charge and the Equivalence Principle

cosmik debris

Tom Roberts explained it like this:


"This really hinges on what one means by "radiation", and classically there are
two reasonable but different meanings:

A) a nonzero radiation term in the Lienard-Wiechert fields, which is
proportional to beta-dot, the charge's acceleration

B) a self-propagating disturbance in the electromagnetic field with E,
B, and v mutually orthogonal (v is the direction of propagation)

In addition, we also require radiation fields to be time dependent -- constant
fields are never considered to be radiation. (B) always satisfies this, but in
certain highly-symmetric situations, (A) can have a non-zero beta-dot term and
yet have constant fields and thus nothing we consider to be radiation.


In classical electrodynamics, the claim "any accelerated charge emits radiation"
refers to radiation(A), but is rather simplistic as it ignores the requirement
of time-dependent fields. Radiation(B) is, of course, the type in a light beam
or radio wave. A uniformly accelerated charge emits radiation(A) but not
radiation(B).

In classical electrodynamics, an observer co-accelerated and co-moving with a
uniformly accelerated charge will see constant E and B fields (from the symmetry
of the physical situation), so this observer will see no radiation of either
type. This is the situation that applies via the equivalence principle to a
charged particle sitting on the surface of the earth, observed by an observer on
the same surface.

In the above-referenced forum thread, someone claimed a dc current in a bent
wire is prevented from radiating by quantum effects. This is wrong, and in
classical electrodynamics that current has a non-zero beta-dot term in the L-W
fields, but it is constant in time and thus is not considered to be radiation.
(Nobody in that thread pointed out the two different meanings of "radiation",
and they got confused by puns.)"