This is a follow up on my earlier post on contextuality and non-locality. As far as I can tell, Spekken’s paper is the gold standard for how to think about contextuality in the messy real world. In particular, since the idea of “equivalent” measurements is key, we might never be able to establish that we are making “the same” measurement from one experiment to the next; there could always be small microscopic differences for which we are unable to account. However, Spekken’s idea of forming equivalence classes from measurement protocols that always produce the same results is very natural. It isolates, as much as possible, the inherent ugliness of a contextual model that gives different ontological descriptions for measurements that somehow always seem to give identical results.

I also learned an extremely important thing in my background reading. Apparently John Bell discovered contextuality a few years before Kochen and Specker (KS).^{a } More importantly, Bell’s theorem on locality *grew out* of this discovery; the theorem is just a special case of contextuality where “the context” is a space-like separated measurement.

So now I think I can get behind Spekken’s idea that contextuality is more important than non-locality, especially non-locality *per se*. It seems very plausible to me that the general idea of contextuality is driving at the key thing that’s weird about quantum mechanics (QM) and that — if QM is one day more clearly explained by a successor theory — we will find that the non-local special case of contextuality isn’t particularly different from local versions.… [continue reading]