In QM you often read that apparatus measures the value of an observable (energy, position and so on). This observable may have different values which are the eigenvalues of a hermitian operator. The eigenvectors are orthogonal. We associate projectors Pi such that Pi * Pi = Pi. if i <> j Pi * Pj = 0 Read http://www.phys.tue.nl/ktn/Wim/qm12.htm#illustrations You will see that all that was an idealization. The Pi must be replaced by positive operators Fi which are not necesseraly projectors and orthogonal. the collapse on one of the vectors of a basis is replaced by the random choice of an operator Fi. This does not seem to be only a change of vocabulary! You can find that in http://www.phys.tue.nl/ktn/Wim/muynck.htm#quantum As i discover all that, i am not yet able to ask questions! But i would be interested in your comments.