Re: [Phys-L] consistency: 1/r^2 electrostatics, 1/r radiation field

[John Denker <jsd@av8n.com>]

On 11/16/2015 10:53 AM, Bob Sciamanda wrote:

> Go into an "oscillating frame" and look at the field of a charge
> which is stationary in some inertial frame. For JD this should be a
> simple transformation :>)))

That's an interesting suggestion.

Here's a modification that might be easier to visualize, and
easier to compute:  Start with a dipole at rest in some frame,
and then switch to a /rotating/ frame.  Techniques for dealing
with rotating frames are very well developed in the NMR business.

On 11/15/2015 01:32 PM, Moses Fayngold wrote:

> > a) Can we take the low-frequency limit of the radiation field
> >   and recover the Coulomb field?
> > b) Can we wiggle the Coulomb field and get the radiation field?
> > c) Or are they related in some other way? 
> >
> > The short answers are: (a) no, (b) no, and (c) yes
> >
> > The answers (a) and (b) become obvious from a very simple
> > observation: The Coulomb field is radial (pointing away from or to
> > the source), whereas the radiation field is perpendicular to its
> > propagation direction which is away from the source. The two fields
> > differ not only quantitatively, but also on the qualitative level,
> > so there is no continuous transition between them.

That's a good point.  I think I agree, but not everyone does.

This gets back to a point I made earlier, namely that I've seen
a lot of explanations that don't make sense to me.  In particular,
in almost all textbooks these days you see "spider diagrams" or
what I think of as I'itoi diagrams.  Here is an easily accessible
example:
  http://physics.weber.edu/schroeder/mrr/MRRtalk.html
Search for the word "passes" and look at the diagram that follows,
and perhaps also the pair of diagrams below that.

This is an explicit attempt to explain the radiation field in
terms of the Coulomb field ... plus some hand-waving.  Among
other things, it depicts (and purports to explain) a transverse
field in the "transition" region, where the radiation is.

This diagram has "some" nice features.  In particular:

++ The simple Coulomb description is correct in the bulk of the
 interior region and in the bulk of the exterior region.
++ The assertion that field lines cannot end in empty space is
 correct.

HOWEVER: 

-- "Fixing up" the field lines to handle the transition
 region requires gross violations of Coulomb's law.  Among other
 things, there is a ton of /curl/ in this region.
-- The implicit rule of "fixing up" the field lines by connecting
 them in the simplest, most direct way seems /not/ well founded
 in the laws of physics.  In particular, once you realize that we
 are going to have nonzero curl in the transition region, you can
 add /closed loops/ of E ... and it will take some very fancy
 hand-waving to convince me that the number of closed loops shown
 in the diagram (i.e. zero) is correct.
-- The "kinks" where the field lines enter and exit the transition
 region are unphysical.  They require infinite acceleration, and
 would radiate infinite energy ... not just infinite energy density,
 but infinite energy.
-- At large R, the Coulomb field should be negligible.  Whatever
 remains should fall off like 1/R and be purely transverse.  I 
 don't see how to make this happen using the diagrammatic 
 construction.

I have a hard time understanding why they worry about factors of
2/3 in the Larmor formula (equation 6 on the cited page), when
the whole construction is wrong by a factor of infinity.  Maybe
it's all OK and I'm just to dense to understand it, but let's
just say that they seem to be skipping a lot of steps.

So I leave this as an open issue.  I assume y'all have seen these
I'itoi diagrams a zillion times.  If somebody can explain how to
make sense of them, please share.