Tom Van Flandern wrote:

and Martin Hogbin writes:

[TomVF]: ...Shall we let the readers decide which of us matches
which description?

[Hogbin]: 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'.

Especially for you, Martin, I have resumed adding references to
observations, experiments, argumentation, or citations to back up every
important point. You expressed an opinion without saying anything about
why you hold it.

You suggested letting the readers decide. When they
disagre with you, you call foul.

Martin Hogbin

This replies to Luke Saul, Hans de Vries, Ken S. Tucker, and Steve
Carlip.

Luke Saul writes:

[Saul]: At first it appears that stable elliptic orbits are consistent
with superluminal speed of gravity field, as Van Flandern has presented in
his papers. 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.

That differs from my opinion. Gravitational forces, as required to do
orbital mechanics, must propagate at speeds very much faster than light.
There is no ambiguity or option about that. But gravitational forces are
independent of the so-called "gravitational field".

By contrast, the gravitational potential field, which may be thought of
physically as the light-carrying medium and always propagates changes at the
speed of light, is what is described by retarded potential equations such as
the Lienard-Wiechert potentials. The shape and density of the potential
field is very much dependent on gravitational force because that force
creates a density gradient in the field near large masses.

Amazingly, this simple viewpoint neatly predicts all first-order general
relativity effects exactly, through the phenomenon of refraction in the
potential field, which is envisioned to be a material medium, not some
mystical entity describable only by equations. It takes the mystery out of
"fields". Gravitational force shapes the field, the field has its own small
effects on light and on masses, but the field has no effect on gravitational
force.

[Saul]: Is there any experimental evidence, past or future, that can
decide between these two approaches?

Yes, there are five predictions made by the physical model just
described, predictions that the geometric interpretation of general
relativity does not make. These are described in detail in [Ref. 1] and
[Ref. 2], and are all in accord with current observations, although not so
strongly as to persuade adherents of geometric GR to jump off their sinking
ship. The two primary problems with geometric GR is that curvature alone in
the absence of a force cannot initiate 3-space motion, and the new 3-space
momentum of an orbiting target body must be created from nothing.


and Hans de Vries writes:

[de Vries]: The propagation [of the E-field] is defined by the standard
wave-equation. This is a second order differential equation. One can
rather easily do a computer simulation on a lattice which then shows that
the gradient of the potential field is not directed to the retarded
position but that it has an angle.

Right. We all agree about that. And if the field propagated at speed c,
the potential gradient would of necessity be directed toward the retarded
position, which it is not. That is why the hypothetical "virtual graviton"
force carriers are inferred to have infinite propagation speed -- because
the physics of electrodynamic forces (e.g., conservation of angular
momentum) cannot be explained with speed-of-light propagation.

Thereafter, the textbooks make an error by claiming that, if the source
charge accelerates, there will be a propagation delay at the speed of light.
However, the previously cited Sherwin-Rawcliffe experiment showed that not
even acceleration produces a difference between the force direction and the
source direction, just as is undisputedly true for the gravitational case
too.

[de Vries]: Static potential fields have no radiation components like
photons or gravitons. You are painting a picture which is an unfortunately
wide-spread pop-sci interpretation of Quantum Field Theory.

No, I'm painting a different physical interpretation of the math that
makes much better sense. Forces impose gradients on potential fields, not
vice versa. So real photons, being waves in the potential field, propagate
at speed c; whereas Coulomb force propagates c.

Once you get past the shock, occasioned by the now-falsified "proof"
that nothing can propagate faster than c in forward time, you will find this
physical description of reality simple and elegant, contradicting no
observation or experiment and opening doors to a deeper understanding of all
quantum phenomena.

[de Vries]: Radiation propagates in the direction indicated by the wave-
front. Light (EM radiation) as well as the assumed gravitons have their wave
front pointing along the direction of the retarded location.

But gravitational radiation propagates at the same speed as light, so
why does gravitational force operate in a different direction?

Note that, when I speak of "classical gravitons", I do not mean the
spin-2 gravitons of quantum field theory, which certainly would propagate at
speed c if they existed. I for one predict a total failure of Ligo and other
gravitational wave detectors to discover spin-2 gravitons. Classical
gravitons are not part of the quantum zoo and cannot be characterized by a
spin property. But real "gravitational waves" may be expected to be
very-long-wavelength, spin-1 waves.

[de Vries]: The radiation fields (photons, gravitons) decrease by 1/r
while the Coulomb field and the gravitation field decrease by a factor of
1/r^2

If I said of some application that "velocity decreases as 1/r while
acceleration decreases as 1/r^2", would it not be absurd to conclude that
the propagation velocity of the force causing that acceleration (f = ma) was
the same as the 1/r velocity? Yet you are so accustomed to assuming that the
speed of field changes must be the same as the speed of the associated force
that your mind is resisting the obvious: the two speeds are quite different
and have no connection to one another.

[de Vries]: The propagation of virtual photons is given by the propagator
1/(E^2-p^2) in momentum space. This is just the standard wave equation
which causes propagation on the light cone. There is no infinite
propagation speed in QFT.

You can postulate anything in mathematics, but not in physics. In this
instance, no possible physical cause-and-effect can be imagined, let alone
justified, for a force with a retarded speed to track the extrapolated
source position. That would be like saying you could expect to hit a target
by aiming at where the target is now instead of where it will be when the
projectile arrives. The fact that both gravitational and electrodynamic
experiments show that a second-order extrapolation is needed, not just a
linear one, makes the idea of a physical cause propagating as slowly as
light-speed even more absurd physically.

The key to understanding is to put away the equations and think about
the physics: cause and effect, what collides with what, momentum transfers,
3-space forces. Math follows; it does not lead.


and Ken S. Tucker writes:

[TomVF]: {regarding Ken's proposed experiment to determine who is right]
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.

[Tucker]: How would you detect "Force shuts off"?

The Earth would stop accelerating and instead continue in a straight
line. Measures of the distance to the Sun would soon see this. Also,
measures of aberration of all stars and galaxies would remain constant and
discontinue their annual sinusoidal behavior. Likewise, Earth's motion is
reflected in the measured radial velocities of stars, which would likewise
change. The orbits of the Moon and artificial satellites would change
because the Sun would no longer be perturbing them.

Some effects would take time to build up to where they could be
observed. But the building effect could be traced back to the moment the Sun's
acceleration ceased. And that would coincide with the moment the Sun's
gravity ceased, not the moment (8.3 minutes later) when the Sun's light
showed us the disaster.

[TomVF]: 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.

[Tucker]: 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
Celestial Mechanics on the problem too, did you use lasers?

The mainstream journal article I cited (Physics Letters A) is refereed,
and no one disputes either the argument or the conclusion. Lunar occultation
results are consistent with laser ranging results, but are more sensitive to
angular differences. Here is a brief summary of that particular experiment
from the second reference of my previous post:

The solar eclipse test
Why do total eclipses of the Sun by the Moon reach mid-visible-eclipse
about 40 seconds before the Sun and Moon's gravitational forces align?

Yet another manifestation of the difference between the propagation
speeds of gravity and light can be seen in the case of solar eclipses. The
Moon, being relatively nearby and sharing the Earth's 30 km/s orbital motion
around the Sun, has relatively little aberration (0.7 arc seconds, due to
the Moon's 1 km/s orbital speed around Earth). The Sun, as mentioned
earlier, has an aberration of just over 20 arc seconds. It takes the Moon
about 40 seconds of time to move 20 arc seconds on the sky relative to the
Sun. Since the observed times of eclipses of the Sun by the Moon agree with
predicted times to within a couple of seconds, we can use the orbits of the
Sun and the Moon near times of maximum solar eclipse to compare the time of
predicted gravitational maximum with the time of visible maximum eclipse.

In practice, the maximum gravitational perturbation by the Sun on the
orbit of the Moon near eclipses may be taken as the time when the geometric
lunar and solar longitudes are equal. For those interested in the technical
details, the computed orbit of the Moon uses instantaneous force
transmission between bodies; i.e., forces in numerical integrations are
computed using true, instantaneous positions at a common instant of
coordinate time. This is standard procedure in celestial mechanics. So I did
an analysis to solve for any correction that might exist to the large
perturbations of the Moon's orbit that depend upon the elongation angle D
between the Moon and the Sun. The visible elongation angle is about 20 arc
seconds larger than the computed elongation angle because light takes much
longer to arrive from the Sun than from the Moon. So any transit delay for
the gravitational force of the Sun would show up as a correction to the
adopted value of D based on instantaneous force transmission. In particular,
if gravity propagated at the speed of light, the correction to D as used in
the computations would be 20 arc seconds. But an extensive analysis of lunar
occultation timing data showed that the correction to D is zero to within an
uncertainty of about one arc second. The elongation angle increases at the
rate of an arc second every two seconds of time. So this result implies a
difference between the time of optical and gravitational maxima at the time
of eclipses of 40+/-2 seconds. These results in turn imply that the
propagation velocity of the force of the Sun acting on the Moon is at least
20 times the speed of light. Although this constraint is far less severe
than some others, it uses three bodies (Sun, Moon, Earth) instead of two and
changes in gravitational fields instead of static fields. Yet, it still
constrains the speed of gravitational interaction to exceed the speed of
light.


and Steve Carlip writes:

[Carlip]: If you disagree with this result, then you disagree with the
math.

I disagree with your interpretation of the math. I do not disagree with
your math. I may agree with you that 3+3=6, but may also dispute it if you
claim that 6 is therefore the square of 3. I sharply disagree with the words
you choose to describe what your math means.

[Carlip, after outlining mathematical GR once again]: Do you agree that GR
specifies these steps?

Yes.

[Carlip]: Do you agree that once the stress-energy tensor is specified,
the remaining mathematical equations have unique solutions?

The field equations are fine. Their solutions, the geodesic equations,
are fine. The derivation of equations of motion from those equations is not
unique until one specifies the speed of interactions. That speed has always
been taken as instantaneous by GR, which is the correct assumption. So I do
not disagree with the GR equations of motion either. But I do disagree about
the interpretation of that non-unique step, because if the speed of gravity
were c, the equations of motion would produce spiral orbits, and the present
equations of motion derived using instantaneous interactions would be wrong.

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

As you see, we do agree about the math, and do disagree about the
interpretation. Specifically, when one uses spatial partials in a Laplacian,
a Lagrangian, a Hamiltonian, or simple in forming a gradient, these spatial
partials take the general form f(X, 0, T), where X indicates a particular
field point location relative to the source mass, "0" means the field point
is non-moving (V=0), and T represents a particular time in case the field is
not static. However, a material target body moving through the field will
sense different spatial partials and a different gradient at point X and
time t than a non-moving body will. So The correct form of the spatial
partials should be f(X, V, T).

And when these corrected spatial partials or gradients are used instead,
we see the explicit appearance of transverse velocity V in the aberration
term. So V always appears as V/Vg, where Vg is the speed of gravity. The
equations GR uses are valid solely because the real Vg is so close to
infinity that the aberration drops out even for moving target bodies. But
the GR equations would be false and incomplete is Vg were as small as the
speed of light c, and orbits would spiral as a consequence.

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.

I agree that the direction of the gradient of the potential field will
continue to point toward the *linearly* extrapolated position of the Sun
until one light-time later. We agree about the field equations, the geodesic
equations, and what they say about the field.

Next, you wish to append an assumption to GR that is not, in fact, any
part of general relativity: that gravitational force is the gradient of the
potential field as sensed by any non-moving body in that field. In reality,
a moving target body senses a different gradient than a non-moving one.
Using your wrong assumption that moving and non-moving bodies sense the same
gradient, the potential field determines the force and mandates that it also
point at the linearly extrapolated source mass position. That erroneous
assumption has been incorporated into the geometric interpretation of GR so
that GR can claim to be an explanation for gravitational force too. But
there are several things wrong with that:

.. In physics, if only natural processes operate, higher-order derivatives
(such as acceleration) determine lower-order functions (such as velocity),
not vice versa. So force must determine potential, not the reverse. Math can't
tell the difference, but it makes a huge difference to the physical
interpretation of the equations.

.. Neither space curvature nor spacetime curvature can explain why a body at
rest on a potential hill begins to move through 3-space. The initiation of
3-space motion requires a force by definition. So the geometric
interpretation cannot, in principle, explain gravity as geometry because
geometry cannot initiate 3-space motion in the absence of a force acting.

.. The field provides no source for the new 3-space momentum acquired by the
target body, and must create it from nothing.

.. The Greenberger-Overhauser experiment shows that the weak equivalence
principle ("gravity is just geometry") is experimentally disproven. [Ref. 3]

[TomVF]: 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?

[Carlip]: 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.

Yes, the equations are the same. No, the predictions are not the same.
Yes, we are arguing over the physical interpretation.

I agree that Einstein and Dirac did not know of any different
predictions between the two interpretations of GR, geometric and field.
Today, we do know of differences. When the direction of the arrow of
causality changes (force causes potential gradients, not vice versa),
certain predictions change. One of the most interesting is in the rate of
perihelion advance when both masses are significant. (This is a consequence
of the way the superposition principle is used --yet another assumption that
must be tacked on to basic GR's accurate descriptions of the fields around
individual masses.) We should have an answer about that prediction very
soon. Sometimes I wonder if the delay in publishing newer binary pulsar
results is occasioned by the authors being unable to account for what they
see happening.

[Carlip]: 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.

This description contains errors of interpretation, perhaps based on a
lack of familiarity with celestial mechanics -- something you never claimed
to have. The "acceleration" noted by Hulse and Taylor came from a
friction-like force that removes angular momentum from the system (by
radiating away gravitational waves). This is similar to the effect that
would occur if the Sun's gravity came from a slightly *retarded* (not
advanced) position. It operates in the opposite direction of aberration, and
has nothing to do with our "speed of gravity" issue.

The gain in angular momentum the binary pulsars would experience if the
force had any propagation delay would be much greater than the tiny reverse
effect found by Hulse and Taylor. And the same binary pulsar data shows that
gravitational aberration clearly does not exist at a detectable level,
meaning the propagation speed of gravitational force Vg must be c because
aberration is just V / Vg, where V is the transverse component of orbital
speed. -|Tom|-


REFERENCES

[1] "21st century gravity: a deeper understanding of why apples fall from
trees", J.Wash.Acad.Sci. 90#3, 108-125 (2004). Also in J. Vectorial
Relativity JVR 2#3:29-41 (2007).

[2] "Possible new properties of gravity", Astrophys.&SpaceSci. 244:249-261
(1996); also at
http://metaresearch.org/cosmology/gr...sofgravity.asp

[3] D. M. Greenberger and A. W. Overhauser, Rev.Mod.Phys. 51:43 (1979). This
was also written up by the same authors in easier-to-read language in "The
role of gravity in quantum theory", Sci.Amer. 242 (May):66-76 (1980).


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

On Aug 2, 11:42 pm, "Tom Van Flandern" wrote:
This replies to Luke Saul, Hans de Vries, Ken S. Tucker, and Steve
Carlip.

Luke Saul writes:
[Saul]: At first it appears that stable elliptic orbits are consistent
with superluminal speed of gravity field, as Van Flandern has presented in
his papers. 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.

That differs from my opinion. Gravitational forces, as required to do
orbital mechanics, must propagate at speeds very much faster than light.
There is no ambiguity or option about that. But gravitational forces are
independent of the so-called "gravitational field".


Thanks for your reply Tom!

Forgive my simplistic approach, but I thought that the field is by
definition the direction of force at every point. The force tells us
what the field is. Is there some definition of either that allows
for a difference?


By contrast, the gravitational potential field, which may be thought of
physically as the light-carrying medium and always propagates changes at the
speed of light, is what is described by retarded potential equations such as
the Lienard-Wiechert potentials. The shape and density of the potential
field is very much dependent on gravitational force because that force
creates a density gradient in the field near large masses.

Amazingly, this simple viewpoint neatly predicts all first-order general
relativity effects exactly, through the phenomenon of refraction in the
potential field, which is envisioned to be a material medium, not some
mystical entity describable only by equations. It takes the mystery out of
"fields". Gravitational force shapes the field, the field has its own small
effects on light and on masses, but the field has no effect on gravitational
force.

[Saul]: Is there any experimental evidence, past or future, that can
decide between these two approaches?

Yes, there are five predictions made by the physical model just
described, predictions that the geometric interpretation of general
relativity does not make. These are described in detail in [Ref. 1] and
[Ref. 2], and are all in accord with current observations, although not so
strongly as to persuade adherents of geometric GR to jump off their sinking
ship. The two primary problems with geometric GR is that curvature alone in
the absence of a force cannot initiate 3-space motion, and the new 3-space
momentum of an orbiting target body must be created from nothing.


I thought that the new momentum is only observed because we have
taken a coordinate system which is not inertial. If we assume the
laboratory frame on the surface of the earth is inertial, we will see
momentum appearing from nowhere - the Coriolis force acting on test
particles, because actually our laboratory is on the surface of a
rotating sphere. We also see momentum appearing from nowhere.. the
gravitational force.. because our laboratory is being accelerated
upward due to electrical forces of the ground pushing upward on the
floor.

In any case, I need to read the relevant papers more thoroughly and
"do the math" before I respond to your other comments and those of
your critiques.

Best Regards -

Luke Saul writes:

[TomVF]: Gravitational forces, as required to do orbital mechanics, must
propagate at speeds very much faster than light. There is no ambiguity or
option about that. But gravitational forces are independent of the
so-called "gravitational field".

[Saul]: Forgive my simplistic approach, but I thought that the field is by
definition the direction of force at every point. The force tells us what
the field is. Is there some definition of either that allows for a
difference?

Admittedly, many textbooks are vague on this point, or provide only
mathematical definitions such as the one you describe. But there is no
physics and no understanding behind your description. For example, how can a
field be just a set of directions? Moreover, the direction of a force is
frame-dependent and depends on the motion of the observer.

Einstein himself first suggested the idea that the gravitational field
is equivalent to an optical medium. For example, in Einstein's "Ether and
the theory of relativity" [Springer, Berlin (1920), reprinted Dover (1983),
p. 23], we read: ". according to the general theory of relativity space is
endowed with physical qualities; in this sense, therefore, there exists an
ether. According to the general theory of relativity space without ether is
unthinkable; for in such space there not only would be no propagation of
light, but also no possibility of existence for standards of space and time
(measuring-rods and clocks), nor therefore any space-time intervals in the
physical sense." According to Einstein, aether could be equated to the
gravitational field. "The aether of the general theory of relativity is a
medium without mechanical and kinematic properties, but which codetermines
mechanical and electromagnetic events." In "Einstein: the first hundred
years", ed: M. Goldsmith, A. Mackay, J. Woudhuysen, Pergammon Press, Oxford
(1980), pp. 58-59, we read: "Thus [Einstein] regarded his field theory as in
essence a kind of revival of the notion of a space-filling ether, which is,
however, relativistic rather than non-relativistic. But somehow Bohr could
never take such views seriously and probably regarded them as naïve, a
return to 'primitive realism'."

Today, we know enough to state simply that the local gravitational
potential field is equivalent to the local light-carrying medium, with
potential being a measure of field/medium density. Then the relativistic
effects of GR are simply refraction effects in this optical medium.
Gravitational force creates the density gradients in the potential medium
near masses (just as it does in atmospheres), which explains the
mathematical "coincidence" that gradient of potential equals force.

[TomVF]: The two primary problems with geometric GR is that curvature
alone in the absence of a force cannot initiate 3-space motion, and the
new 3-space momentum of an orbiting target body must be created from
nothing.

[Saul]: I thought that the new momentum is only observed because we have
taken a coordinate system which is not inertial. If we assume the
laboratory frame on the surface of the earth is inertial, we will see
momentum appearing from nowhere - the Coriolis force acting on test
particles, because actually our laboratory is on the surface of a rotating
sphere. We also see momentum appearing from nowhere.. the gravitational
force.. because our laboratory is being accelerated upward due to
electrical forces of the ground pushing upward on the floor.

These are 4-space mathematical devices to try to explain gravity
geometrically. They do not change the behavior of 3-space or the laws of
motion. In Euclidean 3-space, where all astronomical observations are made,
an orbiting body moving along a geodesic path is being accelerated by
gravitational force and is acquiring new 3-space momentum. 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. As
in Coriolis force, if the observer has 3-space acceleration, he will see
non-inertial effects. But an inertial 3-space observer will not. The key is
to avoid mixing 3-space and 4-space concepts and definitions. To avoid
confusion, I normally say "3-space" when using words with different
definitions in 3-space and 4-space. My statements were about 3-space, and
your examples use 4-space definitions "inertial" and "accelerating". The two
do not mix well.

Consider your last example. Our laboratory is not being accelerated
upward at all in 3-space. Those "electrical forces of the ground pushing
upward on the floor" do not have independent existence because the ground
does not fly into space when the floor is removed. In 3-space, this example
is simply one of action and reaction. And the law of momentum conservation
applies only in 3-space. So IMO, using the 4-space definition of
acceleration obfuscates more than it illuminates. -|Tom|-


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

On Aug 11, 7:52 pm, "Tom Van Flandern" wrote:
Luke Saul writes:
[TomVF]: Gravitational forces, as required to do orbital mechanics, must
propagate at speeds very much faster than light. There is no ambiguity or
option about that. But gravitational forces are independent of the
so-called "gravitational field".
[Saul]: Forgive my simplistic approach, but I thought that the field is by
definition the direction of force at every point. The force tells us what
the field is. Is there some definition of either that allows for a
difference?

Admittedly, many textbooks are vague on this point, or provide only
mathematical definitions such as the one you describe. But there is no
physics and no understanding behind your description. For example, how can a
field be just a set of directions? Moreover, the direction of a force is
frame-dependent and depends on the motion of the observer.

Einstein himself first suggested the idea that the gravitational field
is equivalent to an optical medium. For example, in Einstein's "Ether and
the theory of relativity" [Springer, Berlin (1920), reprinted Dover (1983),
p. 23], we read: ". according to the general theory of relativity space is
endowed with physical qualities; in this sense, therefore, there exists an
ether. According to the general theory of relativity space without ether is
unthinkable; for in such space there not only would be no propagation of
light, but also no possibility of existence for standards of space and time
(measuring-rods and clocks), nor therefore any space-time intervals in the
physical sense." According to Einstein, aether could be equated to the
gravitational field. "The aether of the general theory of relativity is a
medium without mechanical and kinematic properties, but which codetermines
mechanical and electromagnetic events." In "Einstein: the first hundred
years", ed: M. Goldsmith, A. Mackay, J. Woudhuysen, Pergammon Press, Oxford
(1980), pp. 58-59, we read: "Thus [Einstein] regarded his field theory as in
essence a kind of revival of the notion of a space-filling ether, which is,
however, relativistic rather than non-relativistic. But somehow Bohr could
never take such views seriously and probably regarded them as naïve, a
return to 'primitive realism'."

Today, we know enough to state simply that the local gravitational
potential field is equivalent to the local light-carrying medium, with
potential being a measure of field/medium density. Then the relativistic
effects of GR are simply refraction effects in this optical medium.
Gravitational force creates the density gradients in the potential medium
near masses (just as it does in atmospheres), which explains the
mathematical "coincidence" that gradient of potential equals force.


That seems to be what a recent "Cassini" experiment demonstrated
but it will be hard to pick out such plain language in the
analysis offered by Bertotti et al.
http://physicsworld.com/cws/article/news/18268


When a car is pushed, it pushes back ~instantly~, and with a
much more force than we normally attribute to the random
air molecules between the car and the road. Planetary motions
are guided by similar forces in much thinner gas.
So density gradient is not an effective player for conducting
the gravto-inertial forces between massive bodies.

The powerful Coulomb force which, from time to time
exists between neutrally charged gas molecules in
even the thinnest gas in the universe, exerts forces
greater than 10^32 times the force measured for gravity.

It is only necessary for nature to have a mechanism
to choose and maximise times of favourable molecular
alignment, to forge stiff conductors of the
gravito-inertial force from a thin cloud of
gas molecules.

Just such a mechanism can be seen working at its limit
when a pot of water comes to a boil.

--Visser
http://relativity.livingreviews.org/...l#x34-720006.3

--Kouropoulos
http://arxiv.org/abs/physics/0107015
http://arxiv.org/abs/physics/0107015v1

http://en.wikipedia.org/wiki/Induced_gravity

The speed of gravity?
It is fast enough if it only has to be conducted
to the nearest massive bodies.

Sue...


[TomVF]: The two primary problems with geometric GR is that curvature
alone in the absence of a force cannot initiate 3-space motion, and the
new 3-space momentum of an orbiting target body must be created from
nothing.
[Saul]: I thought that the new momentum is only observed because we have
taken a coordinate system which is not inertial. If we assume the
laboratory frame on the surface of the earth is inertial, we will see
momentum appearing from nowhere - the Coriolis force acting on test
particles, because actually our laboratory is on the surface of a rotating
sphere. We also see momentum appearing from nowhere.. the gravitational
force.. because our laboratory is being accelerated upward due to
electrical forces of the ground pushing upward on the floor.

These are 4-space mathematical devices to try to explain gravity
geometrically. They do not change the behavior of 3-space or the laws of
motion. In Euclidean 3-space, where all astronomical observations are made,
an orbiting body moving along a geodesic path is being accelerated by
gravitational force and is acquiring new 3-space momentum. 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. As
in Coriolis force, if the observer has 3-space acceleration, he will see
non-inertial effects. But an inertial 3-space observer will not. The key is
to avoid mixing 3-space and 4-space concepts and definitions. To avoid
confusion, I normally say "3-space" when using words with different
definitions in 3-space and 4-space. My statements were about 3-space, and
your examples use 4-space definitions "inertial" and "accelerating". The two
do not mix well.

Consider your last example. Our laboratory is not being accelerated
upward at all in 3-space. Those "electrical forces of the ground pushing
upward on the floor" do not have independent existence because the ground
does not fly into space when the floor is removed. In 3-space, this example
is simply one of action and reaction. And the law of momentum conservation
applies only in 3-space. So IMO, using the 4-space definition of
acceleration obfuscates more than it illuminates. -|Tom|-

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

Tom Van Flandern wrote:

and Steve Carlip writes:

[Carlip]: If you disagree with this result, then you disagree with the
math.

I disagree with your interpretation of the math. I do not disagree with
your math. I may agree with you that 3+3=6, but may also dispute it if you
claim that 6 is therefore the square of 3. I sharply disagree with the words
you choose to describe what your math means.

I very nearly didn't respond to this -- it's hard to know how to respond to
someone who doesn't even understand the math well enough to recognize
that there's a disagreement. I'll try one more time...

[Carlip, after outlining mathematical GR once again]: Do you agree that GR
specifies these steps?

Yes.

[Carlip]: Do you agree that once the stress-energy tensor is specified,
the remaining mathematical equations have unique solutions?

The field equations are fine. Their solutions, the geodesic equations,
are fine.

Yikes! The geodesic equations are not the solutions of the field equations!
This is an *elementary* misunderstanding of the math.

The derivation of equations of motion from those equations is not
unique until one specifies the speed of interactions.

The geodesic equations *are* the equations of motion.

That speed has always
been taken as instantaneous by GR, which is the correct assumption.

Nonsense.

Here is the math. (I'm going to have to use TeX notation, because you
can't write equations clearly in plain ASCII.)

1. The Einstein field equations are
G_{ab} = 8\pi T_{ab}
Here T_{ab} is the stress-energy tensor, and G_{ab} is the Einstein tensor.

More specifically,
G_{ab} = R_{ab} - 1/2 g_{ab}g^{cd}R_{cd}
where g_{ab} is the metric tensor, and
R_{ab} = \partial_c\Gamma^c_{ab} - \partial_a\Gamma^c_{bc}
+ \Gamma^c_{ab}\Gamma^d_{cd} - \Gamma^c_{ad}\Gamma^d_{bc}
is the Ricci tensor. Gamma is the Christoffel connection,
\Gamma^c_{ab}
= 1/2 g^{cd}(\partial_a g_{db} + \partial_b g_{da} - \partial_d g_{ab})

According to theorems dating back to Yvonne Choquet-Bruhat's work in the
1960s, given a stress-energy tensor, initial data for the metric, and suitable
boundary conditions (no incoming gravitational radiation), the solution of
the Einstein field equations is unique. (For Tom's benefit: "unique" means
"there's only one solution.")

2. The geodesic equations are
d^2z^a/ds^2 + \Gamma^a_{bc}(dz^b/ds)(dz^c/ds) = 0
Here z^a is the position of a test body moving in a spacetime with a given metric,
where the metric appears, as above, in Gamma.

According to theorems for ordinary differential equations that date back to
the late 1800s, given initial data -- that is, the initial position and velocity of
the test body -- the solution is unique. (For Tom's benefit: "unique" again means
"there's only one solution.")

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

As you see, we do agree about the math, and do disagree about the
interpretation.

The equations have *unique solutions.* In particular, for a source that is
initially moving at a constant velocity and then abruptly stops, *either* the
test body's acceleration instantly points to its stopped position *or* it
continues to track the "extrapolated" position for a while. The math has
ONLY ONE SOLUTION. If you disagree with the result, you disagree with
the math.

Specifically, when one uses spatial partials in a Laplacian,
a Lagrangian, a Hamiltonian, or simple in forming a gradient, these spatial
partials take the general form f(X, 0, T), where X indicates a particular
field point location relative to the source mass, "0" means the field point
is non-moving (V=0), and T represents a particular time in case the field is
not static.

This is word salad, not mathematics.

The Einstein field equations and the geodesic equation contain partial derivatives
of the metric. These are defined, for a partial derivative of a function F with
respect to x, for instance, as
\partial f(x,y,z,t)/partial x = lim_{a-0} ( f(x+a,y,z,t) - f(x,y,z,t))/a)
This is an unambiguous operation. No "interpretation" is necessary to perform
the mathematical calculation.

However, a material target body moving through the field will
sense different spatial partials and a different gradient at point X and
time t than a non-moving body will. So The correct form of the spatial
partials should be f(X, V, T).

The partial derivatives in the geodesic equation appear in the connection Gamma.
As I said above, this is defined as
\Gamma^c_{ab}
= 1/2 g^{cd}(\partial_a g_{db} + \partial_b g_{da} - \partial_d g_{ab})
Partial differentiation is a mathematical operation with a single definition, the
limit I just gave.

Do you or do you not agree that the geodesic equation, with "partial differentiation"
defined the way it is in any calculus textbook (or, for example, as defined at
http://en.wikipedia.org/wiki/Partial_derivative in the sixth equation under
"Definition"), is correct?

[...]
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.

I agree that the direction of the gradient of the potential field will
continue to point toward the *linearly* extrapolated position of the Sun
until one light-time later. We agree about the field equations, the geodesic
equations, and what they say about the field.

Next, you wish to append an assumption to GR that is not, in fact, any
part of general relativity: that gravitational force is the gradient of the
potential field as sensed by any non-moving body in that field.

The "assumption" is that the geodesic equations describe the motion of a test body.
If you reject this, you reject the math of general relativity. Period.

(You also then reject the Einstein field equations, since the geodesic equations
for a test body are a mathematical consequence of the field equations.)

[...]
[TomVF]: 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?

[Carlip]: 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.

Yes, the equations are the same. No, the predictions are not the same.

This is a statement that you don't understand the math, pure and simple.
The equations have unique solutions. Those solutions *are* the predictions.
If the equations are the same, the predictions are the same.

Steve Carlip

Steve Carlip writes:

[Carlip]: it's hard to know how to respond to someone who doesn't even
understand the math well enough to recognize that there's a disagreement.

Math has no intelligence and may have many different physical
interpretations. One relevant example here is that the math of GR has a
geometric interpretation and a field interpretation. The physics is very
different for the same math. These different physical models (remembering
that physics drives math, not vice versa) once were thought to make the same
predictions. But now we see ways in which their predictions differ.

You are confining your arguments, and apparently your thinking, to the
math of GR. If we are going to reach agreement, you will have to think again
as a physicist, considering cause and effect, the direction of the arrow of
causation, the nature of the momentum and force carriers, what contacts what
to make bodies follow geodesics -- concepts about which the math of GR is
silent or ambiguous. We simply have no disagreements about the math, despite
a few differences about nomenclature that are ultimately unimportant. All
our disagreements are about the physics driving the math.

[Carlip]: The geodesic equations are not the solutions of the field
equations! This is an *elementary* misunderstanding of the math.

This is an elementary nomenclature issue. The point of relevance is that
I agree with the field equations and their solutions. We have no differences
about the math. What you call "understanding the math" really means
understanding the physics driving the math. We most definitely disagree
about that, as the rest of this response will make clear.

[TomVF]: The derivation of equations of motion from those [solutions of
the field] equations is not unique until one specifies the speed of
interactions. That speed has always been taken as instantaneous by GR,
which is the correct assumption.

[Carlip]: Nonsense.

That's your argument? Nonsense? You don't even say what point you
consider nonsense: that the equations of motion depend on an assumption
about the interaction speed, or that GR makes the correct assumption. You
will have to do better.

[Carlip]: Here is the math.

Other than showing your talent for writing TeX equations, what was your
point? There is nothing in any of the math of GR about which we disagree.

[Carlip]: According to theorems dating back to Yvonne Choquet-Bruhat's
work in the 1960s, ... the solution of the Einstein field equations is
unique.

We agree.

[Carlip]: The geodesic equations are ... [equations omitted]. According to
theorems for ordinary differential equations that date back to the late
1800s, given initial data -- that is, the initial position and velocity of
the test body -- the solution is unique.

The solution is unique for any fixed point in the field. The solution
and its history ignore that a moving point will experience gravitational
aberration of the source mass. You can call this an error in the deviation
if you are so inclined, because the math omitted consideration of important,
non-optional physics.

However, it happens that aberration is zero if and only if the
propagation speed of gravitational force is infinite. So the error in the
derivation of the equations of motion is self-healing because the real,
physical speed of gravity is so fast that "infinite" is still a fully
adequate approximation. The error of omission in the derivation of the
equations of motion is rendered moot because gravitational aberration is in
fact indistinguishable from zero. That lucky accident leaves the equations
of motion correct despite the derivation error. Otherwise, GR would have
been long-ago falsified by observations.

However, the missing step in the derivation (i.e., explicit
consideration of gravitational aberration) is apparently keeping you from
seeing that it is a required step, the omission of which is the physics
equivalent of adopting infinite gravitational propagation speed -- which is
the only reason that GR can reduce to Newtonian gravity in the weak-field,
low-velocity limit. And we all agree Newtonian gravity has infinite gravity
propagation speed.

It would be nice if you could explain in physics terms (no math) why a
spacecraft in a circular orbit around the Sun at a distance of 1200 au
(surely weak field and low velocity) has an infinite gravity propagation
speed by Newton's rules, has gravity propagating at the speed of light in
GR, yet the two are equivalent? The light-time to that distance is about a
week, so the propagation delay would cause the orbit to spiral under Newton's
rules. Why doesn't it do the same in GR? (My answer: GR also has infinite
gravity propagation speed in its equations of motion, which is evident when
they reduce to the same as Newton's equations for this example.)

[TomVF]: As you see, we do agree about the math [of GR as it stands], and
do disagree about the interpretation [of that math].

[Carlip]: ... for a source that is initially moving at a constant velocity
and then abruptly stops ...

Because of their large accelerations, binary pulsars are a rough
approximation of your "stop-motion" example, differing only in the
suddenness of the acceleration. But because the binary pulsar accelerations
are significant during the light-time between them, they tell us what really
happens in your stop-motion case. And what really happens is that the binary
pulsars attract each other from their respective instantaneous positions,
and not from their positions extrapolated ahead linearly over one
light-time. So the same must be true in your example. (The Sherwin-Rawcliffe
experiment shows that electrodynamic forces also respond without propagation
delay when charges accelerate.)

But let's drop this red herring argument for now. Our divergence of
opinion stems from the static field case and carries over to all more
complex cases. If we can't agree about a simple static field case, I hold no
hope for agreement on more advanced examples.

[TomVF]: Specifically, when one uses spatial partials in a Laplacian, a
Lagrangian, a Hamiltonian, or simple in forming a gradient, these spatial
partials take the general form f(X, 0, T), where X indicates a particular
field point location relative to the source mass, "0" means the field
point is non-moving (V=0), and T represents a particular time in case the
field is not static.

[Carlip]: This is word salad, not mathematics.

Translation: "I did not understand your point." Allow me to try again.
If you examine a retarded potential equation such as that on MTW p. 1080, if
describes the potential field at any fixed point as a function of (X, T). If
we generalize that equation to apply also to moving points, it would become
a function of (X, V, T), where V is the moving point velocity. The
dependence on first-order V is simply the dependence on gravitational
aberration. If we make it explicit instead of *assuming* it is zero
(identical to assuming infinite speed of gravity), we then have a valid
equation for a moving point. An orbiting target body is an example of such a
moving field point.

[Carlip]: The Einstein field equations and the geodesic equation contain
partial derivatives of the metric. These are defined, for a partial
derivative of a function F with respect to x, for instance, as \partial
f(x,y,z,t)/partial x = lim_{a-0} ( f(x+a,y,z,t) - f(x,y,z,t))/a). This is
an unambiguous operation. No "interpretation" is necessary to perform the
mathematical calculation.

These calculations are indeed unambiguous, just as you say. The physics
behind them says they are valid for fixed field points. If a moving field
point is used instead, these partials are wrong because they omit
aberration, *unless* the physical force they represent has infinite
propagation speed, in which case gravitational aberration is zero and the
same simplified equations apply.

You can't have it both ways. You can't claim the math is valid because
it works for fixed field points, then apply it to moving field points and
claim the math is still valid. The physics used to derive the math tells us
otherwise.

[Carlip]: Do you or do you not agree that the geodesic equation, with
"partial differentiation" defined the way it is in any calculus textbook
(or, for example, as defined at
http://en.wikipedia.org/wiki/Partial_derivative in the sixth equation
under "Definition"), is correct?

Second verse, same as the first. :-) The math is right for two cases:
(1) fixed field points; or (2) infinite force propagation speeds. GR uses
the latter, so the math of GR is golden. If finite force propagation speeds
were to be considered (a change in the underlying physics), then the math
must change accordingly by introducing a non-zero gravitational aberration.

[TomVF]: you wish to append an assumption to GR that is not, in fact, any
part of general relativity: that gravitational force is the gradient of
the potential field as sensed by any non-moving body in that field.

[Carlip]: The "assumption" is that the geodesic equations describe the
motion of a test body. If you reject this, you reject the math of general
relativity. Period.

The equations of motion describe the motion of a test body because the
physics underlying them has infinite force propagation speed, equivalent to
zero gravitational aberration, equivalent to the force experienced by a
non-moving body.

As to the math, let me state my position using different words to avoid
going in circles endlessly. The math of GR is wrong for moving test bodies
and finite force propagation speeds, as the underlying physics plainly
shows. But GR then assumes infinite force propagation speed, which drives
the missing aberration term to zero, which eliminates the error in the math.
So the math of GR is correct for now because of the lucky circumstance that
gravitational force propagates so fast that no retardation can yet be
detected.

GR's math is right. The opinions of many relativists about what that
math means for the underlying physics are wrong.

[TomVF]: Yes, the equations are the same. No, the predictions are not the
same.

[Carlip]: This is a statement that you don't understand the math, pure and
simple. The equations have unique solutions. Those solutions *are* the
predictions. If the equations are the same, the predictions are the same.

This is a statement that you don't understand the physics behind the
math, pure and simple. The math has more than one physical interpretation.
The physics makes the predictions I spoke of, not the math. The math can
only "predict" (read: calculate) things, such as orbits or light-bending.
The underlying physics can predict things that may require new math, such as
that gravity must have a finite range. Obviously, we cannot learn about the
need for new math from the math alone. -|Tom|-


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

On Thu, 28 Aug 2008 "Tom Van Flandern" wrote:
Steve Carlip writes:
[Carlip]: it's hard to know how to respond to someone who doesn't even
understand the math well enough to recognize that there's a disagreement.

Math has no intelligence...

I think Tom forfeited any presumption of good faith awhile back, when
someone made an interesting observation on the message board of his
web site.

It was pointed out that Tom espouses two flagrently contradictory
things. First (coinciding with his claims about gravity), he claims
that the force exerted by an electrostatic field propagates almost
instantaneously (millions of times faster than light). Second, he
claims that the reason charged particles in particle accelerators
cannot be accelerated to speeds greater than light is that the applied
force only propagates at the speed of light, and hence can't push
anything faster. It was pointed out to Tom that many one-stage
accelerators rely explicitly on an electro-static field to accelerate
the particles, and of course the resulting acceleration is asymptotic
to the speed of light. So it's perfectly clear that Tom's two claims -
on which all his crackpot delusions depend - are mutually exclusive.
(Actually, both of his claims are wrong, but this simple contradiction
suffices to prove that at least one of them must be wrong.)

Tom's reaction was interesting. After a few rounds of his trademark
obfuscations and attempted evasions, denying that particle
accelerators work they way they do (e.g., claiming that they all
accelerate particle by bombarding them with waves, never by an
electrostatic field), he finally ended up deleting the comments of the
critic from his message board, and censoring any further discussion.

On Aug 29, 11:35 am, (Roger Shore) wrote:
On Thu, 28 Aug 2008 "Tom Van Flandern" wrote:

Steve Carlip writes:
[Carlip]: it's hard to know how to respond to someone who doesn't even
understand the math well enough to recognize that there's a disagreement.

Math has no intelligence...

I think Tom forfeited any presumption of good faith awhile back, when
someone made an interesting observation on the message board of his
web site.

It was pointed out that Tom espouses two flagrently contradictory
things. First (coinciding with his claims about gravity), he claims
that the force exerted by an electrostatic field propagates almost
instantaneously (millions of times faster than light). Second, he
claims that the reason charged particles in particle accelerators
cannot be accelerated to speeds greater than light is that the applied
force only propagates at the speed of light, and hence can't push
anything faster. It was pointed out to Tom that many one-stage
accelerators rely explicitly on an electro-static field to accelerate
the particles, and of course the resulting acceleration is asymptotic
to the speed of light. So it's perfectly clear that Tom's two claims -
on which all his crackpot delusions depend - are mutually exclusive.
(Actually, both of his claims are wrong, but this simple contradiction
suffices to prove that at least one of them must be wrong.)

Tom's reaction was interesting. After a few rounds of his trademark
obfuscations and attempted evasions, denying that particle
accelerators work they way they do (e.g., claiming that they all
accelerate particle by bombarding them with waves, never by an
electrostatic field), he finally ended up deleting the comments of the
critic from his message board, and censoring any further discussion.

IMO Flandern is asking good questions.

On Apr.8 in this thread, Tucker published
a proof, based on GR, using both geometry
and algebra to provide an explanation much
more advanced than the old Newtonian ideas,
(where an instanteous speed of gravity can
occur), on the relation of a *speed of
gravity* "c" is compatible with observation,
however Tucker's explanation was for circular
orbits only, and should be extended to highly
ellipitical and hyperbolic orbits.
These should be forth-coming.
Regards
Ken S. Tucker

Roger Shore writes:

[Shore]: I think Tom forfeited any presumption of good faith awhile back
... After a few rounds of his trademark obfuscations and attempted
evasions ... on which all his crackpot delusions depend ... he finally
ended up deleting the comments of the critic from his message board ...

One way our message board (http://metaresearch.org/msgboard/default.asp)
differs from USENET is that ad hominem remarks and character assassinations
are never tolerated. The reasons are obvious. They interfere with any hope
for a teaching/learning environment, and invariably are a frustrated
replacement for a substantive, on-topic response.

The only things we delete from our Meta Research message board are
insults, way-off-topic postings, and ads or spam.

[Shore]: he finally ended up deleting the comments of the critic from his
message board, and censoring any further discussion.

Our Board welcomes and encourages criticism and dissent. We never
"censor". I can offer only two explanations for this "complaint" about a
long-ago discussion, assuming the poster actually believes it to be true:
(1) The critic used abusive language or ad hominem remarks and ignored
warnings to desist; or (2) Shore had his message horizon set to something
short, and older messages disappeared from his view (but not from the board
or the view of anyone wanting to see older messages).

[Shore]: It was pointed out that Tom espouses two flagrantly contradictory
things. First (coinciding with his claims about gravity), he claims that
the force exerted by an electrostatic field propagates almost
instantaneously (millions of times faster than light).

I try not to make unsubstantiated claims such as those Shore just made,
which is why I attach citations to everything important I say here in USENET
for which the source may be in doubt. In this case (the propagation speed of
electrodynamic forces), I rely on the Sherwin-Rawcliffe experiment, which
demonstrated that the propagation speed of Coulomb forces is indeed strongly
faster than the speed of light. [See "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 Clearinghou