# Interpretation of interconnection of alternative macroscopic approaches associated with the Abraham-Minkowski con-troversy using microscopic description

## TL;DR

This paper clarifies the interconnection of different macroscopic electromagnetic momentum approaches by analyzing their microscopic foundations, revealing how Abraham, Minkowski, and total momenta relate to specific forces and energy-momentum exchange.

## Contribution

It provides a microscopic interpretation that clarifies the relationships and differences between alternative macroscopic momentum formulations in electromagnetic theory.

## Key findings

- Material derivative of momentum is preserved across transformations.
- Abraham, Minkowski, and total momenta are linked to specific ponderomotive forces.
- Microscopic interpretation clarifies properties of electromagnetic momentum in media.

## Abstract

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.

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Source: https://tomesphere.com/paper/1905.08426