Difference between revisions 5180715 and 7623324 on enwiki

The '''Wigner - d'Espagnat inequality''' is a basic result of [[set theory]].
It is named for [[Eugene Wigner]] and Bertrand d'Espagnat who (as pointed out by [[John Stewart Bell|Bell]]) both employed it in their popularizations of [[quantum mechanics]].

Given a set S with three subsets, J, K, and L, the following holds:

* each member of S which is a member of J, but not of L 
:: is either a member of J, but neither of K, nor of L, 
(contracted; show full)
# ''N<sub>(hit B) (hit C)</sub> + N<sub>(hit B) (miss C)</sub> + N<sub>(miss B) (hit C)</sub> + N<sub>(miss B) (miss C)</sub> = 1''.


However if the pairwise ''orientation angles'' between these three observers are determined (following 
the inverse of a quantum-mechanical interpretation of [[Etienne-Louis Malus|Malus]]'s definitionLaw) from the measured ratios as

: ''orientation angle( A, B ) = 1/2 arccos( N<sub>(hit A) (hit B)</sub> - N<sub>(hit A) (miss B)</sub> - N<sub>(miss A) (hit B)</sub> + N<sub>(miss A) (miss B)</sub> )'', 
: ''orientation angle( A, C ) = 1/2 arccos( N<sub>(hit A) (hit C)</sub> - N<sub>(hit A) (miss C)</sub> - N<sub>(miss A) (hit C)</sub> + N<sub>(miss A) (miss C)</sub> )'',
(contracted; show full)

====Reference====
* John S. Bell, ''Bertlmann's socks and the nature of reality'', Journal de Physique '''42''', no. 3, p. 41 (1981); and references therein.