Tom Roberts wrote on Fri, 06 Jun 2008 04:15:46 -0500:
Juan R. González-Ãlvarez wrote:
Tom Roberts wrote on Thu, 05 Jun 2008 04:40:03 -0500:
Let me repeat that: there is no ambiguity whatsoever in taking the
gradient at point P and time T, because the potential was evaluated at
time T for every point within the spatial neighborhood of P. In
particular, properties of the source are evaluated only in an
infinitesimal neighborhood of the retarded time T-R(T)/c.
There exists difficulties to evaluate the E field derived from L&W
potentials. This is revised with mathematical detail (just details you
ignore) in
Necessity of simultaneous co-existence of instantaneous and retarded
interactions in classical electrodynamics. 1999: Int. J. of Mod. Phys.
A 14(24), 3789. Chubykalo, Andrew E; Vlaev, Stoyan J.
So you claim. But an examination of that paper shows that nowhere does
it evaluate any source parameter EXCEPT AT THE RETARDED TIME. There is
no "instantaneous interaction" in that paper except in the title. Their
claims, and thus your claims, are not supported by this paper.
But it was done clear then that you did not understand the paper.
Try to learn why they wrote "Necessity of simultaneous co-existence of
instantaneous and retarded interactions in classical electrodynamics" and
why interactions are *not* retarded.
[... further elaboration and references]
I may find time to look at them. But the fact that your first reference
does not support your claims makes me less inclined to spend the time
and effort.
Authors supported their claims with a *rigorous* mathematical analysis,
which you completely ignore.
They proved you are wrong but of course you will continue to say they are
not right whereas you will be *unable* to write a rebuttal paper showing
they really did mistake.
It is also fine you decide to ignore the rest of references. That may be
how science works according to *you* :-)
In GR itself, without approximation, there is no general
Green's-function method to solve the field equation, because it is
nonlinear.
Next is the standard solution to the field equation in *full*
(nonlinear) GR obtained using *Green methods*
h^ab = 4 Int (\tau / r) d^3x
where the source, of course, is evaluated using the past light cone.
You'll have to explain what this means. A reference would help. But I
don't see how an integral can possibly represent a solution to nonlinear
differential equations -- an integral inherently superimposes values
from different sources, and the field equation of GR does not have such
superposition.
Ha ha ha ha ha :-)
Well, above equation is completely standard, well-known, and explained in
many textbooks and papers on GR.
Astronomers as TvF solve it when testing GR, but a self-claimed expertise
as you may perfectly ignore that minor point :-)
Is it possible that like TVF you are confusing an approximation to GR
with GR itself?
It would be possible except by a small detail you igno
"Above equation is an exact solution to full nonlinear field GR equations"
Learn some GR Tom :-)
(next misunderstandings sniped)
Weinberg's section on PPN is indeed an APPROXIMATION.
Read i have really said Tom.
Yes, astronomers use approximations to GR that involve potentials -- the
full theory is too difficult to compute their physical situation(s). So
what? This does not affect the theory itself (which I remind you is what
I was discussing here).
The *full* theory of GR never has been tested Tom. Its main principles as
existence of a dynamical and generally curved spacetime never has been
tested. And the speed of gravity never has been measured Tom.
Your castle is all in the air :-)
Once more again, Tom, *you* confound the field formulation with the
geometrical formulation.
I have said nothing whatsoever about the "field formulation". But if it
is indeed EQUIVALENT to GR, then what I have said about GR applies to
it. If it is not truly equivalent to GR than it is something else, and I
am not discussing it at all.
The geometric and the field formulation are equivalent for many tests
astronomers have worked. But and this is the part you ignore forever they
have tested gravitation *using the field formulation*.
Or you do *not* read TvF?
I also recommend you that would go to next Conference
http://ppc08.astro.spbu.ru/sci_program.html#S_IV
where astronomers will be discussing some novel observational tests
differentiating geometric for the field formulation.
My last knowledge on that topic is that the field formulation is favored
over the geometric one.
(more ad hominem snipped)
--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org