Page:Die Translation deformierbarer Elektronen und der Flächensatz.djvu/2

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-ellipsoid shape when at rest.^[1] When in uniform translation, then according to Einstein the electron undergoes the known Lorentz contraction. Now, is an uniform translation into every direction in a force-free manner for this electron possible, or not?

If it is not possible, then for the sake of the relativity principle, one has to exclude the existence of such electrons in favor of a new hypothesis; otherwise we indeed would possess by them an instrument to demonstrate absolute motion.

If it should be possible, then we would have to show as to how they can be derived from the Einsteinian system, without the use of totally new axioms.^[2]

(Received March 19, 1907.)

↑ See e.g. M. Planck, Verhandl. d. Deutsch. Physik. Gesellsch. Berlin 1906. p. 137: "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."
↑ If (in accordance with the relativity principle) a charged condenser shall have no torque when inclined with respect to Earth's motion, and if a discharging condenser moving with Earth shall have no recoil, then one must use the following hypothesis: that the molecular forces – produced by the charge of the condenser in the constituent parts holding the condenser plates away from each other – provide in both cases the corresponding back reactions. On the other hand, Abraham showed (Physik. Zeitschr. 5. p. 576. 1904; Theorie der Elektrizität 2. p. 205): When one calculates the longitudinal mass of the deformable electron in the usual manner, then one has to ascribe to the electron a non-electromagnetic energy of interior deformation forces, to maintain the energy theorem. Thus one could allow those non-electromagnetic forces (similarly to the molecular forces) to compensate the electromagnetic torque. So one would have given up the (pure electromagnetic) energy- and momentum conservations theorems, and would only maintain the center of gravity theorem. Yet it is only necessary to sacrifice the latter theorem too, as we already sacrificed the energy theorem – then we are able to define any desired apparent mass of the Lorentz electron, thus one can bring any measuring result in agreement with the relativity principle. (However, the value of zero for the apparent mass offers itself as the most simple one; like a macroscopic condenser shall obtain no increase of mass by a charge according to relativity theory.)

[1] See e.g. M. Planck, Verhandl. d. Deutsch. Physik. Gesellsch. Berlin 1906. p. 137: "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."

[2] If (in accordance with the relativity principle) a charged condenser shall have no torque when inclined with respect to Earth's motion, and if a discharging condenser moving with Earth shall have no recoil, then one must use the following hypothesis: that the molecular forces – produced by the charge of the condenser in the constituent parts holding the condenser plates away from each other – provide in both cases the corresponding back reactions. On the other hand, Abraham showed (Physik. Zeitschr. 5. p. 576. 1904; Theorie der Elektrizität 2. p. 205): When one calculates the longitudinal mass of the deformable electron in the usual manner, then one has to ascribe to the electron a non-electromagnetic energy of interior deformation forces, to maintain the energy theorem. Thus one could allow those non-electromagnetic forces (similarly to the molecular forces) to compensate the electromagnetic torque. So one would have given up the (pure electromagnetic) energy- and momentum conservations theorems, and would only maintain the center of gravity theorem. Yet it is only necessary to sacrifice the latter theorem too, as we already sacrificed the energy theorem – then we are able to define any desired apparent mass of the Lorentz electron, thus one can bring any measuring result in agreement with the relativity principle. (However, the value of zero for the apparent mass offers itself as the most simple one; like a macroscopic condenser shall obtain no increase of mass by a charge according to relativity theory.)

[1]

[2]