Dear Flatulent,
I don't agree with "Group has to be equal to or slower than light because it is a physical thing (transmission of information.)"
In fact, in general that is not true. I copied the page 333 and 334 from Stratton, Electromagnetic Theory, McGraw-Hill, to explain it.
Regards.
If the dispersion of the medium is normal and moderate, a pulse or wave packet may travel a great distance without appreciable diffusion; since the energy is presumed to be localized in the region occupied by the field, it is obvious that the velocity of energy propagation must equal at least approximately the group velocity. In a normally dispersive medium an increase of wave length results in an increase of phase velocity and hence the group velocity under these circumstances is always less than the phase velocity. If on the contrary the dispersion is anomalous - as in the case in conducting media - the derivative d v/d lambda
is negative and the group velocity is greater than the phase velocity. There is in fact no lack of examples to show that the group velocity may exceed the light velocity, c.
Since at one time it was generally believed that the group velocity was necessarily equivalent to the velocity of energy propagation, examples of this sort were proposed in the first years following Einstein's publication of the special theory of relativity as definite contradictions to the postulate that a signal can never be transmitted with a velocity greater than c. The objection was answered and the entire problem clarified in 1914 by a beautiful investigation conducted by Sommerfeld and Brillouin, which may still be read with profit.
Sommerfeld, Ann. Physik, 44, 177-202, 1914.
Brillouin, ibid, 203-240.
flatulent said:
There are two delays, group and phase.
Group is the speed that a modulated waveform moves through a system or transmission line or space.
Phase is the speed that a constant phase point moves through the above.
Phase can be faster or slower than the speed of light because it is an artificial thing.
Group has to be equal to or slower than light because it is a physical thing (transmission of information.)
One way to think about this is a pair of scissors. When the two blades approach each other, the point that partitions space between the blades not touching and the blades touching move much faster than the blades approaching each other.
Another example is a spot on a wall made by a laser pointer. If your wrist is fast enough, the spot can go faster than the speed of light, but the photons going to the wall still go at the speed of light.