Re: Examining g0i

On Fri, 28 Sep 2007 15:23:38 -0700, "Ken S. Tucker"
<dynamics@xxxxxxxxxxxx> wrote:

On Sep 28, 2:55 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
Ken S. Tucker wrote:
On Sep 28, 12:00 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
Ken S. Tucker wrote:
The Kerr metric was thoughly studied
by us and was found to be too weakly
founded to be accepted by our theoretical
standards.
http://physics.trak4.com/MST_Kerr.pdf
Your opening statement is false -- it explicitly rejects rotating
coordinates.

No, it rejects a sense of rotation described
by "ds2", even if "g_ij" were nonsymmetrical.

Huh??? I have no idea how "ds2" might "describe" a rotation (though it
depends on any rotation of the coordinates used), and the metric
components {g_ij} are always symmetric (in GR, and in differential
geometry in general).

Ok, I'll presume you're ignorance is honest.
How do you figure the INVARIANT "ds2" depends
on the relative rotation of the CS?

You mean ds^2. Don't expect others to wade through your inability to
express yourself properly.


The summation using "dx^i dx^j" cancels the
spin, even if "g_ij" are antisymmetric.

The issue isn't any supposed antisymmetry in the {g_ij}, it is a
rotation of coordinates. Cartesian coordinates that rotate around z
relative to a locally inertial frame have g_0x and g_0y nonzero (and
equal to each other, and to g_x0 and g_y0). The summation over i and j
does not "cancel" the spin, if the coordinates are rotating.

Yeah it does, do the summation.
It's primitive.
((HINT: Magnetism is relative)).

Hint: You are wrong. The quantity {g_ij} is symmetric /by assumption/.
If you get an antisymmetric or even a non-symmetric metric, then you
are screwing up.

Furthermore, your magnetism example is irrelevant - the antisymmetry
brought on by the Faraday tensor is nuked by the way the stress-energy
tensor for electromagnetism is constructed.


By rejecting any metric with any nonzero g_0i (i=1,2,3), you reject ALL
rotating coordinates. As I said, that's unreasonable.

I rejected "g_0i" in the INVARIANT "ds2",

ds^2

I really do hope you understand that ds^2 is a squared infintesimal
displacement rather than 2*displacement.

whereas Kerr included the relative quantities
"g_0i" to affect the invariant. That's what we
call a "Logic Bomb", i.e. sub-standard theoretics.

Try not to insult what you don't understand [eg, GR], Ken.

Why don't you write down _exactly_ what Kerr assumed and write down
the words that go with it? Then we'll go from there.

Going through the Kerr derivation is something I'd like to do some
time, actually.


You also reject null coordinates, which are extremely
useful in describing some manifolds, such as those
containing only gravitational radiation.

Not sure what you mean, but g-waves appear as
EMR in alternative energies...

http://physics.trak4.com/GR_Charge_Couple.pdf

No, Ken. Gravitational waves are not the same thing as electromagnetic
radiation no matter how many times you spew your idiotic PDF.


We have no problem with rotation using a
2nd rank metric tensor,

I don't understand this -- the metric tensor is ALWAYS 2nd rank. And as
it is independent of coordinates, it is independent of any rotation of
coordinates.

IMO, the whole point of the 2nd rank metric
is to provide for rotations. That's where
Magnetism comes from, a spacetime field.

No, Ken. Wrong again.

The 10 independent quantities provided by the metric are the direction
cosines between the basis vectors.

Not only does the symmetry in those guarantee the symmetry of the
metric, but that's why it is a rank 2 tensor - a rank 2 tensor has the
exact amount of components required and transforms in the correct way.


but even allowing
that rejects the Kerr metric.

When you reject all rotating coordinates, you reject all rotating
systems. But you have not justified this rejection at all.

Explained above.

That's ISU compliant.
What do you mean by that?

A very short brief here,
http://physics.trak4.com/modern-spacetime.pdf

Regards
Ken S. Tucker
...
.

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