Re: Charge without rest mass

[EMAIL PROTECTED] (Imam Tashdid ul Alam) wrote in message news:<[EMAIL PROTECTED]>...
> "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
> 
> Err...probably the question was too basic for the folks. I think you
> have a point there.
> 
> To my (classical + naive) understanding, whenever there is a charge,
> and you try to accelerate it, you face what is called a "radiation
> resistance" or something like that.

That resistance is not always there. In fact if you accelerate the
charge uniformly, i.e. d^2x/dt^2 = constant, then the radiation
reaction vanishes.

> In every aspect it acts as the
> "mass" of the particle, and if I am not totally wrong, this "mass"
> depends on the charge, and perhaps proportional to it.

This does not hold for point particles. E.g. the energy in an electric
field is the work done in assembling the charges to create that field.
If is a result of sources which were not assembled then there is no
meaning to the energy of the field. One cannot assemble a point charge
so it is meaningless to think of the field having energy.
 
> This should answer your question. But probably the answer is wrong. It
> has been known for over a century that a point charge has infinite
> energy associated with it, and presumably an infinite radiation
> resistance as well. I don't know anything about what happened to the
> proposition.

Consider what the mass is of a two charge system.

First consider the electric field energy of two point particles which
carry a non-zero charge. When the particles are brought together the
work done is found in the change in the electric field. The total
field after they are brought together is

E = E1 + E2

The energy density, u, is proportional to E^2 so

u ~ E^2 = (E1 + E2)^2 = E1^2 + E^2 + 2E1*E2

The change in the field energy is due to the interaction term 2E1*E2.
If you integrate 2E1*E2 over all space then you'll find that it has
the value kq1*q2/r where q1 and q2 are the values of the charges and r
is the distance between the charges. The mass of the two particle
system is then

m = m1 + m2 + kq1*q2/r

So, as usual, the change in mass of the system equals the work done on
the system.

Pmb