Question

Explain why the conservation laws of physics are not violated when a positron and an electron annihilate each other. (Note there are more conservation laws in physics than charge)

Answer 1

A position is the antiparticle of electron, i.e. it has same mass as an electron but opposite charge. Now when the annihilation occurs, high energy photons are emmited. As already noted in question charge conservation is not violated as photons have no charge and initially we had a total charge of zero. Now other conservation laws we have to look at are energy conservation and momentum conservation. We know that photons don't have mass but they do have energy and momentum, so the total energy of the system initially which will include the rest mass energy as well will be same as the total energy of the photons. To look at how the momentum is conserved..Suppose initially the system had total momentum to the right and after the annihilation two photon is produced, one moves to left and other to the right, then for momentum to be conserved the photon moving to right will be more energetic or will carry more momentum than the one moving to the left. Spins of the total system is also conserved in an elementary particle interaction.. Both electron and positron are spin 1/2 particles so the total spin of the system will either be 0 or 1, as it should be an integer otherwise we couldn't have the same spin after The annihilation as photons are spin 1 particles, and their Total spin must be an integer..If initially we Had Angular Momentum, don't worry, it's strange but photons do have angular momentum..Even static electromagnetic field too have angular momentum. So after annihilation photons will save us from violating any of the conservation laws. Although seeing that is not trivial at all..I have given a very brief and rough qualitative description of how conservatives remains intact.