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Originally Posted by lyndonashmore
It also states that it will ignore the recoil, i don't and get the redshift.
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I may have missed the post were you do the same calculation and include the recoil.
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The energy is retained by that electron and not dispersed within the plasma. It is re-radiated as a single photon.
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In previous posts you seemed to be bringing in the rest of the plasma in an attempt to balance the budgets. Now it seems that the rest of the plasma plays no part in the fundamental interaction (other than to add to the number of scattering events). So, again, how do you balance the energy and momenta of the electron and photon coming in, and the electron and photon coming out?