special relativity - Photons have no mass. So, why does $E = pc$ hold?

It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The energy $E$ turns out to be 0 always. So, why does this equation hold?

Answer

Momentum in this case is: $p = h / \lambda$ for a massless particle. The momentum is related to the De Broglie wavelength of the particle with this formula. If you plug it in the equation you have stated you will get back the Energy equation of a massless particle:

$E = hc/\lambda = hf$