# Photon to electron + positron

DuckAmuck
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?

## Answers and Replies

soothsayer
Photons don't have mass, but they DO have momentum! ;) This is sneaky, but it comes from Special Relativistic equations. In fact, this is measurable, if you shine a light on a surface, the light will actually apply a force on that surface! F=dp/dt

check out some of these formulas:
http://en.wikipedia.org/wiki/Photon#Physical_properties

The equation for relativistic momentum is
where

If v=c, such is the case for a photon, the gamma term goes to infinity, and when multiplied with zero, well, the result is not easily determinable, but it often equals a real number, such as is the case here with photons.

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niklaus
You are missing that for pair production to occur, another particle (usually an atomic nucleus) must be nearby to contribute momentum. Pair production does not occur in vacuum.