Electrodynamics of Moving Media
For more than fifty years there has been a controversy about the correctness of several apparently different electrodynamic formulations for moving media. The research reported here has resolved this controversy.
In 1908 H. Minkowski proposed his formulation, in which Maxwell's equations have the same form as for stationary media. Later, the formulation of M. Abraham appeared, with a different expression for electromagnetic momentum and, therefore, small relativistic differences in the force predicted. About ten years ago, L. J. Chu developed a new formulation, with significant nonrelativistic differences in the force. Chu's formulation has several advantages, including simplicity, ease of learning, and especially its simple model for magnetization. But before this or any other formulation could be taught or used with confidence, the question of the different force distributions had to be resolved.
Experiments have not been successful in resolving the controversy because many of the differences concern small relativistic effects. The resolution had to come from more complete theoretical understanding. The authors have found that none of the force expressions “is complete; each must be modified, and when so modified all are in agreement.”
The authors were led to this conclusion by carefully identifying the energies and powers, and by establishing a law of conservation of energy consistent with thermodynamics, continuum mechanics, and special relativity. Electrostriction, magnetostriction, piezoelectricity, dispersion, and other nonrelative effects were taken into account. Two techniques were used to predict force. One is Hamilton's principle. The other is a new technique developed by the autos, the “principle of virtual power.” This is based on the principle of virtual work, a well-known principle of classified mechanics.
This work will be of decimal interest to those who teach electromagnetic field theory. A knowledge of special relativity is not required to understand the non-relativistic results.