Translation:H.A. Lorentz: Electromagnetic Phenomena

by Richard Gans

H.A. Lorentz: Electromagnetic phenomena in a system moving with any velocity smaller than that of light. (Versl. K. Ak. van Wet. 12, p. 986-1009. 1904)

The following is not explained by the original electron theory of Lorentz: 1. That Earth's motion has no influence on the interference of light (Michelson and Morley). 2. That no angular momentum acts upon a charged plate condenser (Trouton and Noble).

The first fact was explained by the new hypothesis of FitzGerald and Lorentz, namely, that the dimensions of solid bodies are getting slightly smaller in the direction of Earth's motion.

3. This hypothesis requires double refraction of light in isotropic bodies due to Earth's motion; the experiments gave a negative result (Lord Rayleigh, Brace).

To remove these contradictions, the author makes the following considerations:

If the electromagnetic system experiences a constant velocity $w$ in the direction of the $x$-axis, and if $c$ is the speed of light, furthermore if we set

${\frac {c^{2}}{c^{2}-w^{2}}}=k^{2},$

and are mapping this space by the transformation $x'=kx,\ y'=y,\ z'=z$, and are introducing instead of time $t$, the "local time"

$t'={\frac {t}{k}}-{\frac {kwx}{c^{2}}}$,

then we obtain, when we introduce slightly different vectors ${\mathfrak {d}}'$ and ${\mathfrak {h}}'$ instead of the electric and magnetic field strength ${\mathfrak {d}}$ and ${\mathfrak {h}}$, equations in the moving system (transformed by mapping) which are as exactly formed as the Lorentzian equations in the originally resting system. From that if follows, that the field (${\mathfrak {d}}'$, ${\mathfrak {h}}'$) is strictly equal to the field in the resting system at corresponding points, i.e., no influence of motion of any order can be found in the electrostatic or optic field. The ponderomotive forces in unit volume, however, suffer a small change corresponding to the volume change, it is

$f'_{x}=f_{x}\qquad f'_{y}={\frac {f_{y}}{k}}\qquad f'_{z}={\frac {f_{z}}{k}},$

where the primed letters apply to the moving system.

This transformation leads to the hypothesis, that the dimensions of electrons are changed by the previously given transformation in the same way as the space, however, the charge of corresponding volume elements stays the same.

Furthermore, also non-electric (for example elastic) forces shall experience the same change by the translation, as previously the ponderomotive forces of electric origin.

From that if follows, that a body in equilibrium by the attractions and repulsions of its inner forces, by itself changes its dimensions by the motion, because if the resulting force in the resting system is 0 (thus in equilibrium), then it is 0 in the moving transformed system (thus in equilibrium).

So, the interference experiment of Michelson and Morley is explained, furthermore that of Trouton and Noble on the angular momentum of a charged plate condenser, and also the unsuccessful double refraction experiments by Lord Rayleigh and Brace, because the theorem (already given earlier by the author up to magnitudes of second order) that brightness, darkness, and rays in the resting system, correspond to brightness, darkness, and rays in the moving transformed system, strictly applies to terms of all orders by the current transformation.

The formulas for the electromagnetic mass are changing in consequence of the oblateness of the electrons, however, they represent Kaufmann's experiment on Bequerel rays with satisfying precision as shown by detailed number calculations.

Gans

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