Скачать или смотреть Phase, group and signal velocities : does phase or group velocity exceeding c violate relativity?

In this video we discuss the notion, or rather notions, of speed of propagation of a wave in a dispersive medium. We start by explaining the two most commonly explored concepts involved - that of phase and group velocities, respectively.

Now, the special theory of relativity impose a universal speed limit - a causal influence can not travel faster than c - the speed of light in free space. If it did, the causality principle will be violated.


Now, there are quite a few scenarios where the phase velocity of light traveling in a medium may exceed c. This apparent conflict with the causality principle is often explained away by invoking the idea that the group velocity and not the phase velocity is more relevant in this case - and since that is less than c, there is no problem. However, there are quite a few scenarios where the group velocity exceeds c as well. We will describe one such scenario obtained using a simple model of light matter interaction in this video. Obviously, the appeal to group velocity also fails to reconcile this with causality - and we need to look deeper into what exactly does the universal speed limit tell us about wave propagation. This is the main topic that we deal with in this video. We mainly describe the work of Sommerfeld and Brillouian (I now realize that I spelt his name wrongly in the video!) on this topic - but we mostly follow the slightly simplified treatment from the textbook by Stratton. To give the ending way - the upshot is that once we understand the notion of wave propagation properly, there is no threat at all to causality.