Quantum Physics as a Computer Science

Scott Aaronson, a postdoc at the University of Waterloo, teaches a class on the history of quantum computing -- starting from time of Democritus -- or so the course title claims. He has made his lecture notes available online, and lecture 9 provides an interesting perspective on quantum mechanics, that most of us who took QM, may not have encountered previously. I don't know about you, but if you were like me and had the joy of studying QM, you may have been thrilled to have been part of that fine class of students who could boast about being in QM, while at the same time, secretly harbouring doubts -- maybe the whole thing was just a joke physicists were playing on the world.

Aaronson sets out the make it all clear to the masses -- well, mathematicians and computer scientists anyway -- by doing something quite unremarkable -- something I've always wondered about. Do you remember how you were taught science? You were taught it the way it was historically developed -- including mad rushes down blind alleys that led only to dead ends, and had you gibbering like a mad idiot in the dark. That's how quantum mechanics is taught -- and that's how every QM book I've seen has laid out the concepts.

You have to dutifully follow along the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex.

So Aaronson has decided to clear the air. His lecture drops the history, starts at the conceptual core then add the physics. It makes for an interesting read. Except for the math -- which still hurts -- especially if you've been away from it for years.