Page:Das Relativitätsprinzip und seine Anwendung.djvu/13

as long as only current ${\mathfrak {C}}$ exists; i.e. an observer $A$ will declare the body as charged, while it is uncharged for an observer $B$ moving relative to him. This can be understood when it is considered, that positive and negative electrons of same amount are present in every body, which compensate themselves at uncharged bodies. If the body is moving with velocity ${\mathfrak {w}}$, then (when a conduction current is present) both kinds of electrons will obtain different total velocities, thus also the quantity $\omega =a-b{\tfrac {{\mathfrak {v}}_{z}}{c}}$ will have different values for both kinds. Now, if an observer $B$ which is moving with the body, is calculating the average of charge density ${\overline {\varrho '}}={\overline {\omega \varrho }}$ for both kinds of electrons, then he can obtain the sum zero, even when for an observer $A$ (in whose reference system the body is moving) the averages ${\bar {\varrho }}$ of the positive and negative electrons are not compensating themselves.

This circumstance causes a reminiscence of an old question. Around the year 1880, there was a great discussion among physicists concerning Clausius' fundamental law of electrodynamics. At that time, it was tried to derive a contradiction between this law and the observations by concluding that according to this law, a current-carrying conductor on earth shall exert an action upon a co-moving charge $e$ due to Earth's motion, which could possibly be detected. That the law actually doesn't require this action, was noticed by Budde; it stems from the fact, that the current is acting upon itself due to Earth's motion, and is causing a "compensation charge" upon the traversed conductor, which exactly compensates the first action. The theory of electron leads to similar conclusions, and I find for the density of the compensation charge, when the velocity has the direction of the $z$-axis,

${\frac {1}{c^{2}}}{\mathfrak {w}}_{z}{\mathfrak {C}}_{z}$;

this must be assumed as existent by an observer $A$ who doesn't share the motion with Earth, while it doesn't exist for a co-moving observer $B$. The given value exactly agrees with the formula derived from the relativity principle; if $\varrho '_{l}=0$, then one finds from this formula

$\varrho _{l}={\frac {b}{ac}}{\mathfrak {C}}_{z}{,}$

and since ${\mathfrak {w}}_{z}={\frac {bc}{a}}$ is the mutual velocity of both reference systems according to the things previously said (p. 75), then one indeed finds

$\varrho _{l}={\frac {1}{c^{2}}}{\mathfrak {w}}_{z}{\mathfrak {C}}_{z}.$