The primary reason that the electron is considered to be elementary is that experimentally it appears to be point-like, and hence structureless, down to length scales below 10-18 meter. At the same time, it has a rich set of properties that are fundamental to its nature. It has an elementary charge, a half-integral spin, a definite mass, a well defined magnetic dipole moment, an anomalous spin factor g-2 and of course a wave-particle nature.
Since a point cannot have such properties as spin or a dipole moment, the electron must have extent or structure of some kind. Also, the electron's charge should cause it to fly apart, unless some internal binding forces are present. By comparing the energy contained in the electron's Coulomb field to the electron mass, a lower limit on the electron size can be found to be of the order of 10-15 meter, the so-called classical electron radius. On the face of it, this appears to contradict the experimental observation that shows that it is less than 10-18 meter.
In this talk I will present the idea of a simple semi-classical model of a photon confined in periodic boundary conditions of one wavelength, which seems to have electron-like properties and to be able to deal with the problems stated above. The model indicates that both topology and the non-commutativity of rotations in 3-space and space-time must play an essential role in any theory supporting it. The following attempt has been made.
Guided by the Einstein condition for a purely electromagnetic particle and using a geometric Dirac algebra, a set of non-linear equations can be found, which are an extension to Maxwell's equations and incorporate a generalised Lorentz force. As well as the known solutions to the source-free Maxwell equations these equations appear to allow new dynamical solutions with non-zero charge density. These new solutions correspond to electrically charged toroidal vortices.