Quantum Mechanics and Experience

One of the classes I'll be taking this semester is 24.111 - Philosophy of Quantum Mechanics. Today I just bought the required text, Quantum Mechanics and Experience by David Z. Albert. The book looks pretty good, with a solid layman introduction to the foundational principles of quantum mechanics.

My dance with Quantum Mechanics (QM) has been a really interesting one. Prior to my coursework this past year at Cambridge, I objected to the conclusions of quantum mechanics advertised in popular science books because it ran against my mental model of the universe. My struggles with the conceptual foundations of QM were very much in the same vein as Einstein's critique of the theory. The idea that probability has a real existent status deeply troubled me. Always before, probability was a description of averages and distributions. A coin toss -- the idol of probability -- was still fundamentally governed by Newton's Laws, the forces in the room, the initial configuration of the coin in your hand, the torque, the impulse of your thumb on the coin, the chaotic turbulence of the air molecules in the room, the list goes on but all the initial configurations and momenta could theoretically be specified and then the entire motion could be simulated as the solution of a large system of nonlinear ordinary differential equations (ODEs) -- Laplace's Demon all over again. But QM is a whole different bag of nuts... Instead of solving specifically for things like position and momentum and energy, you have state vectors, and your eigenfunctions of these operators form the basis of an infinite-dimensional space known as Hilbert space. What's new about all of this is that our description of a particle is described by the time evolution of the coefficients of each of these eigenfunctions. Now we can't perceive this superposition, but rather -- and this is the really crazy bit of the whole theory -- only the eigenfunctions can be measured. So our particle is like a point wandering around in infinite dimensional Hilbert space when no one is looking. It's like Mr. Observer finally shines his flashlight in the car window and asks "Hey!?! What are you kids doing?!?" and our couple is always caught in any one of these (usually an infinite number of) compromising positions, but they're never caught scrambling to put clothes on or in a acrobatic transition or superposition of pages of the Kama Quantum Sutra.

So it will be interesting to see what insights 24.111 will bring, and complemented with 18.102 - Introduction to Functional Analysis, this should be a tantalizing semester spent exploring Hilbert space!