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A photon is the force carrier of an electromagnetic wave and it consists of an electric and a magnetic field propagating through space at the speed of light in vacuum.

It exhibits wave-particle duality and does not interact with another photon. The fact that it interacts only with charged particles also implies that it does not interact with magnetic fields.

A photon has an entourage of electrons and perhaps other stuff around it and, especially, in a particle accelerator energetic photons may collide in this way.

Questions:

Q1. How is this possible?

Q2. Why do photons only interact with charged particles?

P.S: A picture is worth a thousand words: I don't have quantum physics background. I read Maxwell's equations and they only apply to waves. I peeked at Einstein's photoelectric effect paper but it only describes how light behaves like a particle.

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Q1: For photons of energies much less gamma rays, the quantum mechanical photon-photon interaction is negligible. This is consistent with the classical electrodynamic description where the principle of superposition holds (electromagnetic waves pass through each other unchanged, as well as through electric/magnetic fields).

Q2: in reality, charge is defined as how strongly a particle interacts with photons, so this question is not valid.

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