/ 01 07 02 5 v 1 5 J ul 2 00 1 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 v w is Ψ f in |v|Ψ in /Ψ f in |Ψ in , where v is the velocity operator and |Ψ in and |Ψ f in are, respectively, the states of a particle before and after a velocity measurement. We discuss the consistency of weak values and show that weak superluminal speed is consistent with relativistic causality.