We discuss and clarify the concept of dephasing in the many-Hilbert-sp
ace approach to the quantum measurement problem. We argue that the pha
se randomization provoked by a detecting macroscopic device is respons
ible for the loss of quantum coherence, and that the ''collapse of the
wave function'' is to be regarded as a statistical process for the ac
cumulated distribution over many events. In stressing the fundamental
differences between our approach and the Copenhagen interpretation, we
counter the objections put forward by Johnston [preceding Comment, Ph
ys. Rev. A 48, 2497 (1993)], whose stand-point is essentially similar
to the Copenhagen one.