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 $c$.


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...