How do we know that charges interact by photons? Has it been observed or is it an assumption in quantum electrodynamics?
The force carriers between two charges are virtual photons which cannot be directly observed. However, the theory that describes this interaction (QED) does make many predictions that have been experimentally confirmed with incredible precision, see Wiki: Precision tests of QED.
How do we know that charges interact by photons? Has it been observed ...?
It is observed that during the approach of an electron to the nucleus photons are emitted and it is observed that During the exposition of atoms by EM radiation electrons could be released from the nucleus.
Furthermore it is observed that during the deflection of moving electrons in an external magnetic field this electrons emit photons.
What is observed throwing two electrons to each other? They loose at once their velocity and spread out again. No EM radiation is observable. To explain the varying forces one could use the imagination of virtual photons. For an other than explanation we have to define the electric field as real and to give this field the characteristics of "where one body is an other body can't be" in analogy to elastic bodies.
The problem is that our today's curiosity stops in front of the question from what an electric as well as a magnetic field is made.