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Detecting the particle spin is somewhat different than detecting
its position components. To measure the position of a particle we
can use a photographic plate or a bubble chamber. In such a case a
simple mathematical model of a detector is obtained by associating
with each active center of the detector a fuzzy, bell-type
function with its half-width corresponding to the active region of
the center ( for instance about for an AgBr grain of a
photographic emulsion). What would correspond to such a "fuzzy"
projection operator in the case of a spin measurement? We do not
have much of a choice here. Due to symmetry reasons there is only
one formula possible, namely one given by Eq. ().