Electromagnetic energy and momentum in moving media

Abstract

The problem of the electromagnetic energy-momentum tensor is among the oldest and the most controversial in macroscopic electrodynamics. In the center of the issue is a dispute about the Minkowski and the Abraham tensors for moving media. An overview of the current situation is presented. After putting the discussion into a general Lagrange-Noether framework, the Minkowski tensor is recovered as a canonical energy-momentum. It is shown that the balance equations of energy, momentum, and angular momentum are always satisfied for an open electromagnetic system despite the lack of the symmetry of the canonical tensor. On the other hand, although the Abraham tensor is not defined from first principles, one can formulate a general symmetrization prescription provided a timelike vector is available. We analyze in detail the variational model of a relativistic ideal fluid with isotropic electric and magnetic properties interacting with the electromagnetic field. The relation between the Minkowski energy-momentum tensor, the canonical energy-momentum of the medium and the Abraham tensor is clarified. It is demonstrated that the Abraham energy-momentum is relevant when the 4-velocity of matter is the only covariant variable that enters the constitutive tensor.

22 pages, Latex AdP-style, to appear in Minkowski's centenary issue of Annalen der Physik

References in corpus (7)

• Momentum of an electromagnetic wave in dielectric media
• Radiation pressure and the linear momentum of the electromagnetic field
• Electromagnetic energy-momentum and forces in matter
• Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric
• The Covariant Description of Electromagnetically Polarizable Media
• Dimensions and Units in Electrodynamics
• Electrodynamics of moving magnetoelectric media: variational approach

Cited by in corpus (17)

• First principles approach to the Abraham-Minkowski controversy for the momentum of light in general linear non-dispersive media
• Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors
• Variational Principles for Reduced Plasma Physics
• Lorentz covariance of the mass-polariton theory of light
• Lagrangian dynamics of the coupled field-medium state of light
• Covariant theory of light in a dispersive medium
• Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations
• Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields
• Covariant Response Theory and the Boost Transform of the Dielectric Tensor
• Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field
• Symmetric energy-momentum tensor: The Abraham form and the explicitly covariant formula
• Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches
• General expansion of time transfer functions in optical spacetime
• Electromagnetic momentum and the energy-momentum tensor in a linear medium with magnetic and dielectric properties
• Static solutions in Einstein-Chern-Simons gravity
• Remarks on the Abraham-Minkowski problem, from the formal and from the experimental side
• Chiral-stress-energy-momentum tensor for covariant description of spin and torque densities of light