next up previous
Next: 3. Importance of fuzziness Up: 4. Notes Previous: 1. Pure states as

2. Fuzzy projections

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 $1\mu m$ 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. ([*]).