An important technical difference between decoherence and the collapse of the wave function is that decoherence actually doesn’t decide which result will be measured. It just diagonalizes the density matrix to diag(p1,p2,…,pN) where p_i then play the role of the probabilities that the individual preferred basis vectors will be detected. Because the information about the relative phases is getting quickly lost, the off-diagonal elements rapidly converge to zero. But decoherence never transforms the density matrix with the many p’s to something like (0,0,1,0,…,0). Never, ever. Quantum mechanics remains the only player here and its predictions remain and will always stay probabilistic. One can never and one will never restore determinism and decoherence doesn’t try to do anything of the sort.

— Lubos Motl

2012.08.28 Tuesday ACHK