So, this is the new book from the authors of Why Does E=mc2?, covering quantum mechanics in a roughly similar manner. This book, or, rather, Brian Cox talking about some material from this book, created a bit of controversy recently, as previously discussed. But other than that, Mrs. Lincoln, how did you like the play?
The big hook here is that they set out to discuss quantum mechanics for a popular audience using a Feynman-type picture from the very beginning. This is an intriguing idea, and sort of appealing in the same basic way that Sakurai’s famous graduate text in quantum mechanics and Townsend’s undergraduate version appealing. Those books are interesting because they come at the subject from a different angle, formulating everything first in terms of spin-1/2 particles, rather than wave mechanics. This makes certain types of problems much easier to deal with, and lets students see the subject in a very different light.
So, the general idea of a book on quantum physics that starts with Feynman’s path integral formulation of the theory– other than, you know, Feynman’s own book on QED— is an interesting idea. The Feynman approach is the starting point for a lot of modern approaches to the theory, and looks very different than the Schrödinger wave mechanics most popular treatments (my own included) take. I got some useful stuff out of their book on relativity, so I was hoping for some useful insights from this one.
Like its predecessor, though, I want to like this book more than I do.
Part of the problem with this is that the subject matter is just inherently messier than relativity. You can easily boil relativity down to a single sentence– the laws of physics do not depend on how you are moving– and everything else follows logically from that. That simple central idea makes it easy to tell a clear and coherent story about the theory.
Quantum mechanics, on the other hand, is more complicated, and kind of a hodge-podge of different things. When I was writing it up around the release of How to Teach Physics to Your Dog, I wound up with seven essential elements. You can cut it down a little more than that, particularly if you skip some of the side branches of the theory, but it’s not as easy to boil down as relativity. And that means telling a story about the theory is much harder to do.
The end result of this is a book that feels much more uneven, with lots of little “Oh, and another thing you need to know is…” transitions when new ideas need to be brought in. I’m not sure it’s actually longer than their first book, but it certainly feels longer.
This is compounded by the fact that they don’t really manage to stick to the Feynman style approach all the way through. They spend a bunch of time setting up an elaborate analogy for the path integral approach in terms of little clocks that get transported from one place to another, subject to a set of somewhat arbitrary seeming rules, and work out some basic elements of the theory. They even “derive” the de Broglie relationship between momentum and wavelength, which is something I hadn’t seen before, and probably the best part of the book.
But when it comes time to apply the rules to systems that are more interesting than a free particle, they more or less chuck the whole moving-clocks-around business, and go back to talking about waves. Their explanation for why atoms have discrete energy states is just the standard particle-in-a-one-dimensional-box model, followed by the usual handwaves about how while the potential energy for an electron in a hydrogen atom doesn’t really look like an infinite square well, it’s the same basic idea. They go back to the moving-clocks-around stuff later, but the overall effect is even more disjointed than a quantum book needs to be, with elaborate models set up at length, then discarded and replaced with different elaborate models for the next thing, which is in turn tossed aside in favor of something else.
I realize that it’s really difficult to explain how to calculate bound states of anything with the Feynman path integral approach, which is why even graduate textbooks don’t spend very much time on it– you get the same answer more quickly with simpler methods. But if that’s the case, then you’re probably better off not trying to use that formalism, particularly if you’re going to set it aside when you actually calculate anything.
And there are some problems with even the straight-up moving-clocks stuff. They’re really sloppy with the way they talk about the clocks, switching between talking about single clocks at specific locations, and small arrays of clocks spread over regions of space whenever it’s convenient, without consistently acknowledging that they’re doing this. And this is particularly problematic when they start talking about everything being interconnected, which they try to do while also maintaining the pretense that individual particle states are perfectly localized. Which isn’t entirely coherent.
But the biggest problem I end up having with the material is that it’s, well, old. They don’t talk about anything all that recent, save for a really oblique mention of the anomalous magnetic moment of the electron. The basic Feynman picture they’re using dates from around 1940, and even QED is from the late 1940’s. Even the grand calculation that highlights the end of the book, of the Chandrasekhar limit for the mass of a white dwarf, was first worked out in 1930.
There’s one hand-wavy mention of EPR (from 1935), but nothing at all about Bell’s theorem (from 1964), or demonstrations of non-locality (first done in the late 1970’s), or quantum information (sometimes attributed to Feynman in the early 1980’s), or any of the exciting work on quantum foundations that has been done in the last 30 years. This is quantum physics as a dusty old theory pressed under glass, not an exciting and active field of research.
It’s a little awkward to write this, of course, because I risk having my criticisms brushed off as the quibbles of somebody whose own book on the subject is directly in competition with this. And there are things I do like about the treatment, particularly the Feynman-to-de-Broglie bit at the beginning. As a whole, though, it wound up being a disappointment.
If you want to read a Feynman-style treatment of the subject, you’re still better off going with QED. And if you want to get a better feel for what’s currently interesting in the field, Anton Zeilinger’s Dance of the Photons is excellent.
Feynman does, as you said, use that approach in QED, but he very notably does not in The Feynman Lectures on Physics, where he instead starts out with finite-dimensional Hilbert spaces. That strikes me as a sounder approach for dealing with things that are not basically scattering or optics problems.
The lack of any recent developments is fairly typical in books about quantum theory written by particle physicists. For them, quantum theory really is a dusty old theory pressed under glass and the interesting developments are elsewhere. In Manchester there really is no interesting quantum information or foundations research going on, so it is not too surprising that Brian and Jeff didn’t include anything about those subjects. This is one of the reasons why I left Manchester after my undergrad.
I am still waiting for the perfect popular science book about quantum theory. Maybe I should look at Zeilinger’s book, although I suspect it might be a bit Copenhagenish for my tastes.