A suggested experiment to measure part of the transverse electromagnetic mass of the electron

Abstract

The changes in self energy of a non-relativistic charged particle are calculated where such changes are due to confinement of the charge within conducting plates. This confinement will alter the mode structure of the virtual photons involved in the transverse self-energy calculation: it will lead to a reduction in the number of modes at the long wavelength limit and, where the modes have a wavelength comparable to the distance, L , between the plates, the normal integrals over virtual momenta are replaced by sums over the integers describing the modes. It is found that mass changes of 1 part in 10 10 can be induced by plate separations of the order of 1 mm. It is suggested that such relative mass shifts could be measured by the use of high precision atomic beam techniques, such as those used in ‘atomic clocks'. The atomic beam would be directed between two closely spaced parallel conducting plates (or through long cylindrical tubes) located between the oscillating fields used to excite a transition between the hyperfine structure levels. The mass change will be reflected in frequency shifts of the h. f. s. separation of the same order as the mass change. With a high precision cesium beam apparatus, such as those at the National Bureau of Standards, it should be possible to demonstrate not only that changes do indeed occur but also obtain a quantitative estimate of such effects as a function of the plate separation, L . It is predicted that the frequency shifts will be inversely proportional to L .