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I am a little confused over the terminology of the rest frame. Say a photon collides with a massive particle then from the rest frame of the massive particle would it be the photon or the particle that has momentum?

i.e. in the rest frame of the massive particle is it the photon that travels to the particle or the particle that travels to the photon.

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  • $\begingroup$ The particle has one rest frame before the collision and a different rest frame afterward. Which rest frame are you asking about? $\endgroup$ – WillO Jan 7 '19 at 6:18
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Choosing a photon in this example could result in a dangerous example but, in your sentence the answer is that from the rest frame of the massive particle the photon has momentum.

You see, in general momentum is (for massive particle) how much force you have to apply in one second to put to rest (in your frame) the incoming particle, in fact $mv$ has dimensions $kg\cdot m\cdot s^{-1}$ that is newton$\cdot$second.

In a similar way, the angular momentum is the torque you have to apply in one second to put to rest an object with linear momentum $mv$ at distance $r$ from you.

If the incoming particle is a photon it's travelling at speed $c$ (unless we are in matter, then if the material is homogeneous and isotropic the speed is $c/n$) and its momentum is $p=h/\lambda$ and thus energy $E=pc$.

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In the rest frame by definition the momentum vanishes. In the particle rest frame only the photon moves. However, before and after the collision, it will have different rest frames. It is better to work in the combined rest frame as this remains the same. In this frame $\hbar \vec k + m \vec v = 0$. The particle moves but slowly in this frame. The photon of course still moves at speed c but has a slightly lower frequency.

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