Phenomenon of mobility in non-linear theories

Homeomorphisms of the unit-sphere of states are studied. Generalizations of the Piron statement and Wigners' theorem are obtained. It is shown that if the semigroup of the unitary operations of quantum theory were extended by introducing any non-linear operation, a mobility phenomenon would occur consisting of a possibility of moving any two states to any two surroundings on the unit sphere. For the resulting ''non-linear wave packets'' the complementarity doctrine would become impossible because of ''fluidity'' of the space of states under the dynamical transformations. (orig.)