As a direct result of [the way quantum mechanics is usually taught in textbooks], the subject acquired an unnecessary reputation for being complicated and hard. Educated people memorized the slogans — “light is both a wave and a particle,” “the cat is neither dead nor alive until you look,” “you can ask about the position or the momentum, but not both,” “one particular instantly learns the spin of the other through spooky action-at-a-distance,” etc. But they also learned that they shouldn’t even try to understand such things without years of painstaking work.
The second way to teach quantum mechanics eschews a blow-by-blow account of its discovery, and instead starts directly from the conceptual core...
Just for the heck of it, here’s another passage from that chapter:
So what is quantum mechanics? …In the usual “heirarchy of sciences” — with biology at the top, then chemistry, then physics, then math — quantum mechanics sits at a level between math and physics that I don’t know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn’t yet been successfully ported to this particular OS). There’s even a word for taking a physical theory and porting it to this OS: “to quantize.”
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.
My contention in this chapter is the following: Quantum mechanics is what you would inevitably come up with if you started from probability theory, and then said, let’s try to generalize it so that the numbers we used to call “probabilities” can be negative numbers. As such, the theory could have been invented by mathematicians in the nineteenth century without any input from experiment. It wasn’t, but it could have been.
And yet, with all the structures mathematicians studied, none of them came up with quantum mechanics until experiment forced it on them. And that’s a perfect illustration of why experiments are relevant in the first place! More often than not, the only reason we need experiments is that we’re not smart enough.
Wow! Is the rest of the book that good? I’ve read some of Aaronson’s lecture notes and blog (and largely approve of his interpretation of QM as probability with a 2-norm), but I didn’t know he could write like this.
I think he might be simplifying it a little bit. As I understand QM, it’s more like probability with complex numbers, rather than with negative numbers.
The book is cleaned up and updated. There’s a section at the beginning explaining all the new results that have come out since 2006, requiring updates to the lecture notes when he was turning them into a book.
I think he might be simplifying it a little bit. As I understand QM, it’s more like probability with complex numbers, rather than with negative numbers.
Yes, he is. Must be for rhetorical purposes, because elsewhere he says exactly that.
Aaronson takes a similar approach to explaining quantum mechanics in chapter 9 of Quantum Computing Since Democritus (2013):
Just for the heck of it, here’s another passage from that chapter:
Wow! Is the rest of the book that good? I’ve read some of Aaronson’s lecture notes and blog (and largely approve of his interpretation of QM as probability with a 2-norm), but I didn’t know he could write like this.
I think it’s been up for a long time on his website as a lecture series. http://www.scottaaronson.com/democritus/
I think he might be simplifying it a little bit. As I understand QM, it’s more like probability with complex numbers, rather than with negative numbers.
The book is cleaned up and updated. There’s a section at the beginning explaining all the new results that have come out since 2006, requiring updates to the lecture notes when he was turning them into a book.
Yes, he is. Must be for rhetorical purposes, because elsewhere he says exactly that.
Ah, okay. It’s been a while since I read it. I remember it being excellent though.
Yeah, I think the book will be a pretty great read for the most mathematically capable LWers. (Most of it is, alas, over my head.)