Tom Van Flandern wrote:
Tom Roberts writes:


In this discussion, one of us is answering every point by addressing
observations, experiments, citations, or argumentation. And one of us is
simply repeating bold claims without any new attempt to justify them.
Shall we let the readers decide which of us matches which description?
:-) -|Tom|-


I, for one, think that you (Tom Van Flandern) are the
one who is 'simply repeating bold claims without any
new attempt to justify them'.

Martin Hogbin

On Jul 27, 12:40*am, "Ken S. Tucker" wrote:
On Jul 26, 8:05 pm, "Pmb" wrote:





"Ken S. Tucker" wrote in ...

On Jul 26, 5:48 pm, Tom Roberts wrote:
Ken S. Tucker wrote:
Hi Steve, Tom and all. I can suggest a means of resolution by
experiment, but it is complicated so stay with me on the bends.

Robert's, somehow you've screwed up
your replies below. My post was directed
to Tom VvF and Steve Carlip, perhaps having
an extra Tom messed things up.
From now on it's Tucker, Carlip, Flandern,
Roberts etc.
Anyway I'm a GRist on this issue and generally
agree Carlip.

Actually, it isn't complicated at all, and HAS ALREADY BEEN DONE.

I see that Tom is still using capitals to provide emphasis even when it is
almost always interpreted by the general reader as yelling. *I wonder if Tom
actually cares about things like how people feel about caps!? Nah.
Pete

Hi Pete.
I don't give a rat's ass about caps,

Of course Ken. However you're not a newbie. You are all too familiar
with Tom's strange posting habits. A new person who does not know
Tom's quirks and his reasons for violating newsgroups etiquette would
generally have a much greater repulsion to Tom's cap problem. Plus,
reading caps is a pain in the ass. I hate it when I get snaim mail
letters which contain all caps. They're really irritating to read.

Pete

Hi Hans

On Jul 28, 3:46 am, wrote:
On Jul 27, 6:13 pm, "Ken S. Tucker" wrote:

Hi Pete and Hans.

Hans has an excellent diagram 16.1 I've been
studying, Pete, how about rendering an opinion.
Ken

That's from chapter 16 on the Hamiltonian and
Lagrangian densities:http://physics-quest.org/Book_Chapter_Lagrangian.pdf

There's a significant update on the derivation
of the Lienard-Wiechert E & B fields demonstrating
that the E field points towards the extrapolated
position instead of the retarded position.http://physics-quest.org/Book_Chapte...rentzContr.pdf

Thanks Hans. I admire Fig 2.5, it makes
good sense seeing it that way. I was
thinking of a radiating or receiving antenna
dipole while reading it, but then you used
the Sun as a radiation emitter and the location
of it's gravitational influence perfectly.
It's good to see a bigger picture.

I made a similiar argument on Apr.8 in this
thread using GR geodesics, accounting for
aberration and rotation, but didn't apply
it to electric fields.
Regards
Ken S. Tucker

Regards, Hanshttp://physics-quest.org
Cheers

Hi Pete.

On Jul 28, 9:54 pm, pmb wrote:
On Jul 27, 12:40 am, "Ken S. Tucker" wrote:



On Jul 26, 8:05 pm, "Pmb" wrote:

"Ken S. Tucker" wrote in ...

On Jul 26, 5:48 pm, Tom Roberts wrote:
Ken S. Tucker wrote:
Hi Steve, Tom and all. I can suggest a means of resolution by
experiment, but it is complicated so stay with me on the bends.

Robert's, somehow you've screwed up
your replies below. My post was directed
to Tom VvF and Steve Carlip, perhaps having
an extra Tom messed things up.
From now on it's Tucker, Carlip, Flandern,
Roberts etc.
Anyway I'm a GRist on this issue and generally
agree Carlip.

Actually, it isn't complicated at all, and HAS ALREADY BEEN DONE.

I see that Tom is still using capitals to provide emphasis even when it is
almost always interpreted by the general reader as yelling. I wonder if Tom
actually cares about things like how people feel about caps!? Nah.
Pete

Hi Pete.
I don't give a rat's ass about caps,

Of course Ken. However you're not a newbie. You are all too familiar
with Tom's strange posting habits. A new person who does not know
Tom's quirks and his reasons for violating newsgroups etiquette would
generally have a much greater repulsion to Tom's cap problem. Plus,
reading caps is a pain in the ass. I hate it when I get snaim mail
letters which contain all caps. They're really irritating to read.
Pete

Carlip and Flandern have access to the most
update data bases available, and have available
advanced computational facilities.
Pete, I used what you term the "tidal effect"
(the 4th rank R_abcd), simplistically detailed
on Apr. 8 this thread to predict how GR should
tidally shift the semi-major axis of the tidal
induced orbit anomally to point to the APPARENT
position of the Sun.
A 20 arc sec shift in the orbit of a satellite
is difficult to detect, so I'm stuck right now.
Regards
Ken S. Tucker

On Jul 29, 6:10*pm, "Ken S. Tucker" wrote:
Hi Hans
There's a significant update on the derivation
of the Lienard-Wiechert E & B fields demonstrating
that the E field points towards the extrapolated
position instead of the retarded position.

http://physics-quest.org/Book_Chapte...rentzContr.pdf

Thanks Hans. I admire Fig 2.5, it makes
good sense seeing it that way. I was
thinking of a radiating or receiving antenna
dipole while reading it, but then you used
the Sun as a radiation emitter and the location
of it's gravitational influence perfectly.
It's good to see a bigger picture.

I made a similiar argument on Apr.8 in this
thread using GR geodesics, accounting for
aberration and rotation, but didn't apply
it to electric fields.
Regards
Ken S. Tucker



Cheers

Hi, Ken

If people would simply understand figure 2.5
then this whole recurring discussion about
the speed of gravity wouldn't be necessary. :^)


Regards, Hans
http://physics-quest.org

On Jul 29, 9:10 pm, "Tom Van Flandern" wrote:
This replies to Steve Carlip, Hans de Vries, Ken S. Tucker, Tom Roberts,
and Martin Hogbin. REFERENCES appended at the end.



Steve Carlip writes:
[TomVF]: The direction of the source mass as sensed by an orbiting target
body is toward its true instantaneous position when the target body or
field point is at rest. And it is toward the source mass's retarded
position (retarded by the speed of gravitational force) when the target
body is orbiting. That's elementary physics. The exact same statement is
equally true if the source mass is moving, then stops (your example).
That "move, then stop" distraction just makes a simple problem more
complicated.
[Carlip]: Tom, this is simply wrong. According to general relativity, when
the source mass stops, the acceleration of the test body will continue to
track its "extrapolated" motion, until a time equal to the light-travel
time from the source to the test body, at which point the acceleration
will rapidly swing back to the actual direction of the source mass. This
isn't a guess or an opinion. It's a calculation. Stop talking through your
hat, and do the math!

Steve, once again I insist, we have no issues with the math. None. This
discussion and the issues of importance are all about the interpretation of
the math, the physics behind the math, what the math means for reality. It
would be nice if we could begin getting our heads together about this. Can
you see your way to acknowledging that general relativity has two different
physical interpretations, the geometric and the field? That is not just my
opinion, but one well known through the early and middle 20th century,
suppressed only following the MTW bid to make the geometric interpretation
dominant. But major physicists as recent as Feynman reaffirmed this duality
of interpretation, reminding us that the geometric interpretation is not
really needed for anything in particular. [Ref. 1] All of relativity can be
described with classical forces in a Euclidean 3-space context, which is the
field interpretation of general relativity.

Or do you wish to redefine "general relativity" to exclude the field
interpretation? :-(

Once we agree on this indisputable fact that the geometric
interpretation is not the only way to understand the math of GR, then you
will readily see that my statement was true for the field interpretation,
and yours for the geometric interpretation. The field equations of GR
describe only the gravitational potential field, so the claims you make are
true for the potential field. Whether or not they apply also to force or
acceleration requires an additional assumption about how force relates to
potential. In the geometric interpretation, whatever is true for the field
is also true for gravitational force/acceleration (your view). But in the
field interpretation, force/acceleration drives the field, not the other way
around (my view).

The next step is to notice that what you claim (that gravitational
acceleration of a target body will suddenly stop tracking the instantaneous
position of the source mass if the source experiences a sudden acceleration)
violates the clear evidence from binary pulsars, which show that the
acceleration continues to track the instantaneous position of the source
mass even when the source mass accelerates by a substantial amount. You
apparently wish to claim that there will be a major difference in behavior
of the target body if the source mass acceleration experiences a "sudden"
(i.e., unanticipated) acceleration instead of just a "substantial"
acceleration. But you have no leg to stand on in making such a claim. Not a
shred of evidence supports it [Ref. 2]; the lifting of the universal speed
limit removes any logical reason to expect it [Ref. 3]; and it is also
untrue in electrodynamics, where sudden accelerations of charges are still
tracked essentially instantaneously [Ref. 4].

You learned only one way to interpret the math of GR. I learned two
ways. If you became more familiar with the way relativistic celestial
mechanics operates, I think you will be (pleasantly?) surprised. It opens up
a lot of doors to a deeper understanding of gravity, and settles a lot of
paradoxes, especially in QM.

and Hans de Vries writes:

[TomVF]: On the contrary, binary pulsars prove that when the source mass
accelerates (as in Steve's example), the target body responds almost
instantly.
[de Vries]: The EM case is much simpler with the essentially same result.

On Jul 30, 2:44 am, wrote:
On Jul 29, 9:10 pm, "Tom Van Flandern" wrote:

This replies to Steve Carlip, Hans de Vries, Ken S. Tucker, Tom Roberts,
and Martin Hogbin. REFERENCES appended at the end.

Steve Carlip writes:
[TomVF]: The direction of the source mass as sensed by an orbiting target
body is toward its true instantaneous position when the target body or
field point is at rest. And it is toward the source mass's retarded
position (retarded by the speed of gravitational force) when the target
body is orbiting. That's elementary physics. The exact same statement is
equally true if the source mass is moving, then stops (your example)..
That "move, then stop" distraction just makes a simple problem more
complicated.
[Carlip]: Tom, this is simply wrong. According to general relativity, when
the source mass stops, the acceleration of the test body will continue to
track its "extrapolated" motion, until a time equal to the light-travel
time from the source to the test body, at which point the acceleration
will rapidly swing back to the actual direction of the source mass. This
isn't a guess or an opinion. It's a calculation. Stop talking through your
hat, and do the math!

Steve, once again I insist, we have no issues with the math. None. This
discussion and the issues of importance are all about the interpretation of
the math, the physics behind the math, what the math means for reality. It
would be nice if we could begin getting our heads together about this. Can
you see your way to acknowledging that general relativity has two different
physical interpretations, the geometric and the field? That is not just my
opinion, but one well known through the early and middle 20th century,
suppressed only following the MTW bid to make the geometric interpretation
dominant. But major physicists as recent as Feynman reaffirmed this duality
of interpretation, reminding us that the geometric interpretation is not
really needed for anything in particular. [Ref. 1] All of relativity can be
described with classical forces in a Euclidean 3-space context, which is the
field interpretation of general relativity.

Or do you wish to redefine "general relativity" to exclude the field
interpretation? :-(

Once we agree on this indisputable fact that the geometric
interpretation is not the only way to understand the math of GR, then you
will readily see that my statement was true for the field interpretation,
and yours for the geometric interpretation. The field equations of GR
describe only the gravitational potential field, so the claims you make are
true for the potential field. Whether or not they apply also to force or
acceleration requires an additional assumption about how force relates to
potential. In the geometric interpretation, whatever is true for the field
is also true for gravitational force/acceleration (your view). But in the
field interpretation, force/acceleration drives the field, not the other way
around (my view).

The next step is to notice that what you claim (that gravitational
acceleration of a target body will suddenly stop tracking the instantaneous
position of the source mass if the source experiences a sudden acceleration)
violates the clear evidence from binary pulsars, which show that the
acceleration continues to track the instantaneous position of the source
mass even when the source mass accelerates by a substantial amount. You
apparently wish to claim that there will be a major difference in behavior
of the target body if the source mass acceleration experiences a "sudden"
(i.e., unanticipated) acceleration instead of just a "substantial"
acceleration. But you have no leg to stand on in making such a claim. Not a
shred of evidence supports it [Ref. 2]; the lifting of the universal speed
limit removes any logical reason to expect it [Ref. 3]; and it is also
untrue in electrodynamics, where sudden accelerations of charges are still
tracked essentially instantaneously [Ref. 4].

You learned only one way to interpret the math of GR. I learned two
ways. If you became more familiar with the way relativistic celestial
mechanics operates, I think you will be (pleasantly?) surprised. It opens up
a lot of doors to a deeper understanding of gravity, and settles a lot of
paradoxes, especially in QM.

and Hans de Vries writes:

[TomVF]: On the contrary, binary pulsars prove that when the source mass
accelerates (as in Steve's example), the target body responds almost
instantly.
[de Vries]: The EM case is much simpler with the essentially same result.
Did you ever try to derive the direction of the E-field from a moving
charge?

Of course. That was featured in my joint paper with J.P. Vigier [Ref.
3]. And it is indeed closely parallel with the gravitational case, where
even accelerations of charges are tracked instantaneously [Ref. 4], even
though many textbooks assert the opposite without any experimental support
for that assumption at all. Experimental evidence trumps textbook claims.

[de Vries]: I wrote a derivation of the Lienard-Wiechert potentials in
chapter 2 of my book which is step-by-step with comments ...

And I published a detailed explanation of why such retarded potentials
describe only the behavior of the potential field, but say nothing about the
forces (gravitational or electrodynamic) that shape potential fields. [Ref.
5]

As I said to Steve: Don't befuddle yourself by making this complicated.
Consider a static potential field around an unmoving source mass. If a
photon (speed c) and a classical graviton (speed undetermined) leave a
source mass at the same instant and travel the same linear path to the same
orbiting target body, the photon arrives from the retarded source direction
(naturally), whereas the classical graviton arrives from the instantaneous
source direction (unexpectedly). The only physical difference available to
account for this change in the action direction is that they travel the same
path with different speeds.

If you substitute "virtual photon" for "classical graviton" and "charge"
for "mass", the same reasoning applies to electrodynamics. Virtual photons,
as you might have heard, are alleged to have infinite speed to "explain"
this unexpected behavior.

and Ken S. Tucker writes:

[Tucker]: suppose the Sun was to instantly convert to light energy. Since
Earth is in free-fall, that event (aside from the flash) would be
undetectable by gravitation except by a tidal variation. ... Either Steve
or Tom may predict when that tidal variation could be detected.

My prediction is already on record. Force shuts off instantly (assuming
your "light energy" has no mass), whereas the field change takes 8.3 minutes
to arrive at Earth. See [Ref. 6].

[Tucker]: Suppose we examine the geodesy of a satellite in a normally
circular orbit, orbiting Earth. The gravitational effect of the Sun will
cause a tidal effect on the orbit of that satellite, such that the
circular orbit will be pulled to an ellipse. The semi-major axis of that
elliptical orbit will point to either the "absolute" position of the Sun
as Flandern predicts or it will point to the "apparent" position of the
Sun as Tucker and Carlip predict. The diff between those two predicted
axes is ~ 20" arc.

The solar eclipse experiment already showed precisely what your example
suggests as a test, where the Moon is the satellite in question. And the
answer is unambiguous and undisputed: the bulge in the Moon's orbit is
toward the instantaneous Sun, not the retarded Sun. [Ref. 2]

[Tucker]: The data base exists, 1st guy to tease out the data accurately
gets my nomination for a Nobel.

Thank you. ļ But I'll be even happier if you do not change your test in
some way, now that it has gone in an unexpected direction for you. That is
what "controls against bias" is all about in scientific method - not
discounting test results when they go against expectations.

[Tucker]: What I'm pointing out to Steve and Tom is the means to
experimentally resolve this ongoing argument, prior to them sitting in an
old folks home throwing false teeth at each other.

It was a nice thought. But we still have to find some way to entertain
ourselves in the old folks home. And I'll throw my false teeth at you if you
don't get my last name right: "Van Flandern" (note capital "V"). ļ

and Tom Roberts writes:
[Roberts]: The actual observations for EVERY ONE of the experiments TVF
cites are in accord with the predictions of GR.

Of course. No one has suggested otherwise. [shrug] But you still don't
get what the discussion is about.

[Roberts]: So when he says "binary pulsars prove that when the source mass
accelerates (as in Steve's example), the target body responds almost

instantly", you should recognize: ... the source NEVER accelerates "as in
Steve's example", the two objects merely orbit each other.

Now you are talking nonsense. Look up the definition of "accelerate" and
remember we are having a 3-space discussion. Anything in orbit is
accelerating by definition of the word: the time rate of change of (3-space)
velocity (a vector).

[Roberts]: In GR, nothing that carries energy, momentum, or information
can travel with local speed c relative to any locally-inertial frame..
TVF's "speed of gravity" would violate this, IF IT WERE GR. He is wrong,
because he is not actually applying GR. That is Steve's point, and mine.

And you will remain of that unsupportable opinion all your life unless
you start to appreciate that there is a difference between math and the
physical interpretation of that math. Learn the field interpretation of GR.
Study some celestial mechanics. THEN let's talk.

As to the substance of your point, for the benefit of others uninhibited
by being...

read more

Thanks for your posts Tom et al.
I have been following this discussion for years.

Sorry to not address your points specifically, but my question is
perhaps simpler.
At first it appears that stable elliptic orbits are consistent with
superluminal speed of gravity field, as Van Flandern has presented in
his papers.

Stable elliptic orbits are also consistent with:

inductive coupling [which] takes place in the
near field £h¡Ó c/r12 between coherently
coupled individual dipoles, through their red-shifted
local antipodal image. This allows the exchanged photons
to be virtual and the coherent modes to genuinely
belong to the coupled oscillators while ensuring that
the range of gravity spans the Universe. In this sense,
the Zitterbewegung of all matter near and far can be felt
here, in the far infrared (£fred shifted 1010 LYrs),
by the Zitterbewegung of a test charged particle or dipole,
in direct proportion to the rate of both, that is, to their
energy, owing to their common coherent modes with the
universe at large, through red-shifted tunneling photons.
This is in agreement with the equivalence principle.
http://arxiv.org/abs/physics/0107015v6
http://en.wikipedia.org/wiki/Induced_gravity

Hydrogen and helium is far more common than examples
of superluminal propagation.


Carlip's paper showed that orbits are also consistent
with light speed propagation, due to a subtlety of retarded potentials
also present in the Lienard-Wiechert potentials of electromagnetism.

Is there any experimenatal evidence, past or future, that can decide
between these two approaches? The speed of gravity being equal to
that of light fits in better with current theory and so unless there
is some real test between the interpretations that will remain the
more accepted version. However it would sure be nice to rule out
superluminal propagation.. would a change in the propagation speed
change the observable behavior of tight binary systems? It seems a
laboratory test is well beyond our current technology..

Atoms are massive particles. They are therefore
accelerated by gravity. A matter wave beam will fall
like a beam of ordinary atoms.
http://cua.mit.edu/ketterle_group/Pr...ser_comm..html

Sue...


Thanks -

On Jul 30, 3:10 am, "Tom Van Flandern" wrote:
[de Vries]: The EM case is much simpler with the essentially same result.

Hi Flandern, I did not intend to intrude into
your and Carlips discussion, you guys are busy.

On Jul 29, 6:10 pm, "Tom Van Flandern" wrote:
This replies to Steve Carlip, Hans de Vries, Ken S. Tucker, Tom Roberts,
and Martin Hogbin. REFERENCES appended at the end.
...
and Ken S. Tucker writes:
[Tucker]: suppose the Sun was to instantly convert to light energy. Since
Earth is in free-fall, that event (aside from the flash) would be
undetectable by gravitation except by a tidal variation. ... Either Steve
or Tom may predict when that tidal variation could be detected.

My prediction is already on record. Force shuts off instantly (assuming
your ¡§light energy¡¨ has no mass), whereas the field change takes 8.3 minutes
to arrive at Earth. See [Ref. 6].

How would you detect "Force shuts off"?

[Tucker]: Suppose we examine the geodesy of a satellite in a normally
circular orbit, orbiting Earth. The gravitational effect of the Sun will
cause a tidal effect on the orbit of that satellite, such that the
circular orbit will be pulled to an ellipse. The semi-major axis of that
elliptical orbit will point to either the "absolute" position of the Sun
as Flandern predicts or it will point to the "apparent" position of the
Sun as Tucker and Carlip predict. The diff between those two predicted
axes is ~ 20" arc.

The solar eclipse experiment already showed precisely what your example
suggests as a test, where the Moon is the satellite in question. And the
answer is unambiguous and undisputed: the bulge in the Moon¡¦s orbit is
toward the instantaneous Sun, not the retarded Sun. [Ref. 2]

Apart from self-referencing is there a refereed
agreement to that measurement?
My suggestion sounds simple, and I've studied the
problem, it's tough, so I need the details.
I've consulted with other Celestrial Mechanics
on the problem too, did you use lasers?

[Tucker]: The data base exists, 1st guy to tease out the data accurately
gets my nomination for a Nobel.

Thank you. ƒº But I¡¦ll be even happier if you do not change your test in
some way, now that it has gone in an unexpected direction for you. That is
what ¡§controls against bias¡¨ is all about in scientific method ¡V not
discounting test results when they go against expectations.

[Tucker]: What I'm pointing out to Steve and Tom is the means to
experimentally resolve this ongoing argument, prior to them sitting in an
old folks home throwing false teeth at each other.

It was a nice thought. But we still have to find some way to entertain
ourselves in the old folks home. And I¡¦ll throw my false teeth at you if you
don¡¦t get my last name right: ¡§Van Flandern¡¨ (note capital ¡§V¡¨).

LOL, I though Van was your middle name, like maybe
your Dad was into trucks or something :-).
Regards
Ken S. Tucker


REFERENCES

[1] Feynman Lectures on Gravitation, R.P. Feynman, Addison-Wesley, New York
(1995). Section 8.4, p. 113: ¡§It is one of the peculiar aspects of the
theory of gravitation, that it has both a field interpretation and a
geometrical interpretation. ... the fact is that a spin-two field has this
geometrical interpretation: this is not something readily explainable -- it
is just marvelous. The geometrical interpretation is not really necessary or
essential to physics.¡¨

[2] ¡§The speed of gravity ¡V What the experiments say¡¨, T. Van Flandern,
Phys.Lett.A 250:1-11 (1998). Also athttp://metaresearch.org/cosmology/speed_of_gravity.asp.

[3] ¡§Experimental Repeal of the Speed Limit for Gravitational,
Electrodynamic, and Quantum Field Interactions¡¨, T. Van Flandern and J.P.
Vigier, Found.Phys. 32:1031-1068 (2002). Preprint under title ¡§The speed of
gravity ¡V Repeal of the speed limit¡¨ available athttp://metaresearch.org/cosmology/gravity/speed_limit.asp.

[4] ¡§Electromagnetic mass and the inertial properties of nuclei¡¨, C.W.
Sherwin and R.D. Rawcliffe, Report I-92 of March 14, 1960 of the
Consolidated Science Laboratory, Univ. of Illinois, Urbana; obtainable from
U.S. Department of Commerce¡¦s Clearinghouse for Scientific and Technical
Information, document AD 625706.

[5] ¡§Reply to comments on ¡¥The speed of gravity¡¦¡¨, T. Van Flandern,
Phys.Lett.A 262:261-263 (1999).

[6] See animation #6 and its caption athttp://metaresearch.org/media%20and%20links/animations/animations.asp

[7] ¡§Is faster-than-light propagation allowed by the laws of physics? (A
primer on Lorentzian relativity)¡¨, Infinite Energy 59, 31-33 (2005). Also athttp://metaresearch.org/cosmology/gravity/LR.asp.

Tom Van Flandern ¡V Sequim, WA - see our web site on frontier astronomy
research athttp://metaresearch.org

Tom Van Flandern wrote:

Steve Carlip writes:

[TomVF]: The direction of the source mass as sensed by an orbiting target
body is toward its true instantaneous position when the target body or
field point is at rest. And it is toward the source mass's retarded
position (retarded by the speed of gravitational force) when the target
body is orbiting. That's elementary physics. The exact same statement is
equally true if the source mass is moving, then stops (your example).
That "move, then stop" distraction just makes a simple problem more
complicated.

[Carlip]: Tom, this is simply wrong. According to general relativity, when
the source mass stops, the acceleration of the test body will continue to
track its "extrapolated" motion, until a time equal to the light-travel
time from the source to the test body, at which point the acceleration
will rapidly swing back to the actual direction of the source mass. This
isn't a guess or an opinion. It's a calculation. Stop talking through your
hat, and do the math!

Steve, once again I insist, we have no issues with the math. None.

Don't be silly, Tom. Of course we have issues with the math.

Look at the case you just quoted -- a gravitating object moving at a constant
velocity that abruptly stops. Now, *do the damn math!* The result is completely
unambiguous, and it's exactly what I described. If you disagree with this result,
then you disagree with the math.

This discussion and the issues of importance are all about the interpretation
of the math, the physics behind the math, what the math means for reality.

A gravitating object moving at a constant velocity abruptly stops. Either
the acceleration of a test body immediately points toward the "stopped"
position, or it continues to track the extrapolated motion before swinging
back to the "stopped" position. This is not a question of "interpretation"
-- it is two physically different predictions. The math either leads to one
prediction or the other.

Now, do the math. You will see that GR unambiguously predicts the second
option.

It would be nice if we could begin getting our heads together about this. Can
you see your way to acknowledging that general relativity has two different
physical interpretations, the geometric and the field?

Sure. This is true, and completely irrelevant. In either interpretation, the
equations are the same, and the predictions are the same. We are not arguing
over interpretation; we are arguing about the physical predictions of the
theory. Once again: do the damn math!

[...]
Once we agree on this indisputable fact that the geometric
interpretation is not the only way to understand the math of GR, then you
will readily see that my statement was true for the field interpretation,
and yours for the geometric interpretation. The field equations of GR
describe only the gravitational potential field, so the claims you make are
true for the potential field. Whether or not they apply also to force or
acceleration requires an additional assumption about how force relates to
potential.

Lets try this once again. A gravitating object moving at a constant velocity
abruptly stops. General relativity, in whatever interpretation you like,
provides a mathematical algorithm for predicting the resulting motion of
a test mass:

1. Write down a stress-energy tensor for the gravitating source. (Of
course, you have to include all sources -- if A stops because it hits a
wall, you'd better include the field of the wall as well.)

2. Solve the Einstein field equations to determine the metric, given
this stress-energy tensor. (There are nice existence and uniqueness
theorems, going back to Yvonne Choquet-Bruhat's work in the '50s,
that guarantee that this can be done, although in practice you often
need an approximation procedure.)

3. Given the metric from step 2, write down the geodesic equations.
(Once you have the metric, these are unique.)

4. Solve the geodesic equations to determine the motion of body B.
(Here, the existence and uniqueness theorems are centuries old; given
an initial position and velocity for B, the equations uniquely determine
its future motion.)

Do you agree that GR specifies these steps? If not, which one do you
disagree with, and in precisely what way?

Do you agree that once the stress-energy tensor is specified, the remaining
mathematical equations have unique solutions? If not, which particular
step do you think is not unique, and in precisely what way.

If you agree with these steps -- as steps in a mathematical procedure
for computing the prediction of the theory -- then we agree on the math.
In that case, once again, just do the damn calculation!

If you do not agree with these steps, we are not arguing about an
"interpretation," we disagree about the mathematics of general relativity.

[...]
The next step is to notice that what you claim (that gravitational
acceleration of a target body will suddenly stop tracking the instantaneous
position of the source mass if the source experiences a sudden acceleration)
violates the clear evidence from binary pulsars, which show that the
acceleration continues to track the instantaneous position of the source
mass even when the source mass accelerates by a substantial amount.

No. Once again, do the damn math! The GR prediction is that the
acceleration of each pulsar is *not* precisely toward the instantaneous
position of its companion, but toward a slightly advanced position. This
is, in fact, what is observed -- Hulse and Taylor won a Nobel Prize for this.

Steve Carlip