Page:AbrahamMinkowski1.djvu/3

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in Lorentz's theory, they represent the electric and magnetic excitation of the aether; while they are lacking an illustrative meaning in Minkowski's theory. In my opinion, exactly in this abandonment of an illustrative interpretation, lies the actuality of Minkowski's theory. After the theory of electrons has borne rich fruit, electrodynamics appears to be entering into a phenomenological phase of its development.

Also the method of the present investigation is a phenomenological one. In view of the perplexity, which is caused by the increasing number of rival theories, it appeared to me as desirable, to possess a system of electrodynamics of moving bodies on a Maxwellian basis, which at first is free from special assumptions of the individual theories. The presuppositions of the system represented here, are contained in the momentum theorems and the energy theorem (§ 3) and also in certain equations, which we denote as "main equations" (§ 4.). Two of them connect – as analogous generalization of the main equations of Maxwell's theory which hold in the case of rest – the line integrals of vectors and (the force upon moving electric and magnetic unit poles) with the temporal changes of the surface integrals of vectors and (the magnetic and electric excitation). Together with the supplemented three main-equations, which express by those vectors the Joule-heat, the relative ray, and the relative electromagnetic stresses in moving matter, they form a mathematical frame into which the different images of electromagnetic processes can be placed. Any such image is (in the sense of our system) characterized by two relations between the four vectors ; by addition of these relations, the two first main equations pass into the differential equations, which represent (in agreement with the corresponding theory) the temporal change of the electromagnetic field, while the other three main equations determine the energy processes and the ponderomotive forces. However, it is remarkable, as to how far one is able to follow the consequences from the main equations, without using the special connecting equations of the corresponding theory. In particular, the deviations between the different theories in the expression of ponderomotive force (§ 12), are only marginally; in the case of rest, the ponderomotive forces of the theories of Lorentz, Cohn, and Minkowski even become mutually identical.

By placing the different theories of electrodynamics of moving bodies in a general system, I remove those properties of the individual image, which are not determined by the characteristic connecting laws of electromagnetic vectors. That I performed such modifications at some of the mentioned theories, will surely be excused; because in the given mode of representation, the essential points of the concerned images are emphasized even more clearer.