D O C . 1 7 G R AV I TAT I O N A N D E L E C T R I C I T Y 4 3 which, according to Maxwell, should vanish, do not necessarily vanish according to (17) and (19), but their divergences of the type certainly do. Consequently, (17) and (19) are basically identical to the Maxwell equations for empty space. Regarding the assignment of the to the electric and magnetic vectors (i.e., a and h), I would like to make a remark that claims validity independently of the theory discussed here. According to classical mechanics, which operates with cen- tral forces, for every sequence of states of motion V there is an inverse . which contains the same states in the opposite order. This inverse sequence is formally obtained from the original V by applying to the latter the substitution . Things are similar in the general theory of relativity in the case of a pure gravi- tational field. In order to derive from a solution V the corresponding solution , one must insert in all field functions and additionally change the sign of the field components and of the energy components . This is the same as applying the above transformation to the original process V. The change in sign of as well as of automatically arises out of the transformation rule of tensors. This ability to generate the inverse process by transformation of the time coor- dinate has to be regarded as a general law that can claim validity with re- gard to electromagnetic processes as well. There, inversing the motion of an electron brings about a change in the sign of the magnetic components but not one of the electric components. Therefore, we should assign the components to the electric field, and the components to the magnetic field.[9] The conventional reverse assignment must be given up. Evidently, it has been preferred up to now because it appears to be more convenient to express the current density by a vector (tensor of first rank) rather than by an antisymmetric tensor of third rank. In the theory presented here, (7), resp. (17), is hence the expression for the law of magnetoelectric induction. This also fits with the fact that there is no term on the right-hand side of this equation that could be interpreted as the electric current density. ∂xα© ∂xα ∂φμν ∂xμ ∂φνα ∂xν ∂φαμ· + + ¹ ¨ ¸ § φμν V V [p. 419] x′ x = y′ y = z′ z = t′ t –= V t′ t –= g14g24g34 T14, T24, T34 g14g24g34 T14, T24, T34 t′ t) –= ( φ23, φ31, φ12 φ14, φ24, φ34
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