SneerClub

Glob help me, but I've actually been reading Quantum Computing Since Democritus, and I've been sorely tempted to write an effortful post about it. In particular, it is appealing to ask whether the book delivers on its professed theme. Here's Aaronson in the preface, laying out what he considers the book's "central message":

But if quantum mechanics isn’t physics in the usual sense – if it’s not about matter, or energy, or waves, or particles – then what is it about? From my perspective, it’s about information and probabilities and observables, and how they relate to each other.

This is a defensible claim. All the way back in the 1930s, Birkhoff and von Neumann were saying that we should understand quantum physics by modifying the rules of logic, which is about as close to "quantum information" thinking before the subjects of computer science and information theory had really been invented. Later, E. T. Jaynes was fond of saying that quantum mechanics is an omelette that mixes up nature and our information about nature, and in order to make further progress in physics, we need to separate them. When undergrads came to John Wheeler asking for summer research projects, he liked to suggest, "Derive quantum mechanics from an information-theoretic principle!" But the question at hand is whether Aaronson's book succeeds at making a case. You can talk a lot about quantum information theory or quantum computing without convincing anyone that it illuminates the fundamental subject matter of quantum mechanics. Knuth's Art of Computer Programming is not an argument that classical electromagnetism is "about information".

Here's Aaronson a bit later:

Here, the physicists assure us, no one knows how we should adjust our intuition so that the behavior of subatomic particles would no longer seem so crazy. Indeed, maybe there is no way; maybe subatomic behavior will always remain an arbitrary brute fact, with nothing to say about it beyond “such-and-such formulas give you the right answer.”

Then he argues,

as the result of decades of work in quantum computation and quantum foundations, we can do a lot better today than simply calling quantum mechanics a mysterious brute fact.

What is this new improved perspective? Here's how his italicized paragraph about it begins:

Quantum mechanics is a beautiful generalization of the laws of probability: a generalization based on the 2-norm rather than the 1-norm, and on complex numbers rather than nonnegative real numbers.

That isn't just a "brute fact". It's the same "brute fact" that an ordinary textbook will tell you! It's the "fourth postulate" in Cohen-Tannoudji et al., equation (1.3) in Griffiths and Schroeter, page 9 of Zwiebach. All that Aaronson has done is change the jargon a tiny bit.

Aaronson declares himself indifferent to the needs of "the people designing lasers and transistors". And fair enough; we all have our tastes for topics. But he has set himself the challenge of demonstrating that studying how to program computers that have not been built, and comparing them to computers that physics says can never be built, is the way to the heart of quantum mechanics.

Aaronson quotes a passage from Carl Sagan, thusly:

Imagine you seriously want to understand what quantum mechanics is about. There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidean geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory . . . The job of the popularizer of science, trying to get across some idea of quantum mechanics to a general audience that has not gone through these initiation rites, is daunting. Indeed, there are no successful popularizations of quantum mechanics in my opinion – partly for this reason. These mathematical complexities are compounded by the fact that quantum theory is so resolutely counterintuitive. Common sense is almost useless in approaching it. It’s no good, Richard Feynman once said, asking why it is that way. No one knows why it is that way. That’s just the way it is.

Aaronson follows this by saying that he doesn't need convincing: "Personally, I simply believe the experimentalists" when they say that quantum physics works. Again, fair enough on its own. But I think this is poor media literacy here. Sagan's Demon-Haunted World is all about the public understanding of science, the difference between authorities and experts, the challenge of becoming scientifically literate, and that kind of thing. What Sagan means by "what quantum mechanics is about" in this context is what physicists use the theory to do, day by day, and why we have confidence in it. Even if you come along with a better explanation of where the mathematics comes from, all that won't go away!