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Algemeen Natuurkunde Colloquium 8 februari 2001
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The
electron's paradox reveals a new paradigm

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Martin van der Mark

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Philips Research Laboratories

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.

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