Ken S. Tucker wrote on Sat, 31 May 2008 11:58:18 -0700:

On May 31, 10:44 am, "Juan R." González-�lvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 10:26:58 -0700:



On May 31, 9:58 am, "Juan R." González-�lvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 09:19:15 -0700:

Hi Juan, a quick question below...

On May 31, 6:13 am, "Juan R." González-�lvarez
wrote:
carlip-nospam wrote on Sat, 31 May 2008 01:17:57 +0000:
...
Your computation of 'gradients' were corrected in several cited
references.

This statement demonstrates clearly that you don't understand
basic general relativity. The geodesics of the metric *are*
the paths of the target bodies. Once you know the path -- the
position as a function of time -- you can use any coordinate
system you like, and any definition of acceleration you like.
The answer is uniquely determined.

In the field formulation? Sure. In the geometrical (geodesic)
one? Sure it is not because the path is coordinate dependent.

That is one of main reasons that one can speak about a
gravitational force in the field formulation. The force is
uniquely determined as orbits of test bodies are also.

Where U^i is contravariant 3-velocity, then the geodesic is
defined in GR by an "absolute derivative" like,

DU^i/ds =0,

and that is the equation of motion in GR. Juan, do you understand
that equation? Regards

I wonder by your insistence on posting about stuff you ignore.

Of course, the equation of motion in the geometrical theory of
gravity is geodesic

*But* i wrote

(\blockquote
That is one of main reasons that one can speak about a
gravitational force in the *field* formulation.
)

I can write the geodesic equation of motion in different ways. I
like the expression (in concise notation)

a = - Gamma v v

and i can write it in other ways (ways you do not know :-))

Your query is really funny when one notices i have been writing
geodesic equations both here and in spf.

But could you write the *field* theoretic equation of motion?

No! Well that is not a surprise :-)

--
Center for CANONICAL |SCIENCE) http://canonicalscience.org

Ok fine, you Juan, TVF and Eugene appear to be unable to grasp the
GPoR emobodied within,

DU^i/ds =0,

succinctly. If you guy's can understand that, then tell us how to
revise that simple equation.

In Eq.(6) at this cite,
http://physics.trak4.com/modern-spacetime.pdfabsolute motion vanishes,
in accord with International Standards.

You see, a good fella like myself, can easily define the "state of
the art", where GToR is concerned, and all you need to do is show me
where I'm mistaken, go and do it.
Regards
Ken S. Tucker
PS: Stop wasting my time.

Ok, a) you cannot write the field theoretic equation, b) you cannot
understand how the geodesic equation of motion follows from the field
theoretic one in the geometric limit and c) you cannot understand that
extension of SR and GR means :-)

P.S: Your geometric "modern-spacetime.pdf" is useless but you already
were said that in spf, true?

Juan, from the standpoint of objective science, I've attempted to extend
to you TVF and Eugene, the benefit of doubt, and I can argue, on your
behalf for you, given any plausible argument. The MST
"modern-spacetime.pdf" is the best we have so far, improvements are
welcome sir.

But, at least I can provide good theoretics in 2 pages, posted!

You boys (Juan, TVF and Eugene) need 200 pages to make your point, what
ever the **** it is, I've still haven't figured out what your trying to
do except being infactuated with Minkowski's Group(oo), well I know
everything about that Group, so what. Maybe I should advise you guys on
G(oo)!

I agree that one can write a 2 pages 'article' (and even one with zero
pages) iff one decides to ignore all the fundamental questions and just
repeat the *mistakes* were already corrected in print (e.g. in the cited
articles in Physical Review and other top journals).

P.S: Ken, your misunderstanding about groups was addressed three or four
times before.


--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org

On Jun 1, 12:47 am, Koobee Wublee wrote:
On May 31, 11:58 am, "Ken S. Tucker" wrote:

You boys (Juan, TVF and Eugene) need 200 pages
to make your point, what ever the **** it is,

Well, after several thousands of posts, you still don’t have a point.
shrug

LOL, I'll buy a pencil sharpener.
Ken

On Jun 1, 6:38 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 11:58:18 -0700:
...
Juan, from the standpoint of objective science, I've attempted to extend
to you TVF and Eugene, the benefit of doubt, and I can argue, on your
behalf for you, given any plausible argument. The MST
"modern-spacetime.pdf" is the best we have so far, improvements are
welcome sir.

But, at least I can provide good theoretics in 2 pages, posted!

You boys (Juan, TVF and Eugene) need 200 pages to make your point, what
ever the **** it is, I've still haven't figured out what your trying to
do except being infactuated with Minkowski's Group(oo), well I know
everything about that Group, so what. Maybe I should advise you guys on
G(oo)!

I agree that one can write a 2 pages 'article' (and even one with zero
pages) iff one decides to ignore all the fundamental questions and just
repeat the *mistakes* were already corrected in print (e.g. in the cited
articles in Physical Review and other top journals).

I usually don't cite Physical Review as it
is not available online.

P.S: Ken, your misunderstanding about groups was addressed three or four times before.

I'm afraid the Group(oo) is implausible
and without any physical empiricism so far.
However as a mathematical tool, it does
have advantages in some simplistic problems,
which is 99.9% of physics.
It's when you (Juan and gang) sell your ideas
as a *new truth* when in fact it's currently
a simplification of very old ideas.
Cheers
Ken

Ken S. Tucker wrote on Sun, 01 Jun 2008 08:43:04 -0700:

On Jun 1, 6:38 am, "Juan R." González-�lvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 11:58:18 -0700:
...
Juan, from the standpoint of objective science, I've attempted to
extend to you TVF and Eugene, the benefit of doubt, and I can argue,
on your behalf for you, given any plausible argument. The MST
"modern-spacetime.pdf" is the best we have so far, improvements are
welcome sir.

But, at least I can provide good theoretics in 2 pages, posted!

You boys (Juan, TVF and Eugene) need 200 pages to make your point,
what ever the **** it is, I've still haven't figured out what your
trying to do except being infactuated with Minkowski's Group(oo),
well I know everything about that Group, so what. Maybe I should
advise you guys on G(oo)!

I agree that one can write a 2 pages 'article' (and even one with zero
pages) iff one decides to ignore all the fundamental questions and just
repeat the *mistakes* were already corrected in print (e.g. in the
cited articles in Physical Review and other top journals).

I usually don't cite Physical Review as it is not available online.

Now understand :-)

P.S: Ken, your misunderstanding about groups was addressed three or
four times before.

I'm afraid the Group(oo) is implausible and without any physical
empiricism so far. However as a mathematical tool, it does have
advantages in some simplistic problems, which is 99.9% of physics.
It's when you (Juan and gang) sell your ideas as a *new truth* when in
fact it's currently a simplification of very old ideas.

You got all wrong again Ken, "extension" is the contrary of
"simplification" :-)


--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org

On Jun 2, 3:50 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Sun, 01 Jun 2008 08:43:04 -0700:



On Jun 1, 6:38 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 11:58:18 -0700:
...
Juan, from the standpoint of objective science, I've attempted to
extend to you TVF and Eugene, the benefit of doubt, and I can argue,
on your behalf for you, given any plausible argument. The MST
"modern-spacetime.pdf" is the best we have so far, improvements are
welcome sir.

But, at least I can provide good theoretics in 2 pages, posted!

You boys (Juan, TVF and Eugene) need 200 pages to make your point,
what ever the **** it is, I've still haven't figured out what your
trying to do except being infactuated with Minkowski's Group(oo),
well I know everything about that Group, so what. Maybe I should
advise you guys on G(oo)!

I agree that one can write a 2 pages 'article' (and even one with zero
pages) iff one decides to ignore all the fundamental questions and just
repeat the *mistakes* were already corrected in print (e.g. in the
cited articles in Physical Review and other top journals).

I usually don't cite Physical Review as it is not available online.

Now understand :-)

P.S: Ken, your misunderstanding about groups was addressed three or
four times before.

I'm afraid the Group(oo) is implausible and without any physical
empiricism so far. However as a mathematical tool, it does have
advantages in some simplistic problems, which is 99.9% of physics.
It's when you (Juan and gang) sell your ideas as a *new truth* when in
fact it's currently a simplification of very old ideas.

You got all wrong again Ken, "extension" is the contrary of
"simplification" :-)

Well you Juan are right, I did make a mistake.

I published a book, "Slide Rule OR Abacus, the
Truth of the Best". What I can't understand is
why it didn't get on the New York Times best
seller list.
You see the Slide Rule is based on a continuum,
while the Abacus is quantized.

Obviously, my unification of the Slide Rule
and the Abacus quantizes the continuum, but
nobody listens to me, they insist on using
those new fangalled calculator thing-me-bobs.

My next best-seller will be applying a circular
slide rule to rotational problems, like a
channel changer that clicks 2,3,4...13.
Regards
Ken

[This replies to Saul and Steve Carlip.]


Saul writes:

[Saul]: As I understand the math of GR ... the same physics applies to
the Lienard-Weichert potential of E&M.

Of course it’s not the same physics. Very different physical entities
and properties are involved. But the math of retarded potentials is closely
parallel for gravity and electrodynamics. For GR, that math describes the
gravitational potential field, which governs small relativistic effects such
as light-bending. But the field equations and their solutions tell us
nothing about orbital motion until we take spatial partials to form
gradients. The force (meaning the time rate of change of 3-space momentum)
acting on a target body happens to be equal to the gradient of the
potential, and determines the orbital motion.

It is only when we use information from the Einstein field equations in
conjunction with an assumption about forces (to describe the orbital motion
of target bodies in Euclidean 3-space for the purpose of comparing to
observations) that any disagreement arises. But that particular usage
(unlike other GR effects such as light-bending) requires taking spatial
partial derivatives to get a gradient. This process in turn requires making
an assumption about “instantaneous� vs. “retarded� gradient because the
direction of the gradient is frame-dependent, especially if the propagation
speed of changes in the field is as slow as light-speed.

[Saul]: Let me try to make a layman's explanation of Carlip's argument...
Is the idea that the space-time ahead of the Earth, where the Earth has
not yet reached in its orbit, has already been affected by gravitational
force of the sun, and therefore the force is in a slightly different
direction making our orbit stable?

Carlip has changed his argument over the years. At one time, he argued
for the existence of a “velocity-dependent force� to cancel the effect of
propagation delay (aberration). But in his latest post, he stated: “The
force is the gradient of the potential. If the potential doesn't change, its
derivatives don't, either.� As you saw in my reply, that’s a wrong
statement. The gradient (which is formed from the spatial partial
derivatives of the potential) is a vector, and is ever changing its
direction as viewed from the frame of a moving target body.

And that is where the issue arises here. You describe a version of
Carlip’s argument that the source mass does not attract target bodies toward
itself now, but toward its own future position. But physically, how can we
explain that the force always acts almost exactly in the direction of the
true, instantaneous source mass rather than the direction of the light-time
retarded source mass, even when the source mass is accelerating? The only
explanation that does not use physical miracles (such as the creation of new
momentum from nothing) is forces propagating strongly FTL.


and Steve Carlip writes:

[Carlip]: Now, at time t=0, make the following change in R: stop the
motion of M. You apparently agree that this change will have no affect
at p until the time for a light signal to reach p from R.

[TomVF]: What I agreed to was that the gravitational potential field at
p would not change until one light-time later than t = 0. However, it
is clear from logic, observation, and computer experiments that the
force operating at point p changes almost instantly,

[Carlip]: The "force" is the gradient of the potential. If the potential
doesn't change, its derivatives don't, either.

[TomVF]: Consider a body on a circular orbit. [The] gravitational
potential [it experiences] is constant. Yet the gradient of that
potential (a vector) is ever-changing. Your claim is wrong. You are
apparently unfamiliar with the physics of gradients, having learned only
the trivial math.

[Carlip]: This is silly. The potential at the location of the object ...
is never constant.

First, you seemed to think I might have been talking about the potential
of the target body, but I was not. So I fixed my statement and your answer
to omit remarks about the target body potential, leaving only our remarks
about the source mass potential. Obviously, your statement is wrong because
the source mass’s potential at a target body moving on a circular orbit *is
constant*, contrary to what you say. You do realize potential is a scalar,
not a vector, right?

[Carlip]: For Newtonian gravity, the derivative of the potential *in the
direction of the orbiting object* is zero, which is why there is no
tangential force.

I wish you would choose your words more carefully. I read this several
times, interpreting “in the direction of the orbiting body� as the direction
for the source mass to the target body. Then I realized you must have meant
to say “in the direction the orbiting body is moving�.

But interpreted in that way, your statement is just a verification of my
statement, that the source mass’s potential at the target body on a circular
orbit is constant.

[Carlip]: But at each point in the orbit, the derivative of the potential
in the direction perpendicular to the orbit is nonzero. To call such a
potential "constant" is a word game.

No, you are making careless choices of words. “Perpendicular� should be
replaced by “radial�. (For example, “normal� is also perpendicular.) And I’m
guessing you meant “gradient� when you said “derivative� in your previous
sentence. We are obviously talking about spatial derivatives, and the
partial of potential with respect to coordinate x can be zero or non-zero
depending on what reference frame – the source mass’s or the target body’s –
we are using.

I think I was pretty clear in saying that the potential at a target body
in a circular orbit is constant, even though its gradient is not. No one
reading this is uneducated enough to think the potential in the radial
direction is constant. So who is playing word games?

Fixing all these poorly worded statements in the way I just described (a
risky thing to do, I admit, because this assumes I know what you were trying
to say), I think your main point is that the potential field as a whole is
unchanging as long as the source mass is unchanging, and that therefore
gradients of that potential field everywhere are likewise unchanging. That
much is trivially true, but ignores the case that matters. The gradient of
that same potential field as seen and experienced by a moving target body is
ever varying in direction, and therefore has instantaneous and retarded
directions that differ.

Is there any chance we have straightened out terminology problems and
agree up to this point?

[Carlip]: Note that when the orbiting object is at a position (x,y,z), the
force is determined by the gradient of the potential at (x,y,z), at the
time the object is at that location.

What you say is certainly true for a non-moving target body. But why
would the gradient of the potential in the source mass’s frame be more
important to a moving target body than the gradient of the same potential as
seen and experienced by the moving target body?

[Carlip]: That's what the gradient is.

Only in the source mass’s frame of reference.

[Carlip]: Please tell me what the "retarded gradient" is.

The same mathematical function calculated in the frame of the moving
target body, assuming the gradient must always be toward the source mass.
Because the source mass direction varies as seen from the target body, so
goes the field gradient direction vary from moment to moment. The spatial
partials change with time.

[Carlip]: For example, here's a function: F(x,y,z,t) = 1/sqrt{ (x-at)^2 +
(y-bt)^2 + (z-ct)^2} I know how to compute its gradient at any position
and time. Please write down its "retarded gradient."

You have mentioned only one coordinate system. The question itself
betrays that you don’t understand retarded gradients. Now if we imitated the
case of a target body on a circular orbit, then we would introduce the
target’s body’s frame wherein the source mass has coordinates (X,Y,Z,t), and
X = r sin nt, Y = r cos nt, Z = 0, r^2 = x^2 + y^2 + z^2, n = angular
velocity of source mass around target body. Then when we do a coordinate
transformation from (x,y,z,t) to (X,Y,Z,t), your function F becomes a
function of time, and so does any derivative of F taken in the (X,Y,Z)
frame.

[TomVF]: *After* you determine the geodesics in that metric, you must
still compute a gradient (or take the equivalent spatial partials) to get
the 3-space force/acceleration.

[Carlip]: This statement demonstrates clearly that you don't understand
basic general relativity. The geodesics of the metric *are* the paths of
the target bodies. Once you know the path -- the position as a function of
time -- you can use any coordinate system you like, and any definition of
acceleration you like. The answer is uniquely determined.

Maybe all our issues are terminology. The (time-like) geodesic equations
are not the path, but merely allow the path to be determined by taking
partials to form a gradient and *assuming* that this gradient represents a
force. Otherwise, the target body would remain in its initial state relative
to the source mass, as it must if no force acts on it. 3-space dynamics are
not present in the geodesic equations. Let me use an example, because we
keep arguing about the strict meaning of words.

The (time-like) geodesic equations describe the potential field
everywhere. That is analogous to describing the shape of a hill. Knowing the
shape of a hill, we can determine the speed and direction of a ball placed
on it at any later time. But that is only because we know about the force
acting on the ball. A hill with no force acting cannot initiate any motion
in a ball. So a geodesic equation without some further assumption about
force (such as “gradient of the potential) likewise cannot initiate 3-space
motion. That is why a lot of work goes into deriving 3-space equations of
orbital acceleration from geodesic equations, and why the starting point is
some assumption about dynamics such as “force is the gradient of potential�.

[Carlip]: The geodesic *is* the path. It's (x(t),y(t),z(t)). Once you give
an initial position and velocity, this path is completely and uniquely
determined by the geodesic equation. No further assumptions are needed.

Are you talking about trivial cases such as space-like geodesics or null
geodesics here? Are you talking about a spacetime path instead of a 3-space
path? Those cases are irrelevant to orbital motion, our topic here. So
please look at the geodesic equations at
http://metaresearch.org/cosmology/gravity/spacetime.asp and tell me how to
compute a simple circular orbit from those equations without making some
assumption about force.

Geodesic equations per se contain no 3-space dynamics. They merely tell
us how proper time differs from coordinate time along any path. We must add
an assumption about force before we can derive 3-space (Euclidean)
acceleration from geodesic equations.

I’m guessing you must have never understood what the
Einstein-Infeld-Hoffmann or Robertson-Noonan or Damour-Deruelle papers,
deriving 3-space equations of motion, are all about. Why do those papers
exist if the geodesic equations contain all the information we need about
orbits?

[Carlip]: You claim that there is a mathematical operation called
"retarded gradient." Define it! Given a field, as a function of position
and time in a given coordinate system, tell me the mathematical procedure
for computing its "retarded gradient."

For a moving target body, the instantaneous gradient points toward the
instantaneous direction of the source mass, and the retarded gradient points
toward the retarded direction of the source mass. Surely you don’t need me
to write the corresponding ASCII equations for you to grasp such a simple
physics concept.

[TomVF]: But then, my paper with Vigier in Foundations of Physics is now
six years old, and already back then showed the definition of gradient
and how to apply it to the case of a dynamic target body.

[Carlip]: I have looked at that paper, but apparently missed the
definition. Please give me the equation number for the equation in that
paper that defines the "retarded gradient" of a function.

The first equation in section 3 gives the mathematical definition of a
gradient for a single coordinate system. We then go on to explain why
physics has an issue that math does not, with these words:

“Note that the gradient of a scalar field is a vector, not another
scalar. But if the field source begins to move, does the field gradient
point toward the instantaneous or retarded position of the source? That
depends on whether the field updates or regenerates instantly or with delay.
So when we say that the gravitational acceleration of a test body follows
the field gradient, we must ask which gradient it will follow --
instantaneous or retarded. Physics has an issue that math does not. Retarded
potentials in math allow for delays only in the mass distribution and in
changes of distance between masses in a scalar field. Retarded potentials in
physics must allow also for delays in the vector direction of the field –
normally the dominant effect of retardation.�

Why is it that whenever we switch from talking math (equations) to
talking physics (concepts, properties, principles), we seem to have so much
difficulty communicating? -|Tom|-


Tom Van Flandern – Sequim, WA - see our web site on frontier astronomy
research at http://metaresearch.org

On Jun 3, 3:49 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Mon, 02 Jun 2008 11:51:59 -0700:



On Jun 2, 3:50 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Sun, 01 Jun 2008 08:43:04 -0700:

On Jun 1, 6:38 am, "Juan R." González-Álvarez
wrote:
Ken S. Tucker wrote on Sat, 31 May 2008 11:58:18 -0700:
...
Juan, from the standpoint of objective science, I've attempted to
extend to you TVF and Eugene, the benefit of doubt, and I can
argue, on your behalf for you, given any plausible argument. The
MST "modern-spacetime.pdf" is the best we have so far,
improvements are welcome sir.

But, at least I can provide good theoretics in 2 pages, posted!

You boys (Juan, TVF and Eugene) need 200 pages to make your point,
what ever the **** it is, I've still haven't figured out what your
trying to do except being infactuated with Minkowski's Group(oo),
well I know everything about that Group, so what. Maybe I should
advise you guys on G(oo)!

I agree that one can write a 2 pages 'article' (and even one with
zero pages) iff one decides to ignore all the fundamental questions
and just repeat the *mistakes* were already corrected in print (e.g.
in the cited articles in Physical Review and other top journals).

I usually don't cite Physical Review as it is not available online.

Now understand :-)

P.S: Ken, your misunderstanding about groups was addressed three or
four times before.

I'm afraid the Group(oo) is implausible and without any physical
empiricism so far. However as a mathematical tool, it does have
advantages in some simplistic problems, which is 99.9% of physics.
It's when you (Juan and gang) sell your ideas as a *new truth* when
in fact it's currently a simplification of very old ideas.

You got all wrong again Ken, "extension" is the contrary of
"simplification" :-)

Well you Juan are right, I did make a mistake.

Everybody makes mistakes Ken.

The problem is when you misread others, make false accusations about the
work of others (work you do *not* know) and *repeat* the accusations even
after being kindly pointed about the mistake.

As i already pointed here several times, I am working in an *extension*
of both SR and GR. The theories of SR and GR are recovered in a well-
defined limit of a more general and sophisticated theory.

The theory reduces to GR and explains *why* the speed of gravity in GR
coincides with the speed of gravity. However this is not true in the
generalized theory.

The new theory is a sophisticated formulation based in mathematics and
physics developed in last few years. Technically it is a nongeometrical
DPI many-body theory in Liouville space with universal evolution
parameter.

As already said GR results are obtained as special case and the limits of
geometry and spacetime fixed :-)

Your accusation of using 1908 physics and maths looks thus completely
irrelevant and your re-accusations look very unfair :-)

Ok, who is your target market, (evidentally
not me, as you Juan insist).
I'm interested in the new predicticts your
theory makes, apart from our classicals.
Ken

[I ignore the embroidery and only discuss Van Flandern's primary confusion.]

Tom Van Flandern wrote:
We then go on to explain why
physics has an issue that math does not, with these words:
“Note that the gradient of a scalar field is a vector, not another
scalar. But if the field source begins to move, does the field gradient
point toward the instantaneous or retarded position of the source? That
depends on whether the field updates or regenerates instantly or with
delay. So when we say that the gravitational acceleration of a test body
follows the field gradient, we must ask which gradient it will follow
-- instantaneous or retarded. Physics has an issue that math does not.
Retarded potentials in math allow for delays only in the mass
distribution and in changes of distance between masses in a scalar
field. Retarded potentials in physics must allow also for delays in the
vector direction of the field – normally the dominant effect of
retardation.�

Why is it that whenever we switch from talking math (equations) to
talking physics (concepts, properties, principles), we seem to have so
much difficulty communicating? -|Tom|-

[For simplicity, I'll discuss the Lenard-Wiechert
potential of classical electrodynamics (ignoring
magnetism). I'll relate this to GR below.]

"We" don't have "so much difficulty", only YOU do, probably because your
description above is just plain wrong. Your question "does the field
gradient point toward the instantaneous or retarded position of the
source?" is SUPERFLUOUS AND MAKES AN INVALID ASSUMPTION -- the math is
unambiguous, and the answer is: NEITHER, the field gradient points to
the retarded source position EXTRAPOLATED LINEARLY to the time at which
the gradient is evaluated.

The correct way to use the L-W potential for a single point source, and
to compute the E field from its gradient, is as follows:

To determine the E field at spatial point P and time T (both specified
in a given inertial frame which is used throughout) one needs to know
the potential at every point within a spatial neighborhood of P at time
T. One does that using the L-W formula, noting that the retardation is
different for each point in the neighborhood of P, so that the source
position is evaluated at slightly different times for each point in the
neighborhood (one can relate this difference to the velocity of the
source at the retarded time). Now one takes the gradient of the
potential at P. Note there is no ambiguity whatsoever in taking that
gradient, because the potential was evaluated at time T for every point
within the spatial neighborhood of P.

Let me repeat that: there is no ambiguity whatsoever in taking the
gradient at point P and time T, because the potential was evaluated at
time T for every point within the spatial neighborhood of P. In
particular, properties of the source are evaluated only in an
infinitesimal neighborhood of the retarded time T-R(T)/c.

[The spatial neighborhood of P is 3-dimensional; the
neighborhood of the retarded time is 1-d; for each
point in the latter there is a 2-d locus in the former.]

When one does this, one finds that for a moving source (i.e. moving
relative to the inertial frame used above), E does not point at the
location of the source at the retarded time. When one linearly
extrapolates the position and velocity of the source at the retarded
time in the obvious way to time T, one finds that E points at this
latter point.

I'm saying nothing new, and this is explained in every
graduate-level textbook on classical E&M.


In the weak-field linear approximation to GR the situation is more
complicated, but basically the same. The gravitational force vector at
point P and time T points to the QUADRATICALLY EXTRAPOLATED position of
the source at time T. That is, the position, velocity, and acceleration
of the source are involved in an infinitesimal neighborhood of the
retarded time.

In GR itself, without approximation, there is no general
Green's-function method to solve the field equation, because it is
nonlinear. There can be no scalar "gravitational potential" because in
GR gravitation has more degrees of freedom and a scalar field is
inadequate to represent it. In some sense the metric can be considered
to be a "generalized gravitational potential", and the analogy to the
gradient is the Christoffel symbols -- this has the necessary property
that the "generalized gravitational force" is zero when evaluated in
locally-inertial coordinates.



This has been explained to you numerous times. I don't know why it is so
hard for you to understand this. Apparently you don't actually have the
requisite background: this E&M is very basic physics taught to every
graduate student of physics (ditto for the GR, but not every graduate
student takes that course).

[Your problem seems to be that you cannot imagine that the
gradient does not point at the source. It doesn't -- this
is NOT a central force, and your notion that retardation
screws up planetary orbits is just plain wrong. Indeed,
the quadratic extrapolation is PRECISELY what is needed
to make such orbits almost but not quite stable (e.g. the
precession of perihelia).]


Tom Roberts

Ken S. Tucker wrote on Wed, 04 Jun 2008 13:20:16 -0700:

On Jun 3, 3:49 am, "Juan R." González-�lvarez

As i already pointed here several times, I am working in an *extension*
of both SR and GR. The theories of SR and GR are recovered in a well-
defined limit of a more general and sophisticated theory.

The theory reduces to GR and explains *why* the speed of gravity in GR
coincides with the speed of gravity. However this is not true in the
generalized theory.

The new theory is a sophisticated formulation based in mathematics and
physics developed in last few years. Technically it is a nongeometrical
DPI many-body theory in Liouville space with universal evolution
parameter.

As already said GR results are obtained as special case and the limits
of geometry and spacetime fixed :-)

Your accusation of using 1908 physics and maths looks thus completely
irrelevant and your re-accusations look very unfair :-)

Ok, who is your target market, (evidentally not me, as you Juan insist).

Simple, people who do not make unfair criticisms about works he never
read first :-)

Also, people who take five minutes to read references provided instead
repeating mistakes were corrected in print :-)

I'm interested in the new predicticts your theory makes, apart from our
classicals. Ken

Oh, i am too :-)

The dual theory make several interesting predictions (for both
electrodynamics and gravity) and also solves well-known difficulties with
the former theory (when interactions travel at c).

That is, the new theory gives right answers for questions that former
theory gives us wrong.

If you had taken a look to references cited you would already know at
least this part :-)


--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org

Tom Roberts wrote on Thu, 05 Jun 2008 04:40:03 -0500:

(snipped ad hominem)

Tom Van Flandern wrote:

[For simplicity, I'll discuss the Lenard-Wiechert
potential of classical electrodynamics (ignoring magnetism). I'll
relate this to GR below.]

(sniped naive discussion)

Let me repeat that: there is no ambiguity whatsoever in taking the
gradient at point P and time T, because the potential was evaluated at
time T for every point within the spatial neighborhood of P. In
particular, properties of the source are evaluated only in an
infinitesimal neighborhood of the retarded time T-R(T)/c.

There exists difficulties to evaluate the E field derived from L&W
potentials. This is revised with mathematical detail (just details you
ignore) in

Necessity of simultaneous co-existence of instantaneous and retarded
interactions in classical electrodynamics. 1999:
Int. J. of Mod. Phys. A 14(24), 3789. Chubykalo, Andrew E; Vlaev, Stoyan
J.

with the conclusion that fields E and B are *not* retarded but contain an
irreducible component with (speed c). That instantaneous component
correspond to the dual potential introduced in

Action at a distance as a full-value solution of Maxwell equations: The
basis and application of the separated-potentials
method. 1996: Phys. Rev. E 53, 5373. Chubykalo, Andrew E; Smirnov-Rueda,
Roman.

Other mathematical ambiguities *you* completely ignore in your naive
(textbook like) discussion are revised in other papers, e.g see

http://arxiv.org/pdf/math-ph/0204043.pdf

and references cited therein.

In the weak-field linear approximation to GR the situation is more
complicated, but basically the same.

Indeed same difficulties than in EM and basically the same dual
generalization is needed

h^ab(r,t) -- h^ab(r,t) + h^ab(R(t))

I introduce gravitational dualism in my paper "Newtonian limit
difficulties of General Relativity".

The dual generalization implies that fundamental speed of gravity is not
c as incorrectly believed in GR :-)

In GR itself, without approximation, there is no general
Green's-function method to solve the field equation, because it is
nonlinear.

And you claim expertise? :-)

Next is the standard solution to the field equation in *full* (nonlinear)
GR obtained using *Green methods*

h^ab = 4 Int (\tau / r) d^3x

where the source, of course, is evaluated using the past light cone.

(snipped ad hominem)

Well, I know *for sure* that Vigier was aware that a pure scalar theory
of gravity is not enough. Vigier itself was working a non-scalar theory,
and i think Tvf knows that also.

But saying that cannot be scalar "gravitational potential" is completely
false.

The scalar is usually identified with h_00. Take a look to Moller
textbook or to Weinberg section in PPN formalism or just ask some
astronomer (e.g. TvF) on how they have tested GR using potentials :-)

In some sense the metric can be considered
to be a "generalized gravitational potential", and the analogy to the
gradient is the Christoffel symbols -- this has the necessary property
that the "generalized gravitational force" is zero when evaluated in
locally-inertial coordinates.

Here i would recover a classic from sci.physics.research:

"Yours is a statement of profound ignorance in all of its parts."
--- Uncle Al to Tom Roberts in sci.physics.research Feb 2008


Once more again, Tom, *you* confound the field formulation with the
geometrical formulation. Astronomers are not so ignorant and unlike you
they know they are speaking. This is standard stuff and may be found in
many textbooks. A resume is:

(G) -- Geometric formulation

(F) -- field "

Metric (G): g_ab = n_ab + h_ab

Field potential (F): h_ab

Analogy to the gradient (F):

(1/2) \gamma (\partial h_ab \over \partial x^k) v^a v^b

If either often astronomers simply this expression for weak fields and
introduce a set of potentials \phi, A^i, etc.

(rest of rants snipped)


--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org