In article , Randy Poe writes:
On Wed, 22 Oct 2003 13:32:31 -0500, Richard
wrote:
J?rgen Clade wrote:
Hello Richard,
[...]
Now as I see it, a group velocity was measured at greater than c, and
thus, in contrast to the Fizeau near fit, the relativistic velocity
addition equation fails in this current experiment. Not only that, but
the whole of special relativity has been proved false.
No, it hasnīt. SR forbids *transport of energy-momentum at
superluminal speeds*, and in the case of anomalous dispersion, as in
this experiment, energy-momentum is not transported with the group
velocity of the wave package. So superluminal group velocities donīt
violate SR.
Where in the lorentz transform is it implicit that v corresponds only to
tangible particles?
In working out the consequences. You can easily add up a bunch of
waves with subluminal speeds and get a superluminal group velocity.
It's simple addition. Therefore it follows that subluminal phase
velocity does not prohibit superluminal group velocity.
You are only repeating what you've heard over and
over.
No, you are attempting to do mathematical derivation without
mathematics. It's a simple consequence of the mathematics: If under
the postulates we find that something like superluminal group velocity
is allowed, we say "under the postulates, superluminal group velocity
is allowed". Because we show that under the postulates you can get
superluminal group velocity.
I'll add here as a comment that the issue of group velocity is
generally misunderstood, perhaps due to the fact that lower level
textbooks don't explain it well. Group velocity *is not* signal
velocity. Under some circumstances, when the dependence of phase
velocity on frequency over the bandwidth of the signal is weak, group
velocity is a good approximation to signal velocity over distances
short enough so that the pulse shape does not change appreciably in
propagation. That's all. The conditions listed above are reasonably
well satisfied in most practical situations, but they totally fail
under anomalous dispersion situation.
Mati Meron | "When you argue with a fool,
| chances are he is doing just the same"