 Quote by Saw
you say that here there is a couple of mutually generating fields, but in my frame there is only one... But can that happen? Now I tend to think it can't, that whenever there is an EM wave (or a photon), there are both things, E and B field... even if different observers label them differently?
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You are correct, this cannot happen. Suppose in some frame you have E and B fields which satisfy Maxwell's equations and form a plane wave in vacuum (no currents or charges). If you boost those fields by the Lorentz transform you will get different fields, but those fields will still be a valid plane-wave solution to Maxwell's equations in vacuum.
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