Re: Dipoles in X-Ray Scattering
From: ZZBunker (zzbunker_at_netscape.net)
Date: 08/25/04
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Date: 25 Aug 2004 12:33:11 -0700
zigoteau@ausi.com (zigoteau) wrote in message news:<9da9cba1.0408250402.4e6dee8c@posting.google.com>...
> glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message news:<cge5kt$1hn$1@hood.uits.indiana.edu>...
>
> Hi, Greg,
>
>
> > Most physicists work with materials. Funny thing about this newsgroup is
> > you can ask the most esoteric questions about general relativity,
> > wormholes, string theory, and so on, and get insightful replies. But ask
> > for a recommendation for a solid-state book or something, and nobody seems
> > to know.
>
> A throw-away remark, but worth analyzing. Could it be any other way?
>
> I have quite a few textbooks on my shelves, but I don't memorize the
> names of their authors. I try to understand their contents, and when I
> have understood them, I don't need to refer back to them. I can
> recreate a range of different results from first principles. Of
> course when I recreate results from first principles, I very often
> make mistakes, which is perhaps not the most impressive, or the best
> way to become considered as an authority. Luckily on Usenet there is
> no penalty for this. If someone asks me for the name of a textbook, I
> have to go to my shelf or to the library and see what there is on any
> given subject. Usually I find that I don't fully agree with the
> presentation in any of the books on offer, so how can I recommend one?
>
> The motto of the Royal Society is "Nullius in verba", which may be
> translated freely as "Don't take anybody's word for it". Of course,
> everybody relies on authority at some point or other - modern science
> has just so much content that you can scarcely do anything else.
> However I do think that understanding is an important part of science,
> and this is in conflict with the community of science with its
> research funding committees, their chairmen, etc. In science, the
> subject matter is so arcane that outsiders can scarcely judge who is
> right in any given difference of opinion, and it seems most prudent to
> give the benefit of the doubt to the plausible man in the neat suit
> who has written the textbook and been given lots of research funding,
> not to that scruffy individual whose research proposals are always
> turned down. In my experience, the plausible man in the neat suit
> usually can't recreate results from first principles, but always knows
> where to find a textbook on the subject. You will not find him
> contributing to Usenet.
We know that, which is why we created Internet.
Since the plausible man only wants to hear
what The New Yorks Times wants To Hear, which
is want Chairmen of Science Committee's
want to hear, which is Cha-Ching. They doen't want to
hear things like New York Book Editors and their
Theory Of Evolution blow, like the wind of
The Big Fart that is funding the theory.
Of that Set Theory was invented by
people who should get a job, rather
than publish "new" math. Which is
not only not new, it's not even math.
>
> Have you ever been associated with the writing of a textbook? Usually
> a publisher approaches you first, but then you have to write a
> proposal to the publisher saying what you would put in the book, and
> it gets sent out to referees. Typically, it's the plausible men in the
> neat suits whose proposals get accepted. They don't have any rough
> edges, no strong views on scientific subjects that other people can
> violently disagree with. They can be guaranteed to come up with the
> party line on any subject. And their books will sell. They are
> mainstream, smooth, professional, and recommended by all the other
> spokesmen.
>
> If you remember, some time back I was trying to explain to you the
> basics of the stability of control systems. I was quite happy to go to
> great lengths to get you to understand, but you did upset me by asking
> me to debug your program for you. I want my relationship with you and
> other contributors to Usenet to be one between equals. I am eager to
> learn, too. I like the motto, "Teach what you know, learn what you
> don't" (it seems to have disappeared from Usenet now that Google has
> taken over). And I enjoy rethinking through problems which I solved
> years ago but where I have become rusty on the fine details. I think
> everyone else on Usenet who provides answers to other people's
> questions (as opposed to just talking around the point without ever
> getting anywhere) has exactly the same motivation.
>
> So, to cut a long story short, that's why you will get answers to
> esoteric questions but very few recommendations of specific textbooks.
>
> Another point is that a small fraction of the replies you get will be
> insightful, while the rest will be misleading, erroneous, obfuscatory,
> insulting, scandalous, total nonsense, . . .
>
> By the way, if and when you become Chairman of that Committee, please
> remember to divert some of the money under your control in my
> direction, won't you?
>
>
> > This seems like it pretty much sums it up. The near-field interactions
> > between electrons is the multiple scattering that can often be safely
> > neglected. And even when they can't be, as for a large single crystal,
> > the problem is often powder diffraction, or diffraction from a
> > polycrystalline or mosaic material, and so single scattering is good
> > enough anyway. Perfect crystals are weird things, diffractionly speaking.
> >
> > My experience is more with neutron optics, and nuclei are so small
> > compared with their separation that there's really no question that S-wave
> > scattering is a fine approximation. You might have interesting optical
> > effects, but you just don't have to worry about one nucleus seeing an
> > octupole term of another nucleus.
>
> I think you're fixating on multipoles. Yes, there is an approximation
> in which the radiation from an object is expressed as the sum of
> dipolar, quadrupolar, octupolar terms, etc. Actually I said it wrong
> in my last post. It's not the charge distribution which is a power
> series, whose coefficients are each 2^N-pole strengths, but the
> Fourier transform of the charge distribution.
>
> There is a simple exact expression for the EM field from a general
> distribution of charge. It is written down most neatly in terms of the
> 4-potential A_i. If the distribution does not vary with time you don't
> get any magnetic field, and hence no power flow, no radiation, but
> there's always an effect at large distances. Considering the
> complexities you can get into when you start analyzing it, the basic
> relationship is surprisingly simple, a one-liner (no, I can't give
> you a reference!).
>
> I don't know if you've noticed another thread to which I have
> contributed recently about Doppler distortion from loudspeakers. If a
> loudspeaker is simultaneously called upon to reproduce a low frequency
> tone and a high freqency tone, the low-frequency tone moves the
> loudspeaker cone through a distance which may be large compared to the
> wavelength at the high frequency. The distance from the cone to your
> ear varies signficantly over the period of the low-frequency tone, and
> Doppler-shifts the high frequency tone. The whole system is apparently
> in its "linear regime", but this mechanism means that the signal which
> reaches your ear is distorted. It's just struck me that there is a
> relationship between the two threads.
>
> You normally think about a loudspeaker as being fixed (and your ear
> for that matter), and the signal gets transduced from electrical form,
> voltage as a function of time at each point in the circuit which is
> fixed, to acoustic form, pressure as a function of time at each fixed
> point. But in fact you can't produce sound without moving something,
> leading to this nonlinearity, which in the normal course of events is
> completely negligible. The multipole approximation is exactly
> analogous. You can't produce EM radiation without moving charges, but
> a whole mass of physics is based on Hamiltonians which are independent
> of time and commute with partial d/dt, which you can't do if objects
> in your setup are moving with respect to one another, so the normal
> approach is to replace it by a setup which is to all intents and
> purposes identical, but where things remain fixed.
>
> This is perfectly justified when all the action takes place in a
> region much smaller than a wavelength. You can then approximate to the
> field by the sum of contributions from an infinite series of
> 2^N-poles, all located at the origin. In the case of an electron acted
> on by an external X-ray beam, you replace the wiggly motion of the
> electron by a fixed electron, plus a time-dependent dipole, and if you
> need too, time dependent quadrupoles, octupoles, etc. The fixed
> electron does not radiate. The dipole radiation is significant, so you
> don't have to think about the quadrupolar term.
>
> In your book by Warren, I think you will find that not all your
> dipoles are located at the origin, so that there is no problem at all.
>
> Cheers,
>
> Zigoteau.
- Next message: Mitchell: "Re: Reflections on Aether"
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