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Re: Group velocites greater than the speed of light



The shear example I remember from a Sci. Am. article some time ago. An
additional one they gave was shining a light at one planet to another. The
speed from planet to planet is much faster than C, but no info is transmitted
from and to the respective planets.

Regarding the faster moving disappearing peaks in the wave in the tank, do not
the peaks reappear at the beginning of the wave?

I suspect that the above is not analogous to the initial post, but homologous.

bc



John Denker wrote:

At 11:09 PM 1/9/01 -0700, Eric Asselin wrote:
I don't understand what he means by "The contradiction is only an apparent
one, arising from the fact that although a monochromatic wave can indeed
have a speed in excess of c, it cannot convey information".

Here is a well-known analogy that may help:

Consider a giant shear with two blades that cross at a small angle (theta),
and imagine that each blade is moving perpendicular to its edge, which is
typical of an industrial shear (unlike the pivoting action of household
scissors).

Now, as the blades move, consider the motion of the point where the blades
cross. This point will "move" at a speed greater than the blade speed, by
a factor of something like the cotangent of theta. You can easily imagine
the intersection "moving" faater than the speed of light, even though the
blades aren't. This superluminal "motion" carries no information beyond
the information carried by the subluminal motion of the individual blades.

So it is with the monochromatic light wave. Since the wave has small
spread in frequency, it must have a gigantic duration in time (and
therefore space). The wave must have been (almost) everywhere for (almost)
all time. The arrival of one hump of the wavetrain carries no information
beyond what was carried by the previous hump.

In contrast, if you try to send information by modulating the (heretofore
monochromatic) light wave, you will find that the modulations travel at
less than the speed of light.