On Fri, 24 Aug 2007 14:40:13 -0600
Michel Fodje <[EMAIL PROTECTED]> wrote:
The mathematics works but doesn't necessarily mean the current
interpretation of the mathematics has any resemblance to what actually
happens in reality.
Sure, it does. Crystallography is traditionally derived using classical wave
mechanics,
but you can take a quantum approach, using the First Born approximation (a
single photon
scatters elastically from a point source exactly once). If you want to speak
about what a
single photon does, then you have to resort to that approach. Except in rare
instances,
the photon interferes only with itself, regardless of how many or how few are
present.
The particle is the photon, and the wave is the propensity for the photon to
appear at a
given position on the detector. QM teaches us that the entire experiment, in
this case the
crystal lattice, has to be taken into account, (which simply means you have to
add amplitudes
rather than intensities). It is the same thing with a single particle going
through a double slit.
BOTH slits must be taken into account, as both are possible paths. A crystal is
simply a
near-infinite diffraction grating in three dimensions, but the physical
interpretation is identical.
Feynman developed the most intuitive way of looking at this, which is to sum
over all possible
paths before squaring the wave. Unfortunately, the accompanying mathematical
treatment is
a bit hairy.
Bill
