Superluminal Signal Velocity and Causality

Abstract

A superluminal signal velocity (i.e. faster than light) is said to violate causality. However, superluminal signal velocities have been measured in tunneling experiments recently. The classical dipole interaction approach by Sommerfeld and Brillouin results in a complex refractive index with a finite real part. For the tunneling process with its purely imaginary refractive index this model obtaines a zero-time traversing of tunneling barriers in agreement with wave meechanics. The information of a signal is proportional to the product of its frequency band width and its time duration. The reasons that superluminal signal velocities do not violate causality are: (i) physical signals are frequency band limited and (ii) signals have a finite time duration.