I wanted to understand Rob Spekkens’ self-described lonely view that the contextual aspect of quantum mechanics is more important than the non-local aspect. Although I like to think I know a thing or two about the foundations of quantum mechanics, I’m embarrassingly unfamiliar with the discussion surrounding contextuality. 90% of my understanding is comes from this famous explanation by David Bacon at his old blog. (Non-experts should definitely take the time to read that nice little post.) What follows are my thoughts before diving into the literature.

I find the map-territory distinction very important for thinking about this. Bell’s theorem isn’t a theorem about quantum mechanics (QM) per se, it’s a theorem about locally realistic theories. It says if the universe satisfies certain very reasonable assumption, then it will behave in a certain manner. We observe that it doesn’t behave in this manner, therefore the universe doesn’t satisfy those assumption. The only reason that QM come into it is that QM correctly predicts the misbehavior, whereas classical mechanics does not (since classical mechanics satisfies the assumptions).

Now, if you’re comfortable writing down a unitarily evolving density matrix of macroscopic systems, then the *mechanism* by which QM is able to misbehave is actually fairly transparent. Write down an initial state, evolve it, and behold: the wavefunction is a sum of branches of macroscopically distinct outcomes with the appropriate statistics (assuming the Born rule). The importance of Bell’s Theorem is *not* that it shows that QM is weird, it’s that it shows that the *universe* is weird. After all, we *knew* that the QM formalism violated all sorts of our intuitions: entanglement, Heisenberg uncertainty, wave-particle duality, etc.; we didn’t need Bell’s theorem to tell us QM was strange.… [continue reading]