Page:Grundgleichungen (Minkowski).djvu/20

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and the equations (III) and (IV), are


§ 8. The Fundamental Equations for Moving Bodies.

We are now in a position to establish in a unique way the fundamental equations for bodies moving in any manner by means of these three axioms exclusively.

The first Axion shall be, —

When a detached region of matter is at rest at any moment, therefore the vector is zero, for a system x, y, z, t — the neighbourhood may be supposed to be in motion in any possible manner, then for the spacetime point x, y, z, t the same relations (A) (B) (V) which hold in the case when all matter is at rest, snail also hold between , the vectors and their differentials with respect to x, y, z, t.

The second axiom shall be : —

Every velocity of matter is < 1, smaller than the velocity of propagation of light.

The third axiom shall be : —

The fundamental equations are of such a kind that when x, y, z, it are subjected to a Lorentz transformation and thereby and are transformed into space-time vectors of the second kind, as a space-time vector of the 1st kind, the equations are transformed into essentially identical forms involving the transformed magnitudes.

Shortly I can signify the third axiom as ; —

and are space-time vectors of the second kind, is a space-time vector of the first kind.

This axiom I call the Principle of Relativity.