Superluminal but causal wave propagation

Abstract

A series of experiments in recent years have shown that under carefully designed circumstances the group velocity, or even more surprisingly the energy velocity can exceed the speed of light in vacuum or become negative (abnormal velocities). These abnormal results have led some researchers to question the validity of special relativity, or at least cast doubt on the relevance of these principles to the aforementioned experiments. In this work series of experiments with single electromagnetic pulses measured in both time and frequency domain are described. It is seen that while these experiments verify the aforementioned abnormal velocities, they are not in contradiction with the principles of special relativity (Einstein causality). In this regard, the important concept of “front” or “Sommerfeld forerunner” is reintroduced, and it is argued that the only physical velocity required to obey the Einstein causality is the “front velocity.”