Michel Fodje wrote:
>> For every direction where there is destructive interference and a
>> loss of energy there is a direction where there is constructive
>> interference that piles up energy. If you integrate over all directions
>> energy is conserved.
>
> 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.
You seem to be operating under the impression that there are two diffracting
waves that later destructively interfere. All constructive and destructive
interference occurs at the point of scattering. There is no energy that
heads off in a direction that later disappears - Nothing ever went in
that direction.
You have the same problem with your idea of two waves, out of phase
but identical in wavelength, that scatter off an electron. The two waves,
if they are coherent, would interfere with each other long before they
reach the electron and become a single wave. If they are not coherent
they will interact with the scatter independently and produce incoherent
diffraction waves, which will sum by intensity independent of phase.
I can get into deep trouble with this next point so I hope a physicist
jumps on me where I'm wrong. All light sources are coherent to a degree.
A laser is pretty much 100% coherent and my pocket flashlight is hardly
coherent at all. I seem to recall that there is a parameter called
the coherence length that measures the distance within a beam that
the light is coherent. The coherence length of a rotating anode
X-ray generator is small but unit cells are smaller so there are plenty
of unit cells to form a nice diffraction pattern.
Your second paragraph is just the Copenhagen Interpretation of the
wave function. If you want to think of photons then the diffraction
wave we are talking about is the wave function and that function maps
the probability of finding a photon. Wave/particle duality says we
can look at the experiment either way.
Dale Tronrud
