Page:Zur Elektrodynamik bewegter Systeme I.djvu/6

Therefore, in the stationary state they do not depend on the translation at all, and with respect to radiation processes only in so far, as for every point a corresponding displacement of time takes place: the "local time" $t_{1}$ replaces the "general" quantity of time $t_{0}$.

Equations (C') were derived by us from the modified theory of electrons, which was recently given by Lorentz, to adapt them to the results of the experiments. These equations are now completely identical to those, which follow from my general equations for the special case of uniform velocity, which is treated here. They can be found in my treatise "On the Equations of the Electromagnetic Field for Moving Bodies"^[1] under (B₂) (C₃). When they are compared, it is only to be noticed that (with respect to the denotations employed there) we actually presupposed: $\mu =\mu _{0}$, $K=0$, and we have arbitrarily written:

$\sigma ,\ 1-\eta ,\ 1,\ 1,\ w$

instead of

$\lambda ,\ \epsilon ,\ \epsilon _{0},\ \mu _{0},\ p.$

§ 3. However, the interpretation of these equations by Lorentz and by me is different. In the case of Lorentz, is is about the representation of the two field strengths $E$ and $H$ as functions of $xyzt$ that define location and time. This is done by (L₁) and (L₂). The system, to which these equations apply, has the following properties: is is deformed in consequence of the motion in agreement with (2); it simultaneously changes its dynamical properties in agreement with the unified meaning of equations (2) (3) (4); it becomes anisotropic in the sense of a crystal of one axis, as it is indicated by equations (L'₃). In order to vividly present the electrodynamics of this system, the substitutions (L₃) and (L₄) were introduced. The $x_{0}\dots t_{0}$ are mere calculation quantities at the moment. However, at the same time they have a simple physical meaning. According to (2), $x_{0}\ y_{0}\ z_{0}$ are those measuring numbers being read at an "initially correct" measuring-rod (initially = when at rest), after it was introduced into the system and was accordingly deformed. And according to (2) (3) (4), $t_{0}\!$ are those time intervals indicated by an "initially correctly ticking" clock, after it was inserted into the system and accordingly has changed its rate.

In my view of equations (C'), the quantities E, M mean the field strengths, $x_{0}\dots t_{0}$ true coordinates and true times. They are identical with the measured coordinates and times. The moving

1. Göttinger Nachrichten 1901, Heft 1; also Ann. der Physik 7, p. 29. 1902. (Mainly already in Arch. Neerland. (2) 5, p. 516, 1900.)