Question

Why momentum squared is zero for photons?

Answer 1

For relativistic particles, dispersion relation reads

$$p_\mu p^\mu = \frac{E^2}{c^2}-\vec{p}^2=m^2c^2$$

where $p_\mu$ is momentum 4 vector, $E$ is energy of particle, $\vec{p}$ is momentum , m is the mass and c is speed of light.

For photons, mass equals to zero - because they travel with maximum possible speed c.

Therefore

$$p_\mu p^\mu=0$$