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Electron is a particle with momentum $p$ and it spins up. Positron is its antiparticle having momentum $-p$ and it spins down. "A positron is an electron travelling backwards in time" said by Feynman. Therefore how an electron and positron annihilate producing photons since total momentum is $p-p=0$. Therefore how they produce photon with momentum?

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A positron is an electron travelling backwards in time" said by Feynman.

This is the Feynman diagram for electron positron annihilation at low momenta of the electron and positron.

e+e- annihilation

Therefore how an electron and positron annihilate producing photons since total momentum is p-p=0 therefore how they produce photon with momentum

The diagram is a prescription of how to calculate the probability that the electron and positron when meeting will annihilate. Note the arrow in time. That is what Feynman meant by "backwards in time", that mathematically a positron is an electron going backward, simply mathematics.

Note the two photons. In the center of mass system momentum would not be conserved if only one photon came out, as there is about a 1 MeV in the rest mass of the electron and the positron, a lower limit to the energy to be divided, and conservation of energy with conservation of momentum will divide it to the two photons in the center of mass system.

You should read up a bit on special relativity and how it differs from classical mechanics notions.

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