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Some plasmas have a refraction index of less than 1. In these plasmas the phase velocity of light can be faster than light-speed. But the phase itself won't transfer information, so no paradox occurs here. But what if I constructed a tube filled with plasma with a torch on one end and a photon sensor on the other. When I see a beam of red light travelling past me, I lit up the torch, and some guy at the other end can know there's red light coming at him before the red light arrives. Isn't that an FTL occasion?

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One way to look at that:

  • The envelope of the red light pulse travels at the group velocity, less than $c$.

  • The fast oscillations within the main pulse travel faster than $c$.

In the end, the torch "lighting up" is given by the group velocity, because the envelope of the pulse is what you receive.

This animation showing a train of pulses is pretty clear. You can see that each pulse goes slowly, but the fast oscillations go fast.

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protected by ACuriousMind Jan 17 '17 at 22:36

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