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A bit on NonSymmetrical Metrics.



 
 
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  #1  
Old March 28th 08 posted to sci.physics.relativity
Ken S. Tucker
external usenet poster
 
Posts: 7,341
Default A bit on NonSymmetrical Metrics.

(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
Ads
  #2  
Old March 29th 08 posted to sci.physics.relativity
xxein[_2_]
external usenet poster
 
Posts: 422
Default A bit on NonSymmetrical Metrics.

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 symetrical fashion that can reproduce -1.
  #3  
Old March 29th 08 posted to sci.physics.relativity
Eric Gisse
external usenet poster
 
Posts: 16,782
Default A bit on NonSymmetrical Metrics.

On Mar 28, 10:32*am, "Ken S. Tucker" wrote:

[...]

You never actually answer questions. You are the USNET squid - when
confronted, you blow **** everywhere and attempt to run away from the
issue.

As is pointed out to you every time you bring this issue up: A
NONSYMMETRIC METRIC DOES NOT MAKE PHYSICAL SENSE.
  #4  
Old March 29th 08 posted to sci.physics.relativity
Edward Green
external usenet poster
 
Posts: 3,336
Default A bit on NonSymmetrical Metrics.

On Mar 28, 10:30*pm, Eric Gisse wrote:
On Mar 28, 10:32*am, "Ken S. Tucker" wrote:

[...]

You never actually answer questions. You are the USNET squid - when
confronted, you blow **** everywhere and attempt to run away from the
issue.

As is pointed out to you every time you bring this issue up: A
NONSYMMETRIC METRIC DOES NOT MAKE PHYSICAL SENSE.


If you can stand it, and I don't mean this rhetorically, ur... why?

IIRC, focussing on the 3-stress, a non-symmetric 3-stress implies a
body-torque. Body torques are a bit bothersome if we imagine them as
truly infinitesimal in extent, but we've already discussed several
cases where they might make sense (actually, we've discussed body-
angular momenta, but that directly suggest we also allow body torques
to change 'em).

I'm not sure that a magnetic field applied to a region with free
electrons -- where the electrons are below resolution (I guess I may
mean a plasma) might not be modeled as a body torque: the electrons
all spin up into small orbits, and definitely acquire angular
momentum. Am I missing something?

Then again, if we put propeller blades on my famous distribution of
pebbles, and blow over them...

[I'm not defending anything Ken Tucker might have written, but I'm
independently interested in this issue... and have spilled a lot of
bits over it].
  #5  
Old March 29th 08 posted to sci.physics.relativity
Edward Green
external usenet poster
 
Posts: 3,336
Default A bit on NonSymmetrical Metrics.

On Mar 28, 10:30*pm, Eric Gisse wrote:
On Mar 28, 10:32*am, "Ken S. Tucker" wrote:

[...]

You never actually answer questions. You are the USNET squid - when
confronted, you blow **** everywhere and attempt to run away from the
issue.

As is pointed out to you every time you bring this issue up: A
NONSYMMETRIC METRIC DOES NOT MAKE PHYSICAL SENSE.


Oops... I read that as "antisymmetric stress/energy tensor" (that's
two read-o's). sigh.

But perhaps you can answer my question anyway. Thanks.

Hmm... say x1,x2 were spatial coordinates, and g^12 /= g^21 . Then
tangent vectors (a,b,..) and (b,a,..) and not the same magnitude.
Weird, but there is lots of weird stuff out there.

Now let's decompose g into symmetric and antisymmetric parts. The
antisymmetric contribution to |x|^2 is now flipped by -1 between
(a,b,..) and (b,a,..). Perhaps that implies, contrary to assumption,
that they are not both spatial, but one is time like, the other space
like. And now what happens when we mix in the symmetric part? They
are mixed in character? Partially comprised of null vectors?
  #6  
Old March 29th 08 posted to sci.physics.relativity
Ken S. Tucker
external usenet poster
 
Posts: 7,341
Default A bit on NonSymmetrical Metrics.

Hi Xxein

On Mar 28, 5:41 pm, xxein 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 symetrical 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

  #7  
Old March 30th 08 posted to sci.physics.relativity
xxein[_2_]
external usenet poster
 
Posts: 422
Default A bit on NonSymmetrical Metrics.

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.



  #8  
Old March 30th 08 posted to sci.physics.relativity
JimJast
external usenet poster
 
Posts: 9
Default A bit on NonSymmetrical Metrics.

On 30 Mar, 05:44, xxein wrote:
[...]
So let's start with gravity. *We don't know what it is! *
[...]

I had an impression that Einstein have aready found out (almost 100
years ago) and we are just finding the places where he was not precise
enough mathematically, and slowly fixing these places. As e.g. his
notion of "gravitational energy". Now, thanks to Landau, we know it is
just mc^2 since (d/dx)(mc^2)=-(gravitational force), which Einstein
might have also known as it is a direct result of his theory (see
Landau and Lif****z, Theory of Fields, around p. 285).

So why you still don't know what gravity is? What is so mysterious
about it? What is what you don't know? Why don't you ask someone who
knows? Which might be true for most people in sci.physics.relativity
even those (like trully yours) who was banned from it for asking why
this group believes that energy can be created which was apparently
(according to Jonh Baez) established already by the members of this
group and so it couldn't be discussed any more here. But questions
about gravity are probably still most welcome.
  #9  
Old March 30th 08 posted to sci.physics.relativity
xxein[_2_]
external usenet poster
 
Posts: 422
Default A bit on NonSymmetrical Metrics.

On Mar 30, 5:17*am, JimJast wrote:
On 30 Mar, wrote: [...]
So let's start with gravity. *We don't know what it is! *
[...]


I had an impression that Einstein have aready found out (almost 100
years ago) and we are just finding the places where he was not precise
enough mathematically, and slowly fixing these places. As e.g. his
notion of "gravitational energy". Now, thanks to Landau, we know it is
just mc^2 since (d/dx)(mc^2)=-(gravitational force), which Einstein
might have also known as it is a direct result of his theory (see
Landau and Lif****z, Theory of Fields, around p. 285).

So why you still don't know what gravity is? What is so mysterious
about it? What is what you don't know? Why don't you ask someone who
knows? Which might be true for most people in sci.physics.relativity
even those (like trully yours) who was banned from it for asking why
this group believes that energy can be created which was apparently
(according to Jonh Baez) established already by the members of this
group and so it couldn't be discussed any more here. But questions
about gravity are probably still most welcome.


xxein: You almost nailed it with "energy can be created". It is
harvested.

How can an atom exist without falling apart in the orbital clouds that
would presumably fly off in a straight direction? It perpetually
gains enough energy to keep the orbits in tow.

Another way of looking at it is simply to say that gravity represents
energy. A flow, an exchange. What initiates this flow? Is there a
drain/sink to which this energy flows? This is where I think that
atoms require harvested energy to exist. But this is also the
question that quantum theories refuse to consider.

According to cosmological theories, there is a vast amount of energy
that resides in the so-called "empty" space. Relativity also defines
it as a field. So what is it exactly? The energy is there, but why
does it act the way it does (both expansion and gravity)?

Run out of gas and push your car. You use/waste energy. Why? If you
did not push your car, there is energy saved. To where? From where?
Yeah, I know the box of Wheaties has energy. Where did that come
from? We could say the sun. Where did that energy come from? And so
we can go all the way back to 'a' big bang (maybe in a hierarchy).

But what it means is that energy was released from a rather small
structure that was already gravitationally bound. So? How did it
form the present universe? Something about energy (and an imperfect
outflow) allows it to sort of coagulate into what we call mass.
Various theories try to explain this behavior, but nonetheless it
happens.

Would the same thing happen with another BB? Presumably there was a
gravity, but what about the other structural forces like e, w and s?
Would they be replicated?

Still, gravity remains as a function that provides both a genesis and
remains in the aftermath. And so describing it as a mathematical
function does not do it a justice at all.

Repeating over and over again "what is gravity and how does it work"
is not answerable in the present-day physics. It is glossed over by
our theories and just accepted as a function to be described by a
mathematic.

What can cause the energy to move contrarily to expansion? How does
an atom exist? What IS gravity?

I don't expect you to have an answer. I expect you to have a question.
  #10  
Old March 31st 08 posted to sci.physics.relativity
Ken S. Tucker
external usenet poster
 
Posts: 7,341
Default A bit on NonSymmetrical Metrics.

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
 




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