EM/GR Radiation as Scattering?

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Main Question or Discussion Point

Is it accurate in any sense of the word to think of electromagnetic radiation, ala chapter 7-8 of Landau, and gravitational radiation, ala https://n.ethz.ch/~usoler/download/GR/Spacetime%20and%20Geometry.pdf [Broken], as the classical field theoretical analogue of inelastic (& elastic?) scattering, the way you could loosely think of electromagnetic waves (free field solutions of Maxwell) as the field theoretical analogue of the harmonic oscillator of particle Lagrangian mechanics? Is it too much of a stretch to call gravitational waves an analogue of the Harmonic oscillator as well?
 
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  • #2
PeterDonis
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Gravitational wave solutions of the Einstein Field Equation, just like electromagnetic wave solutions of Maxwell's Equations, can be thought of as the field analogues of oscillators, yes. However, unlike Maxwell's Equations, the Einstein Field Equation is nonlinear, so strong-field wave solutions will not be harmonic. Weak gravitational waves can be treated using linearized GR, so they are (effectively) harmonic just like EM waves are, but they have spin 2 rather than spin 1.
 
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Great, thanks very much, hopefully someone has comments on the radiation issue.
 
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PeterDonis
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What radiation issue? Gravitational waves are radiation, so my comment applies to radiation.
 
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I mean for thinking of radiation as the analogue of inelastic & elastic scattering.
 
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PeterDonis
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I'm not sure how to address that beyond the fact that radiation, i.e., wave solutions to field equations, can be viewed as analogous to oscillators. What other model of scattering are you thinking of, besides oscillators?
 
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Well I'm thinking of the fact that you have Coulomb elastic scattering & disintegration-type inelastic scattering in classical (particle) mechanics, then you have Compton, Bhabba, Moller scattering in quantum field theory (using Green functions as you do with classical field theory radiation problems), so it looks like they all fit into the same thought-process category, i.e. radiation is the classical field theory counterpart of these ideas (not some fundamentally new concept), the way you can think of the harmonic oscillator category in classical mechanics generalizing to EM/GR waves in classical field theory as well as applying to QM & QFT, rather than viewing waves as some totally new concept (perhaps only pedagogically, but I'm not sure about that tbh).
 
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PeterDonis
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you have Coulomb elastic scattering & disintegration-type inelastic scattering in classical (particle) mechanics,
I assume by this you mean that the scattering is being modeled using a classical interaction force, like the inverse square Coulomb force, and no fields are being used anywhere, correct?

you have Compton, Bhabba, Moller scattering in quantum field theory (using Green functions as you do with classical field theory radiation problems), so...radiation is the classical field theory counterpart of these ideas (not some fundamentally new concept)
It's certainly true that the same math that is used for classical radiation fields is also used in quantum field theory. It is also true that, once you have a QFT model of some scattering process, you can take its classical limit and come up with a model that looks like a classical scattering process (with an inverse square force law and no fields anywhere). Is this what you're getting at?
 
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Yes about the inverse square Coulomb force.

While your QFT example is very interesting, I was more looking at CFT radiation and just asking if you could reduce it to a CM scattering process (even if only conceptually). In Jackson's Classical Electrodynamics (no need to check it), chapter 9 is on 'radiating system's and 10 is on 'scattering', as if they are different/distinct concepts. I'm just wondering if I could potentially put the title "inelastic scattering" on chapter 9 and "elastic scattering" on chapter 10, or simply 'scattering' as the title on both, because no source I've read has actually explicitly said radiation is (at least kind of) the classical field theoretical analogue of scattering, my only clue is that QFT scattering uses the same math so perhaps the words radiation and scattering are mathematically synonymous?
 
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PeterDonis
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I was more looking at CFT radiation and just asking if you could reduce it to a CM scattering process (even if only conceptually)
Classically, radiation is made of waves and waves are distinct from particles, and scattering is a process that applies to particles, not waves. (For one thing, waves don't have a "center of mass" the way particles do.) The fact that the force between the particles that are scattering is caused by the same underlying field as the radiation does not make radiation and scattering the same. That's why Jackson treats the two separately.

In QFT, there is only one kind of thing, quantum fields; what we ordinarily think of as "waves" and "particles" are just particular states of quantum fields. It turns out that the math that describes quantum fields is basically the same as the math that describes classical waves; so QFT uses the same math to describe scattering because it uses the same math to describe everything. Note, however, that in order to get processes in QFT that look like scattering (when you adopt a particle interpretation of the field states), you have to have anharmonic terms in the Lagrangian; pure harmonic oscillators can never produce scattering-type solutions, because pure harmonic waves superpose linearly, and you need nonlinearity to get scattering.
 
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PeterDonis
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seem to say radiation = scattering in the sense I meant
The book says that radiation can be scattered by matter, which is certainly not controversial (although the meaning of "scattering" here is not the meaning you were using earlier in this thread--it has nothing to do with an inverse square force between particles); but to say that means "radiation = scattering" seems strange.
 
  • #13
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I never said scattering is just an inverse square law of force, I just said I was thinking of elastic Coulomb scattering as well as inelastic disintegration scattering as well as Compton, Bhobba etc... scattering (concepts that can be handled from a relativistic quantum mechanics perspective with Green functions as though they were particles btw, c.f. Bjorken & Drell vol. 1) trying to see whether the analogue of these concepts in CFT was radiation, and I definitely never said partices = waves. The book says "Oscillating charges radiate electromagnetic waves, a fundamental property of such charges with its origins in the finite speed of light. These radiated electromagnetic waves are scattered waves, ...", I'm not trying to say anything controversial I'm just looking for a loose way of thinking about the concept, the same way you can think of diffraction as the notion of scattering simply applied in geometrical optics (an approximation to free Maxwell equations, and there's a big comment about this in the book as well).
 
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PeterDonis
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trying to see whether the analogue of these concepts in CFT was radiation
Other than the fact that QFT uses the same math as classical waves, I don't really see an analogy worth pursuing. But that's always a matter of opinion.

"Oscillating charges radiate electromagnetic waves, a fundamental property of such charges with its origins in the finite speed of light. These radiated electromagnetic waves are scattered waves, ..."
I need more context to be sure about what the book is trying to say here (I don't have Bjorken & Drell). The part about oscillating charges radiating EM waves because of the finite speed of light is simple (and appears in many textbooks), but I'm not sure what they mean by saying that these radiated waves are scattered waves. The EM waves would be radiated even if the oscillating charge were alone in the universe (at least that's the prediction of standard classical EM), so there's nothing else for the waves to scatter off of.
 
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That quote is from the book I linked to, it's on the first page of chapter 3 (directly linked to), the first 4 pages of the chapter talk about it, and say the distinction between inelastic and elastic is whether the frequency changes or not. If you define scattering specifically in terms of solutions of pde's I can now see why they can say this about radiation.
 
  • #16
PeterDonis
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If you define scattering specifically in terms of solutions of pde's I can now see why they can say this about radiation.
Yes, that's a more general definition that basically makes "scattering" equivalent to "interaction". But which specific PDE's are involved will depend on which specific interaction you are studying.
 
  • #17
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Thanks, I was just kind of shocked at the notion that you could think of EM radiation in such familiar conceptual terms allowing one to see even more unity throughout physics, hence was checking to be sure!
 

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