Quantum Computing since Democritus

by Scott Aaronson

In the usual “hierarchy 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.”

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.

So, in this chapter, we're going to ask – and hopefully answer – this question of whether there's free will or not. If you want to know where I stand, I’ll tell you: I believe in free will. Why? Well, the neurons in my brain just fire in such a way that my mouth opens and I say I have free will. What choice do I have?