The electromagnetic field due to a uniformly and rigidly electrified sphere in spinless accelerated motion and its mechanical reaction on the sphere—I

Abstract

1—It is well known that the Quantum Theory has failed to account for many nuclear phenomena, particularly those connected with the emission and absorption of β particles, e. g. , their passage through considerable thickness of lead in spite of radiation damping. This failure can fairly be attributed to faulty methods in classical electrodynamics, on which quantum mechanical methods have been largely based by alanlogy. In an attempt made some years ago to explain the continuous β-ray spectrum on the basis of classical electrodynamics, I was confronted by the difficulty that the so-called radiation pressure on a fast, electron, which I wished to take into account in a second approximation, actually turned out to be greater than the supposedly principal term of the mechanical reaction of the electromagnetic field—the term which accounts for the electromagnetic momentum and mass. Thus the usual hypothesis of quasi-stationary motion, on which this kind of approximation is based, broke down completely near the nucleus, where the acceleration of the β-particle was very large, so that it became necessary to search for a more powerful method than the classical one of determining the mechanical reaction on an accelerated electron due to its motions, own field, if possible one which will avoid all expansions or other approximations, or at least defer them to a late stage of the investigation when investigation we need a new method of calculating the electromagnetic field of moving electrified system with as few restrictions as practicable; such a one an be based on a recent investigation of my own, which makes it possible to determine it exactly for a uniformly and rigidly electrified sphere moving in any manner, subject only to the restriction that its speed must be always less than that of light, the usual Lorentzian expressions for the potentials being assumed. It may be objected that so specialized a system is unlikely to satisfy the requirements of atomic theory as a representation of the particles postulated in it; whilst this objection must be admitted, it is more important for our purpose to treat one such system, however artificial it may be, rigorously and completely than a more general one only approximately with the aid of additional simplificatory hypotheses of doubtful validity, such as the quasi-stationary hypothesis employed in classical electrodynamics. The sphere in question admits of rigorous and complete treatment, and so far it is the only system that I have found to do so, although I hope to extend some of the results obtained for it to other systems by applying the Lorentz transformation. We may expect that the exact solutions found for it with an unrestricted motion will prove useful in illustrating, qualitatively at least, the behaviour of electrified systems in general. This expectation has already been justified by the discovery that this particular system possesses periodic orbits of comparatively small dimensions, whose frequencies are integral multiples of a fundamental frequency peculiar to the sphere, but which are otherwise unrestricted as to form and mode of description and posses a static distant, field, so that they do not lose energy irreversibly by radiation. This behaviour—no radiation in spit of often large acceleration—has been unsuspected hitherto and contradicts the generally accepted conclusions of classical electrodynamics. Some more new results of this kind will be found in Paper II of this series.