Instantaneous spreading and Einstein causality in quantum theory

In nonrelativistic quantum mechanics the wave-function of a free particle w hich initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same ins tantaneous spreading can occur in relativistic quantum theory and that tran sition probabilities in widely separated systems may instantaneously become nonzero. We discuss how this affects Einstein causality.