> > I'm a bit rusty but isn't it the other way around? Phase velocity may
> > exceed 55mph( 25 in a school zone ) but group velocity ( information,
> > energy ) is limited? I thought the envelope was what carried energy.
>
> Group velocity is the speed at which the envelope moves. Phase velocity
> is the speed at which the peaks move, and is constrained to be the speed
> of light in the medium. Group velocity is the speed at which energy is
> transported, but signalling cannot be done at greater than the phase
> velocity.
No, you've got it backwards. Phase velocity is irrelevant, group
velocity is the speed at which signals travel. See the sci.physics
FAQ at http://math.ucr.edu/home/baez/physics/FTL.html#5:
"The paradox is resolved by distinguishing this velocity which is known as
the phase velocity vph from another velocity known as the group velocity
vgr which is given by,
"vgr = c / vph
"If a wave solution has a frequency dispersion it will take the form of
a wave packet which travels at the group velocity which is less than
c. Only its wave trains travel at the phase velocity. It is only possible
to send information with such a wave equation at the group velocity so
the phase velocity is yet another example of a speed faster than light
which cannot carry a message."
The actual resolution of the paradox in the NY Times article is that the
pulse changes shape but its leading edge does not advance. The peak
of the pulse arrives sooner but that its because the peak is shifted
forward within the pulse itself. The energized medium is acting like
an amplifier, raising the early trailing edge of the pulse up to the
level of the peak:
--- --------
-- -- ==> - --
--- --- - ---
The front edge is steeper, that's all.
