Classical Electron Model Research Articles

Electromagnetic mass, relativity, and the Kaufmann experiments

This paper presents the theoretical background for and the detailed analysis of Kaufmann’s 1901–1905 experiments to determine the e/m ratio for fast electrons. Far from providing the first experimental confirmation of Einstein’s special theory of relativity, as is often claimed in physics textbooks today, these data were initially interpreted as confirming Abraham’s classical model of a rigid spherical electron and as providing evidence against special relativity. Only in 1906–1907, upon Planck’s subsequent reanalysis of Kaufmann’s 1905 data, did these experiments become evidence marginally in favor of relativity over classical models of the electron. This particular issue, of the superiority of special realtivity over classical theory in providing a fit to e/m determinations, was not definitely settled until 1914 with new extensive and accurate data obtained by Neumann. The entire episode provides another example that science does not proceed by a strict falsificationist methodology. It shows rather that a great scientist such as Einstein at times gives more weight to a theory that has a certain beauty and produces equations simple in form than he does to experimental results that apparently conflict with such a theory.

When can a classical electron accelerate without radiating?

A classical point electron radiates when it accelerates. However, there are classical electron models with extended charge distributions which can accelerate and/or deform without radiating. Can a model be contrived that will undergo radiationless motion while accelerating (on the average) over a distance large compared to its size? The answer is no: we prove that the “center” of the electron is always closer than the electron “diameter” to a fictitious point undergoing constant-velocity motion, if the electron's motion is radiationless.

Canonical formalism and relativistic invariance of the Grossman-Peres classical electron model

The Grossman — Peres classical electron model is not explicitly a relativistic invariant. The relativistic invariance of the Grossman — Peres model is proved in this paper by the direct construction of Poincare-group generators from integrals of the motion of the model under consideration. The generators found afford the possibility of obtaining also an expression for the 4-vector of coordinate-time.

Pion-muon mass ratio and classical electron models

At present, one regards the muon and electron as closely related particles because of their quantum electrodynamie and leptonie similarities. In contrast to this very reasonable view, this note will describe a model in which the pion and muon are treated as closely related particles, while the ordinary electron is left to a future development of the theory. The pion-muon model is based part ly on the classical Lorentz electron, but certain ambiguities involved in compensating the self-stress are utilized to introduee nonclassical ideas. The basic advantages of the model are the simplicity with which it resolves the charged pion-muon mass ratio, utilizes isospin in the eompensation mechanism, introduces the neutral pion, and admits of possible extrapolation to other particles. We recall the standard noneovariant expressions for the transformation of the energy and momentmn of the Lorentz electron, with the understanding that the divergent electrostatic self-energy in the rest frame has been cut off, and the finite quantity is denoted by U0, then with c = 1, we have

Explicit Representation of the Transformation Property of Physical Quantity of Dirac Electron with the Hyperbolic Metric of Velocity

This paper aims, in the theory of Dirac electron, at the deliberate use of the hyperbolic metric of velocity, the effectiveness of which Smorodinski1 has recently emphasized in rela­ tivity. The metric of velocity is fully used together w~th a proper spin direction vector, to represent explicitly spinor cf; and vector, tensor, etc., of cf;* (matrix) cf;, of free Dirac electron. The 3-vector polarization operator is confirmed to correspond to the proper spin vector. For the electron in a square well potential, cf; is a product of hyperbolic function of the metric with trigonometric or the Bessel function, etc., and the metric turns out to be imaginary or complex in the case of the bound state or free negative energy state. A classical model of Dirac electron is established concretely by obtaining simple time derivatives of the metric and spin vector, from the covariant equations of a spinning particle under general fields, suggested by Frenkel, Kramers and others. The so-called Thomas factor 1/2 is brought inevitably in the equation of the spin vector itself, regardless of the time average motion. These explicit representations may facilitate the visualization of Dirac electron.

Chemical Shifts in C5H5 − and C7H7 + Ions: the Free Electron Model

IN an earlier communication1, the classical free electron model proposed by Pople2 was modified and successfully applied to the description of the nuclear resonance spectra of hydrocarbons containing six-membered aromatic rings. It was then noted that results on a five-membered aromatic ring did not appear to be in good agreement with this theory. We now wish to report complete data on the aromatic systems C5H5 − and C7H7 + (cyclopentadienide ion and tropylium ion, respectively), and to compare them with theoretical expectations. The aromaticity of these two species is generally accepted3–5.

A new model of classical electron

The theory we developed in this paper appears to be interesting as it overcomes some typical difficulties of the preceding ones by Lorentz and Dirac. For these reasons our formalism is able to give a consistent classical model of electron.