Even leaving aside the web bot issue, the OP requirements, as far as I can see, cannot be met without loading and parsing the whole file in some way, since you have to randomly select a word. If the file is sorted by initial letter (as at least one of the ones linked to in the OP is), you might...
I'm not sure I understand. The only mathematical quantity involved is the operator ##\hat{Q}##. The "observable" ##Q## is not something you can do math with, so I don't understand how you could even make sense of an expression like ##\partial / \partial t (x p)## (without the hats).
As I understand it the MWI was the interpretation that inspired the concept. I don't know if that's the only interpretation that allows it, though. In any case the discussion of it belongs in this subforum.
I don't know if this is true for all KVFs, but we know ##X## is a commutator of two KVFs whose asymptotic behavior is known, which makes things simpler:
$$
\nabla X = (\nabla T) \Phi - (\nabla \Phi) T
$$
So if ##\nabla T \to 0## and ##\nabla \Phi \to 0## in the asymptotic limit, that would be...
True, but you have specified that the spacetime is stationary and axisymmetric. You have also implicitly specified that it is asymptotically flat. Wald, in section 7.1, defines "stationary and axisymmetric" to include the property that ##\Phi## commutes with ##T##. (Wald then goes on to show how...
The relevant properties in the asymptotic limit are that ##T## has unit norm in that limit and ##\Phi## is orthogonal to ##T## in that limit. That is different from them being coordinate basis vector fields only in that limit.
Can you find a chart in which ##T = \partial / \partial t## and ##\Phi = \partial / \partial \phi## everywhere? If the two KVFs commute in that chart, they would have to commute in any chart, since any valid coordinate transformation will have to preserve commutators of vector fields.
Ok. But note that that is not the same as what is done to test the Bell inequalities, or other related ones such as CHSH. To do such a test you need to make measurements of all of the possible combinations and then do the appropriate calculations from the results.
In other words, once you specify which measurements are being made. Yes, but the probability you calculate is only valid for that specific setup. You appeared to be claming that you could calculate some sort of "total probability" that applied to any experimental setup. You can't.