Physics Banter - View Single Post - Empirically Confirmed Superluminal Velocities?

EL

wrote in message ...

[Mati Meron]
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.

[EL]
You sound like you do know what is a group velocity so why do you also
sound as if you are endorsing the superluminal lie?

I am not going to write the equations or derivations but to give you a
hinting example:

v_g = v_p - [Lambda (div-v_p/div-Lambda)]

also

v_g = dw/dk

Without going into meticulous details, a pure sign wave is not a
natural phenomenon but we usually have interference or a packet of
interacting waves and this is not a light in vacuum or gases exclusive
thing.

For example in deep water v_p = c.k^(-1/2), where c is a constant.
Thus w= c.k^(1/2) and v_g =dw/dk = 0.5 v_p.
These waves are strongly dispersive, and the individual wave crests
slide through the group at twice the group speed.

Those of you who still do not get it and find it hard to imagine why
it is a very funny lie or simply ignorance from those who claim
superluminal velocities, please recall Lord Kelvin's smoke rings.

Air is a dispersive medium and smoke is a visual indicator of the flow
of a wave.

The air compression along the axis of symmetry of the wave is at a
maximum and the velocity too is at its maximum along that axis.
However, the ring demonstrates velocities reduction as we step away
from that axis until they turn negative, which means that smoke
particles move backwards relative to the (Ring) group even though the
whole group is advancing forward, and this particular phenomenon is
observed on the outer shell topology of that smoke ring group.

The contrary may be observed on the smoke particles at the core of the
ring, where those particles would be moving at twice the group
velocity being accelerated on there way in and decelerated on there
way out at the group-wave-front.

Can any of you claim that a smoke ring may move in air faster than
sound can move in the same medium?

No, certainly not, because you are all wise and sane.

LASSER light pumping is neither better nor worse.

Caesium atoms undergo similar dispersion anomalies and a magnetic
field of 1Gauss is maintained parallel to the direction of light
packet propagation to define an axis.

Obviously, caesium atoms are huge particles that attain velocities far
slower than c.

While light propagates at c exactly along the empty axis that caesium
atoms do not enter due to preparing them by preparatory light pulses,
the group velocity is expected to be at half c but very roughly.

If the atoms absorb all the energy or the medium become saturated we
have no anomalies.

The anomaly is a replication of Lord Kelvin's smoke ring in a wave of
air gist but this time using a caesium ring-group hoping to accelerate
LASSER light packets at the core axis of the wave group.

So yes, indeed the light speed at the core axis is at a maximum and it
is at c but the group velocity is much lower.

The terrible mistake is to assume that the light packet is a group
that is propagating at c and then one discovers that relative to that
velocity a much faster speed is detected.

The equations are supposed to find the group velocity not to assume
it.

The group velocity by definition must be a fraction of the maximum
velocity that the medium allows.

Vacuum allows a maximum of c.

Caesium gas at 30 degrees Celsius should slow down light to a maximum
less than c.

The new refractive index may not be a fraction less than unity or it
would be a calculation mistake.

So what they really have is a set of data that they fail to interpret
properly and an oscilloscope that they have no freaking idea about
interpreting its screen or recorded tapes.

Those clowns need to go back to school and they disgrace their
credentials and smear our credentials too by being so irresponsible
and reckless.

EL