Simple question about photons turning into electorn positron pairs.

[cpfoxhunt]

Homework Statement

This is a really easy one, goodness only knows why I can't think of how to do it, here goes

" Explain why a photon in free space cannot turn into an electron-positron pair."

Homework Equations

I assume E^2- P^2 = 0 will be of some help

The Attempt at a Solution

I'm stuck - why on Earth shouldn't it if it has sufficient energy to provide the necessary rest masses? Why don't photons do this all the time?

Cheers
Cpfoxhunt

 

[pam]

E^2-p^2=0 for a photon, but it must be positive for an electron-positron pair.
That is $$(E_1+E_2)^2-({\vec p}_1+{\vec p}_2)^2>0$$.