Hidden momentum in continuous media and the Abraham-Minkowski debate

Abstract

We perform a detailed study of the connection between hidden momentum and the Abraham-Minkowski debate about the electromagnetic momentum density in material media. The results of a previous work on the subject [P. L. Saldanha and J. S. Oliveira Filho, Phys. Rev. A 95, 043804 (2017)] are extended to the continuous medium limit, where some subtleties arise. We consider a polarized and magnetized continuous medium with applied electric and magnetic static fields, where the medium polarization can be due to either an electric charge density or a hypothetical magnetic current density and the medium magnetization can be due to either an electric current density or a hypothetical magnetic charge density. Each model leads to a different expression for the system material hidden momentum and for the electromagnetic momentum density in the medium. We show that the main results of the cited reference are sustained in the continuous medium limit: Abraham momentum is compatible with a model for the medium where the polarization is due to electric charges and the magnetization is due to magnetic charges, Minkowski momentum is compatible to a model where the polarization is due to magnetic currents and the magnetization is due to electric currents, and the expression ${\epsilon }_0\mathbf{E}\times \mathbf{B}$ is compatible with a model where the polarization is due to electric charges and the magnetization is due to electric currents, which is the natural model. These results are illustrated with the example of a uniformly polarized and magnetized sphere.

arXiv comment11 pages, 1 figure

References in corpus (20)

• Momentum of an electromagnetic wave in dielectric media
• Optical Momentum, Spin, and Angular Momentum in Dispersive Media
• Photon recoil momentum in dispersive media
• Optical momentum and angular momentum in complex media: From the Abraham-Minkowski debate to unusual properties of surface plasmon-polaritons
• Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
• Photon mass drag and the momentum of light in a medium
• Comment on "Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation"
• Mass-polariton theory of sharing the total angular momentum of light between the field and matter
• Energy-momentum balance in quantum dielectrics
• Mass-polariton theory of light in dispersive media
• Division of the momentum of electromagnetic waves in linear media into electromagnetic and material parts
• Radiation Forces and the Abraham-Minkowski Problem
• Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"
• Lorentz covariance of the mass-polariton theory of light
• Lagrangian dynamics of the coupled field-medium state of light
• Division of the Energy and of the Momentum of Electromagnetic Waves in Linear Media into Electromagnetic and Material Parts
• Hidden momentum and the Abraham-Minkowski debate
• Photon reflection by a quantum mirror: a wave function approach
• Hidden momentum in a hydrogen atom and the Lorentz force law
• Hidden momentum of electrons, nuclei, atoms and molecules

Cited by in corpus (6)

• Standardizing Platinum Dainotti-correlated gamma-ray bursts, and using them with standardized Amati-correlated gamma-ray bursts to constrain cosmological model parameters
• Time-dependent theory of optical electro- and magnetostriction
• The Microscopic Ampère formulation for the electromagnetic force density in linear dielectrics
• Remarks on the Abraham-Minkowski problem, from the formal and from the experimental side
• Recoil momentum of an atom absorbing light in a gaseous medium and the Abraham-Minkowski debate
• Optical force density and surface displacements in transparent dielectrics due to non-ionizing sub-picosecond laser excitation