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added this:
Relation to (identification with) much older inequalities in classical probability theory, due to George Boole was pointed out by (among others, called the “probabilistic opposition” in Khrennikov 2007, p. 3):
Luigi Accardi, The Probabilistic Roots of the Quantum Mechanical Paradoxes, in: The Wave-Particle Dualism, Fundamental Theories of Physics 3 Springer (1984) [doi:10.1007/978-94-009-6286-6_16
Itamar Pitowsky, From George Boole To John Bell — The Origins of Bell’s Inequality, in: Bell’s Theorem, Quantum Theory and Conceptions of the Universe, Fundamental Theories of Physics 37 Springer (1989) [doi:10.1007/978-94-017-0849-4_6]
reviewed in
Elemer E Rosinger, George Boole and the Bell inequalities [arXiv:quant-ph/0406004]
{#Khrennikov07} Andrei Khrennikov, Bell’s inequality: Physics meets Probability [arXiv:0709.3909]
Andrei Khrennikov, Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?, Entropy 10 2 (2008) 19-32 [doi:10.3390/entropy-e10020019]
Incidentally, I notice that besides this entry Bell’s inequalities we have Bell’s theorem, and the two should be merged.
Looking over the latter, I find that the text offered there needs attention. (This originates from a user 12+ years ago who caused us some trouble back then, I seem to remember.)
I won’t do the merging right now, though (am on my phone in a plane descending onto Dubai…).
added pointer to today’s
added pointer to today’s:
As announced there, I have merged the material previously at Bell’s theorem into here, in order to merge the duplicate entries.
That original material had references to equation numbers coded by hand(!), which I have now adjusted to automatic numbering, hoping I got it all right.
(A strange technical glitch is that in the original entry all the equations were numbered automatically, while in the new entry the numbers appear only for equations that also carry a label. While that clearly makes sense, I am puzzled that the rendering can change just by copying material to another entry as if dependent on some preamble context, which I thought doesn’t exist for nLab entries(?).)
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