If quantum mechanics is interpreted as an objective, complete, physical theory, applying to macroscopic as well as microscopic systems, then the linearity of quantum dynamics gives rise to the measurement problem and related problems, which cannot be solved without modifying the dynamics. Eight desiderata are proposed for a reasonable modified theory. They favor a stochastic modification rather than a deterministic non-linear one, but the spontaneous localization theories of Ghirardi et al. and Pearle are criticized. The intermittent fluorescence of a trapped atom irradiated by two laser beams suggests a stochastic theory in which the locus of stochasticity is interaction between a material system and the electromagnetic vacuum.