I suggest that quantum mechanical nonlocality may in a certain sense allow a particle to be in two places at the same time, without violating causality. I discuss the measurable consequences of such a feat, and speculate about possible statistical tests which could distinguish this view of quantum mechanics from a “corpuscular” one. In particular, I describe some experiments being set up at Toronto which will investigate atomic tunneling, looking among other things for a signature of such alkali schizophrenia.