Re: Charge without rest mass

"Lord Snooty" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> There are no known particles that have zero rest mass and finite charge.
> Is there any fundamental reason known why such particles cannot exist?
> 
> -Andrew

The answer it would appear is unknown. It is possibly untrue (if a
massless charge were someday detected); or true as a mere accident
(like a boundary condition.) Theoreticians want very much to find deep
connections and they are sometimes right.

An almost facetious arguement against them is that: if you boost a
massive charge to near the speed of light, then the Gaussian volume
that in part determines the charge is Lorentz contracted to zero.
Integrating a charge density through a zero gaussian volume would give
zero charge. However one could surround a light pulse with a gaussian
surface for a little while. During that time why couldn't the gaussian
suface register a non zero charge?

Electric and magnetic field lines are supposed to be either unending
or begin and end on charges. This is not exactly true. Integrating the
electric field intensity over a gaussian surface gives the charge
contained, so it is really only 2-D area's worth of field lines that
begin and end on charges. Consider the electric field of two identical
positive point charges. Midway on the line between the charges there
is a point where the total electric field vanishes. At this point the
field lines along the line between the charges stop. So we have a
point's worth of field lines stopping and no negative charge. Consider
the electric field around this "stagnation" point. Here, perpendicular
to the line between the charges, is a plane that separates the field
lines that begin on one charge from the field lines that begin on the
other. The field lines that fill this plane originate in a ring around
the "stagnation point". So here is a line's worth of field beginning
and there is no positive charge at the "stagnation point".

Looking at Maxwell's equations; F = dA, d*F = *J. We see that forcing
the electromagnetic field F to have a global vector potential A
eliminates magnetic charges. Raising the observation of no massless
charges to a principle, would require modifying Maxwell's equations
for radiation. The usual source free equations F = dA, d*F = 0, permit
*F to be closed and not exact. Just this feature permits an area's
worth of field lines to begin or end and gives the charged black holes
their charges. A closed *F that was not exact could give rise to a
topological electric charge that travelled at light speed. Just as the
global vector potential A eliminates magnetic monopoles, a similiar
global potential B eliminates any massless electric charges. Raising
the observation of no massless charges to a principle, requires
splitting Maxwell's equations into F = dA and d*F = *J for matter with
rest frames or *F = dB for masslesss matter with no rest frame.

There are profound differences between matter with a rest frame and
radiation that has no rest frame. Any theory such as the Einstein-de
Broglie relations (E = hf, p = h/lambda) that applies to both is very
deep and rests on what is the same about the two types of matter. The
desire by theoreticians to unify matter would cause most to argue that
splitting Maxwell's equations was not justified. However if such a
splitting could lead to new experimental findings, one would be forced
to concede it. Unfortunately looking for massless charges is like
looking for magnetic monopoles, in that just because you haven't found
one, doesn't mean they don't exist. It is also different in that
finding a magnetic monopole requires modifying Maxwell's equations
while finding a massless charge requires no modifiction. It is only
the impossibility of finding a massless charge that requires modifying
Maxwell's equations.

Fermi observed a long time ago that the half life for radioactive
decay meant that radioactive matter carried a clock. Since all clocks
have rest frames, all radioactive matter must have a rest frame. A
"clock" boosted to light speed would never tick and so masslees matter
cannot be radioactive. If all charges were radioactive, then there
could be no massless charges. Although recent theories have suggested
that the proton is unstable, a finite half life has yet to be
observed.