# Why doesn't anomalous dispersion allow faster-than-light propagation?

It seems that the phase velocity of light could be greater than $c$, if $\sqrt{\epsilon \mu} < 1/c$, i.e. for anomalous dispersion.

1. Are there examples of such media? For diamagnetics it seems possible since $\mu < \mu_0$.

2. And what is the physical meaning of phase velocity in this case, besides being speed of wave surface? Why it cannot be seen as a physical entity that is traveling faster than light?

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Related question –  Vijay Murthy Apr 6 '12 at 14:00
This is the historical motivation for the Kramers-Kronig dispersion relation, which completely explained causality with a varying complex dielectric constant and susceptibility, and replaced causality in S-matrix theory. –  Ron Maimon Apr 7 '12 at 4:25