Re: Light slows down in glass?

[Maurice Barnhill <mvb@UDel.Edu>]

SCIAMANDA@edinboro.edu wrote:
> Ludwig complained:
>
> > As I wrote several days ago, I am no longer satisfied with the
> "absorbed,
> > reemitted, absorbed again" explanations. Any comments on what is
> below?
>
> How about "scattered"?  I think most people involved in this field
> would
> refer to their work as a "scattering theory/model" (either Maxwellian
> or
> QED).  But it's not just semantics; I think you need to consider the
> "steady state" solution vs the "transient buildup" to that situation.
> (Can we treat this transient in our QED model?  I think we can - at
> least
> in principle - in the Maxwellian model.)
> -Bob

It is possible to rigorously define a time delay in a scattering process
in Quantum Mechanics.  In my old copy of Goldberger and Watson
[Collision Theory, Wiley, 1964] the theory is discussed in section 8.5,
starting page 485.  They state that Wigner first published the
definition and derivation [Phys. Rev. 98 (1955), 145.  The derivation as
given by Goldberger and Watson is straightforward, but not necessarily
all that easy to follow.  The bottom line is that that the time delay is
proportional to the derivative of the scattering phase shift with
respect to energy.  Away from resonances of the scatterer, this time
delay could be very, very short, which would make the "absorbed,
re-emitted, absorbed" model of the slowing of light in a medium a pretty
good qualitative model of what is going on. G&W clearly use an
approximation that the passage of the wave packet across the scatterer
takes a time *long* in comparison to the time delay due to the
scattering.  The formalism uses wavepackets, so there is no need to
distinguish between steady states and transient states leading to an
eventual steady state.

Caveats: Goldberger and Watson clearly have in mind electrons scattering
off atoms or nucleons scattering off nuclei.  In a quick read I see
nothing that could imaginably go wrong using photons, or unquantized
electromagnetic waves for that matter, but I haven't worked through the
details.  G&W call the delay time a "lifetime," but explicitly define
the lifetime in question as being the time delay between the arrival at
a position outside the scattering zone of an unscattered and a scattered
particle.  Also, the formalism involved in getting from the time delay
to an index of refraction never comes up.  Using a large number of wave
packets to recreate a pseudo-steady state is not addressed. 

-- 
Maurice Barnhill, mvb@udel.edu                
http://www.physics.udel.edu/~barnhill/          
Physics Dept., University of Delaware, Newark, DE 19716