Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , -h$\nu_2$/c , 0 , 0). Each are null vectors. The norm squared of the vector sum of the two vectors yields 4$h^2\nu_1\nu_2/c^2$ using the (+---) metric. If the sum of the energies of the two photons is greater than 1.022 MeV and pair production results then the norm squared of the vector sum of the 4-momenta of the positron and the electron after the interaction in a frame of reference where their total momentum is 0, would yield 4$m_e^2c^2$. Since the morm of the 4-momentum is lorentz invariant and a conserved quantity, this would lead to a useful result like calculating the minimum energy needed for a gamma photon interacting with a CMB photon to lead to pair production.

I understand mathematically that it is possible to get a vector whose morm is not 0 from the addition of two null vectors. However, I have some trouble understanding from a physics perspective how two photons about to collide would have a non-zero rest mass, at least in some lab frame of reference before the collision.

I am guessing that the interaction is a process, and not simply vector addition at a point in time.