  Interconnection of alternative equations of conservation of the momentum
related with different interpretations of equations of the electromagnetic
field is an essential aspect of the Abraham-Minkowski controversy, which is
associated in the first place with rivalry of alternative definitions of
optical momentum of the electromagnetic wave in a medium. Assuming significance
of alternative equations of momentum conservation in accord with their
interconnection, potential functional equivalence of alternative descriptions
of optical momentum is examined in the context of the radiation pressure. In
accordance with conducted examination, the material derivative of the momentum
of a closed medium-field system is preserved in transformations linking
alternative equations of momentum conservation, whereas the optical momentum is
changed in compliance with alternative approaches. It is found that Abraham's,
Minkowski's, and the total momenta are inherently linked with specific
ponderomotive forces, which are not interchangeable in spite of interconnection
of involved forms of field equations and equations of conservation of the
momentum. Interconnection of alternative macroscopic approaches is clarified
using microscopic interpretation of the energy and the momentum of the
electromagnetic wave in a host medium. Contradictory references to microscopic
aspects associated with alternative approaches, including assumptions in regard
to manifestation of the Lorentz force on the level of macroscopic description
and nature of inertial properties of electromagnetic wave in a host medium, are
evaluated in this context. It leads to clarification of properties of
ponderomotive forces as well as concepts of momentum and pseudomomentum of the
electromagnetic wave in a host medium, which are essential for explanation of
interconnection of alternative macroscopic approaches.
