The Theoretical Minimum by Leonard Susskind and George Hrabovsky

This is the physics book that’s generating the most buzz just at the moment, by noted string theorist Leonard Susskind and George Hrabovsky, based on a general-audience course Susskind’s been running for years. It’s doing very well, with an Amazon rank in the 300’s, which is kind of remarkable for a book with this many equations. Using calculus, even.

Odd though it might seem given the mathematical content, this is a book that has a lot in common with Cox and Forshaw’s Why Does E=Mc2?. By which I mean that it sets out to present a very particular take on theoretical physics to a general audience, working at a very high level of abstraction. Susskind and Hrabowsky have a somewhat wider scope than Cox and Forshaw, attempting to cover all of classical mechanics rather than just relativity, but the general concept in very similar: Cox and Forshaw give a high-level overview of relativity from the perspective of spacetime geometry, where Susskind and Hrabowsky give a high-level overview of classical mechanics from the perspective of Lagrangian and Hamiltonian mechanics.

As a bird’s eye view of the subject, it’s quite good, and if I ever find myself teaching our intermediate mechanics course, in which we cover this same material, I’ll probably assign it as a supplement. While it has equations galore, it doesn’t get into the mathematical weeds very much, sticking instead to what I might call a conceptual overview, though if I were to call it that I would have to hasten to distinguish this from “conceptual physics,” which is one of the euphemisms used to describe the classic “Physics for Poets” courses, which this manifestly is not. Anyway, if you want a nice, clean description of what’s really going on when you talk about a Lagrangian or a Hamiltonian, this is outstanding.

At the same time, though, despite the subtitle “What You Need to Know to Start Doing Physics,” it’s blissfully unconcerned with actually calculating anything practical. Which, you know, is fine as far as it goes– the real goal is to give a broader audience some hint of how professional theoretical physicists think about the world. But I’m an experimentalist by training and inclination, and I can’t help thinking that while the mathematical formalism is all elegant and stuff, it doesn’t really capture everything that’s cool about physics. As I said above, I think this would be an excellent companion to a real classical mechanics textbook, in that the above-the-treetops view could help prevent students losing sight of the bigger purpose while they struggle with calculational details, as an overview of physics per se, it is itself in need of a companion volume, something more grounded in the actual motion of objects, and what we can learn from and about the real world. Something like, say, Rhett “Dot Physics” Allain’s forthcoming Angry Birds book (OK, I don’t know what’s actually in Rhett’s book, but I’m a huge fan of his blog, which is pretty much the exact opposite of the approach this book takes).

So, as I said, while the conceptual coverage is outstanding– really, it clarified some points I’ve been unsure about since I took classical mechanics as an undergrad, back when dinosaurs roamed the Earth– the particular stance it takes leads to some curious choices. As I mentioned on Twitter, at one point when they need to include units of length, they make a reference to the meter being defined by a platinum-irridium bar, which it hasn’t been since 1960. They include a footnote noting that this isn’t the current definition, and alluding to a more recent definition “in terms of the wavelength of light emitted by atoms jumping from one quantum level to another.” Which, it’s true, is the definition that replaced the platinum bar, but hasn’t been the definition of the meter since 1983– the meter is currently defined in terms of the speed of light, as the distance light travels in 1/299,792,458th of a second. It’s very puzzling to see a book whose purpose is to present a modern view of physics using a definition that’s thirty years out of date. (When I mentioned this on Twitter, Matthew Francis quipped “[Susskind]’s a string theorist. Reality is something that happens to other people.”)

Or, for a more substantive example, when they want to show the power of the Poisson bracket formulation of mechanics for dealing with rotation, the system they go to is a spinning charged sphere in a magnetic field. Which is obviously setting the stage to talk about electron spin in a future volume, but as a physical system, it’s not something that’s familiar to anyone, so the general reader isn’t going to have any idea what to expect. They also need to assert the properties of the system more or less by fiat– what the form of the Hamiltonian is and how to write it in terms of the angular momentum– none of which is likely to provide any insight to people who haven’t worked with magnetic fields before (this is also the first mention of magnetic fields in the entire book), further limiting its ability to illuminate the general principles.

When attempting to explain what’s going to happen, though, they make the appropriate analogy, namely a gyroscope, which nearly everyone has seen at some point, and toy versions of which can be picked up for a couple of bucks at any toy store. But, of course, there wouldn’t be much practical difference to taking the gyroscope as an example, because they haven’t talked about the necessary properties of familiar systems, either. They’d end up needing to do the same by-fiat assertions to get in the properties of gravitational forces and physical rotating objects, at which point I doubt they’d be confusing readers all that much less than they do by dragging in spin.

Which is a long way of saying that, from my very-much-an-experimentalist perspective they made some curious choices. Which isn’t a bad thing per se— again, the point is to show how theorists think, and it does a bang-up job of that– but, you know, it felt weird. Especially because I’m currently teaching intro classical mechanics for the fourth time in the last two years, and very much bound up in the gory details of real objects.

So, circling back to my opening comment, I think that this book does an excellent job of what it’s trying to do, but for all the equations it contains (and despite the subtitle), it doesn’t teach anybody to do physics in a significantly more substantive sense than Cox and Forshaw’s vastly less mathematical take on relativity. It gives a flavor for how a certain subset of theoretical physicists look at the world, which is a useful and valuable goal, but not the whole of physics, and not even classical physics.

This is ending up sounding like the worst kind of bad review, I realize, the one that blasts a book for not being a completely different book than the authors set out to write, and I feel a little bad about that. But, you know, it’s my blog, and what you get here is my opinion, which is a conflicted muddle. Again, I think the book is outstanding at doing what they set out to do, and I think it would be great as a companion to a course on Lagrangian and Hamiltonian mechanics. But what they set out to do imposes certain limits, and I think it’s important to point out what those are in evaluating the book as a whole.

10 Replies to “The Theoretical Minimum by Leonard Susskind and George Hrabovsky”

  1. “the meter is currently defined in terms of the speed of light, as the distance light travels in 1/299,792,458th of a second”

    Which raises the question: how is a second defined?

  2. A second is 9,192,631,770 oscillations of the light emitted by cesium-133 atoms moving from one hyperfine ground state to the other. This is now routinely measured with an uncertainty of a couple parts in 10^16 (that is, +/- 0.0000000000000002), so it makes sense to define the speed of light as a specific value, and use the outstanding accuracy of time measurements to produce a highly accurate and universal length standard.

  3. 9.2GHz isn’t exactly “light” as, say, an engineer would think of it. That’s not meant as a quibble — I’ve seen other descriptions of cesium clocks use the same word, so I wondered if there is a specific sense of the word in play here.

  4. Chad

    You make some very fair points. Definitely the book puts a premium on the theoretical aspects of physics. One of the reasons why the appendix on Kepler’s laws was included was to give readers a feel for a more real-world feeling for the formalisms they were introduced to in the main part of the text. What I like best about the book–as a totally biased person, namely the editor of the book (and in the interest of complete openness of your relativity book)–is that it introduces in detail what a Lgrangian is. Few people learn about this formalization in high school and they become one of the magic wands of popular physics books. But they are amazing, more so I think than the Newtonian formalization most people know.

  5. I would’ve sworn I’d posted a reply to weirdnoise and TJ yesterday, but apparently not. Anyway:

    9.2GHz isn’t exactly “light” as, say, an engineer would think of it. That’s not meant as a quibble — I’ve seen other descriptions of cesium clocks use the same word, so I wondered if there is a specific sense of the word in play here.

    I use “light” there to emphasize that it’s the same physical phenomenon, just at a different frequency range. From a more practical standpoint, it makes sense to divide up regions of the electromagnetic spectrum in terms of the technologies you use to manipulate them, so 9.192 GHz would be microwaves, in contrast to, say, visible light with a frequency in the 10^14 Hz range. But the process by which microwaves are emitted by a cesium atom moving between ground-state hyperfine levels is no different than the process by which infrared light is emitted by a cesium atom moving between the first excited state and the ground state.

    Few people learn about this formalization in high school and they become one of the magic wands of popular physics books. But they are amazing, more so I think than the Newtonian formalization most people know.

    Yeah, and I think that having a good popular treatment of Lagrangian and Hamiltonian mechanics out there is a great thing. They’re really cool, and it’s valuable to see that perspective in contrast to a more standard Newton’s Laws treatment. In more or less the same way that Cox and Forshaw’s spacetime geometry treatment of relativity is a valuable contrast to the infinite-grid-of-clocks-and-meter-sticks perspective.

    I just think that both the more abstract and more grounded approaches have value. Which is why I gave both of them a bunch of space in How to Teach Relativity to Your Dog. If Emmy ever takes an interest in classical mechanics, I’m sure we’ll talk about both versions.

  6. Still am looking forward to reading this. What’s kinda funny though is that I found the book today, and now this is up haha.

  7. One of my psychologist colleagues told me once that what we learn first of something is what sticks even when we learn better/different later. This has all sorts of implications for disciplines that are dynamic or taught in an historical progression.
    And as a theoretician, I can confirm that a great deal of theory formulation is “curious choices”, which is a lovely turn of phrase that I shall have to incorporate in my vocabulary.

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