Cherenkov radiation of superluminal particles

Any charged particle moving faster than light through a medium emits Cherenkov radiation. We show that charged particles moving faster than light through the vacuum emit Cherenkov radiation. How can a particle move faster than light? The weak speed of a charged particle can exceed the speed of light. By definition, the weak velocity [Formula Presented] is [Formula Presented] where [Formula Presented] is the velocity operator and [Formula Presented] and [Formula Presented] are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that superluminal weak speed is consistent with relativistic causality. 5555 2002 The American Physical Society.