I have been solving a problem where you should derive the formula for doppler effect when a source of light is an atom moving at a relativistic velocity v. I understood everything in the solution except for why was the formula for impulse of the atom used as if it's not relativistic i.e. p=m*v? Is it maybe because the atom is so heavy that the lorentz factor wouldn't change the momentum noticeably?

  • $\begingroup$ Someone made some error somewhere :) Maybe recoil effect was calculated in the atom frame, that's what I would do. $\endgroup$
    – stuffu
    Feb 5 '21 at 21:23

There is nothing wrong on writing the relativistic momentum as $p = mv$ as long as you are saying that $m = \gamma m_0$, where $m_0$ is the rest mass (inertial mass). In other words, the equation $p = mv$ is relativistic, the Lorentz factor is simply compacted onto the mass, meaning that the mass you are using to calculate isn't the rest mass but rather the relativistic mass.

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    $\begingroup$ You might want to point out that most physicists no longer use the concept of relativistic mass as pointed out by many other answers for example: relativistic mass and graivty. $\endgroup$
    – M. Enns
    Feb 5 '21 at 13:31
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    $\begingroup$ @M.Enns I know. But that's not the case for most undergrad books (I'm here assuming that the asker is an undergrad) $\endgroup$ Feb 5 '21 at 13:34
  • $\begingroup$ Thank you, everyone, it turns out that the author actually used relativistic mass which we didn't use before for the reasons you already mentioned and I didn't even think of using it. $\endgroup$ Feb 6 '21 at 14:59

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