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.
I think this is consistent with the math.
James
Jacob Keller wrote:
For the total integrated energy to be conserved, energy will have to be
created in certain directions to compensate for the loss in other
directions. So in a direction in which the condition is met, the total
will have to be more than the sum of the waves in that direction.
How about considering the possibility that all photons coming into the
sample are diffracted -- just in different directions. So that what is
happening is not constructive and destructive interference but a kind
sorting of the photons based on a certain property of the photons, maybe
the phase.
*****
I think of it that each photon that happens to be perturb an electron, i.e.,
Thomson scattering,
sends out a spherical wave, which has anisotropy to it, i.e., the wave front is
more concentrated
in the forward direction. These spherical waves interfere with each other,
making the diffraction
pattern.
Something for you to chew on: how is it that the electrons of the protein, which are presumably not
in phase with each other nor in exactly the same place in their orbitals from unit cell to unit
cell (maybe they are?) when they scatter the photons, they result in
interference? What are the
chances that the scattering electrons are exactly in the same place as the
electrons in another
unit cell, or of the same phase? And would they not need to be in the same
place to sub-angstrom
precision to scatter coherently? I would suggest two possible answers, neither
of which am I
entirely satisfied:
1. Something about the crystalline state induces the protein molecules'
molecular orbitals to be
totally in synch with each other. This seems too miraculous to be true, in a
way. Nevertheless, it
would account for the data, I think.
2. The scattering electrons are elusive probablistic entities which are really
no place at all.
This, however, does not solve the problem of the phases (not in the usual sense
of finding fourier
phases) which is that it seems unlikely that electrons in multiple unit cells
should be exactly in
phase with each other, something which it seems would be necessary to produce
interference.
NB this issue came up in a crystallography class several years ago, and I have
been ruminating on
it, on and off, since then.
JPK
***********************************
Jacob Keller
Northwestern University
6541 N. Francisco #3
Chicago IL 60645
(847)467-4049
[EMAIL PROTECTED]
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--
James Stroud
UCLA-DOE Institute for Genomics and Proteomics
Box 951570
Los Angeles, CA 90095
http://www.jamesstroud.com/
