From: aephraim@physics.Berkeley.EDU (Aephraim M. Steinberg)
Newsgroups: sci.physics
Subject: Re: Questions of transparency
Date: 15 Oct 1992 18:40:20 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: physics.berkeley.edu

In article <1992Oct14.022256.11742@prim> prim!dave@germany.eu.net (Dave Griffiths) writes:
>In article <1992Oct13.022709.21439@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>>In article <1992Oct10.234101.9875@prim> prim!dave@germany.eu.net (Dave Griffiths) writes:
>>
>>>If a beam of light passes through a glass block, are the majority of the
>>>photons which emerge on the other side the very same ones that entered? Or
>>>are the photons absorbed and retransmitted?
>>
>>There is no such thing as "the very same photons".  Photons being
>>identical bosons, and light being a collective state of such, it really
>>makes no sense I can see to try to answer this question.  
>>
>
>Sorry, I'll rephrase the question. If one single photon enters the glass
>block, is it absorbed and retransmitted en-route, or does it pass straight
>through unimpeded? Seems like quite an important point since much
>discussion about QM inteference experiments assume single photons passing
>through polarizers, beam splitters and so on.
>
>If the photon _does_ fly straight through, why does it slow down? The gaps
>between atoms are a vacuum and it should whizz through at the speed of light!
>
>Finally, if the hand-wavy argument is that the energy of the photon is
>transferred into oscillating fields of charges in the glass block... how?
>If nobody had yet discovered transparency, could QM have predicted it,
>together with the index of refraction and speed of light given the
>molecular structure?
>
>Dave Griffiths

I think this question really is a semantic one, but I'll take advantage
of the continued non-existence of the crackpot index to force my own
views upon people anyway.

First of all, in QED, the identity of a photon is really nothing more
than the identification of its mode.  As pointed out above, a given
photon with wave vector k and polarization e cannot be distinguished
from any other like photon, although the phase of the wavefunction may
change.  (Note I did not say the phase of the light, since for a single
photon, that is not a meaningful quantity.  There is, however, a difference
between |1> and |1>exp(i\phi), which is why single photons can interfere.)

Even classically, there are ambiguities revolving around whether one should
consider the momentum as belonging entirely to the field or as being
shared between the field and the matter (by using a susceptibility model,
you essentially ignore the details of what the matter does and place
it all on the shoulders of the re-written field), but no final results depend
on which way you choose to write this.

In a piece of glass, the absorption at optical wavelengths is relatively
negligible.  This does not rule out "virtual absorption processes," which
you could term being "absorbed and retransmitted en-route."  If you try to use
QED to calculate the index of refraction, the important thing is to calculate
the forward scattering amplitude for the light, so I would agree with your
phrasing.  The amplitude for scattering at non-zero angles interferes
destructively if you are not sitting on top of an absorption line, so
no resonance fluorescence is observed, and the amplitude for scattering
at zero degrees (whatever that means) is imaginary, yielding a change in
phase, making the effective wavelength smaller than the vacuum wavelength,
by a factor we can identify with the index of refraction.

A word of warning-- only in the simplest structures (say, an alkali vapor)
can a really good first-principles derivation of the index of refraction
be performed, as far as I know.  I'm sure that solid state people come up
with good approximations for crystals, but probably only after fitting
certain experimental parameters.  (I welcome corrections on this point.)

Finally, only very recently has there been a paper to claim to have come
up with a quantum optical description of the interaction between light
and a dispersive medium: Huttner & Barnett, Europhysics Letters 18, 487 ('92).
This work relies upon what is known in solid state as the polariton model,
and is exactly diagonalizable.


-- 
Aephraim M. Steinberg                    | "WHY must I treat the measuring
UCB Physics                              | device classically??  What will
aephraim@physics.berkeley.edu            | happen to me if I don't??"
                                         |       -- Eugene Wigner