the electron; a pure electromagnetic foundation of the mechanics of the electron, and by that also of mechanics at all, would be proven to be impossible if new measurements should demonstrate the validity of Lorentz's theory. This conclusion would of course still be valid, when instead of the work of an unknown inner energy of the electron, an also unknown universal external pressure (following Poincaré's[1] proposal) would by introduced, which provides the necessary compression work on the electron.
Besides that of Abraham, also a third fundamental hypothesis on the electron is free from this difficulty, which was introduced[2] by Bucherer[3]; he assumes that the electron is deformed at constant volume, namely in a way, so that the ratio of axis of the emerging ellipsoid always agrees with the so called "Heaviside ellipsoid"[4]. Since the same ratio of axis also applies to Lorentz's electron, one can derive the equations given by Bucherer for mass, energy, and momentum of the electron, without further ado from the ones of Lorentz, when one introduces, instead of the invariable transverse diameter of the electron that occurs as a parameter in the equations of Lorentz, a transverse diameter depending on the velocity, so to be measured that the volume of the ellipsoid is equal to the original sphere. When differentiating with respect to velocity – when calculating the longitudinal mass – then also the variability of the transverse dimensions must of course be considered too.
Although it is immediately clear due to the unambiguity of the reasoning of Lorentz and Einstein, that Bucherer's electron cannot strictly remove the influences of the absolute velocity,
- ↑ H. Poincaré, Compt. rend. 140. p. 1504. 1905.
- ↑ I was informed by M. Abraham by letter, that the deformation-work with respect to Bucherer's electron is equal to zero.
- ↑ A. Bucherer, Math. Einführung in d. Elektronentheorie p. 53. Leipzig 1904.
- ↑ i.e., that , where .
