Re: [Phys-l] zero width?

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

On 10/15/2007 05:24 PM, Michael Porter wrote:

> Okay, just to play devil's advocate here, how are you defining the  
> boundary? Chalk is made of atoms and atoms don't have a well-defined  
> edge.

  Apart from the notion that it is perfectly OK to think of a 
zero-width boundary as idealization of a real boundary, I think there 
is a real physical object with the zero-width boundary. This is a 
leading edge (wave-front) of any real perturbation. According to the 
Sommerfeld-Brillouin theorem, it always propagates with the invariant 
speed. If we have a laser pulse that can be used as a signal, 
then it has sharply-defined front with no precursor. The corresponding 
wave-function is exactly zero ahead of the pulse and non-zero in the 
region of the pulse. The corresponding shape must be described by a 
function that is non-analytic - there has to be a discontinuity 
starting from derivative of a certain order.
  To tell the truth, I did not think much about it before Michael's 
question, but from what I know today I think the propagating edge of
ANY real pulse must be a real zero-width boundary.
  Unless or until we experimentally discover tomorrow the quanta of
spacetime! 

Moses Fayngold,
NJIT