Mach's Principle, intertia, and radiation reaction

From: Blake Winter (blake.winter_at_houghton.edu)
Date: 10/25/04 

Date: Mon, 25 Oct 2004 13:09:51 +0000 (UTC)

I've been reading about various explanations for Mach's principle and
inertia, and a lot of them referred to the radiation reaction problem.
 I read that this problem entails some difficulty with conservation
laws unless treated very carefully, and so on. I also read that
Mach's principle is usually thought to only work along spacelike
hypersurfaces or else to be due to some time-symmetric
"Wheeler-Feynman" effect.
However, I was thinking, if I remember correctly Thirring and Lense
showed that rotational inertia could result from a spinning shell of
matter around the object (e.g. the distant stars, approximated as a
spinning shell). If this is so, then could we not describe an object
which is initially not rotating, then starts to rotate, then stops
again also by describing the "outer shell" suddenly starting to spin
at some previous time, and stopping again, in such a way as to have
the spinning perceived by the object at the same time as we claim he
starts spinning, and stopping in the same manner? This would not
involve the interaction going over the spacelike hypersurface but
rather be a result of a "previous" acceleration of the matter shell,
followed by a "previous" stopping of it. Likewise, couldn't we
describe linear acceleration as being equivalent to having a large
matter field all about suddenly start accelerating and then stop again
(but of course, the field would have to start sometime in the past, so
that its effects reached the object at the same time as we claim it
started accelerating)?
And couldn't a similar effect be responsible for the electromagnetic
radiation reaction problem? Of course, it would react a lot less,
because there are two types of EM charge which mostly cancel, but
would still leave some small net field due to nonuniformity in the
distribution of positive and negative charge.