About conservation the angular momentum for asymmetric tensors in electrodynamics

Abstract

It is customary to assume that the law of conservation of the angular momentum is violated for an asymmetric energy-momentum tensors. This is the reason for criticizing the Minkowski tensor and other asymmetric energy-momentum tensors. In this paper, it is shown that the laws of conservation of energy and momentum following from an asymmetric tensor in the form of its total divergence are equivalent to the divergence of its symmetric part. It is shown that the total divergence of the antisymmetric part of the asymmetric tensor is identically zero. From this, it follows that for the asymmetric energy-momentum tensor the law of conservation of the angular momentum is also fulfilled. It is shown that the linear invariant of the Minkowski tensor for a vacuum does not correspond to the quadratic invariant of the electromagnetic field. This indicates that the linear invariant of the Minkowski tensor and the three-dimensional stress tensor are not correct.

arXiv comment10 pages

References in corpus (15)

• Resolution of the Abraham-Minkowski Controversy
• Revisiting the Abraham-Minkowski Dilemma
• Division of the momentum of electromagnetic waves in linear media into electromagnetic and material parts
• Minkowski Momentum Resulting from a Vacuum-Medium Mapping Procedure, and a Brief Review of Minkowski Momentum Experiments
• Optomechanical Measurement of the Abraham Force in an Adiabatic Liquid Core Optical Fiber Waveguide
• Detection of the Abraham force with a succession of short optical pulses
• Forces and momenta caused by electromagnetic waves in magnetoelectric media
• Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches
• Is the Abraham electromagnetic force physical?
• A new form of the energy-momentum tensor of the interaction of an electromagnetic field with a non-conducting medium. The wave equations. The electromagnetic forces
• Electromagnetic Momentum in a Dielectric: a Back to Basics Analysis of the Minkowski-Abraham Debate
• The energy-momentum tensor of electromagnetic fields in matter
• The Role of Conservation Principles in the Abraham--Minkowski Controversy
• About the Abraham force in a conducting medium
• Equation for the Abraham force in non-conducting medium and methods for its measurement