Quantum interpretations and Buddhism Part 9: Interlude: Contextuality

 A special note on contextuality would be appropriate here. 

From Wikipedia, Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other observables which are simultaneously measured (the measurement context). 

After Bell, there are many different kinds of theorems and no-go things around. One of them is Kochen–Specker theorem. This works similar to Bell’s theorem, but in a more complicated scale, if you’re interested, you’re welcome to read it up on your own. Sufficient to say that this theorem rules out quantum interpretations involving hidden variables (wavefunction is not complete) which is not contextual. 

So measurement answers depend on the set of measurement being done, we cannot have pre-fixed answers for everything. Quantum non-locality of the entanglement types explored before can be considered as a special case of contextuality. 

Another interesting inequality is Leggett’s inequality. Leggett’s inequality violation is said to rule out counterfactual definiteness in hidden variable interpretations, whereas Bell’s inequality violation can only rule out the combined local reality hidden variable types. 

Leggett’s inequality is indeed violated by experiments, showing that quantum wins against a type of theories called crypto non-local hidden variable theories. Jim Baggott calls it somewhat halfway between strictly local and completely nonlocal. 

This seems to imply that quantum interpretations without assuming hidden variables underneath the wavefunction (realism/ counterfactual definiteness) can stay in the non-signalling comfort of the non-local entanglement. However, once we insist on having realism, we need to seriously consider that the interpretation also has signalling of faster than light within its mechanics. And indeed this is what Bohm’s pilot wave interpretation does. The price of realism is high.