Re: The speed of gravity revisited

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
.

Relevant Pages

  • Re: The speed of gravity revisited
    ... to distinguish the speed of gravity from oo, ... points at the EXTRAPOLATED retarded position of the source ... "gravitational force" is central. ... ACCELERATION of the target object, not "force", and he discusses a DELAY ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... Einstein himself first suggested the idea that the gravitational field is equivalent to an optical medium. ... according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. ... Gravitational force creates the density gradients in the potential medium near masses, which explains the mathematical "coincidence" that gradient of potential equals force. ... A conceptual straight line between any two points along the orbit represents the path a taut rope takes, and is obviously not experiencing 3-space acceleration. ...
    (sci.physics.relativity)
  • Re: Flaw in Stowe/LeSage Heating
    ... what I wrote is the formula for gravitational force. ... or shedding this energy must be radiated from the surface. ... >> How do you go from capital F which looks like momentum flux, ... >> velocities required to avoid tangential acceleration and the ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... it asks that you describe how to measure the "gravitational force" on an orbiting satellite, not any implications of it (such as acceleration, or an equal-and-opposite reaction). ... measurement of force can be performed. ... geometry can be used to explain the measurements of acceleration, without any "gravitational force" at all. ... Some people in this thread claimed that geometry is "refuted", but they are unable to meet this challenge, which would be required to "refute" a geometrical explanation of gravity in favor of a "force" model. ...
    (sci.physics.relativity)
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