A bit on NonSymmetrical Metrics.

**Pmb[_2_]** · #11 March 31st 08 posted to sci.physics.relativity

"Ken S. Tucker" wrote in message
...
On Mar 29, 7:44 pm, xxein wrote:
On Mar 29, 1:22 am, "Ken S. Tucker" wrote:

HiXxein

On Mar 28, 5:41 wrote:

On Mar 28, 2:32 pm, "Ken S. Tucker" wrote:

(Ken posted this to SPF).

Hi Dr. Francis.
I was confused, perhaps still am.
My OP on NonSymmetric Christoffel's presumed that
the semantic "NonSymmetric metrics" was standard,
and understood. So I think I see now that the subject
is shifting to a definition of NS metrics.

Recent work on NS metrics, was done and published
by J.W.Moffat and his team, and is available in ArXiv.
I'll provide specific refs if you want.
(Incidentally, Dr. Moffat and his wife came to dinner at
our place, and we discussed the subject).

On Mar 26, 9:40 am, Oh No
wrote:

Thus spake Ken S. Tucker

Charles, if you think that's an "oxymoron" I'd like to know how
you
would define "charge" as a spacetime
invariant.

I think we are completely at cross purposes. I was thinking
solely of
how one defines a metric on a vector space with an inner product,
and
how one defines metric space in mathematics.

Semantics again, the inner product is an outer product
followed by a contraction, that's from chp7 of GR 1916
and it may be obsolete.
(That part of your post confused me too).

As it seems to me, if it
not symmetric, it is not a metric. That doesn't mean in might not
be a
useful or interesting idea, but if so it is wrongly named, and if
it is
wrongly named it will be difficult to communicate.

Ok, let's go to example, using g_uv = e_u dot e_v
with e_u being unitary basis vectors.

Let's use a phonograph record, and work g12 = e1.e2
at a point on the circumference.
(Contravariant/Covariant, are not important here).

(0) In this case the record is not rotating, a laser is
directed radially from the center of the record, being
in direction "e1" to said point, will be perpendicular to
a circumferential vector "e2", therefore g12 = e1.e2 =0.

(1) The record is now spun Clock-Wise (CW).
Due to the aberration of the laser relative to said
point the vector e1 projects onto the vector e2
with g12 = e1.e2 = velocity/c = v/c.

(-1) The record is now spun CCW.
Due to the aberration of the laser relative to said
point, the vector e1 projects onto the vector e2
in the opposite direction on the circumference of
the point compared to (1),
with g'12 = e1.e2 = -velocity/c = -v/c.

Using that data, g12 = -g'12
is a function of rotational direction provides,

g12 = (x1/r) (dx2/ds) - (dx2/r) (dx1/ds)

= (x/r) (dy/cdt) - (y/r) (dx/cdt) = -g21.

Physical proof can be found in this thread I
posted to SPF,
"Asymmetric metrics/Speed of Gravity".

And also in a current loop in the EM tensor
F12, wherein the reversal of current direction,
causes F21. The difference between F12 and
F21 is caused by direction of the rotation of
the current, ie. F12 = -F21 is a function of
rotation.

Regards
Charles Francis
http://www.teleconnection.info/rqg/MainIndex

Those are fairly straighforward examples, it can
become much more detailed, which I try to post
in the future.
Regards
Ken S. Tucker

xxein: As you know, I don't delve into math (much). The idea of a
"record" being created does imply an asymmetry. But "recorded" in
one
direction does not imply the reverse "playing" will be the direct
(symmetrical) opposite (as usually measured).

I understand the underlying point. It will occur with even a
phonograph needle. There is no way that the needle can follow
gravity
through the bumps in a symmetrical fashion that can reproduce -1.

Interesting lead, obviously you know about
these things, (probably more than I
do),http://en.wikipedia.org/wiki/Loudspeaker#Driver_design

By reversing the direction of current in the
voice coil, the speaker moves in and out, and
that effect is communicated via the spacetime
field with no mechanical linkage.

We have learned (at least we think we have)
that the effect of gravitation is transmitted
via the spacetime field curvature, without
mechanical linkage.

So it stands to reason that magnetic force is
communicated via the spacetime field.
That is consistent with the "speed of gravity".
Regards
Ken S. Tucker- Hide quoted text -

- Show quoted text -

xxein: I mean much more than that. Although the universe has no
sense of time (it just follows laws of causation), the cause itself is
a temporal event. When can it reverse and how? I don't think it can.

A set of circumstances is fleeting at best. If any laws were to
apply, they would act to different circumstances.

Short of some sort of perfectly reflecting boundary conditions (and
even with configured ones), you will have a hard time trying to put
the toothpaste back into the tube.

Yeah, we got atoms. But HUP. We got a solar system. Let's boost our
Earth orbit by 1 km/sec. and see what happens. Now reduce it back.
NOTHING of the solar system will reverse with it.

It is not about a feigned curvature. That's why I am x x ein
(stein). We apply false boundaries that allow us to subjectively
'see' a curvature. Without a math abstraction/extraction, the
curvature disappears. It will still have 'fields' of influence that
depend only on the present circumstance of where things are.

Math is a useful tool, don't get me wrong here. I use it all the
time. It is a good predictor for what we have put into it. But what
'have' we put into it? I may put something into it that is different
from yours. I understand why there appears to be a spacetime
curvature. I also understand that it is a mathematical artifact
brought about by boundary conditions. There are none in a strict
sense. They can change with circumstance.

Our present view of this universe is based only on our present view.
Despite supercolliders and telescopes, the present universe is still
modeled only by what we extract. If we get one thing wrong, the whole
barrel of apples is spoiled.

So let's start with gravity. We don't know what it is! While we say
that SR is fully compatible with Lorentz, it has a different
interpretation. GR attempts to be fully compatible with SR. We don't
know where we are without a math and the universe doesn't use it. But
we're getting closer.

We're getting closer with the aid of math. It is not the only tool at
our disposal, though. We have put a lot of subjective measurement
into a math and tried to extract some objectiveness. But not enough.
We tend to quit when it satisfies us. "Eat your hamburger and shut-
up" will satisfy a stomach.

Yeah. I know we do more. But we really haven't gotten into the
objective mode yet. We can't really think that way yet. Einstein was
a help, but in the long run a hindrance.

He perpetuates subjective measurement as the tool (math). While the
several new theories tend to go away from this they tend to do this by
radical means. Not bad in itself, but they seem to lose track of what
we DO measure. Quantum theories are an exception to this, but only
because they CAN measure. But still in the subjective mode, with
tighter boundaries and no gravity.

So, I do understand that GR provides the best explanation so far. But
we are not limited to any theory/model. The universe acts as it does
despite what we think about it.

That's why not knowing what gravity IS is the 'objective' stumbling
block. That's why exotic theories were invented, like strings. Deep
down, we are not satisfied with any theory and we know it. But a TOE
is impossible.

But we can do better than what we have. That's why I post. I can
give a better objective description of gravity. It is not formal and
you do not have to believe it. It's just here.

I walked into a meeting with the late Prof. Grueb of
the U of Toronto, he is a very strict mathematician.
He advised me (admonished is more like it) that
D g_uv=0 is a presupposed condition and is not
true in general.
Later I read the Principle of Equivalence (PoE), was
required to justify D g_uv =0, otherwise D g_uv=0
will not hold.

The PoE provides a ref, such that D g_uv=0, as in
freefall, commonly called "geodesical motion".

The up-shot is in a freely falling FoR the g_uv
are constant thus D g_uv =0 hold in that FoR.

From D g_uv=0 we also derive the common def of
the standard Christoffel symbol (connection), and
then get the geodesic from the absolute derivative
of the 4-velocity vanishing, ie, DU^u=0.

That, to me, is a very powerful explanation of the
conversion of the Principle of General Relativity
(PoGR) to the mathematical Theory of General
Relativity (ToGR), that are distinct.

The PoGR is philosphical, the ToGR is a symbolic
conversion of the PoGR into the ToGR.
That conversion is limited by our use and knowledge
of the theories of mathematics.

To me, going from PoGR to ToGR is like a transformer
inducing power from a primary coil to a secondary
coil.
In that conversion are nonsymmetrical relations.

In my view, I can set the origin of a CS on
to a charged particle, because it is subject
to the PoGR, and thus the physical laws of
nature. Therefore, the ToGR should apply to
that said particle, such that,

D g_uv =0 and DU^u=0

applies to FoR's with origins centered on
charged particles.

In conclusion, I think I can explain how
a transformer works!
Regards
Ken S. Tucker

Ken - I sent you an E-mail. Did you get it?

Pete

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