Re: Radiation reaction for a uniformly accelerated charge
- From: "Ken S. Tucker" <dynamics@xxxxxxxxxxxx>
- Date: Wed, 22 Feb 2006 00:47:13 +0000 (UTC)
Re: Radiation reaction for a uniformly accelerated charge
Dear Mr. Parrott
Re: Your original post.
I follow Edward Purcell on the problem of radiation.
In his book "Electricity and Magnetism", pg 8 ,
"The only way we have of detecting and measuring
electric charges is by observing the interaction of
charged bodies".
That implies radiation requires an interaction of charges,
since radiation reveals the presence of charge(s).
In simplistic terms, that would require an electrical
potential energy p= -a*b/r such as an electron with
charge "a" in a relatively +Electric nuclear field with charge
"b" to reduce energy by emitting a photon, with a reduction
in radius "r". In an advanced treatment using Quantum
Theory that observation is spectral.
It appears to me an underlying civil war has been waging
where the Equivalence Principle and GR is applied to
Lorentz Force (LF).
In AE's classical GR1916 treatment (Dover Principle
of Relativity pg 155, Eqs. 65, 66), requires the LF to
vanish, in the statement kappa_sigma=0.
That is in accord with the GR requirement that no
absolute acceleration (ergo force) is invariant, IOW's
a Frame of Reference (FoR) may be found where the
acceleration is zero, such as choosing the particle
apparently being accelerated as the FoR.
((The context following AE's Eq.66 is somewhat
ambiguous, I quote "if kappa_sigma vanishes",
but then relies on that for the needed conservation
of energy and momentum in GR, and then steers
us back to the energy components of the g-field
in Eq.(56))),
That is embodied in the absolute derivative of the
4-velocity in the equation,
DU^u /ds =0
and leads easily to the geodesic equation.
Moving forward, Tolman in "Relativity Thermodynamics...
(Eq.103.1,2 ) and Weinberg in "Grav&Cosmo" Eq.(5.1.11)
set forth a variation to AE's original treatment, by setting
an absolute acceleration caused by the LF "f^u"
DU^u/ds = f^u / m ,
to produce what appears to be an absolute acceleration.
So I think the question becomes, is the LF an absolute
and invariant force as Tolman and Weinberg imply or
does it vanish as AE implies?
I think this is an important consideration to understand
GR and EM relations, and QT, so what follows is my
reasoning. Given the fracture of thought dividing Nobel
prize winners (Einstein & Weinberg) we should be very
careful.
First I dismiss Tolman's and Weinberg's geodesic
solutions since their mass "m" was added by hand,
into the geodesic equation without regard to a
2 body solution that is rather more sophisicated than
the intention of the geodesic (actually equations of motion)
in AE's 1916 Eq.(45), just after stating "the equation of
motion of a point". "Point" was specified.
That's important because in a Lorentz force situation,
we have the masses of the relating charged particles
and the stored energy in the EM-field that is ultimately the
source of photonic energy emissions, that's not a simple
"point".
As you may recall, classical EM theory allows charged
particles to spiral inwards by continuously reducing the
radius and continuously transmitting energy. That means
a charge may move in the direction "V" in the electric field
"E" to provide a continuous force "f" such as
f = q*E dot V ,
following the LF,
f_0 = q*F_0i U^i
where E = F_01 and V = U^i.
However, following AE, we get, f_0 =0, in accord with
0 = q*E dot V,
meaning charge "q" cannot continuously vary it's energy
level, and that is physically in accord with QT.
((I term that GR conjecture a "quantum geodesic")).
In my personal opinion, I think Einstein was acutely aware
of the application of GR to the basis of the QT, I described
above in his GR1916 applied to LF and atomic orbitals.
My email is dynamiXs@xxxxxxxxxxxx , where X=>c.
Regards
Ken S. Tucker
.
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