sci.physics.electromag

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. Lorenz 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. Yes, 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. Of 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
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