sci.physics.electromag

On Mar 12, 11:05=A0pm, Timo Nieminen wrote:
> On Sun, 9 Mar 2008, maxwell wrote:
> > Although Lorenz and Maxwell both ended up with
> > similar mathematical FIELD-like equations they were very different
> > physics theories, as E. T. Whittaker pointed out. =A0Lorenz had a causal=

> > SOURCE theory that generated potentials AT the receiving charges.
> > Maxwell had no sources (charge density was a later Helmholtzian style
> > add-in) and his FIELDS were defined EVERYWHERE throughout ALL of
> > space. =A0Yes, Maxwell could derive his fields from potentials like
> > Lorenz but Lorenz's potentials were retarded (hence causal); Maxwell's
> > were not - in fact, he only developed a magnetic theory and just
> > imported Coulomb's electrostatics to make it an ELECTRO-magnetic
> > theory. =A0Of course, this brings in the Coulomb (or Maxwell gauge) with=

> > its instantaneous changes in potential everywhere.
>
> The joy of gauge invariance! (Btw, Jackson's paper on the history of gauge=

> invariance is worth reading [J. D. Jackson and L. B. Okun, Rev Mod Phys
> 73, 663-680, 2001].)
>
> Which brings us to another part of the discussion: is the electromagnetic
> potential "real" in a physical sense? (I intended "field" in the thread
> title in the more general sense of field, including the potential(s), not
> just E,D,H,B.)
>
> Aharonov-Bohm would suggest that, yes, the potential is real. Lorenz's
> potential would be an ideal candidate for the "real" potential. I've just
> read one of Carpenter's papers on electrodynamics taught in terms of
> potentials rather than the conventional EM fields. Using the potential
> gives a very different picture of where the energy is (again, this is the
> ambiguity that results from the Lagrangian+Noether conservation laws only
> telling us _total_ quantities, not densities). Alas, the paper only dealt
> with static/DC current cases.
>
> --
> Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
> E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
> Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html
Now you're getting it, Timo. The Lorenz potential is not a continuous
function (so it's not differentiable - although Lorenz thought it was)
but it does reflect the asynchronous transfer of momentum (and thus
energy) between the two electrons (true action-at-a-distance).
Noether and Lagrange are only valid for continuous interactions, as
everyone has assumed (which is why no one has ever solved the
classical two particle EM problem).
Yes, I would recommend Jackson & Okun's paper to everyone who is
interested in EM - it corrects a gross historical injustice made by
Maxwell against Lorenz.
I would also strongly recommend all of John Carpenter's papers on EM.
JC is a GOM who has spent his life trying to get people to look at
charges & potentials, but then he is an EE so he is plugged into the
real world & not the platonic world that physics has become since it
got hijacked by the mathematicians, who KNOW that reality is only
mathematical ("ideal forms", remember?).