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## Main Question or Discussion Point

I'm confused about how photons are able to split into electrons and positrons. Learning about four dimensional vectors, but it's still not clear how this happens.

The photon will have a vector of P=(E,p), where p^2=E^2, so P^2=0, since photons don't have mass.

It must be that P = P1 + P2, where P1 and P2 are electron and positron.

P1 = (E1,p1), where E1^2 = p1^2 + m^2.

So (E,p) = (E1,p1) + (E2, p2) = (E1+E2,p1+p2)

So (E,p)^2 = 0 = m^2 + m^2 + E1*E2 - p1*p2

So is the product of p1 and p2 really equal to m^2 + m^2 + E1*E2?!

That would suggest that either p1 or p2 is greater than it's corresponding energy, which would make mass negative.

What am I missing?

The photon will have a vector of P=(E,p), where p^2=E^2, so P^2=0, since photons don't have mass.

It must be that P = P1 + P2, where P1 and P2 are electron and positron.

P1 = (E1,p1), where E1^2 = p1^2 + m^2.

So (E,p) = (E1,p1) + (E2, p2) = (E1+E2,p1+p2)

So (E,p)^2 = 0 = m^2 + m^2 + E1*E2 - p1*p2

So is the product of p1 and p2 really equal to m^2 + m^2 + E1*E2?!

That would suggest that either p1 or p2 is greater than it's corresponding energy, which would make mass negative.

What am I missing?