Photodetection and causality I

We investigate in this paper the link between the measurement process in quantum mechanics and casuality associated to a finite velocity of field propagation. We use models of interaction of a bound state with a scalar field. We first show that in the existing approaches, time delays resulting from the finite velocity of propagation have been obtained only as a consequence of ad hoc approximations. We show that exact causality can be restored in the case of a single photodetection by a slight change of the observable associated to the measurement process. Moreover, this modification may be justified by the introduction of a simple model for the photodetector. We present qualitative arguments to show that this procedure cannot be extended to the case of multiple photodetections. The process of repeated photodetection clashes therefore with causality. This paradox is closely related to the Zeno paradox described by Misra and Sudarshan1). Both may be traced back to the positive definite character of the hamiltonian which is the generator of motion in quantum mechanics.