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[Physltest] [Phys-L] Re: accelerating charge



Carl E. Mungan wrote:

A stationary charge in a gravitational field does not radiate. (That
would be a source of free energy.) But if a uniformly accelerated
charge radiates, then what of the equivalence principle?

An early suggestion in Feynman's Lecture on Gravitation is that a
uniformly accelerated charge does not radiate because the actual
formula for radiated power goes as the first * third derivative of
position (rather than second * second as follows from an integration
by parts), and the third derivative of position is zero for the
special case of uniform acceleration. To put it another way, the work
done against the radiation reaction force is zero for this case.

An alternative and more popular resolution however is that of D.G.
Boulware, "Radiation from a uniformly accelerated charge," Ann. Phys.
124:169 (1980) who argues that uniformly accelerated charges do
radiate, but that cannot be seen by a co-accelerating observer, ie.
the form of a radiation field is relative (observer dependent).

An opposing recent view is that of S. Parrott, "Radiation from a
uniformly accelerated charge and the equivalence principle,"
arXiv:gr-qc/9303025 (2004) who argues not only that a uniformly
accelerated charge radiates, but that that radiation should be
experimentally observable. He therefore feels the equivalence
principle does not hold for electric charges, and claims that doesn't
violate any known mathematical result or physical observation.

I looked at Parrott's article
http://arxiv.org/abs/gr-qc/9303025
and I'm very favorably impressed. The thinking and the writing
are remarkably clear. In particular he patiently and carefully
defines what he means by
-- energy
-- radiation
-- pseudo-energy
et cetera.

I disagree with Carl's description of the work. Parrot shows
that previous alleged proofs that a uniformly accelerated
charge does not radiate are defective, resting on questionable,
previously-unstated assumptions. But he recognizes that
that's not the same as a proof that it does radiate. As he
says on page 29, at some point it comes down to a matter of
definition. Energy (as he defines it) is radiated, while
pseudo-energy is not. The question of which of these is
relevant can be settled by experiment, but the experiment
has not been done and is not easily doable.

Parrott judges it to be _unlikely_ that pseudo-energy is the
relevant quantity, and FWIW I agree.

I really like the fact that Parrott's formalism is general
enough to handle alternative assumptions, thereby making
clear the connection between particular assumptions and
particular results.

BTW you can't have it both ways; either the charge radiates
or it doesn't. This isn't like some "parallel postulate"
that can be freely assumed one way or the other. As Parrott
says, either the rocket runs out of fuel or it doesn't.

=========================

I remind people that the main uncertainty concerns the rather
peculiar case of long (perhaps infinitely long) uniform
rectilinear acceleration.

In contrast, for the case of bounded motion, such as a
charge freely falling in orbit around a planet, it's
entirely clear that there *is* radiation. So a freely-falling
frame is really not the same as an unaccelerated frame.

Some on this list have suggested that it is important to
protect Einstein's equivalence principle, and for this
reason and/or others, they prefer a radiation law that
depends on
(x dot)*(x dot dot) [1]
rather than
(x dot dot)^2. [2]
since [1] vanishes for uniform rectilnear acceleration.

But let me quickly point out that [1] has problems of its
own. It protects Einstein's principle of equivalence, at
the cost of violating Galileo's principle of relativity!
A Galilean change in velocity will change x dot. In
particular, will be some frame in which x dot is zero,
but in other frames it will be nonzero.

Given the choice, my opinion is that it is more important
to keep the laws of physics independent of velocity,
rather than keeping them independent of acceleration.
I can't prove I'm right about this, but I doubt anyone
will prove me wrong anytime soon.

Again, note that for bounded motion, [1] and [2] are
identical, as various people have mentioned.

It is amusing that there could exist such a simple physics
question for which no cut-and-dried answer is known. But
I suspect whenever you have two formulas that differ by an
integration by parts, you can create some kind of mystery
by pushing the boundary terms into the far past and future.
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