Re: [Phys-L] phase velocity, one kind of charge, and other intangibles

[Stefan Jeglinski <jeglin@4pi.com>]

> The canonical analogy is the point of intersection between the blades
> in a shear.  You could use common scissors, where the blades rotate,
> but it is simpler to talk about a guillotine shear, where one blade
> is stationary and the other moves in a straight line.  They meet at
> a slight angle, as you can see here, if you know what to look for:
>  https://www.youtube.com/watch?v=2Cqbl6dY7jM&t=60 <https://www.youtube.com/watch?v=2Cqbl6dY7jM&t=60>
>
> The point of intersection moves very much faster than the blade itself.
>
>   Optionally you can connect this to special relativity, where the
>   top blade is moving vertically at 0.2 times the speed of light,
>   while the point of intersection moves left-to-right ten times
>   faster, i.e. twice the speed of light.  This is 100% true and
>   consistent with the laws of physics.


Not relevant to phase velocity, but since special relativity was mentioned, how about this common "velocity addition” question (or some variation) in special relativity, which gets at the same idea and is a good teaching moment:

Two spaceships travel toward one another at speeds of 0.7c and 0.8c, each wrt to an inertial Earth observer – at what speed does each spaceship observer see the other spaceship approach? Answer is 0.96c, maintaining the necessary result that “no object can travel at the speed of light.” However, wrt Earth observers, the closing speed of the two spaceships is in fact 1.5c. There’s nothing wrong with this, because the “closing speed” is not a “thing.” The best I’ve figured what to tell students is that “closing speed” (change in the gap wrt time) is not an inertial concept, where “inertial” is taken as Newtonian (that is, related to mass). 

Stefan Jeglinski