Tom,

Thanks for your reply. Your discussion of integrating over manifolds is
very helpful, especially since I have been giving a lot of consideration to
how one might think about the topological turbulence at the Planck length
and find consistent mathematical tools to model it.

Best,

Jay.

--
_____________________________
Jay R. Yablon
910 Northumberland Drive
Schenectady, New York 12309-2814
Phone / Fax: 518-377-6737
Email:
"Tom Roberts" wrote in message
...
Jay R. Yablon wrote:
Tom Roberts wrote:
T^uv is local energy-momentum _density_, not _total_energy_.

Agreed.
To obtain
total energy you need to integrate the local density over the region of
interest, and that's the problem: in general for a curved manifold such
an integral is not well defined.

Are you speaking of a curved spacetime problem or a quantum problem?

I am continually amazed at people around here who think they can respond
to articles without reading them. Please elevate your eyes to the part of
my post that you quoted above and actually READ it -- it contains a clear
and direct answer to your question.


For curvature, so long as we have g^uv defined at each point, and the
scalar sqrt(-g), we can in principle take a volume integral "Integral
sqrt(-g) T^00 d^3X" that will relate observed physics to choice of
coordinates.

Sure, you can do anything you like. That does not mean it makes sense. In
this case, the value you get will be dependent on the coordinates you
choose, so the result cannot have any physical significance.

BTW: sqrt(-g) is not a scalar....


The problem seems to be, for ANY tesnor defined at a "local," i.e.,
theoretically infinitesmal point in spacetime, how do we carry out
integration over a finite region when "points" in physics are not
infinitesmal.

This is nonsense. Points in a manifold have zero extent.

The problem is that for a given integral on a manifold to make sense the
integrand must satisfy certain integrability conditions (which basically
ensure that the integrand is a function on the manifold, as opposed to
being something that is path dependent inside the region of integration).
For the kind of integral required to compute "total energy in a region"
those integrability conditions are essentially that the Riemann curvature
tensor vanish throughout the region of integration. This can be traced
back to the fact that the energy-momentum tensor is a rank-2 tensor, and
to obtain a scalar integral of it one must contract it with two vectors,
and that introduces path dependence into the integrand (I'm speaking a bit
loosely here; this is not my area of expertise).


For instance, above you wanted to integrate T^00. That is explicitly
coordinate (basis) dependent. Probably what you really want is to
integrate T_uv U^u U^v where U^u are the components of an observer's
4-velocity -- then you get the energy density as measured by that
observer. But note that expressing it this way in an invariant manner does
not ensure that such a volume integral makes sense; in general it does
not. shrug

There's also the problem that U is defined only along the observer's
trajectory, not throughout the volume over which you want to integrate....


It seems almost a problem with using calculus, where delta x -- dx --
0, and it suggests that in physics, the best we can do is delta x where
delta is small but finite.

Not true. Modern theoretical physics (specifically GR) is fully consistent
with real analysis.

But nobody really expects GR to be valid all the way own
to the Planck scale. _Mathematically_ it is well founded
on the differential geometry of smooth manifolds, but the
world is not expected to be well-modeled by a manifold
at such small scales. You seem to be trying to apply
this model vs world problem to the mathematics of the
model -- that's invalid.


Tom Roberts

Tom Roberts wrote:
Jay R. Yablon wrote:
....
For
curvature, so long as we have g^uv defined at each point, and the scalar
sqrt(-g), we can in principle take a volume integral "Integral sqrt(-g) T^00
d^3X" that will relate observed physics to choice of coordinates.

Sure, you can do anything you like. That does not mean it makes sense.
In this case, the value you get will be dependent on the coordinates you
choose, so the result cannot have any physical significance.

Tom you should read Tucker's essay...

http://www.vacuum-physics.com/KST/GR_Charge_Couple3.pdf
(courtesy of Fred Diether)

If there's something not appropriately defined let me know.
I recommend you learn everything you can about a pair of
charges, because you can sum them to create a universe.
....

But nobody really expects GR to be valid all the way down
to the Planck scale. _Mathematically_ it is well founded
on the differential geometry of smooth manifolds, but the
world is not expected to be well-modeled by a manifold
at such small scales. You seem to be trying to apply
this model vs world problem to the mathematics of the
model -- that's invalid.

Classical descriptions of GR evolved from Newton's *fluxions*
and so inherited the "smooth manifold", but as the essay
shows GR doesn't need a manifold, just a relation, after-all
it's called General Relativity, i.e. it's about relations.
Regards
Ken S. Tucker

Jay R. Yablon wrote:
Hi Hannu, see inline:


I have understood that the total energy is ill defined concept in
General Relativity ?
How you have defined for example total gavitational energy in your
paper ?

Well, total energy is defined mathematically as an energy for which
T^uv_;u=0, and the zero must be ensured identically. That is, T^uv_;u must
be set to a combination of fields which is identically equal to zero, in all
situations, for Abelian and non-Abelian interactions alike.


Steve Carlip wrote "Gravitational Potential in GR" article, 23.02.1998
in sci.physics.relativty:

"The principle of equivalence implies that there can be no covariant
gravitational stress-energy tensor --- one can always choose
coordinates
in which the geodesics are arbitrarily close to straight lines in a
small region,
which implies that the gravitational energy in that region is
arbitrarily
close to zero; but a tensor that vanishes in any coordinate system
vanishes
in every coordinate system."

Is your energy tensor t^u _v of the gravitational field really
covariant
gravitational stress-energy tensor or what it is if not ?


I found one nice explanation also about the problem:
Tom Roberts wrote " Gravitational Potential Energy" article,
27.6.1998
in sci.physics.relativity:

"In GR, if one selects a gven "frame of reference" (in the usual SR
sense),
one can still change coordinates in arbitrary many ways, such that
the new coordinates are still "at rest" in that frame, but yet the
quantities
computed for potential energy and kinetic energy can have ANY possible
values.
In a given set of coordinates these quantities have definite values,
but as
there is no preferred coordinate system so is there no unique value for
PE
or KE. In other words, they are not well defned."



I notice end of your paper the group of equations which sems to have
solution same as Resissner-Nordstrom solution as a line element
( metric of charged black hole), if I looked right ?

Serious Problems with this Reisnerr-Nordstrom solution are that with
time like geodesic it is possible to avoid hitting the singularity
and also that if black hole would have charge then the whole space
would be also charged too which is impossible ?


Well, Hannu, you are right to notice the similarities because I am using the
Schwarzschild solution. But, this is not intended as a real-world solution,

I notice that you mention the Kerr solution in your paper, but this
have
a problem too: H-M explained many years ago that if the black hole
in center of space would rotate then the planet which is center of
coordinative colour
electricity signals (planet orbits the great neutrino crystall
collection (big ball) in
center of the space) would be shifted into the other side of this big
ball. I understood
that this would block colour electricity signals (its mass would change
colour electricity
signals to black colour (= no colour electricity)). This is why at
least this
black hole is not possible to rotate. I assume that this is case for
all
black holes. In other words black holes are not possible to rotate ???


Of course the Schwarzschild solution is special case for both mentioned
black hole types.


but just as an example to give people a concrete idea of what I am talking
about when I say that one can quantize gravity by feeding quantum mechanical
wavefunctions for fields and currents directly into the Einstein equations
at second and third differential order in the spacetime metric g_uv, and
then solving for G_uv to arrive at a metric wavefunction fully grounded in
empirical knowledge from QED and QCD and QWeakD.

Jay.

Ken S. Tucker wrote:
Tom Roberts wrote:
Jay R. Yablon wrote:
...
For
curvature, so long as we have g^uv defined at each point, and the scalar
sqrt(-g), we can in principle take a volume integral "Integral sqrt(-g) T^00
d^3X" that will relate observed physics to choice of coordinates.

Sure, you can do anything you like. That does not mean it makes sense.
In this case, the value you get will be dependent on the coordinates you
choose, so the result cannot have any physical significance.

Tom you should read Tucker's essay...

http://www.vacuum-physics.com/KST/GR_Charge_Couple3.pdf
(courtesy of Fred Diether)

If there's something not appropriately defined let me know.
I recommend you learn everything you can about a pair of
charges, because you can sum them to create a universe.
...

But nobody really expects GR to be valid all the way down
to the Planck scale. _Mathematically_ it is well founded
on the differential geometry of smooth manifolds, but the
world is not expected to be well-modeled by a manifold
at such small scales. You seem to be trying to apply
this model vs world problem to the mathematics of the
model -- that's invalid.

Classical descriptions of GR evolved from Newton's *fluxions*
and so inherited the "smooth manifold", but as the essay
shows GR doesn't need a manifold, just a relation, after-all
it's called General Relativity, i.e. it's about relations.

Hmmm ....
Charge pairs have strong SOL relations and conveinently quantize to
2(0.511MeV).

Induced dipoles have weak bulk_mass_damped relations...
and I doubt there is anything conveinent or even useful
about quantizing them. Just my heritical opinion tho.

Sue...

Regards
Ken S. Tucker

Sue... wrote:
Ken S. Tucker wrote:
http://www.vacuum-physics.com/KST/GR_Charge_Couple3.pdf
(courtesy of Fred Diether)
Classical descriptions of GR evolved from Newton's *fluxions*
and so inherited the "smooth manifold", but as the essay
shows GR doesn't need a manifold, just a relation, after-all
it's called General Relativity, i.e. it's about relations.
Ken

Hmmm ....
Charge pairs have strong SOL relations and conveinently quantize to
2(0.511MeV).
Induced dipoles have weak bulk_mass_damped relations...
and I doubt there is anything conveinent or even useful
about quantizing them. Just my heritical opinion tho.
Sue...

Quantization per say, is not really that difficult, it's detailed.
An example would be the emission of a photon, that requires
the relative movement of two charges. Doing that by "hand"
is one way but I think it's easier to use computers.
Ken

conveinently - conveniently
conveinent - convenient
heritical - heretical

per say - per se
difficult, - difficult;

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you foken stoopid bitch spell cheking usenet....ahaha my dick

not words, ****head

you are more ugly then ****, i saw your picture, get lost
ugly bitch

then - than
you are - I am
****, - ****;
i - I
your - my

I don't have a picture online. You're as much of a liar as you are a
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have got - have gotten

Ken S. Tucker wrote:
FrediFizzx wrote:
"Jay R. Yablon" wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.

V = dr/ds

dp/dr = - {uv,u} U^v V

The Looks like Newton, Einstein and EM in a neat package!

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker