Why must all operators in QM be linear (and therefore able to be represented by matrices). What is the physical reasoning behind this?
Is it be possible that the non-unitary nature of quantum collapse could be described physically by a non-linear quantum theory where the coupling of a system to a measuring device (composed of a large (thermodynamic limit) number of particles) 'massages' the state into one of the observable eigenstates. (i.e. the large number of particles in the measuring device make any state but the observable eigenstates statistically impossible to be 'massaged' into)
I am (obviously) assuming that these suggestions are incorrect, but I think I could learn a lot about the nature of QM by understanding exactly why.