Modern electroweak theory, which unifies the electromagnetic and weak-nuclear forces, says that electrons are actually have no mass at all at energies of 100 GeV or higher .At these energies, the vacuum itself takes on a different energy state and this causes the symmetry between electromagnetism and weak forces to break down. Electrons get their rest mass from the interaction of the massless electron field with the Higgs field in the vacuum. String theory says that electrons have no internal structure until you get to Planck Energies of 1019 GeV where their string-like characteristics become obvious. So, an electron is basically a 'knot' of energy in the electromagnetic field, and the field itself is produced by the emission and absorption of virtual particles from 'within' the electron itself.
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This answer was updated in 2011.
See my books:
The Astronomy Cafe (1998) and
Back to the Astronomy Cafe (2003) for more FAQs in printed form. Author: Dr. Sten Odenwald, Copyright 2011
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