sci.physics.electromag

Not a specific comment on any single post, but a general comment on the
reality of EM fields.

Part the First
==============

The standard introduction of electric fields into physics teaching is
pretty much as an auxiliary mathematical device. The usual procedure is to
start with Coulomb's law (i.e., F = k q1 q2 / r^2) as the fundamental law,
and to then split this into E=kq/r^2 and F=Eq, apparently for some
non-obvious convenience. At this point, the student may well doubt the
existence of fields in any "real" sense - interaction between charges is
the fundamental element.

On the other hand, magnetic fields might be introduced as the fundamental
magnetic entity, being easily visualisable with iron filings, etc.
However, the mathematisation of magnetism typically comes much later, so
this doesn't seem to have much impact on the teaching of and perception by
students of electric fields. There's the further question of whether to
introduce the concept of magnetic charge.

Anyway, at this point, electric fields have little reality for the
student.

More significant for the reality of fields in teaching is the introduction
of Gauss's law, perhaps in a first-year university introductory/general
physics course. If fields are just a mathematical convenience, at this
point they become a tremendously convenient convenience, replacing rather
difficult integration over a source distribution with a very simple 3-line
procedure. For simple geometries, of course, but the integration over
source distribution is also for simple geometries.

But this still doesn't mean that fields really exist. One can still take
Coulomb's law as the absolute fundamental law, at this point in education.

However, Coulomb's law is _not_ a fundamental law - it's only a special
case. Gauss's law gives Coulomb's law for a special case, that of a
stationary spherically symmetric charge distribution. If the charges
within the Gaussian surface are moving, or have moved, E is not
necessarily perpendicular to the Gaussian surface, if the the charge
distribution is currently spherically symmetric.

Part the Second
===============

The retardation of electromagnetic effects presents a direct challenge to
the view of electromagnetism as solely an interaction between charges and
currents, with fields merely as a mathematical auxiliary. This is
especially the case for radiation.

Charge/current distribution radiates, and loses energy, momentum, and
angular momentum. This has immediate local effects - the kinetic energy
gained by charges is less than the work done by the accelerating force,
there are reaction forces and torques. Sometime later, the radiation can
be absorbed elsewhere, with the absorber gaining (a portion of) the
energy, momentum, and angular momentum.

We have some possible choices:

(a) Throw away our conservation laws.

The problem with this is that conservation laws are very useful, and
describe much of observed reality very well. For example, Newton's laws of
motion are an indirect statement of the conservation of momentum. This
choice pretty much involves throwing almost all of theoretical physics
into the bin. Given that all, or at least almost all, of theoretical
physics is known or suspected to not be ultimately correct, this, in
itself, is not necessarily a problem. But the various approximate or
probably approximate theories making up theoretical physics are useful,
accurate within their regimes of applicability, and discarding them - with
no available replacement - just because one doesn't believe that fields
are "real" doesn't look like a very productive path.

The conservation laws are on a much stronger foundation than any of the
individual theories.

(b) Assume the field carries the energy, momentum, and angular momentum
from one place to another.

This is the simple and direct solution that retains our conservation laws.
We have two paths to follow. Firstly, there is Poynting 1884 (or Heaviside
1884), where it is assumed that the field carries the energy and momentum,
and the energy and momentum fluxes and densities are found from the power
and force applied to a charge by the field. This is the usual derivation
for the Poynting vector and momentum flux given in textbooks (e.g.,
Jackson). Secondly, we can go along the route of Lagrangian field theory +
Noether's theorem and out pop the conservation laws (also in Jackson).

Following the standard methods in the two cases, one obtains different
results for the angular momentum density, and can obtain different results
for the momentum density. Fun! However, I think these are nice educational
features rather than fundamental problems.

What is a fundamental problem is the failure to deal with the apparently
point-like electron. Even if the electron radius is finite, it's too small
for the classical theory to work. If the radius is zero, the resulting
infinite energy (and infinite inertia) is theoretically problematic.

What is better/worse: discarding our conservation laws, or infinite
self-energy that isn't observed? The latter puts the problem into the
specific theories concerned, keeping the possibly-fundamental concervation
laws intact. The former discards the conservation laws in order to avoid
difficulties in a theory known to not be strictly correct.

(c) Revise our idea of conservation laws.

Feynman-Wheeler electrodynamics, anyone? No self-interaction, so not
infinite self-energy. Conservation laws still included, but via light-like
connections rather than at all times.

Part the Third
==============

When asking "Are fields real?", perhaps we should ask just what fields are
we talking about. We have two distict formulations, in terms of the field
vectors in the usual Maxwell equations (or the antisymmetric 4x4 field
tensor), and in terms of potentials.

Given that any expression in terms of E and B can be readily converted
into one in terms of potentials, there's no difficulty in coming up with
energy, momentum, and angular momentum densities in terms of potentials
(indeed, a common criticism aimed at the usual Lagrange+Noether result for
electromagnetic spin (ExA) is that the potential appears in it).

Interesting to note that many who are quite insistent that EM fields
(i.e., E and B) are real are equally insistent that the potentials are not
real in the same sense. However, we can note that if the potentials are
real, then E and B are real too, as derivatives of the potentials.

Part the Fourth
===============

As a final historical note, we can note that the first two successful
electromagnetic theories of light came as field theories, not as theories
of interaction-at-a-distance, despite the larger effort that went into
IAAD theories. We have Maxwell's theory, converted into a E,B,D,H-only
theory in its later Hertz-Heaviside revisions, and Lorenz's theory, with
potentials only (in the Lorenz gauge, of course).

Later, we have the introduction of other field theories, such as quantum
mechanics, which seem to work well. Very relevant is QED, based as it is
on the supposed reality of EM fields. How can we have photons, EM field
quanta, if fields are not real?

While fields introduce some problems into physics, I believe they resolve
more than they introduce. The mathematical convenience is immense. Whether
they are "real" or not, they are certainly useful. The only stance that is
certain to be properly aligned with reality is agnosticism wrt the reality
of fields or otherwise. However, I'd say that, on balance, it's reasonable
to assume that fields exist. This opinion may well be coloured by the
practical engineering usefulness of assuming that they exist.

--
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