Can quantum objects be point-like particles?

The possible nature of the nonlinear evolution of quantum systems is explored from the point of view of nonlocal effects under the conditions of EPR paradox. It is shown that both stochastic and deterministic mechanisms of nonlocal evolution should consider a quantum particle as a material field in order not to contradict special relativity. It is assumed that there is an experiment allowing to find out which of the mechanisms of nonlinear evolution is realized in nature