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*

- ↑ M. Abraham, Ann. d. Phys. 10. p. 174. 1903; see also Theorie der Elektrizität 2. p. 170 — 173. In the case of motion, the forces exerted upon each other by the volume elements of the electron, are not directed any more in the direction of the connecting line. Thus every element-couple provides a torque. Only in the case of translation parallel to the major axes, the whole torque is zero due to symmetry.
- ↑ A. Einstein, Ann. d. Phys. 18. p. 639. 1905.
- ↑ See especially W. Kaufmann, Ann. d. Phys. 19. p. 487 and 20. p. 639. 1906.