The reality of charge

[Leigh Palmer <palmer@SFU.CA>]

At 12:40 PM -0700 8/5/99, Jim Green wrote:
> At 11:20 PM 8/4/99 -0700, Leigh wrote:
> > I have a small quibble with Jim which I will raise here. Jim said
> > charge doesn't flow; I disagree. I can make a propellor which
> > measures the passage of charge, a loop which exploits Ampere's law
> > to measure DC current.
>
> I acknowledge that any discrepancy between me an Leigh is only a
> quibble:  In the case of "heat" and "energy" we agree.
>
> Leigh, let us have a short sidebar:  You can detect the flow of charged
> _particles_  these particles have the _property_ of "charge", but you can't
> measure "pure charge" in deed there is no such thing -- just as there is no
> such thing as "pure energy" or "pure mass" or "pure  blue" (unless you find
> one of those ancient bottles of bluing in the laundry aisle in the grocery
> store -- the stuff my mother used to use in the wash)

It is not the case that I can detect charge flow (or charge itself)
only if it is attached to particles. My detectors detect the charge
itself directly; there is no operational distinction between a flow
of, say, positrons and a flow of protons. My detectors are insensitive
to such differences; they react only to charge, or in the case of
electric current in a conductor, to the flow thereof.

> You can't have a "property" without a "system" to exhibit the property.

Electrical charge is localizeable operationally by Gauss's Law. You
can tell how much charge you have within a given closed surface by
performing a measurement of the normal component of the electric
field over the surface. Charge is locally conserved.

Energy, for another example, cannot be localized. For that reason
it is locally conserved only within a model. For example, if one
considers a system two gravitating particles in eccentric orbits
about their common focus, one can write the system energy in terms
of two kinetic energy terms and a gravitational potential energy
term. In doing so it is appealing to localize the kinetic energy of
each body in the body itself, and to divide the potential energy
between the particles, perhaps in direct proportion to their
masses. This division will result in the total energy localized in
each mass remaining constant as the bodies orbit; energy is
manifestly locally conserved.

The reason for the apportionment of the potential energy as I did
it was solely to achieve the goal of having a local conservation of
energy. Any other division will result in energy having to be
instantaneously (in the nonrelativistic sense) transferred from one
body to the other. This can be got around in the same way as it is
done in electromagnetism, of course, by putting some or all of the
potential energy in the field. If one does that one acknowledges
the nonlocalizability of energy!

Localizing a deficiency of something (gravitational field energy is
negative) is, I suppose, conceptually possible. I wonder what
gravitational mass density distribution, rho, might appropriately
be associated with negative gravitational field energy density u ?
                                                                g
                                    u
                                     g
                             rho = ----
                                     2
                                    c

Proper mass is real in my cosmology, by the way, but I know of no
instances of negative mass. Eh?

> And now to beat the list with this again:  the idea of "energy" can only
> make sense as it is a property of a system:  it can not exist, move, or
> flow, by itself.
>
> And, Leigh, in the same light, I don't have a meaning for "charge flow"
> unless there is a "charged particle" which moves.

When it comes to flow I will invoke my flowmeter criterion. I can
measure charge flow independent of any other system parameters.

Leigh