The ESR model has been recently proposed in several papers to offer a
possible solution of the problems raising from the nonobjectivity of physical
properties in quantum mechanics (QM) (mainly the objectification problem of the
quantum theory of measurement). This solution is obtained by embodying the
mathematical formalism of QM into a broader mathematical framework and
reinterpreting quantum probabilities as conditional on detection rather than
absolute. We provide a new and more general formulation of the ESR model and
discuss time evolution according to it, pointing out in particular that both
linear and nonlinear evolution may occur, depending on the physical
environment.Comment: 36 pages, standard LateX, minor revisions in Section 7,
Acknowledgments and some References adde