The draught of a draught

Book review: The First Three Minutes, by Steven Weinberg

The title seems to say it all: this is a book about what happened during the first three minutes of the universe. That's a fair summary, but it's both incomplete and imprecise. A better description is this: it's a 1977 book about what happened during those first three minutes, and the reasons we had back then for believing it.

Another thing the title won't tell you, nor could you guess from its short length and its status as a classic, is that this is not an easy read. Weinberg, the author, warns in the preface that he expects the reader to "puzzle through some detailed arguments", and he means it. It's still an enjoyable book if you don't make that effort, but in that case you won't get half of what it has to offer.

The question then is why spend time reading an old, challenging book? Wouldn't it be better to get something up to date, and perhaps more easy-going? Maybe. But this is a book written by a unique author. In fact, I believe you'll enjoy the book in direct proportion to how much you like Weinberg. And I loved him.

Before trying to explain what makes him such a good author, let's get the obvious out of the way. Yes, Steven Weinberg was one of the most important physicists of the 20th century. Yes, as the book mentions three times on the front and back covers, he was a Nobel laureate. (I remember reading, in a side note of some undergraduate physics book, about the achievement of unifying the electromagnetic and weak forces; Weinberg got the Nobel for that.) These are impressive credentials, and I won't pretend that's not why I got the book in the first place. But it's not what makes him great.

One of the reasons I like him is that he seems to be as interested in the discoveries as in the process behind them. A good chunk of the book is closer to the history of science than science, even if he discloses that he doesn't consider himself a historian:

This is not to say that I regard this book as a definitive history of these developments—I have far too much respect for the effort and attention to detail needed in the history of science to have any illusions on that score.

Nevertheless, this passion means you learn not only about the idea that the universe is expanding, but how we arrived at that conclusion: from the 19th century hypothesis and confirmation of the Doppler effect, through the measurement of redshift in spectral lines from stars, to Hubble's celebrated law. Similarly, there's a whole chapter on the cosmic microwave background, discussing both its significance to the theory of the early universe and its accidental discovery in 1964. This is one of the most fascinating episodes in the history of science, and it comes with the unforgettable image of two physicists wondering whether a mysterious, isotropic signal (which turned out to be leftover radiation from the early universe) was not just electric noise caused by pigeon poop.

That's not to say that the science itself takes a backseat; far from it. The core of the book is still the theory and the arguments in its favor. And this is where the reader is expected to make an effort. Weinberg tries to present it in the simplest way that doesn't cheapen the explanation, while also convincing you that it makes sense. He has an immense respect for the reader, along with intellectual honesty and critical thinking of the first order. That's why engaging with the book, instead of just nodding along pretending you get what he's saying, is so rewarding.

This content—the theory itself and the history behind it—would be enough to make the book worth reading, but on top of that you get some really good writing:

Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world.

He can be deep without being pompous:

The universe will go on expanding and cooling, but not much of interest will occur for 700,000 years. […]. After another 10,000 million years or so, living beings will begin to reconstruct this story.

He is duly modest when necessary:

Can we really be sure of the standard model? Will new discoveries overthrow it and replace the present standard model with some other cosmogony, or even revive the steady-state model? Perhaps. I cannot deny a feeling of unreality in writing about the first three minutes as if we really know what we are talking about.

And he has a witty, dry sense of humor, which he uses sparingly but effectively:

We don't know enough to rule out the possibility that it is antimatter instead that would have survived, but, in such a case, antiphysicists on antiearth would naturally call it matter, not antimatter.

My main problem with the book is its intended audience. Weinberg mentions in the preface that he imagines his reader as "a smart old attorney who does not speak my language", and that no mathematics will be used. That's fair. The thing is... he does use mathematical formulas, but he disguises them as prose. For example:

[…] the increase in the separation between a pair of typical galaxies will be given by the product of their relative velocity and the elapsed time, or, using the Hubble law, by the product of the Hubble constant, the separation, and the time. But then the ratio of the increase in separation to the separation itself will be given by the Hubble constant times the elapsed time, which is the same for any pair of galaxies.

This is much easier to understand if you instead write, or at least add, the same idea in mathematical notation:

  Δr   = v Δt
  v    = H r
  Δr   = H r Δt
∴ Δr/r = H Δt

In fact, I ended up scribbling the book's margins with these translations. Otherwise it was hard to follow the wordy arguments.

What I wonder is whether someone who doesn't understand these simple formulas will get the meaning of the argument anyway just because it uses words. After all, math is a way of thinking as well as a language. Perhaps there are people that can't read math at all, but who can nonetheless think in a mathematical way ("if two things depend on the same thing, then the ratio of those things doesn't depend on that third thing"), but my guess is that's a rather small subset of potential readers.

(I must mention that the book does include an appendix with a "Mathematical Supplement", which elaborates on the math behind some explanations. It's useful and not very hard to follow. But it's more like deeper dives into specific arguments, rather than a reformulation of the core narrative in math form.)

As mentioned at the beginning, another problem with the book is that it's outdated. The first edition was published in 1977. There is a second edition from 1993, but it doesn't change anything in the main text; it just adds an afterword by Weinberg explaining the main developments that happened during those sixteen years.

I'm not in a position to list what has changed in cosmology down to this blessed minute, but from reading other people's comments, these seem to be the most relevant developments:

Besides these missing concepts, another factor that makes the book outdated is its uncertainty about certain values. The most important of these is a critical parameter, the baryon-to-photon ratio, on which the text relies a lot (although it doesn't use that name). Weinberg assumes a value of 1 in 1 billion for it, but he always makes it painfully clear that this estimate could be off by an order of magnitude. Today it seems well-established that the actual value is 1 in 6 billion. This doesn't change anything of substance in the theory, but many of the values derived from that ratio are of course different.

As far as I know, no updated version of The First Three Minutes was published after 1993, but this book is so good that I wish a proper new edition came out. Sadly, Steven Weinberg passed away in 2021. Any new afterword would have to be written by someone else, and those are big shoes to fill.