Pulse propagation with group velocities that exceed the vacuum speed of light c, or even become negative, has been a subject of a number of works in the last 100 years (Brillouin has given an excellent account of the early work in his book. It is a phenomenon that might appear to violate the special theory of relativity's pillar statement that no signal can be transmitted faster than c. However, Brilloum and later in a series of works Chiao (see [2] and references therein) argued, that the "faster-than-c" propagation is perfectly in accord with special relativity. They reasoned that the signal velocity should be properly defined not as the velocity of a smooth pulse but as that of a step-function-like signal. One can show that the latter one is always limited by c.
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