Re: Gravitational Field


physicsboy wrote:
Ken S. Tucker wrote:
physicsboy wrote:
That's not quite a paradox, but cheating. :-) The discrepancy
is a thin gap in the reassembly.
http://www.ics.uci.edu/~eppstein/junkyard/rect.html
shows the dissection, about a third of the way down.

I am always very careful when I use Geometry to "prove" any claim,
theory, etc. Geometry is founded on many assumptions. Geometric axioms
are built upon certain "truths" that we have come to accept as
"self-evident" but have never been realitiscally proven.

I find many of your posts stimulating, and as a geometry
student, I'd find an example of a "self-evident truth" welcome.

Usually everything is proven using surveying methods that
today rely on lasers and even when extended to GR such
as the deflection of light rays, use their course to chart a
gravitational field that is distinctly different from Newtons,
and proves to be a triumph of modern applications of
non-euclidian geometry in a real experimental test.

Regards
Ken


Thank you. I will give you an example of an assumption made in
non-eucledian geometry. The assumption of Maximal Symmetry is one of
the biggest one that comes to mind.

I think "Maximal Symmetry" (MS) uses *conditions* of
isotropy, homogenity and continuity imposed upon
a non-euclidian geometry and then deduces the
results of that, in that well defined framework,
((that's not "self evident truth")).

One noteable result of the application of "MS"
is in Weinberg's "Grav & Cosmo" Eq.(13.4.11).

f,w =0 ,

implies all norms (scalar invariants) vary incrementally,
and therefore discontinuously, and has been well verified
by testing the Quantum Theory, that also predicts the
same thing.

Regards
Ken S. Tucker

.

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