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Quantum Field Theory - The Photon Is Massless, and It Has No Potential Energy
Quantum field theory says the mass of a field is the energy you get just from having a value, not necessarily from changing. But for something like the photon, there's no potential energy. There's no energy associated with the field having a value. That's why the Higgs field takes on a non-zero value in empty space. The lowest energy state is not at zero field value.