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Why EM waves having only x momentum transfers to electron z momentum? Electron begins oscillating along z, so will not radiate EM waves along z direction, to compensate its z momentum. It seems that it is violated conservation of momentum?

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For the opposite process, see – Qmechanic Jul 6 '11 at 15:10
Why do You ask the same question two times? Were the answers out of Your reach?… – Georg Jul 6 '11 at 16:49
There is no correct answer – grigori Jul 7 '11 at 10:52

In the particle formulation of electromagnetism, light is carried by photons. Momentum is absolutely conserved. If a photon hits an electron, there will be momentum balance.

In the wave formulation of EM the electric field,( supposed it is a polarized beam), oscillates in the z direction. An electron that acquires a momentum will take part of the energy of the beam and the beam will acquire a small z component to conserve momentum. On the average,since the electron will be hit in both z directions by the incoming beam, the effect will be that the beam will spread/degrade, to conserve momentum and energy.

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From your explanation it follows that if we consider in terms of photons, the electron will acquire mainly x momentum (cos(teta) from x direction), if consider in terms of waves, electron will acquire mainly z momentum (cos(teta) from z direction). What will be in reality? – grigori Jul 7 '11 at 10:57
@grigori No. One has to solve the specific scattering with Feynman diagrams that are consistent with both the wave and particle picture to see what a specific scatter will do. You have to give the energy of the photon etc to speak about what "an electron will acquire", and that will be probabilistic. If we are talking about optical frequency photons on electrons at rest the amount of momentum and energy transfered will be minimal: – anna v Jul 7 '11 at 11:06
continued:a small delta(p_z)+delta(p_x) for the electron which will almost remain at rest and the photon will be steered a tiny bit away from the x direction. That is what I meant by dispersion of the beam – anna v Jul 7 '11 at 11:07
anna, no. The amount of transfered momentum can be large if we use strong optical frequency waves. By this oscillating along z electron will not radiate along z, so its z momentum is not compensated by radiated field. – grigori Jul 8 '11 at 16:26
Do you have a link to this claim? A specific experiment? – anna v Jul 8 '11 at 19:51

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