Would it be taking it too far to suggest that one could go all the way
and consider that each electron diffracts not as groups in a plane but
as individual electrons and a photon impinging on an electron with with
a specific phase will be diffracted in a specific direction. However the
lattice arrangement of the electrons will statistically accumulate
photons which impinged on electrons on a specific family of planes in
one direction at the detector. Such that the crystal is a phase sorter.
In which case diffraction is not based on constructive or destructive
interference but on conservation of some property of the photon, such as
angular momentum? IANAM either.
On Fri, 2007-08-24 at 15:36 -0700, James Stroud wrote:
> Without resorting to a circular argument? You are asking too much.
>
> However, this probability distribution is perfectly described by
> considering a component wave model wherein coherence of the component
> waves correlates with peaks in the probability distribution--i.e.
> Bragg's Law.
>
> IANAM (I am not a mathematician), but, if pressed, I would posit that
> one could decompose the fun description just a little bit and consider
> the lattice not as *groups* of reflecting planes, but as individual
> planes. In such a case, each single reflecting plane would contribute a
> probability distribution with an angular dependence. The total
> probability distribution would then be the sum of the probability
> distributions for every plane in the lattice.
>
> Your next question might be, "what's the probability distribution for a
> single plane". Well, I would imagine that it has a maximum where the
> angle of incidence equals the angle of reflection and that the phase of
> a component probability distributions is spatially (i.e. angularly)
> directly related to the phase of the originating photon.
>
> The sum distribution of the reflected photon takes into account the
> angular phase dependence of its components and so one gets positive and
> negative interference between component distributions.
>
> James
>
> Jacob Keller wrote:
> > Yes, but why should the directions of diffraction conditions be most probable (one of your premises)?
> >
> > ==============Original message text===============
> > On Fri, 24 Aug 2007 4:54:53 pm CDT James Stroud wrote:
> >
> > Here's a fun way to think of it:
> >
> > A photon hits a crystal and will diffract off in a certain direction
> > with the same energy as the original photon. The direction is subject to
> > a probability distribution based on the lattice, with angles at the
> > diffraction conditions being most likely and the broadness of the peaks
> > in the distribution arising from imperfections in the lattice. The
> > photon propagates as this probability distribution and then is forced to
> > select from the distribution because we stuck a detector up. The
> > diffraction pattern we observe is the sum of many such photons
> > interacting with the crystal.
>
>
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