On the Electrodynamics of Minkowski.
Memoir by Max Abraham (Milan)
At the meeting on January 23, 1910.
§ 1. Introduction.
In a preceding paper[1] I have developed a system of electrodynamics of moving bodies, which – being in accordance with the general principles of the theory of Maxwell and Hertz – embraces the modern theories of E. Cohn, H. A. Lorentz and H. Minkowski. Regarding the special case of Minkowski's theory, an expression of the ponderomotive force resulted, which differs from the expression given by Minkowski himself; I have asserted that this expression satisfies the principle of relativity.
In this present note, this assertion will be confirmed. I will start in § 2 with some theorems related to the four-dimensional vectors, which are essentially already contained in the memoir of Minkowski[2], that will be applied later; I believed that it was useful to give a four-dimensional vector form to the analysis, which, adapting itself to three dimensional analysis, allows us to quickly get from the four-dimensional variation of space and time to three-dimensional space.
Variables are introduced in § 3, which I will call "four-dimensional tensors." They are a generalization of three dimensional tensors[3], which characterize, for example, the state of stress of an elastic body. The four-dimensional tensor that should be considered in electrodynamics, contains – in its ten components – the six components of electromagnetic pressure, and the three components of the energy current and the electromagnetic energy density. It will be formed by a four-dimensional tensor, whose components are identical to the values of pressure, the flow of energy,
- ↑ M. Abraham, Zur Elektrodynamik bewegter Körper [Rendiconti del Circolo Matematico di Palermo, t. XXVIII (2° sem. 1909), pp. 1-28].
- ↑ H. Minkowski, Die Grundgleichungen far die elektromagnetischen Vorgänge in bewegten Körpern [Nachrichten von der Kgl. Gesellschaft der Wissenschaften zu Göttingen, Jahrgang 1908, pp. 53-111].
- ↑ M. Abraham, Geometrische Grundbegriffe [Encyklopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, IV, 2, pp. 3-47].
