Re: Tom Van Flandern and Newtonian Gravity

From: Tom Van Flandern (tomvf_at_starpower.net)
Date: 06/03/04 

Date: Wed, 2 Jun 2004 23:28:19 -0400

            This replies to Tom Roberts and Mike.

"Tom Roberts" <tjroberts@lucent.com> raises a few interesting discussion
points. It is regrettable that they are somewhat buried in diatribe.

>> [tvf]: Gravitational forces are absent only in the geometric
interpretation of GR, which has now (arguably) been falsified in favor
of the field interpretation for violating the causality principle and
for needing to create changes in the 3-space momentum of target bodies
from nothing.

> [Roberts]: Nonsense . Physical theories yield mathematical predictions
for the results of physical measurements. When one does the comparison
correctly between theory and experiment, no interpretation is needed.

            Your statement is a non-sequitur to mine. Many different
physical theories, even some drastically different ones (such as "dark
matter" versus MOdified Newtonian Dynamics -- MOND) have the same
mathematical representation, at least to observational accuracy. So
getting the right physical theory is very much a matter of
interpretation.

            In the case under discussion, GR, the distinction between
the original field interpretation and the latter-day geometric
interpretation is not mine, but was an historical development commented
on most recently by no less a notable than Richard Feynman in Feynman
Lectures on Gravitation, Addison-Wesley, New York (1995). Section 8.4,
p. 113: "It is one of the peculiar aspects of the theory of gravitation,
that it has both a field interpretation and a geometrical
interpretation. ... the fact is that a spin-two field has this
geometrical interpretation: this is not something readily explainable --
it is just marvelous. The geometrical interpretation is not really
necessary or essential to physics."

            To take just one aspect of GR, Einstein and Eddington were
already aware 80-90 years ago that "refraction in an optical medium"
gave a mathematically equivalent result to "curved spacetime". Would you
still say "no interpretation is needed" about that difference?

            The complete, intuitive gravity model in [Pushing Gravity:
New Perspectives on Le Sage's Theory of Gravitation, M. Edwards, ed.,
Apeiron Press, Montreal, 93-122 (2002)] has the same math as GR to first
order in potential and second order in velocity. So it is the same
mathematical theory to that accuracy. Yet it predicts five phenomena
that GR does not. So in physics, mathematical theories definitely need
interpreting, and multiple interpretations need to be distinguished.
That has now happened in GR, and the geometric interpretation has lost
out to the field interpretation. But as Feynman said, the geometric
interpretation is not really necessary or essential to physics anyway.

> [Roberts]: In actual practice, the geometrical interpretation of GR is
live and well, and is ESSENTIAL in all of the current investigations of
quantum gravity....

            Would those be the current investigations that have failed
to produce a quantum gravity model since GR was first introduced nearly
a century ago? Note that Le Sage gravitation ("pushing gravity") has
already produced a *complete* quantum gravity model. As long as it
continues to work well, we really have no need of a second quantum
gravity model. But if one ever does evolve, it will be fun to see which
version is simpler and makes the better predictions.

>> [tvf]: Absent force, the 3-space acceleration of target bodies would
lack a cause, which is one of the reasons the geometric interpretation
is falsified -- curvature cannot initiate 3-space motion, and requires
"magic", which is forbidden in physics.

> [Roberts]: That is just plain false. In spaceTIME, curvature can
indeed "initiate 3-space motion" -- you just chose to ignore it by
focusing only in 3-space curvature.

            As I explained, "curvature" in the absence of a force (force
being the TIME rate of change of momentum) cannot initiate motion from
rest, just as the rubber *** analogy shows. Without gravity (a force)
under the rubber ***, a body on the side of a curved potential hill
will simply remain at rest there forever. What exactly are you proposing
as the causative physical mechanism to change non-motion into 3-space
motion when no force acts? An equation?

> [Roberts]: What you are discussing here has no relation to GR at all,
but is directly related to the APPROXIMATION to GR that you love so much
[equations of motion]

            You have repeated this ad nauseam, rather mantra-like, but
never explained yourself. What difference does it make whether one uses
exact equations or approximate equations to compare against observations
as long as the error in the approximation is far less than the error of
observation?

            What you say here makes no sense unless, by implication, you
also rule our using computers to evaluate sines and cosines or other
functions because these are just approximations, and the computed
approximations of these functions "have no relation at all" to the exact
functions.

            Please do explain yourself.

>> [tvf]: Roberts also writes as if equations of motion did not exist in
GR. But of course, they do, and are required for comparison with
observations. Equations of motion, as on p. 1095 of MTW, are expressions
for 3-space force/acceleration.

> [Roberts]: Please turn to page 1095 of MTW. Now elevate your eyes to
the heading of the chapter (which happens to be on the facing page), and
please read it: "Other theories of Gravity and Post-Newtonian
Approximation". Those equations are NOT the "equations of motion of GR",
they are equations of motion for an APPROXIMATION TO GR.

            Those equations are known throughout the civilized world as
"the GR equations of motion" for the simple reason that is what they
are. They are used in orbit computation and for definitive comparisons
of theory and observation. If they were in any way not representative of
GR, then only the "approximation" would have been observationally
confirmed, and GR would remain an untested theory.

            However, speaking more directly to your point, turn to p.
1069 and read in the first paragraph there (with emphasis added by me):
"Consequently, the analysis of solar system experiments using any metric
theory of gravity can be simplified, WITHOUT SIGNIFICANT LOSS OF
ACCURACY, by a simultaneous expansion . Such a "weak-field, slow motion
expansion" gives . (3) post-Newtonian corrections . The formalism of
Newtonian theory plus post-Newtonian corrections is called the
"post-Newtonian approximation".

            If there is no significant loss of accuracy, how do you
justify your extravagant claims?

> [Roberts]: People around here have told Tom Van Flandern this many
times, and he is still unable to comprehend this important distinction.

            "People around here" refers to Tom Roberts. I concede that I
see no importance whatever to the distinction you wish to make for the
purposes of this discussion. Do other people also have trouble
comprehending your claims, or am I privileged to be the only one?
Perhaps if you did less bashing and more explaining, the point you are
trying to make would emerge. Or perhaps in the effort to explain, you
will discover that you were just beating a strawman.

> [Roberts]: Analyze the approximations to GR leading to these
equations, and you will realize that some aspects of the limit
c->infinity have been included. And this is an ESSENTIAL aspect of
reducing the equations form 4-d spaceTIME to "3-space
force/acceleration".

            I have been through the full derivation of the equations of
motion line-by-line in Einstein-Infeld-Hoffmann, in Robertson and
Noonan, and in Damour's treatment too (which is more general). I have
been saying right along that the speed of gravitational force has been
set to infinity in these equations, not for reason of any convenience or
approximation, but because that step is (as you say) an ESSENTIAL aspect
of the equations, without which they would fail to represent reality.
But that is the only place where an infinite speed is used. The speed of
light always remains c and appears only as c^2 (an energy per unit mass,
not a speed) or higher powers, but the speed of gravitational force is
set to infinity.

            Run through the derivations and see for yourself. I'd then
be interested in your explanation of the physical interpretation of this
use of infinity. You will plainly see that it has nothing to do with
lightspeed and cannot be approximated by c under any circumstances
without turning closed orbits into spirals.

> [Roberts]: The equations of motion of GR are well known: T^uv_;v = 0
TVF ignores this, probably because he knows full well that if he pursued
it he could never conclude that gravity "propagates >> c".

            The equations you mention describe the potential field, not
the 3-space motion of bodies in that field. Changes in the potential
field propagate at speed c. That is now old news. Equally certain is
that the propagation speed of gravitational force, the entity described
by GR's 3-space equations of motion, is infinite in GR and
near-instantaneous in all experiments, as detailed in the references
previously provided.

            So I definitely do conclude that gravity (meaning
gravitational force, the chief determinant of orbital motion in 3-space)
propagates >> c.

>> [tvf]: Yes, you will look in vain for forces in the Einstein field
equations. That is simply because the gravitational (potential) field
described by those equations does not produce forces. After the field is
described, one must form a gradient to get an expression for force to
describe the 3-space dynamics. That "gradient" step, incidentally, is
where the "infinite propagation speed" is introduced into GR.

> [Roberts]: ONLY if you work in a suitable APPROXIMATION TO GR. In GR
itself one NEVER performs such a gradient; one solves the field equation
and/or the geodesic equation. The only reason such approximations are
used is that it is vastly simpler to solve the approximate equations
than the real equations, and in practice the errors due to the
approximation are negligible (i.e. far smaller than measurement
accuracies).

            Perhaps this is at the heart of our failure to communicate.
The field and geodesic equations describe only the potential field. One
cannot calculate orbits from those equations. Orbits and observations
are 3-space entities, and require 3-space equations of motion. Forming
those requires taking a gradient or the mathematical equivalent, such as
forming a Lagrangian or a Hamiltonian. (They all involve 3-space partial
derivatives.) So the purpose of these equations of motion is quite
different from the purpose of field equations. The former equations
involve forces, the latter involve potentials.

            These two sets of equations are not related to one another
as "exact" versus "approximation". They are equations of completely
different kinds used for different purposes. It is unfortunate that you
are not familiar with equations of motion, which are in fact the subject
of my professional specialty (celestial mechanics). For a deeper
understanding of equations of motion and how to compute orbits from
them, I recommend J.M.A. Danby's "Fundamentals of Celestial Mechanics".
Notice especially that interactions between bodies are taken as
instantaneous. A light-speed propagation delay would be fatal because
the computed orbits would spiral.

> [Roberts]: consider Schwarzschild spacetime outside a spherical mass
M. The field in Schw. coordinates is independent of time t. Now boost to
uniformly-moving coordinates, and the field will vary as a function of
time in the moving coordinates. And if one plotted a contour map of the
field wrt the moving coordinates, by golly the contour lines move in
mutual harmony with the mass M. This is an elementary consequence of the
coordinate-independence of GR.

            All true, but also beside the point here. Try adding
gradient lines to your contour map of the field using moving
coordinates. That is where the relevant action occurs. The gradient
lines cannot move in mutual harmony with the mass M unless either (1)
nothing propagates to regenerate the field (no causality, no source of
3-space momentum for target bodies), or (2) the field regenerates with
near-infinite speed. Obviously, only solution (2) is consistent with the
principles of physics. [See
http://metaresearch.org/cosmology/PhysicsHasItsPrinciples.asp.]

            Perhaps you have worked in a GR field-equation world so long
that it has escaped your notice that the real world is not always
Lorentz invariant. The GR 3-space equations of motion are an obvious
example, as you may be able to see for yourself by inspection of MTW p.
1095.

            Only the field and geodesic equations have that neat
covariant property. But once you take the gradient of the potential to
get descriptions of motions in 3-space versus time, you lose Lorentz
invariance. It is important to know that. Someone lacking that knowledge
might be inclined to make inappropriate generalizations about nature.

>> [tvf]: the geometric interpretation of GR is not viable. It provides
no causal connection between source mass and target body, a link that is
essential in physics, even if not in math.

> [Roberts]: You use the naive notion of causality; that is appropriate
in everyday speech, but is utterly absent in any modern theory of
physics. Including GR.

            The causality principle in physics reads: "Every effect has
a proximate, antecedent cause." That arises from logic alone. Any
exception would be a form of "magic", and therefore outside the domain
of physics. As long as we can continue to describe reality in accord
with the causality principle, there will remain no need for miracles --
including a beginning to space or time. I am sorry you are not familiar
with this principle because it is fundamental to constraining
mathematical theories, which might otherwise entertain singularities,
unlimited dimensions, creation ex nihilo, and other miracles as
something more than mathematical abstractions. But then, you would have
lots of company to comfort you.

and "Mike" " <eleatis@yahoo.gr> writes:

> [Mike]: GR offers a geometric model of relativistic dynamics and only
that.

            It sounds as if the field interpretation of GR is a hole in
your knowledge.

> [Mike]: This is the only interpretation (geometric) that satisfies the
epistemological principle in the foundation of GR and which states that
all phenomena must have the same explanation in all moving reference
frames.

            But you don't define what you mean by this coordinate
independence. As noted above, in the simplest interpretation
(covariance/Lorentz invariance), coordinate independence is simply wrong
for all of celestial mechanics and the GR 3-space equations of motion.

            If that is not what you mean, then please provide a clear
definition. The murkiness of definitions of terms is one of the primary
reasons for failures to communicate in forms such as this one.

> [Mike]: I have looked at the paper by Tom Van Flandern and it
appears . that he is using the flat space metric of Minkowski spacetime
to build some arguments involving causality in 3-D space.

            You might want to look again. Causality in 3-space follows
from logic alone, without need for Minkowski spacetime to exist outside
the world of mathematics. And remember that "curved spacetime" does not
involve any curvature of space. (If this is news to you, see "Does space
curve" at http://metaresearch.org/cosmology/gravity/spacetime.asp.)

> [Mike]: Thus, the 3-D world of Van Flandern is just a projection of a
relativistic dynamics. In this projection, one is faced with dilemmas
such as causality. The power of GR is in eliminating the need for causal
agents and superluminal speeds from a model which, despite the
philosophical objections, seems to work very well.

            Apparently, one person's meat is another's poison. Inasmuch
as causality is contrasted with magic, I was always quite partial to the
former, and didn't feel I truly understood a phenomenon until I could
describe cause and effect. And why one would consider eliminating
superluminal speeds an *advantage* I cannot imagine. Look at all the
paradoxes that elimination created in cosmology and quantum physics that
have now vanished.

> [Mike]: I would like to inform Van Flandern that the causal
relationship between force and acceleration cannot even be established
in Newtonian Mechanics he seems to be a master of.

            That is indeed news to me, especially since I have written
papers about that very causal relationship. My Meta Research Bulletin
[vol. 11#4, pp. 49-53 (2002)] article, "Does gravity have inertia",
would be a case in point. Have you an argument, experiment, or citation
to support your opinion?

> [Mike]: I challenge Tom Van Flandern to give me an answer to the
following question or refrain from any reference to causality from his
posts: Tie a stone at the end of a rope and whirl it around Dr. Van
Flandern. Is the tension on the rope the cause of the circular orbit or
the circular orbit causes the tension on the rope?

            I have no idea why you ask this because Newton's first two
laws of motion explain this in classical physics. All bodies at rest in
3-space remain at rest, while those in motion remain in uniform, linear
motion unless a force acts. Your rock does not continue in uniform,
linear motion, so a force must be acting on it -- the tension in the
rope.

            In the following, assume that a hand whirls the rope. Then
here is the sequence. The rock tries to move in a uniform, linear way in
3-space. That causes the distance between rock and hand to increase,
which creates tension in the rope. (I assume that the physics of tension
inside the rope is not the subject of your interest.) The tension
applies a centripetal force to the rock, curving its path into a circle.

            So clearly in this example, tension causes the circular
motion. If the tension is removed by the hand releasing the rope, the
rock will resume its uniform, linear motion. If the rock is removed but
the rope remains, the rock's attempt to travel in linear motion can no
longer act to stretch the rope, so the rope tension (except the small
part from its own weight) is released, and the rope continues to whirl
without tension.

            This seems a complete picture of cause and effect at the
rope-rock interface, with unambiguous causality. So why did you issue
your challenge?

> [Mike]: The failure of NM to provide answers to such basic questions
about its model of the world gave power to GR.

            You and I also apparently were taught history differently as
well. What gave impetus to GR was the success of its three classical
post-Newtonian predictions. Other than for that, there was no "failure
of NM", which was doing just fine at explaining dynamics with Newton's
three laws of motion and his universal law of gravity.

> [Mike]: But when one mixes physics and metaphysics, all sorts of
paradoxes emerge.

            This is something we can agree upon, although we probably
don't agree about who is doing the mixing. But the models I described
have eliminated (as contrasted with "resolved") every related paradox
without exception, as shown in the papers I have referenced. You sure
can't make that claim for your personal world model.

> [Mike]: If you wrote that paper as a midterm project for the course I
took in Modern Physics (that's how SR and GR was called then) you (Van
Flandern) would have gotten a straight F, I'm sorry to say.

            That is an illuminating remark. Often, a poor background in
any subject area can be traced to bad teachers. You have my sympathies.

            Truly, I have an unfair advantage in this area because I was
taught (in the Yale graduate school) by Brower, Clemence, Danby, Deprit,
and Szebehely among others, all authors and world-renowned figures in
celestial mechanics of both the Newtonian and Einsteinian variety; and I
did my dissertation on improvements in the lunar orbit using occultation
data (a "rock" on a "gravitational string", so to speak :-). -|Tom|-

Tom Van Flandern - Washington, DC - see our web site on replacement
astronomy research at http://metaresearch.org