Translation:The Translation of Deformable Electrons and the Theorem of Conservation of Angular Momentum

The Translation of Deformable Electrons and the Theorem of Conservation of Angular Momentum  (1907)
by Paul Ehrenfest, translated from German by Wikisource

The Translation of Deformable Electrons and the Theorem of Conservation of Angular Momentum.

by Paul Ehrenfest.

Abraham alluded to the fact, that for a (rigid) non-spherical electron, uniform translation cannot take place into all directions in a force-free manner. For example, if a rigid, homogeneously charged electron having the shape of an ellipsoid of three axes, shall execute an uniform translation inclined to its major axes, then a torque stemming from external forces must compensate the torque exerted by the field of the moving electron upon the electron itself.[1]

Certain reservations against the ordinary definition and calculation of the apparent mass of deformable electrons are causing me to present the following remark, on whose solution the more accurate formulation of those reservations is depending.

Lorentzian relativity-electrodynamics, in the form as it was formulated by Einstein[2], is quite generally seen as a closed system.[3] Accordingly, it must give in a pure deductive manner the answer to the question, which we obtain by transferring Abraham's problem from the rigid to the deformable electron: Provided that there exists a deformable electron, having any non-spherical and non -ellipsoid shape when at rest.[4] 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.[5]