Friday, 5 January 2018

In superluminal phase velocities, what is it that is traveling faster than light?


I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but the actual content is carried in the modulated wave, the sidebands $\omega_c\pm\omega_m$. The modulation envelop has its group velocity and this is the speed at which information is being transmitted. We also know, for example, that x-rays in glass have a phase velocity which is greater than the speed of light in vacuum.


My question is, what exactly is it that is travelling faster than the speed of light?


EDIT: I know it couldn't be anything physical as its superluminal. My problem is, what is it that has absolutely no information content yet we associate a velocity with it.



Answer



Shine a flashlight on a wall. Rotate the flashlight so the illuminated spot moves.


Q: How fast does the spot move?
A: It depends how far away the wall is.



Q: How fast can the spot possibly move?
A: There is no limit. Put the wall far enough away, and the spot can move with any speed.


Q: What is moving across the wall?
A: Nothing. The light that makes up the spot at one instant is unrelated to the light that makes up the spot an instant later.


This is how a wave can be apparently superluminal: we interpret a series of unrelated events as a continuous 'wave'. Group velocity can also be superluminal; even though the individual chunks of energy are going at roughly $c$, the region where they superpose constructively (the 'crest of the wave') goes faster than $c$.


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