are listed as sections within each chapter, usually focusing on a particular phenomenon or a connected set of phenomena: polytropes, or close binaries, or HII regions, or accretion, or spiral arms of galaxies. The treatment is strongly focused on analytical results, theoretical syntheses, and their exactly solvable models. Some well-known results are derived, some in the manner never published before, although presumably chatted about in cafes frequented by astrophysics theorists.

The book originated in lecture notes for a course in astrophysics given by Weinberg at the University of Texas in Austin in 2016–2017. Obviously, any course of this type has to be a masterpiece of trade-offs and selectivity. Weinberg chooses his topics carefully, but his criteria may not be always transparent, especially not for undergraduate and even graduate students. There will always be readers dissatisfied with the lack of A, B, or C—or with the attention devoted to X, Y, or Z. Even the provocation inherent in such selectivity can be harnessed in service of science education. I found myself trying to conceive how nonexistent sections devoted to some of my own pet topics could be fit into the Weinberg narrative; for instance, could one treat the thermal stability of cold molecular clouds or the cosmic-ray component of the interstellar medium in the same succinct manner as HII regions are dealt with in Chapter 3? Any teacher of astrophysics worth her salt can use Weinberg's primer as a foundation for thinking and rethinking of her own course(s).

Weinberg chooses to treat star formation in the interstellar medium chapter, rather than in the galaxies chapter, so that the treatment is strictly local; we don't get anything on the effects of star formation on the structure and evolution of galaxies. This is in accordance with Weinberg's preference for what could be called well-rounded astrophysical theories: like the theory of binary stars, the quadrupole approximation for gravitational waves, or the Bondi accretion. Since we do not have such a well-rounded theoretical framework for global star formation or cosmic-ray acceleration or even chemical evolution of galaxies, we won't read much on those topics in the book. Clearly, this was a conscious choice on author's part. His is a bottom line which is likely to remain rock-solid 50 years from now, just as almost all pages in Chandrasekhar's textbooks stand now.

And this leads us to another feature of Lectures on Astrophysics that too often is lacking in advanced textbooks: it is great, even provocative, with epistemological clarity. No sections and subsections, no equations, and no individual symbols even are located out of their optimal place and context. The book's mathematical tools are not excessively complex: apart from a brief excursion into tensor calculus necessary for understanding gravitational waves in Secs. 2.3 and 2.4, they boil down to standard algebraic and differential equations, occasionally giving rise to (rather tame) special functions. They are, however, organized and derived with uncanny precision. With just a few tables, lacking figures, Weinberg's book is decisively old school; without much effort, a reader could almost see and hear occasional screeching of his chalk on the blackboard. Just as some chess moves of truly great champions may look unnecessary or pedantic even to observing grandmasters, but everything eventually falls into proper place of an “immortal” combination, so many of Weinberg's auxiliary derivations or change in variables subsequently emerge as indispensable parts of the solvable apparatus of the theory.

The old-fashioned presentation is there on purpose, to remove all unnecessary adornments and all distractions of so much of (post)modern, fancy, and flashy “methods.” It is not an easy ride, and it could occasionally be quite a strain on a student's capacity for abstraction and imagination. For example, to understand different regimes of the cooling function Λ(T) for various metallicities (Sec. 3.3) without a—color-coded!—schematic diagram is a supreme theoretical exercise. To paraphrase Einstein, one needs a deep love for the subject matter in order for the proper mental image to emerge. In that sense, Weinberg's teaching austerity is a clear statement. Probably, it will not be popular, as other kinds of reasonable austerity are never popular, but it is clear and persuasive. It is also provocative in that it actually reiterates our need for well-rounded theoretical frameworks: we need to go a bit off the trodden path of working on local and safe (career-wise) problems and veer toward building wider syntheses. As all great teachers, Weinberg instructs us by what he says—and also by what he does not say. Highly ironically, he shows himself once more as a “philosopher in spite of himself,” as a fellow Nobel laureate Frank Wilczek memorably called him in a review of another book.2 

All this emphatically does not mean that the text itself is an ultra-condensed and extremely concise, dry material; on the contrary, in spite of his tremendous scope, Weinberg finds an opportunity to refer to important empirical discoveries, such as the binary pulsar or LIGO detection of gravitational radiation. And there are other moments of good-natured humor as well. A vignette from the preface is worth quoting in full:

Many years ago, when I was bed-ridden in Berkeley with a bad back, my wife gave me a present, a copy of Chandrasekhar's 1939 classic An Introduction to the Study of Stellar Structure that she had found in a bookshop on Telegraph Avenue. Reading the book saved me from wasting much of my time in bed and gave me a permanent sense of excitement that physics and mathematics could deal effectively with something as mysterious as stars. I don't wish bad backs on today's young physicists, but I hope that they will have some occasion to spend time going through these calculations and will feel some of the excitement with astrophysics that I first felt long ago.

Also, it is to be hoped that observational astrophysicists will not be unduly irritated that several sections conclude with a version of “[T]he general theory of accretion disks described in this section can be applied to accretion disks in binaries, but observations are complicated by the presence of the companion star.” (p. 160)

The book is appropriately simply, yet robustly produced. It has a brief bibliography for each particular chapter, limited to the foundational and key texts. The appendices containing even more advanced material are set within each chapter, which is a neat solution for a perennial problem of interrupting the flow of explanatory material. There is a set of assorted problems at the very end of the book, also in an extremely condensed form (three pages in total). The index is surprisingly accurate, which has become somewhat of a rarity these days.

All in all, Lectures on Astrophysics is an extraordinary book(let), a truly precious new resource in service of a wide range of students and experts alike. It is a successful teaching experiment reaffirming the worth and power of high-profile theoretical astrophysics, and it clearly shows how mastery of analytical calculation is necessary before one embarks in more ambitious numerical work. Finally, the subtlest and yet perhaps the most important and timely aspect of this book is its implicit Enlightenment message: you can still, in 2020, put universal truths—uncompromisingly important and beautiful universal truths, at that—between the two covers of a book.

Lectures on Astrophysics
Cambridge U.P
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Weinberg: A philosopher in spite of himself
Phys. Today

Milan M. Ćirković is a research professor at the Astronomical Observatory of Belgrade (Serbia) and a research associate of the Future of Humanity Institute at the Oxford University (Oxford, UK). His primary research interests are in the fields of astrobiology philosophy of science and risk analysis. He co-edited the widely-cited anthology on Global Catastrophic Risks (Oxford University Press, 2008, with Nick Bostrom), wrote three monographs (the latest being The Great Silence: The Science and Philosophy of Fermi's Paradox, Oxford University Press, 2018), as well as four popular science/general nonfiction books, and authored about 200 research and professional papers.