The question goes like this: Prove that conservation of four momentum forbids a reaction in which an electron and positron annihilate and produce a single photon(gamma ray). Prove that the production of two photons is not forbidden.(adsbygoogle = window.adsbygoogle || []).push({});

The solution is to work in the centre of momentum frame. I understand that, the electron and positron will travel in opposite directions in this frame since they both have the same mass, and the annihilation will conserve momentum by sending out even numbered photons, each pair in opposite directions of the same frequency.

My question is, why can't we not work in the centre of momentum frame. In the frame of the positron, the total momentum before collision is not zero, but after collision, if only one photon is produced with the same momentum as the sum of the four momenta of the electron and positron, things will still look good.

If two photons of the same frequency are emitted as seen in the C.M. frame, for an observer travelling in the MCRF of the positron travelling from right to left, the left going photon will be redshifted and the right going photon will be blueshifted. The resultant of this momentum has to be equivalent to the resultant momentum before collision.

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# Conservation of four momentum question

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