Page:Das Prinzip der Relativität und die Grundgleichungen der Mechanik.djvu/2

that according to the relativity principle a moving electron would be subject to a specific deformation work, I would attach no decisive importance, because in general we can add this work to the kinetic energy of the electron. However, the question of an electrodynamic explanation of inertia remains open; but instead there arises, on the other hand, the advantage that it's not necessary to ascribe to the electron neither a spherical form nor even any other form in order to arrive at a certain dependence of inertia on speed.

However that may be: a physical idea of that simplicity and universality, as contained in the relativity principle, deserves more than to be examined in a single way, and if it is incorrect it deserves to be led ad absurdum; and that can done in no better way than by exploring the consequences to which it leads. So perhaps at least from this point of view, the following investigation can provide some benefit. Therein the task is treated to determine the preferred form of the fundamental equations of mechanics, which take the place of the usual Newtonian equations of motion of a free mass point:

$m{\ddot {x}}=X,\ m{\ddot {y}}=Y,\ m{\ddot {z}}=Z,$

2)

when the relativity principle should have general validity.

According to this principle, those simple equations are only valid for a stationary point $({\dot {x}}=0,\ {\dot {y}}=0,\ {\dot {z}}=0)$. For a finite velocity of the point:

$q={\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}+{\dot {z}}^{2}}}$

3)

they need an extension. However, for arbitrary values of q one could, simply by definition, set the quantities X, Y, Z equal to the product of mass and acceleration, and denote them as the components of the moving force, as this indeed directly happens in many descriptions of mechanics. But then the moving force, as defined, would have no independent physical meaning, in particular,