Several papers have now claimed to have resolved this controversy; e.g., a team from the Aalto University argues that the photon EM field induces a dipole in the medium, where the dipole moment causes the medium atoms to bunch, creating a mass density wave. The EM field carries the Abraham momentum and the combined EM field and mass density wave carries momentum equal to the Minkowski momentum. However, a recent study argues that the physical model set up by the team is not consistent with Einstein's special relativity; and the study further argues that (i) momentum-energy conservation law is consistent with but not included in Maxwell equations, and as a result, the momentum and energy of light in a medium cannot be uniquely defined within the Maxwell-equations frame; (ii) the momentum and energy of a non-radiation field is not measurable experimentally, because the non-radiation field cannot exist independently of the materials which support it, just like one cannot experimentally determine the momentum and energy of the EM field carried by a free electron in free space. In other words, the non-radiation field is the component of the material subsystem, instead of the EM subsystem. This conclusion is apparently supported by Compton photon-electron scattering experiment.