Page:Zur Elektrodynamik bewegter Systeme I.djvu/7

system is not deformed, doesn't possess a specific measure of time, and hasn't become isotropic by motion.

§ 4. The Lorentzian interpretation requires from us, to distinguish between measured lengths and times $x_{0}\dots t_{0}$ and true ones $x\dots t$. But it doesn't give us the means to solve the task experimentally - even under presupposition of ideal measuring instruments. The Lorentzian electrodynamics and mechanics is only developed for $w=const$. Thus we have no other means at all, than to measure the distances with "false" co-moving measuring sticks, and to measure times with "false ticking" co-moving clocks. In order to use "correct" ones, that is, stationary instruments for measurements with respect to our moving system, a mechanics and optics must be given to us, which not only applies to the two ranges $w=const.$ and $w=0$, but which passes from one to the other through the range of variable $w$. - For the time being, the only meaning for the "true" lengths and times $x\dots t$ lies entirely in the fact, that the electrodynamics of equations (L₁)(L₂) applies to it (simultaneously with mechanics), which finds its expression in the hypotheses 1, 2, 3. They cannot be defined by any independent experience.

Thus, concerning Lorentz and me, it's only about two different kinds of expressing the same facts: either by (L₁)(L₂) and mechanics of theorems 1, 2, 3 – or by (C') and ordinary mechanics. No imaginable observation can distinguish between the two systems of explanation.

§ 5. A generalization of equations (C') for the case of velocities arbitrarily distributed in space, is represented by my "equations of the electromagnetic field...". It replaces, without changing anything in addition, the first two of equations (C') by the following ones:^[1]

${\begin{cases}\int \limits _{\circ }{\mathsf {M}}_{s}ds={\frac {d}{dt}}\int \limits _{s}{\mathfrak {E}}_{N}dS+\int \limits _{s}\Lambda _{N}dS\\\int \limits _{\circ }{\mathsf {E}}_{s}ds=-{\frac {d}{dt}}\int \limits _{s}{\mathfrak {M}}_{n}dS\end{cases}}$

(C)

where $S$ is a surface fixed in matter, and $s$ denotes a boundary curve.

These equations give, applied to closed surfaces, the known "equations of continuity" of electricity and magnetism, and lead back to (C') when applied to non-deformable surfaces.

1. Comp. l.c. under (B).