A Critical Analysis of the Classical Experiments on the Relativistic Variation of Electron Mass
Abstract
In the course of a previous mathematical analysis of an improved method for the determination of the ratio em it was suggested that the generally accepted interpretations of the classical experiments of Bucherer and of Neumann might be subject to serious limitations. A similar analysis for the unmodified BuchererNeumann experiment is therefore carried out in the present paper. By this means it is discovered that Neumann's supposed velocity filter, even for the case of negligible scattering of electrons along the condenser plates, must have been completely broken down on the high velocity side, for values of β>0.7 and that, even for the lower velocities observed, the resolution width was approximately as great as that equivalent to the whole relativistic mass effect. Besides, it is found from this analysis that, with a certain choice of geometrical constants, a very poor resolving power may be concealed by spurious focusing effectsand that it was just this choice that Neumann, by trial, found it necessary to make in order to obtain sharp lines. It is also seen that, when the filter is open on the high velocity side, one may still obtain an apparent line, which may be considerably shifted from the position predicted by the simple theory, and which in extreme cases may form the edge of a heavily fogged region extending inward to the central zero line corresponding to β=1. This fogging can actually be seen very clearly in Neumann's photographs for β=0.8. Further, a consideration of the possible effect of scattering on such experiments shows that, when the resolving power is very near the critical limit at which the filter breaks down, the probability of leakage of high velocity scattered electrons through the filter becomes relatively large, especially when the spectrum of the source is distributed largely amongst velocities above that to be observed. Under these latter circumstances it is suggested that one might obtain seriously shifted lines, and even mistake for the expected line a spurious maximum due to the source distribution itself. Since the interpretations of Bucherer and of Neumann are based on such doubtful premises, a short discussion is given of other similar experiments designed to distinguish between the Abraham and the Lorentz electrons. So far as is known to the authors, it appears that, at least for the higher velocities, no very satisfactory experimental distinction between the two types of electron has as yet been made by direct electric and magnetic deflection methods. In view of the fundamental importance of such experiments it seems that much is left to be desired.
 Publication:

Physical Review
 Pub Date:
 April 1938
 DOI:
 10.1103/PhysRev.53.511
 Bibcode:
 1938PhRv...53..511Z