Did Michelson and Morley test the wrong phenomenon?

"Our Universe does not have a real cosmic medium". "Light is fundamentally dual, comprising a wave aspect and a particle aspect". These two statements are jointly present in most physics textbooks, but they are logically incompatible. The argument against mediation is based on the outcome of the Michelson-Morley experiment. It only works under the assumption that light is a running wave in the ether, similar to a sound wave in the air. Without such an assumption, invariance only proves that the speed of light is not the speed of a wave. If light has a dual nature, then the speed of light is the speed of the particle aspect. In quantum mechanics, it can be described as the speed of the photon. Classical models would suggest that the speed of light is equal to the rate of mutual generation of electric and magnetic fields across space. Alternatively, the speed of light can be described as the speed of a train of fields, propagating like a stream of particles. There is no room for running waves in these models, except as a constituent element of static fields. For a coherent account of our knowledge, the second statement should be preserved, and the first one should be rejected.