Difference between revisions 3012256 and 4536800 on enwiki

The '''Wigner - d'Espagnat inequality''' is a basic result of [[Sset 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, 
:: or else is a member of J and of K, but not of L;
(contracted; show full)

The failure of certain measurements (such as the non-negative ratios in the example) to be obtained at once, together from one and the same set of trials, and thus their failure to satisfy Wigner - d'Espagnat inequalities, has been characterized as constituting disproof of [[Albert Einstein|Einstein]]'s notion of ''local realism''.

Similar interdependencies between ''two'' particular measurements and the corresponding operators are the [[
Uuncertainty Pprinciple|Uuncertainty relations]] as first expressed by [[Werner Heisenberg|Heisenberg]] for the interdependence between measurements of distance and of momentum, and as generalized by [[Edward Condon]], [[Howard Percy Robertson]], and [[Erwin Schrödinger]].
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====Reference====
* John S. Bell, ''Bertlmann's socks and the nature of reality'', Journal de Physique '''42''', no. 3, p. 41 (1981); and references therein.