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From: Ken S. Tucker on 27 Sep 2008 07:29
Hi Tom
You should review GR 1916 Chp 3, and learn
about "circumference and diameter" and the
meaning of "pi" in non-Euclidian geometry.

On Sep 26, 7:08 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> Ken S. Tucker wrote:
> > On Sep 24, 4:56 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> >> Ken S. Tucker wrote:
> >>> The fact of light deflection in a g-field proves the
> >>> vectors ExB=C are NOT orthogonal, because
> >>> they aren't perpendicular.
> >> No, it doesn't "prove" that they are not orthogonal. It is perfectly
> >> possible that E.B=0 at every point along the light ray's trajectory, and
> >> yet the light ray is deflected by the gravitation of a massive object,
> >> because of the curvature of spacetime. Indeed, this is precisely how GR
> >> models this: the E and B fields of a light ray ARE perpendicular (==
> >> orthogonal, == E.B=0), at EVERY point along the trajectory; and yet that
> >> trajectory is "deflected" by gravity.
>
> >> Hint: the "deflection" has nothing whatsoever to do with E or B or E.B
> >> or ExB. Hint2: ExB lies right along the trajectory at every point.
> >> Hint3: both "." and "x" involve the metric (here x = cross-product of
> >> 3-vectors).
>
> >> [There are subtle issues related to defining E and B
> >> that I ignore; they do not affect the conclusion. There
> >> are further subtleties related to 3-vectors and cross-
> >> products which also do not affect the conclusion.]
>
> > Ok, perhaps Tom you might provide us with your
> > understanding of how E.B=0 , E.C=0 , B.C=0 and
> > ExB=C, CxE=B , BxC=E in a GR g-field, in view
> > of the Shapiro Effect, the Deflection of light
> > and the "red-shift".
>
> [To make sense of this, I must assume C to be a UNIT 3-vector
> along the trajectory, and E and B to be UNIT 3-vectors along
> the corresponding field directions. In no other way can I
> reconcile units consistently. That's OK.]

Yes, that's agreeable.

> It's quite simple: E.B, E.C, B.C, ExB, CxE, BxC all involve the fields,
> tangent, and metric at a single point along the trajectory. They all
> have values as you say, at each and every point along the trajectory.
> The Shapiro effect, the deflection of light by a massive object, and the
> gravitational redshift of light are all NON-local phenomena -- the
> curvature of the manifold induces them all. But the curvature of the
> manifold does not affect its properties at a given point, which are what
> matters for those dot- and cross-products.

1) The off diagonal conponents of the metric
are used in the dot product.
2) The cross product uses *tensor densities*
(I recommend you review those).

> Simple example: Consider cylindrical coordinates {r,\phi,z}
> on E^3, and the circle r=R,z=0. Let E=d/dz, B=d/dr, and
> C=(1/R)*d/d\phi (all 3 are unit vectors). At each and every
> point of the circle, E.B=0, E.C=0, B.C=0, ExB=C, CxE=B,
> BxC=E. Yet the circle is "curved". Yes, this is not a
> geodesic path, but it illustrates the point that these 3
> vectors can be orthogonal at each point along a curved path.
>
> Exercise for the reader: construct a similar example on
> the surface of a sphere S^2 (omit E and keep B and C on
> the surface); use a circle of constant latitude. This
> shows that a flat manifold is not required.
>
> Note that all those dot- and cross-products hold independent of
> coordinate system (given the proper definition of the cross-product in
> terms of the underlying 2-form).
>
> This also holds for my example, even though E,B,C are
> defined in terms of a particular coordinate system.
> Because they are vectors, and once defined they are
> independent of coordinates.

Gravitation causes non-euclidean geometry, such
as the Vertical speed of light (1-2m/r) is less
than the horizontal speed sqrt(1-2m/r) where
the speed of light defines lengths and thus unit
vectors.
A better example is to do geometry on a rotating
disk. Einstein explains that in the ref I gave.

> > I'll caveat that those 6 equations hold in an
> > Orthogonal space and time, simultaneously, but
> > I maintain those 6 cannot hold simultaneously
> > in a NonOrthogonal SpaceTime.
>
> I don't know what you mean by "orthogonal space and time" or
> "NonOrthogonal SpaceTime". AFAIK the adjective "orthogonal" is
> incommensurate with the noun "manifold". Google gives some opaque usages
> of the phrase that don't appear relevant to me.

Ok, use "euclidean".
Regards
Ken S. Tucker
From: Ken S. Tucker on 29 Sep 2008 00:28
Thanks JRY for cutting me some slack.
(I'm a bit nuttier on Sunday).

On Sep 28, 9:29 pm, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote:
> On Sep 27, 3:05 pm, "Juan R." González-Álvarez
>
> <juanREM...(a)canonicalscience.com> wrote:
> > Ken S. Tucker wrote on Sat, 27 Sep 2008 09:08:01 -0600:
>
> > >> Precisely the main criticism done on GR is in the ill-defined character
> > >> of several fundamental aspects (energy, equivalence principle), its
> > >> conflict with rest of physics (no unification), and its strong
> > >> dependence in a set of non-observables: g_ab, geodesics...
>
> > > Juan
> > > GR is very secure with an observable "geodesic".
>
> > Ken, in GR the geodesic are not observables because are coordinate
> > dependent. Coordinate dependent quantities are also named "unmeasurable
> > quantities" [1].
>
> Correction in Celestrial Mechanics: Use the ratios of orbits,
> and therefore coordinate free invariants. It's a "convenience"
> to use adopt coordinates.
>
> > > See "advance of
> > > perihelion of Mercury's orbit".
>
> > Do not mix apples and oranges; the concept "Advance of perihelion" is
> > different from "geodesic".
>
> Then what is a geodesic?
>
> > > I've worked out the orbit myself using GR, and sim'd it on computers.
>
> > Do not confound computers with Nature!
>
> LOL, in place of calculations what do you recommend,
> tea leaves, or sheep entrails?
>
> > I know people who also simulated
> > wavefunctions using computers but none of them would claim wavefunctions
> > are observables just because displayed in monitor.
>
> That's could be true, the pix of a fella with a 48 inch
> penis is likely not an observable.
>
> > > I strongly recommend you put effort into understanding GR prior to
> > > making what are clearly erroneous statements.
>
> > Thanks
>
> You're welcome
> Ken S. Tucker
>
> ======================================= MODERATOR'S COMMENT:
> Ken, approved, but let's try to keep it clean. ;-) JRY

Ok, no more sheep entrail comments ;-).
I definitely think we are an extremely fortunate
generation, speaking for myself at age 55, to go
from slide rule, to calculator, to digital computer
to simulate physics, and GR orbital anomally's,
for instance, a small 1/r^3 quantity as predicted
by AE's GR does account for the 43" arc/century
of the semi-major axis rotation of Mercury's orbit.

You may be interested to see that all of those
"periods" can be expressed as ratio's, such that
Period1/Period2 = scalar invariant, where the
"periods" themselves are usually measured in
seconds etc. but the unit of time cancels.
Best Regards
Ken S. Tucker
From: Ken S. Tucker on 3 Oct 2008 17:36
Hi Peter and fella's.

On Sep 29, 1:55 pm, Peter <end...(a)dekasges.de> wrote:
> On 28 Sep., 09:05, Raphanus <lester.we...(a)gmail.com> wrote:

> > On Sep 27, 7:42 pm, Peter <end...(a)dekasges.de> wrote:
>
> > > > Compared to modern standards the ancient masters had very little knowledge - but great wisdom.
>
> > > I would agree they knew less than we, but that, what they knew, they
> > > knew better than we do it nowadays
>
> > It is easy to know everything about nothing.
>
> > > Because I feel that some discussions would proceed more smoothly, if
> > > wisdom and knowledge would go together ;-)
>
> > And the attribute of a discussion proceeding smoothly is...?
> > And if there is one, why do wisdom and knowledge going together
> > contribute to that?
>
> Wisdom is understood to include the insight, that - at least for the
> truth itself - it is not important who has found it
> P.

Allow me to preamble my experience.
Around age 4-5, I had a speech problem, and was
considered a bit of a dummy, but I had an interest
in rocketry and astronomy and solving puzzles.
Well I got into solving puzzles as a hobby, probably
to overcome the stigma of being a dummy and to
show-off a bit, but got a *high* solving new puzzles
and problems.
Next, I go to grade school and the education institution
serves IQ tests, based on solving puzzles, which I
found to be fun, and was classified a "genius", because
that's was/is my hobby.
I suppose that puzzle solving requires some insight into
a "truth", though I'd term that "truth" a solution algorithm.
If so then we can redefine wisdom as an "ability to find
solution algorithms".
Ok that works for me.
Regards
Ken S. Tucker
From: Ken S. Tucker on 8 Oct 2008 13:18
Hi Kwan and fellow SPFer's.

On Oct 4, 6:09 pm, qchiang <qchia...(a)yahoo.com> wrote:
> On 9ÔÂ28ÈÕ, ÏÂÎç9ʱ28·Ö, "Ken S. Tucker" <dynam....(a)vianet.on.ca> wrote:
> > On Sep 25, 10:35 pm, qchiang <qchia...(a)yahoo.com> wrote:
> > ...
> > > I can see quite naturally you are less than 100% convinced about the
> > > plane angle space and solid angle rotation because it is a new concept
> > > and not widely recognized just like any new concept.
>
> > The "new concept" you mention evidently relates to
> > geometry. Let me term that "Kwan's New Math".
> > This New Math needs to satisfy the mathematicians
> > (geometrists) who frequent the group, using as far as
> > possible, common terminology, to verify it's logical
> > soundness.
> > Where I stand, I'm unable to apply the New Math to
> > physics until I can understand it.
>
> > > But I am totally
> > > confident on it as I have spent a lot of time studying from various
> > > angles and thinking deeply into the philosophy of physics. I'm
> > > positive you will be gradually convinced,
>
> > I'm rather uncertain if we're working in 5D and whether
> > it's Euclidean, could you answer that please?
>
> > > especially when physics
> > > hasn't gone anywhere under conventional wisdom since the later part of
> > > 20th century.
>
> > Well there are quite a few experiments ongoing that
> > intend to test the new theories.
> > Regards
> > Ken S. Tucker
>
> Hi Ken,
>
> Thanks for your recommendations and sorry for the delayed reply, as I
> had some trouble with posting in the correct ASCII formatting. Hope
> this time it is ok.
>
> Below is the new math which can be defined only in the PLANE ANGLE
> SPACE, where each linear coordinate represents a plane angle scale,
> while the plane angle IN THE PLANE ANGLE SPACE is actually the solid
> angle.
>
> For the Lorentz spacetime, there are x, y, z and t linear coordinates
> and there are 6 plane angle scales for the 6 planes, xy-plane, yz-
> plane, zx-plane, xt-plane, yt-plane and zt-plane. Correspondingly, on
> the PLANE ANGLE SPACE, there are 6 LINEAR coordinates, each represents
> a plane angle scale for the 6 planes, xy-plane, yz-plane, zx-plane, xt-
> plane, yt-plane and zt-plane.
>
> A PLANE angle rotation in the PLANE ANGLE SPACE, say from the axis of
> xy-plane to the axis of yz-plane, is actually a SOLID angle rotation
> from xy-plane to yz-plane as considered (conceptually) from the
> viewpoint of the cartesian coordinates. (While it's termed as SOLID
> angle, it's more like a curved cylinder running from xy-plane to yz-
> plane. However, there is no direct translation of coordinates between
> the cartesian coordinates and the PLANE ANGLE SPACE.)
>
> We may define SOLID ANGLE w_xyyz in the following fashion: An
> arbitrary plane angle arc alpha (ie, line segment in the plane angle
> space) can be projected on the xy-plane and yz-plane through SOLID
> ANGLE w_xyyz as
>
> alpha_xy = alpha . sin w_xyyz
> alpha_yz = alpha . cos w_xyyz
>
> The absolute value of the arbitrary plane angle |alpha| remains a
> constant
>
> |alpha|^2 = (alpha_xy)^2 + (alpha_yz)^2 = (alpha . sin
> w_xyyz )^2 + (alpha . cos w_xyyz )^2 = (alpha)^2 = constant
>
> under any plane angle rotation in the plane angle space (or under the
> solid angle rotation as considered conceptually from the viewpoint of
> the cartesian coordinates). Likewise, for the 3+1 Lorentz spacetime,
>
> |alpha|^2 = (alpha_xy)^2 + (alpha_yz)^2 + (alpha_zx)^2 +
> (alpha_xt)^2 + (alpha_yt)^2 + (alpha_zt)^2 = constant
>
> In this way, we can successfully decompose any plane angle arc into
> components of the 6 planes, xy-plane, yz-plane, zx-plane, xt-plane, yt-
> plane and zt-plane. And any solid angle rotation (or plane angle
> rotation in the PLANE ANGLE SPACE) would not alter a plane angle arc.
> Thus, a new symmetry has emerged. However, this is not a new
> invention but actually a reflection from the Cisimir invariant.
>
> Solid angle and the plane angle rotation is not visulizable from the
> cartesian coordinates, and linear length cannot be conserved under
> solid angle rotation.

Quote,
"We can either work in the PLANE ANGLE SPACE or
in the cartesian coordinates, but not both simultaneously."

> This is
> not a drawback though, as there are times we care only about the plane
> angle and solid angle rotations, but not about the linear space, e.g.
> in particle classifications.
>
> The other major mathmatical aspect is that: for a 4+1 spacetime, a
> point can be identified by identifying through the generalized polar
> coordinates:
>
> the 4-d surface in the 5-space according to the 5-d angles,
> then the 3-d cubic surface in the 4-space according to the 4-d
> angles,
> then the 2-d surface in the 3-d space according to the solid (3-d)
> angles,
> then the 1-d surface (line) in the 2-d space according to plane (2-d)
> polar angle,
> then the 0-d point on the 1-d surface (line) according to the distance
> (1-d angle).
>
> Associated with this decomposition is that the quantum numbers to be
> associated with a particle should be,
>
> ¦· = ¡Æ E ¡Á D ¡Á C ¡Á B ¡Á A (6.1)
>
> where:
>
> is a wave function, exp[-i¦Ð(p^0x^0 -p^1x^1 - p^2x^2 - p^3x^3 -
> p^mx^m)], representing linear (1-dimensional) momentum, including
> energy and mass. x^m is the extra dimension [1] and p^m = mc.
> A spinor representing plane (2-dimensional) angular momentum.
> A solid angle spinor representing solid (3-d) angular momentum. Solid
> angle rotation runs from one plane (2-brane) to another (among the 10
> planes) while preserving plane angular momentum. Symmetry of solid
> angle rotation is suspected to be those of iso-spin, strangeness,
> charm, etc. The interaction through solid angle rotation is believed
> to be weak interaction.
> A 4-d rotation spinor representing 4-d angular momentum. 4-d rotation
> runs from one 3-plane (3-brane) to another (among the 10 3-planes)
> while preserving solid angular momentum. This symmetry probably
> generates K^L and K^S, the mixtures of K^0 and anti-K^0 mesons. The
> interactions may be the CP-violation interactions.
> A 5-d rotation spinor representing 5-d angular momentum. 5-d rotation
> runs from one 4-d plane (4-brane) to another among the 5 4-d planes
> while preserving 4-d angular momentum. Fields in 5-d rotations may be
> causing the strong interactions. The symmetry of 4-d angular momentum
> might be the color symmetry which exists but cannot be observed in
> isolation.
>
> > I'm rather uncertain if we're working in 5D and whether
> > it's Euclidean, could you answer that please?

And then,

> We are still in the 3+1 Lorentz space, but its PLANE ANGLE SPACE is
> 6D. In the case of 4+1 spacetime, the PLANE ANGLE SPACE is 10D. They
> are all Euclidean.
> Best regards,
> Kwan Chiang (9/30/08)

As far as I know, a Euclidean space is characterized
by the Rieman tensor vanishing, ie.
http://en.wikipedia.org/wiki/Riemann_curvature_tensor
R_abcd=0.
Such that the metrics are transformable to constants,
specifically Cartesian CS's.
Naturally we can work with any metrics "g_uv" that
are compatible with R_abcd , "simultaneously", like
polar, cylindrical and on and on...
Does that reasoning always hold?
Regards
Ken S. Tucker
From: Ken S. Tucker on 13 Oct 2008 00:38
> Roger Mr. Moderator.
> As a youngster, I worked out a few different methods
> of calculating out how to derive Mercury's orbital
> anomally, and acquired a great deal of respect for GR,
> so that's a bit of a hobby of mine, so naturally I'm
> interested in pursuing alternatives philosophies.
> Regards
> Ken S. Tucker
>
> ======================================= MODERATOR'S COMMENT:
> This group would surely benefit from an exposition of that :-)

EFEs==Einstien Field Equations
As a student, I encountered the calculations of Mercurys
GR induced orbital anomally with less than adequate
Celestrial Mechanical training. Text book expositions
generally impose an anomally "3mu^2" on the ellipse,
as a result of the effect of the Schwarzschild Solution
(SS) of the EFE's, on the otherwise Newtonian Euclidean
space and time that renders a perfect ellipse (apart
from other planets gravitational inductions).
That method is thorough, but for me, didn't connect the
EFE's to the anomally as directly as I would like.

The next method I used was to vary Newtons Force
Law such as, at Mercury's distance,

F = GMm/ r^(2.000 000 17)

where the exponent varies from a pure square, as a
function of radius.
That uses an interpretation of the SS similiar to
Dr. Francis's and Weinberg's (Grav&Cosmo pg. 181,
R=r - MG).

My favorite is to use the "red-shift" of light, such as
(P is invariant energy),

P_0 = P * sqrt(g_00) , P = P_0/sqrt(g_00)

and then take the derivative dP/dr to get the orbital
anomally. That last method gives the most direct
connection to SS which is based on the g-field effect
on light energy and therefore all energy, including
orbital energy.
Regards
Ken S. Tucker

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