Does the sub-electron exist?

(Millikan, Die Existenz eines Subelektrons? Ann. d. Phys. 1916, 50, p. 729.)

At the present time, the methods for determining the ratio of charge to mass, \(e/m\), and separately \(e\) and \(m\), may be brought up to twenty. Some of them (for example, electrolysis, the deflection of \(+\)- and \(-\)-rays in electric and magnetic fields) are direct; others (for example, the Zeeman effect, dispersion) must be classed as indirect. It should be noted that the dispersion method, by means of which many determinations have been made, generally speaking admits several solutions, and, for example, Lorentz’s measurements give for the dispersion constant

\[ a=\frac{Ne^2\lambda_0^2}{\pi mc^2} \]

a value 200 times smaller than that calculated theoretically.

Ehrenhaft, Millikan, and Ioffe use a specially developed method for determining the elementary electric charge in small metallic or other drops falling in an electric field and detaching free electrons from themselves under the influence of energy incident upon them (for the apparatus see, for example, A. Ioffe, Beobachtungen über den photoel. Elementareffekt, Sitzungsber. der Bayer. Akademie, 1913). But whereas Millikan and Ioffe obtained for the elementary quantum the value established earlier (\(ca.\ 4\cdot10^{-10}\) cgsk), Ehrenhaft, as the result of a similar investigation (Über die Quanten der Elektrizität. Der Nachweis von Elektrizitätsmengen, welche kleiner sind als das Elektron, Wien, 1914), arrives at a much smaller (20–30 times) value of the charge, \(e=1.4\text{–}2.8\cdot10^{-11}\) cgsk, which he calls a sub-electron. In the article named in the title, Millikan subjects Ehrenhaft’s conclusions to sharp criticism. He asserts that in all cases where the experiments do not produce any complications: 1) ions carry a charge equal to, or exactly a multiple of, the Elementarquantum \(4\cdot10^{-10}\) cgsk; 2) static charges retained by and separating from insulators or conductors obey the same rule; 3) the direct tearing off of a negative electron from a “particle” or a “drop” by the Millikan—Ehrenhaft—Ioffe method causes a change in charge equal to the charge of an ion in electrolysis. Millikan explains the deviations of the Elementarquantum from the normal value, which led Ehrenhaft to assert the existence of the sub-electron, by false assumptions concerning the density and spherical form of his particles. At present, in his opinion, there is no evidence for the existence of the sub-electron.

In any case, this question requires further investigations and the establishment of an exact constant for \(e\), especially in connection with the recent work in theoretical physics (although only for the question of the dependence of the electron mass on velocity; see, for example, Nasternak, “On the inconsistency of Einstein’s principle of relativity,” Izv. Ross. Akademii nauk, 1918, Nos. 2–3).

V. V. Ilyin