Dynamic Impossibility of Photon to Electron/Positron Conversion

[Woodzy]

Show that the following process is dynamically impossible: A single photon in empty space is transformed into an electron and a positron.

Hint: use conservation of momentum and energy


for this problem I know a photon has no rest mass and therefore its energy is just equal to pc. However I am unsure about how o go about the proof? I am fairly comfortable obtaining expressions for momentum and energy conservation but what then??

please help

thanks

 

[Hao]

A conceptual approach to solve this can be reached by considering what happens in a zero momentum frame.

A calculational approach is more tedious, and involves proving that it is impossible to satisfy both conservation of momentum and energy simultaneously. You could do this in the zero momentum frame, but it will be physically confusing.