Page:The Meaning of Relativity - Albert Einstein (1922).djvu/58

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THE MEANING OF RELATIVITY

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If there exists with respect to only a magnetic field, , but no electric field, , then with respect to there exists an electric field as well, which would act upon an electric particle at rest relatively to . An observer at rest relatively to would designate this force as the Biot-Savart force, or the Lorentz electromotive force. It therefore appears as if this electromotive force had become fused with the electric field intensity into a single entity.

In order to view this relation formally, let us consider the expression for the force acting upon unit volume of electricity,

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in which is the vector velocity of electricity, with the velocity of light as the unit. If we introduce and according to (30a) and (31), we obtain for the first component the expression

Observing that vanishes on account of the skew-symmetry of the tensor (), the components of are given by the first three components of the four-dimensional vector

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and the fourth component is given by

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