Hi Fellows,
Zbi's response has addressed refs and the technical complexities that arise
when describing
the scattering process on a microscopic QM basis.
I shall tell you why I decided to provide this probabilistic QM
interpretation.
First, a probabilistic approach to empirical science is the overarching
theme of the book.
Examples range from Bayes to ML and necessarily, the interpretation of
quantum mechanics.
Having been tortured in Vienna as experimental physicist with instruments
that Boltzmann built
and probably already Schrödinger broke, when I saw for the first time these
explanations
of Bragg's equation (footnote *) where 2 incoming, interfering waves are
pictured,
I was confused. Can't be.
The first fact to drive across is that there is no coherence between the
photons emitted
from a conventional source (and under normal operations with exceptions and
caveats
I am not going into, also from synchrotrons):
In demonstrations with a laser and a diffraction slide, invariably a
fraction of students exposed to
these Bragg drawings seem to erroneously but justifiably assume that the
coherence
of the laser is relevant to diffraction.
It is the monochromaticity and the brilliance of the laser that makes the
experiment work
so well, not any necessity for coherence between incoming photons.
This is why I avoided throughout the book to show illustrations with 2
incoming
waves or wave vectors, as observant readers may have noticed.
Second, as a fundamental principle, a macroscopic phenomenon based on the
average
of many microscopic processes taking place on a quantum mechanical scale can
often
be well explained with a 'classical' picture. That is why this partial wave
recombination
business for structure factors works.
For me a more logical and consistent approach is to treat diffraction as a
probabilistic
phenomenon, with the underlying probability distribution simply given by the
structure factors. Also the square proportionality between |F| and I follows
naturally
from quantum mechanics as the observable of these complex probability
functions.
So, this quantum mechanical interpretation (note the word interpretation) is
very
consistent and imho unforced and almost beautiful. But, as noted, the
underlying microscopic
process description is less than trivial, and defies our macroscopic
experience. And
beauty is in the eye of the beholder....
Historically, of course, when the first diffraction images were taken and
the Braggs
began to make sense of the images, QM was in its infancy. The ultraviolet
catastrophe
was fresh in the minds, and the photoelectric effect published only in 1905.
The Bohr model
came out in 1913, and it took about another 10+ years for Heisenberg,
Schroedinger
& Cie. to come up with workable theories. So, the Braggs are excused, but
today I think
a more modern picture involving the underlying QM picture can be presented.
*
If you are interested in the philosophical issues w/o becoming a quantum
physicist, there are
interesting accounts about the early history of quantum mechanics which I
find a most
fascinating period in physics. I can provide a few refs off board later when
I am back at my library.
So, yes I am guilty of not providing a more concise intro to QM, but as
Dirty Harrys says:
'Man's gotta know his limits'
Best, BR
* [The brilliance of the Bragg equation imho is to combine the 3 independent
Laue equations
(unhandy) by simply turning the Laue 'pictures' so that reflection on
lattice planes - much
more intuitive - can be used to relate the diffraction angle (nota bene, not
the direction
anymore) to lattice spacings.]
-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
Zbyszek Otwinowski
Sent: Friday, May 22, 2015 4:40 AM
To: [log in to unmask]
Subject: Re: [ccp4bb] X-rays and matter (the particle-wave picture)
The answer to your questions depends on the level of understanding of
quantum mechanics. I am sending info where to find the subject discussed in
more details.
Bernhard Rupp's book page 251 necessarily simplifies a rather complex
subject of the photon's interaction with multiple particles. Quantum
mechanical wave function can be considered virtual from the measurement
process point of view, as the photon (a single quantum) appears in the
detector during the measurement process, but not on the way to it.
> the photon's coherence length
The concept of photon's coherence length involves quantum mechanics mixed
state. For introduction see:
http://en.wikipedia.org/wiki/Quantum_state#Mixed_states
> virtual waves
Quantum mechanical wave function is "virtual" in certain sense. The Feynman
Lectures on Physics Vol 3 covers this subject quite well.
> appears again in some direction
This refers to quantum mechanical wave-particle duality
> Hello Everybody!
> I was trying to make some sense from Bernhard Rupp's book page 251.
>
> I will copy the relevant part...
>
> When photons travel through a crystal, either of two things can
> happen: (i) nothing, which happens over 99% of the time; (ii) the
> electric field vector induces oscillations in all the electrons
> coherently within* the
photon's coherence length* ranging from a few 1000 Angstroms for X-ray
emission lines to several microns for modern synchrotron sources. At this
point, the
> photon ceases to exist, and we can imagine that the electrons
> themselves
emanate *virtual waves*, which constructively overlap in certain directions,
and interfere destructively in others. The scattered photon then *appears
again in some direction*, with the probability of that appearance
proportional to the amplitude of the combined, resultant scattered wave in
that particular direction.......The sum of all scattering
> events of independent, single photons then generates the diffraction
pattern.
>
> I underlined the problematic parts...
>
> can anyone shed some light on this ..or point me in the right direction?
>
>
> Thanks in advance
>
Zbyszek Otwinowski
UT Southwestern Medical Center at Dallas
5323 Harry Hines Blvd.
Dallas, TX 75390-8816
Tel. 214-645-6385
Fax. 214-645-6353
Zbyszek Otwinowski
UT Southwestern Medical Center at Dallas
5323 Harry Hines Blvd.
Dallas, TX 75390-8816
Tel. 214-645-6385
Fax. 214-645-6353
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