As far as I know, the Compton Effect can only be explained by using Quantum Electrodynamics, given an incoming electromagnetic wave there is a probability that a photon with different wavelength than the incoming wave is generated, this effect cannot be explained with classical electrodynamics, which only changes the wave direction but not its wavelength.

My question is, given an incoming wave, we can get the Compton probability density for each possible generated photon, so, can we use these probabilities to figure out the classical electromagnetic field that the Compton Effect will cause?

  • $\begingroup$ One-photon EMF is a volume-dependent quantity and it is useless anyway because we never put it into the classical EOM. $\endgroup$ – Vladimir Kalitvianski Aug 23 '19 at 7:00
  • $\begingroup$ Classical EM theory can explain a lot about the Compton effect including the wavelength variation with scattering angle. Raman has shown one gets quantitative agreement with experiments under assumption that the scattering electron forward momentum in the field of the primary wave is $h/\lambda$: dspace.rri.res.in/bitstream/2289/2125/1/… $\endgroup$ – Ján Lalinský Aug 23 '19 at 9:21

The classical analogue of Compton scattering is Thomson scattering of an electromagnetic wave by a charged particle. It can and does change the wavelength, because the charged particle recoils as it radiates the scattered radiation, causing a Doppler shift. But as the intensity of the wave goes to zero, the recoil and the wavelength shift do as well.

By contrast, in quantum-mechanical Compton scattering, there is a wavelength shift even at low intensity, since the electromagnetic wave can behave like a localized particle that “hits” the charged particle.

So the two descriptions are not equivalent and there is no classical EM field that can explain Compton scattering and the observed wavelength shift at low intensity. Only the QED description can do this. This experiment, like the photoelectric effect, is clear evidence of quantum mechanics.

  • $\begingroup$ Thank you for your accurate response and for correcting me in the fact that Thompson scattering can change the wavelength because of the particle recoil. $\endgroup$ – Sergio Prats Aug 23 '19 at 18:35
  • $\begingroup$ The Lorentz force would not lead to the Compton effect because the classical electromagnetism only allows a very little recoil energy when the intensity grows smaller and the frequency grows bigger, however, could the acceleration caused by the Lorentz-Abraham force radiate in higher frequencies similar to the ones generated by the Compton radiation? $\endgroup$ – Sergio Prats Aug 24 '19 at 9:41
  • $\begingroup$ I’m not sure; I haven’t seen such a calculation. $\endgroup$ – G. Smith Aug 24 '19 at 16:17

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