Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties
In a continuum setting, the energy–momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy–momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material four-divergence of the traceless, symmetric total energy–momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the Abraham–Minkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy–momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.
- OSTI ID:
- 22250766
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
ANGULAR MOMENTUM
BYPASSES
CONTINUITY EQUATIONS
DIELECTRIC PROPERTIES
ELECTRODYNAMICS
ENERGY CONSERVATION
EQUATIONS OF MOTION
FOUR-DIMENSIONAL CALCULATIONS
LINEAR MOMENTUM
MAXWELL EQUATIONS
MINKOWSKI SPACE
PULSES
SYMMETRY
TENSORS
THREE-DIMENSIONAL CALCULATIONS