The relevant physics for photon-photon scattering is Quantum Electrodynamics and is elegantly described by Feynman Diagrams. See the relevant diagrams on this s

The relevant physics for photon-photon scattering is Quantum Electrodynamics and is elegantly described by Feynman Diagrams. See the relevant diagrams on this stack exchange question: https://physics.stackexchange.com/questions/215697/photon-photon-scattering-feynman-diagram https://physics.stackexchange.com/questions/215697/photon-ph... To make a crude description, virtual fermions are exchanged between the two photons and this results in transfer of momentum and energy between them.