Tom Van Flandern wrote:
Steve Carlip writes:
[Carlip]: a gravitating object -- call it A -- moving at a constant
velocity suddenly stops. What happens to the motion of a test body B a
distance R away from the point that A stops?

This has nothing to do with the issue on the table, the propagation
speed of gravitational force. It concerns only the propagation speed of
changes in the gravitational potential field, about which there is no
dispute -- it is speed c.

We don't need A to be moving, then stop, as in your example. The
issue of relevance here is present even when A is permanently at rest
and its field is completely static. 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.

So you claim that the "gravitational force" in Steve's example is not
the "gravitational force" in yours (in general, abstracting away the
differences in physical situations). That is ridiculous.

You claim Steve's example is "propagation speed of
changes in the gravitational potential field". But the
gradient of the potential gives the force (in your
model), so "gravitational force" also "is speed c"
-- either that is true or you disbelieve mathematics.

The problem is: your model is inconsistent with
"gravitational force" propagating at speed c; but the
appropriate approximation to GR is not inconsistent
with that, nor is GR itself. But you refuse to
distinguish among the THREE models: yours, GR itself,
and the approximation to GR (this approximation has
been discussed at length, previously).

Steve's example is a COUNTEREXAMPLE to your claim "The direction of the
source mass as sensed by [the] target body is toward [the source's] true
instantaneous position". That is, of course, why he mentioned it.


You seem to think that "orbiting" is somehow special, and your claims
apply only to that specific physical situation, and not others (such as
Steve's). That is ludicrous for what purports to be a general theory.

As has been repeatedly pointed out, for the situation you
discuss an approximation to GR is valid, and in that
approximation the "gravitational force" points directly
to the EXTRAPOLATED position of the source. For the
situations you consider, that EXTRAPOLATED position is
indistinguishable from its present position [#]. But for
Steve's situation they are different, and clearly show
the error in your claims, WHEN USING THIS APPROXIMATION
TO GR.

[#] This is why the experiments you cite do not refute GR.

Of course Steve was discussing the correct computation in GR itself, not
this approximation, and he shows a similar conclusion (no surprise in a
regime where this approximation is valid).


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.

It is not too complicated for sensible people to think about. And it
clearly and succinctly refutes your claims about "speed of gravitational
force" and the direction of "gravitational force pointing to the
source's true instantaneous position" -- in both the approximation to GR
I mentioned above, and in Steve's description of a complete computation.

I repeat: your basic problem is confusing NG with GR.
Indeed, you even confuse NG with this approximation to GR.


Address your attention
back to the static field problem, a much simpler one, and we will start
to make progress.

It is not possible to ascribe a "speed" to a static field. That is, in a
static situation it simply is not possible to distinguish among models
in which "gravitational force" propagates with different speeds, because
for any propagation speed whatsoever one obtains the same "gravitational
force" and its direction.

The other problem is you keep assuming that "gravitational
force" is a central force, and in the approximation to GR
it simply is not. In GR itself there is no quantity that
can be identified as "gravitational force" (though one
can make an analogy to components of the connection in
Newtonian coordinates).



Your claims about the orbiting body are basic math: in the frame of the
source the "gravitational force" is central. Transform to the
instantaneous rest frame of the orbiting object and of course the
"gravitational force" will still point directly at the source.

The problem is: this is NOT the math of GR. It is the math of Newtonian
gravitation. It is also not the math of the approximation to GR that
I am discussing.


[Carlip]: In general relativity, you solve this problem as follows ...

Most of your message was about this irrelevancy.

If applying General Relativity is an "irrelevancy", then you clearly are
not doing GR. THAT WAS STEVE'S POINT. And mine.


[said to Steve]
That said, what cryptic point were you trying to make?

His point is: you do not understand GR. Which you repeatedly
demonstrate, but refuse to admit.


Obviously, there is no legitimate way out of this dilemma.

The only "dilemma" is YOURS -- why do you keep claiming you are using GR
when you QUITE CLEARLY are not?

You repeatedly claim Steve (and I) are ignoring the "physics behind the
math". The problem is YOURS, not Steve's or mine -- you are confusing
Newtonian gravitation with General Relativity. The physics is DIFFERENT.
Until you actually learn about GR, you will remain confused.


Tom Roberts

Tom Roberts writes:

[Carlip]: a gravitating object -- call it A -- moving at a constant
velocity suddenly stops. What happens to the motion of a test body B a
distance R away from the point that A stops?

{TomVF]: This has nothing to do with the issue on the table, the
propagation speed of gravitational force. It concerns only the
propagation speed of changes in the gravitational potential field, about
which there is no dispute -- it is speed c. We don't need A to be moving,
then stop, as in your example. The issue of relevance here is present
even when A is permanently at rest and its field is completely static.
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.

[Roberts]: So you claim that the "gravitational force" in Steve's example
is not the "gravitational force" in yours (in general, abstracting away
the differences in physical situations). That is ridiculous.

No, it is not ridiculous, and you are apparently not following the
discussion. I objected to Steve's example because it tried to insinuate that
my position required field changes to occur faster than light, which no one
claims. Gravitational aberration much exist even for perfectly static
(unchanging) fields, as well as for fields experiencing a sudden impetus to
change, as in Steve's example. So his example serves to obscure the issue,
not to clarify it.

As is well known, the unique math of GR has more than one physical
interpretation. In particular, physics is concerned about the direction of
the arrow of causality, whereas math is not. So when we say "force is the
gradient of potential", the geometric interpretation of GR simply assumes
that the gravitational potential field, as described by the Einstein field
equations, governs; and that a gradient in that field causes a force.
However, the geometric interpretation of GR is no longer viable because it
violates physical principles. So we are forced to adopt the other physical
interpretation, that gravitational force induces a gradient into the
gravitational potential field. The arrow of causality is reversed. The math,
of course, is insensitive to this and remains unchanged.

So in Steve's example, when a source mass "A" changes its state of
uniform motion (as happens for binary pulsars in their mutual orbits),
observations are very clear that the force on distant target bodies changes
almost instantly, and always operates in the new direction of A. (Any delay
is immeasurably small.) Then this changed force operates on the field, and
alters the density of the physical potential field surrounding A. Field
changes occur at the speed of light, and eventually conform to the new
location and motion of A, but only after a delay, just as the Einstein field
equations specify.

I gather from our past exchanges that you have not been trained in
classical physics, and are familiar only with the geometric interpretation
of GR. I highly recommend you broaden your horizons. True understanding of
nature cannot be achieved through math alone. You need to study the two
different physical interpretations of GR, then come to understand why one of
them (the geometric interpretation) is now off the table, and why the other
(the field interpretation) makes the physics of gravity easier to understand
for everyone.

[Roberts]: You claim Steve's example is "propagation speed of changes in
the gravitational potential field". But the gradient of the potential
gives the force (in your model), so "gravitational force" also "is speed
c" -- either that is true or you disbelieve mathematics.

The field interpretation of GR existed before I was born, and is
therefore not "my model" even though I have published extensively about it.
In the field interpretation, the force causes the gradient in the potential
field instead of vice versa. The force propagation speed (the "speed of
gravity") is much faster than the speed c at which the physical field can
change in response to changes in the force.

In modern expositions of the field interpretation of GR, the
gravitational potential field is synonymous with the light-carrying medium,
now called "elysium". Einstein hinted at this, but did not state it quite so
clearly. Gravitational force is responsible for most orbital motion (except
the perihelion advance), and it makes elysium denser near large masses, just
as it does for planetary atmospheres. The special GR effects such as
light-bending are then simply refraction in elysium because of this density
gradient near masses. This is simple, classical physics, and is well known
in the relativity literature. Even Eddington spoke of it in his 1920 book
"Space, Time and Gravitation".

[Roberts]: The problem is: your model is inconsistent with "gravitational
force" propagating at speed c; but the appropriate approximation to GR is
not inconsistent with that, nor is GR itself.

That statement is flatly wrong. You really need to get yourself
straightened out about that point. Ask Steve Carlip or anyone who knows
relativistic dynamics. No model that has gravitational forces propagating at
speed c can reproduce the orbital motions of the planets. GR itself is about
the field, and says nothing about forces without making additional
assumptions about the nature of potential gradients. What you call the
"approximation" to GR has explicitly instantaneous forces with propagation
delay set to zero. The only light-speed propagation delays anywhere in GR
occur in the field. But the most important manifestation of propagation
delay, gravitational aberration, is set to zero when field gradients are
used to calculate forces or when it is applied to an orbiting body.

To show otherwise, all you have to do is show where the gravitational
aberration exists in the equations of motion. Such a term is easily spotted:
It must be proportional to v/v_g, where v is the relative transverse speed
of any orbiter and v_g is the speed of gravity, which (you wish to argue)
has been set equal to c. No such term exists. Steve Carlip knows that full
well, and he argued that some "velocity-dependent term" must exist to cancel
gravitational aberration. My 2002 paper with Vigier in Foundations of
Physics showed that, while such a hypothesis would be required to conserve
angular momentum when forces propagate at speed c, no possible physical
justification exists.

However, I infer that you would rather continue to hurl insults on
USENET than to read the published literature and judge the merits of the
arguments for yourself, or possibly even make a useful contribution to the
on-going dialogue.

[Roberts]: Steve's example is a COUNTEREXAMPLE to your claim "The
direction of the source mass as sensed by [the] target body is toward [the
source's] true instantaneous position". That is, of course, why he
mentioned it.

On the contrary, binary pulsars prove that when the source mass
accelerates (as in Steve's example), the target body responds almost
instantly. Your impression to the contrary is indefensible, and is keeping
you from seeing the validity of our criticism of the geometric
interpretation of GR. Unless you remedy this knowledge deficit, you will die
no wiser than you are now about relativity and the physical nature of
gravity. No one in the know challenges the fact that much better than a
linear extrapolation of the field is required to explain orbital dynamics.

[Roberts]: As has been repeatedly pointed out, for the situation you
discuss an approximation to GR is valid, and in that approximation the
"gravitational force" points directly to the EXTRAPOLATED position of the
source. For the situations you consider, that EXTRAPOLATED position is
indistinguishable from its present position [#]. But for Steve's situation
they are different, and clearly show the error in your claims, WHEN USING
THIS APPROXIMATION TO GR.
[#] This is why the experiments you cite do not refute GR.

Once again, you are dead wrong on your two major points. (1) For the
situations I consider, one of which is binary pulsars, the linearly
extrapolated position is easily distinguished from the present position. The
difference is major because the accelerations during the light-time between
the two stars are large and significant. (2) Please write a reminder to
yourself, because this is the nth time I've had to remind you: I do not
claim any experiment refutes GR, meaning the mathematical theory. Not one
iota of it needs to change. But one of the two physical interpretations of
GR (the geometric) that have existed for nearly nine decades is now
falsified in favor of the other (the field interpretation).

If you don't know or care anything about the physics behind GR, then
this change of physical interpretation need not concern you. But then you
will never understand what this discussion is about.

[Roberts]: I repeat: your basic problem is confusing NG with GR. Indeed,
you even confuse NG with this approximation to GR.

All of my statements are in a GR context. You seem to be so unfamiliar
with the physics behind GR that you are unable to distinguish GR physics
from NG physics. If so, that's not my problem; it is something you must
remedy.

[Roberts]: It is not possible to ascribe a "speed" to a static field. That
is, in a static situation it simply is not possible to distinguish among
models in which "gravitational force" propagates with different speeds,
because for any propagation speed whatsoever one obtains the same
"gravitational force" and its direction.

When changes are imposed on a static field, they spread out with a
certain speed. In the case of the gravitational potential field, that speed
is the speed of light. But whether the field is changing at speed c or
static with no speed, that has no bearing on gravitational force and its
propagation speed.

Your statement about gravitational force betrays a lack of understanding
of the physics of forces. When two bodies have a relative transverse motion,
and a force (or anything else) passes linearly between them at a uniform
speed, the receiving body will sense the force approaching from the retarded
direction of the source, not its instantaneous direction. That much is
unconditionally true.

The ratio of the relative transverse speed of the two bodies to the
force propagation speed passing between them is called "aberration". If the
force appears to come from the instantaneous position of the transmitting
body (as it does for gravity), the aberration angle (measuring apparent
motion during the light-time) is zero. Since the relative speed is not zero,
the force propagation speed must be infinite (or at least very large) to
make the aberration speed ratio approximately zero. Again, this basic
physics has full generality.

When the propagating force is light (e.g., radiation pressure force) and
travels at light-speed, the aberration angle is large and easily seen. But
for gravity, that aberration angle is zero to the accuracy of our best
observations. Hence, the speed of transmission of gravitational force from
source to receiver must be much faster than light-speed. It simply does not
matter that field changes (if any are needed) happen much slower.

[Roberts]: The other problem is you keep assuming that "gravitational
force" is a central force, and in the approximation to GR it simply is
not. In GR itself there is no quantity that can be identified as
"gravitational force"

What you call "GR itself" appears to refer to the field equations and
their solutions. I agree, these describe only the field, not the forces that
form and change that field. Once again, when thinking physics, "field" can
be considered a synonym for "light-carrying medium".

The GR equations of motion are expressions for the 3-space acceleration
of target bodies with respect to source masses. Because "force" is by
definition the time rate of change of momentum, and momentum is the product
of target mass and target relative velocity, it follows that the force
acting on the target body is given by the product of its own mass and the
3-space acceleration from the GR equations of motion. But those equations of
motion are based on central forces. Any deviations from central forces are
second order in the speed of light (i.e., proportional to 1 / c^2), and are
too small to significantly affect aberration or any of the experiments or
reasoning I described above.

But you know math. You should have been able to see that for yourself,
and not raise this straw man argument about central vs. non-central forces
as if it had some relevance to this discussion. The difference is too small
to affect this discussion by a substantial margin (many orders of
magnitude).

[Roberts]: Your claims about the orbiting body are basic math: in the
frame of the source the "gravitational force" is central. Transform to the
instantaneous rest frame of the orbiting object and of course the
"gravitational force" will still point directly at the source.

This statement refers to a "non-propagating force", something that has
no meaning in physics, where forces involve momentum by definition. If a
force propagates, then a snapshot of the system with nothing moving is
meaningless for understanding its dynamics. For a propagating force, your
statement is false. The direction of the force in the rest frame of the
orbiting body is the retarded position of the source, not its instantaneous
position.

If you might benefit from a refresher on propagation delay and
aberration, see our animation #4 at
http://metaresearch.org/media%20and%...animations.asp

[Roberts]: The problem is: this is NOT the math of GR. It is the math of
Newtonian gravitation. It is also not the math of the approximation to GR
that I am discussing.

What I've said here is in a relativistic context, not a Newtonian one.
If you choose to define GR so narrowly that relativistic physics,
relativistic dynamics, and relativistic celestial mechanics are excluded,
that would make your claim that it "is NOT the math of GR" true but of no
practical value. [shrug]

[Roberts]: you do not understand GR, which you repeatedly demonstrate, but
refuse to admit.

Then why are my papers published and yours are not? And why do you
continue to make claims that are in hard conflict with experimental facts
when attempting to show that you understand GR better than I do?

[Roberts]: why do you keep claiming you are using GR when you QUITE
CLEARLY are not?

Perhaps it is because I deal with the real world and you deal with a
mathematical idealization for which the only physical interpretation you are
familiar with has now been discarded.

[Roberts]: You repeatedly claim Steve (and I) are ignoring the "physics
behind the math". The problem is YOURS, not Steve's or mine -- you are
confusing Newtonian gravitation with General Relativity. The physics is
DIFFERENT. Until you actually learn about GR, you will remain confused.

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|-


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

Tom Van Flandern wrote:
Steve Carlip writes:

[Carlip]: a gravitating object -- call it A -- moving at a constant
velocity suddenly stops. What happens to the motion of a test body B a
distance R away from the point that A stops?

This has nothing to do with the issue on the table, the propagation
speed of gravitational force. It concerns only the propagation speed of
changes in the gravitational potential field, about which there is no
dispute -- it is speed c. So let's stay on topic, please.

I said nothing about potential fields. I asked, what happens to the
actual, physical motion of the test body?

We don't need A to be moving, then stop, as in your example. The issue
of relevance here is present even when A is permanently at rest and its
field is completely static.

Clearly not... Otherwise, you would not have gotten the answer to my
question so wrong.

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.

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!

[Carlip]: In general relativity, you solve this problem as follows ...

Most of your message was about this irrelevancy. But we have no issues
between us about the math.

Clearly not... Otherwise, you would not have gotten the answer to my
question so wrong.

The part of my message that you deleted described the way to do the
calculation. If you agree with it -- if you really think "we have no issues
between us about the math" -- then stop guessing. Just sit down and do
the calculation. I've told you how to do it, and even given you references
to places where you can look up the hard bits.

Let me repeat the basic steps:

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?

If you don't agree, tell me exactly which step you disagree with, and why.
If you do agree, then just *do the damn math*.

Steve Carlip

On Jul 26, 1:53*am, wrote:
Let me repeat the basic steps:

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.)

Steve Carlip

Never giving up hope? :^)

On Jul 24, 12:02 am, "Tom Van Flandern"
wrote:

On the contrary, binary pulsars prove that when the source mass
accelerates (as in Steve's example), the target body responds almost
instantly.

I'm a bit surprised to see that this discussion is still
going on. 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?

I wrote a derivation of the Lienard-Wiechert potentials
in chapter 2 of my book which is step-by-step with
comments he

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

See section (2.10).


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

Hi Steve, Tom and all.

On Jul 25, 4:53 pm, wrote:
Tom Van Flandern wrote:

Steve Carlip writes:
[Carlip]: a gravitating object -- call it A -- moving at a constant
velocity suddenly stops. What happens to the motion of a test body B a
distance R away from the point that A stops?
This has nothing to do with the issue on the table, the propagation
speed of gravitational force. It concerns only the propagation speed of
changes in the gravitational potential field, about which there is no
dispute -- it is speed c. So let's stay on topic, please.

I said nothing about potential fields. I asked, what happens to the
actual, physical motion of the test body?

We don't need A to be moving, then stop, as in your example. The issue
of relevance here is present even when A is permanently at rest and its
field is completely static.

Clearly not... Otherwise, you would not have gotten the answer to my
question so wrong.

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.

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!

[Carlip]: In general relativity, you solve this problem as follows ...
Most of your message was about this irrelevancy. But we have no issues
between us about the math.

Clearly not... Otherwise, you would not have gotten the answer to my
question so wrong.

The part of my message that you deleted described the way to do the
calculation. If you agree with it -- if you really think "we have no issues
between us about the math" -- then stop guessing. Just sit down and do
the calculation. I've told you how to do it, and even given you references
to places where you can look up the hard bits.

Let me repeat the basic steps:

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?

If you don't agree, tell me exactly which step you disagree with, and why.
If you do agree, then just *do the damn math*.

Steve Carlip

On Apr.8 in this thread I posted a complete
geometry and tensor algebra based on GR, so
you fella's know where I stand.

I can suggest a means of resolution by experiment,
but it is complicated so stay with me on the bends.

As means of introduction, 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.
(4th rank RC-tensor R_abcd).
Either Steve or Tom may predict when that
tidal variation could be detected.

Next, the operating term is "tidal", we know
the math.

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. I wonder if a close look at the
geodesy of GP-b might distinguish between the
two? (Yes I know the Moon's an issue).

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

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.
Best Regards
Ken S. Tucker

wrote in message
...
On Jul 26, 1:53 am, wrote:
......

Hans. I noticed that you didn't answer the question that I asked you. May I
be so bold as to ask why?

Pete

On Jul 26, 7:34*pm, "Pmb" wrote:
Hans. I noticed that you didn't answer the question that I asked you. May I
be so bold as to ask why?

Pete

Hi, Pete.

Which question was that? Would you be so kind to repeat
it here or give a link?

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

wrote in message
...
On Jul 26, 7:34 pm, "Pmb" wrote:
Hans. I noticed that you didn't answer the question that I asked you. May
I
be so bold as to ask why?

Pete

Hi, Pete.

Which question was that? Would you be so kind to repeat
it here or give a link?

-----------------------------
I asked you where I could get a copy of your book. I'd love to read it.

Pete

Hi Pete,
I regard you as one of the best experts on
tidals tensors, you know, R_abcd, you've
clued me in sometimes.

Allow me to set up a complicated scenario.

I'll use incremental variations to the gedanken.

To begin: let Earth be free with No Sun and
we have a sat orbiting in a perfect circular
orbit.

Now plup in the Sun such that the *center* of
the Earth is in orbital Free-fall, and any
objects displaced from said *center* are subject
to tidal effects - relatively to the center
of the Earth, by the effect of the Sun.

I presume the tidal effect creates an anomally
in said sats orbit to be elliptical when the
Sun is taken into account, as a tidal effect.

Said ellipse possesses a measureable semi-major
direction, and that axis differs 20" of arc from
the "absolute" Newtonian position compared to the
"apparent" position GR uses.

What do you Pete, and the fella's think?
Regards
Ken S. Tucker




















On Jul 26, 10:34 am, "Pmb" wrote:
wrote in message

...
On Jul 26, 1:53 am, wrote:
.....

Hans. I noticed that you didn't answer the question that I asked you. May I
be so bold as to ask why?

Pete

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.

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

The key is to realize that science is the process of testing theories,
not attempting to "measure" some nebulous "speed of gravity" that
depends in detail on one's model.

The actual observations for EVERY ONE of the experiments TvF cites are
in accord with the predictions of GR (there is also agreement with other
models and theories, but that is not at issue here).

The proper way to do science and compare theory to experiment is to
select a theory and use it to compute the same quantities that are
observed, and then compare the theoretical computations ("predictions")
to the actual measurements. Instead, TvF insists on taking the
observations, computing some model-dependent theoretical quantity
("speed of gravity") from them, and then comparing the result to
theories. THAT IS NOT SCIENCE. The reason his method is invalid is that
it is KNOWN to lead to erroneous conclusions (there are additional
difficulties related to error analysis).

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: a) the observations do not MEASURE
such a "response", they only observe signals from the distant pulsars,
b) those signals are in agreement with the predictions of GR for
such a system, and c) the source NEVER accelerates "as in Steve's
example", the two objects merely orbit each other.

In GR, the "response" is delayed by a time L/c, but TvF
simply does not understand that in GR the acceleration
does not point at the retarded position of the source, it
points at the EXTRAPOLATED retarded position of the source
mass (i.e. extrapolated from its retarded position). For
every physical situation he considers, this extrapolated
position is indistinguishable from the instantaneous
position. When Steve presented a physical situation
for which they are distinguishable, TvF dismissed it as
"irrelevant".


The issue of this thread is TvF's claims that he is using GR, when in
fact his claims are at odds with the underlying structure of GR [#], and
he displays in every post a rather complete ignorance of GR. And, of
course, he has never done the computation in GR (or in an appropriate
approximation to GR).

[#] 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.


Tom van Flandern wrote:
The force propagation speed (the "speed of gravity") is much faster
than the speed c at which the physical field can change in response
to changes in the force.

Hmmm. It's not clear how "force" can "propagate" independent of the
"physical field" in a field theory such as GR. But no matter, let's
stick to the subject:

If what you say is true, then it cannot be possible that all these
statements are true:
A) the "field interpretation" is indeed GR.
B) the "gravitational force" in the "field interpretation" carries
energy and momentum (i.e. it can transfer them from one object
to another).
C) Low's paper has no error, and neither does Carlip's and the
zillions of other papers and textbooks.

Indeed, it is rather clear that your statement is false, because you
make an unacknowledged and implicit assumption that is false: that
"gravitational force" is central (i.e. points directly at the source).
In the appropriate approximation to GR in which there is a gravitational
force, this is not true.


So when we say "force is the gradient of potential", the geometric
interpretation of GR simply assumes that the gravitational potential
field, as described by the Einstein field equations, governs; and
that a gradient in that field causes a force.

YOU might assume that because you clearly do not understand the geometry
of GR, but no GR expert would do so. The "geometric interpretation of
GR" makes no such assumptions, because it has no "gravitational
potential" or "gravitational force". In the situations you consider,
objects follow geodesic paths through spacetime, and there is no "force"
on them at all (that's what "geodesic path" means).

Please don't confuse this with a planet's path through
space (as you have done before). Yes, the path of a planet
in 3-space is not a geodesic in space. But it _IS_ a
geodesic in spaceTIME (assuming the planet is small enough
that its effect on the geometry can be neglected). For
instance, the earth follows a helix through spacetime
centered on the sun, with a radius ~8 light minutes and a
period of one light year; this deviates from a straight
line by a few parts per million, consistent with the
curvature induced by the sun's gravitation (I'm
neglecting small stuff). The axis of this helix is
parallel to the time axis of local Minkowski coordinates
in which the sun is at rest.


the geometric interpretation of GR is no longer viable because it
violates physical principles.

Nonsense. It obeys DIFFERENT "physical principles" than you want to
accept. That's all. This is YOUR problem, not GR's or any "geometric
interpretation's".


So we are forced to adopt the other physical interpretation, that
gravitational force induces a gradient into the gravitational
potential field.

We are not "forced" to do that at all -- on a geodesic path there is no
"force" at all (it's your PUN, not mine).

All you ever do is show that the basics of GR are incompatible with your
closely-held beliefs about "physical principles", and that you don't
really understand GR. Both are YOUR problem.


[Roberts]: The problem is: your model is inconsistent with
"gravitational force" propagating at speed c; but the appropriate
approximation to GR is not inconsistent with that, nor is GR
itself.

That statement is flatly wrong. You really need to get yourself
straightened out about that point. Ask Steve Carlip or anyone who
knows relativistic dynamics. No model that has gravitational forces
propagating at speed c can reproduce the orbital motions of the
planets.

The basic problem is that we use different words and phrases, and have
different sets of implicit assumptions. Note that Steve Carlip discusses
ACCELERATION of the target object, not "force", and he discusses a DELAY
in the effects of stopping the source, not a "propagation speed" of
anything from source to target. His word choice is much better than
yours, as it is significantly more precise (but is still subject to the
implicit assumptions listed below).

A major part of his and my disagreement with your claims are several
implicit assumptions (Steve's computation has no need for these, but the
discussion uses all of them):
A) fields are weak and there is an obvious "background"
Minkowski coordinate system to use.
B) quantities such as time, position, velocity, acceleration, and
direction are referenced to the coordinates of (A).
C) the acceleration of a target body is in the same direction
as any "gravitational force" on that body, at every instant.
D) if any gravitational influence propagates from source to target,
then the speed of propagation is the ratio of the distance
between them to the delay between changes in the source's motion
or position and the effect on the target's motion, with all
quantities measured in the coordinates of (A).

[Note that the acceleration of (C) is nonzero, even though
in GR there is no "gravitational force" and the
4-acceleration of the target body is zero. See (B).]

Steve's computation clearly shows that with these assumptions, in GR the
speed of (D) is c, not c. There is no interpretation in his
computation, and the only interpretations required to relate its result
to this discussion are listed above.

Now consider the physical situation you consider: two isolated objects
in mutual orbit. While I know of no exact computation, I believe there
are computations in an approximation to GR that have the same basic
features of Steve's computation: the acceleration of one object points
toward the EXTRAPOLATED retarded position of the other object. This is a
counterexample to your claim "No model that has gravitational forces
propagating at speed c can reproduce the orbital motions of the
planets." And this also explains how it is that you can be deluded into
thinking the "speed of gravity" is c -- for the physical situations
you consider, the EXTRAPOLATED retarded position is experimentally
indistinguishable from its instantaneous position (using suitable
coordinates, as above).


Tom Roberts