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Electrodynamics in the general relativity theory

1925; American Mathematical Society; Volume: 27; Issue: 1 Linguagem: Inglês

10.1090/s0002-9947-1925-1501302-6

1088-6850

G. Y. Rainich,

Relativity and Gravitational Theory

The restricted relativity theory resulted mathematically in the introduction of pseudo-euclidean four-dimensional space and the welding together of the electric and magnetic force vectors into the electromagnetic tensor. Einstein's general relativity theory led to the assumption that the fourdimensional space mentioned above is a curved space and the curvTature was made to account for the gravitational phenomena. The Riemann tensor which measures the curvature and the electromagnetic tensor seem thus to play essentially different roles in physics: the former reflects some properties of the space so that gravitation may be said to have been geometricized,-when the space is given all the gravitational features are determined; on the contrary, it seemed that the electromagnetic tensor is superposed on the space, that it is something external with respect to the space, that after space is given the electromagnetic tensor can be given in different ways. Several attempts were made to geometricize the electromagnetic forces, to find a geometric interpretation for the electromagnetic tensor, to inicorporate this tensor into the space in the sense in which the gravitational forces had been incorporated. It seemed that in order to do this it was necessary to change the geometry; to abandon the Riemanii geometry and to adopt a more general space with a more complicated curvature tensor, one part of which would then account for the gravitational properties and the other wouild in the same way account for the electromagnetic phenomena. H. Weyl arrived in a most natural way to such a generalization. His theory always will remaini a brilliant mathematical feat, but it seems that it did not fulfil the expectationis as a physical theory and the same seems to be true with respect to other attempts. The electromagnetic tensor is, however, niot elntirely independelnt of the Riemann tensor in the ordinary genieral relativity theory; these two tenisors are connected by the so called eniergy relation; it seemed to be desirable to try, witliout breaking the frame of the Riemann geometry, to study