Particle Theory (QED electrons)
Date: Around 1993
I was wondering if anybody has come up with some proposed models
for the electron that are renormalized and compatible with Quantum
Electrodynamics. In QED, the electron can not be thought of as a spheroid
with an evenly distributed charge because it should then repel and explode.
According to the inverse square law, the formula for charge rests on the
phrase 1/r. As it turns out when all is said and done, the QED electron model
has no radius to boast, and an infinite energy. Also, is it possible that in
same fashion a photon (being a boson) has no rest mass, an electron (being a
fermion), has no , shall we say, "rest radius"? Note the difference in
angular momentum in each family. Might this relate to the"hidden" information
in each case (volume for the fermions and mass for the bosons)?
Basically the standard model regards all the elementary particles
as point particles (i.e. with infinite energy in principle, if the electric
field energy is really included). This is clearly unsatisfactory. Note that
it does not have much to do with spin, though - for example a proton has spin
1/2, but it is a composite particle containing 3 quarks, and so the protons
really does have a certain radius. But, electrons really do behave as point
particles down to the length scales they have been tested on (fractions of the
size of a proton, anyway, and orders of magnitude less than the "classical"
radius of an electron in which its mass arises from its electrostatic energy).
The string theories are intended as a way to depart from the pointparticle
model, not that they do not have problems of their own. But some of them
actually do end up getting rid of the infinities in QED - at least in
principle. No one has actually gotten as far as deriving QED from string
theory (at least that I am aware of) - but in principle the electron would
then be modeled by these strings, with certain kinds of vibrations on the
string. Of course, all sorts of other theories can be imagined - it is really
an open question, but unfortunately one that no experiments are likely to
address for many years.
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Update: June 2012