  A theorem of Hegerfeldt (Instantaneous spreading and Einstein causality in
quantum theory, Ann. Phys. Leipzig vol. 7, 716-725 (1998)) establishes, for a
class of quantum systems, a dichotomy between those which are permanently
localized in a bounded region of space, and those exhibiting instantaneous
spreading. We analyse in some detail the physical inconsistencies which follow
from both of these options, and formulate which, in our view, are the basic
open problems.
