Re: [Phys-l] zero width?

["Fayngold, Moses" <fayngold@ADM.NJIT.EDU>]

Bernard Cleyet wrote:

  "I understood in a dispersive medium (all media are dispersive?) 
pulses can not have sharp edges."

  This is a very strong statement which does not hold for pulses 
that have arrived from an external source that had been turned on 
at a certain moment of time. The Sommerfeld-Brillouin theorem
holds true for any medium (and yes, all of them are dispersive!).
The edge of an arriving pulse necessarily involves Fourier-components
with infinite frequencies, and they interfere destructively ahead of 
the edge. In case of EM-waves, infinite frequencies propagate with
the invariant speed in any medium, so the edge propagates with the
same speed. The pulse can still spread by developing a long tale from
the trailing edge. It can also reshape itself and in particular its top
can get ever closer to the leading edge. In the latter case the speed
of the top will be superluminal, but this does not contradict anything
since the top, being within the region of analyticity of the pulse, 
does not carry a signal. The discontinuity at the edge, on the other 
hand, will in this case become even more pronounced.

 
 Brian Whatcott wrote:

 "This sounds very like the thought about modeling the magnitude of
> the  acceleration when an object, any object, that was stationary,
>  begins to move".

  Exactly! The only difference that in this case we have a discontinuity
in time rather than in space. But again, in this case the object's 
boundary must be sharply defined from the very beginning, or else
it should be a point-mass object.


Moses Fayngold,
NJIT