From: cflatter@nrao.edu (Chris Flatters)
Subject: Re: The Hole Story
Reply-To: cflatter@nrao.edu
Organization: NRAO
Date: Mon, 21 Dec 1992 00:34:40 GMT

In article 355@well.sf.ca.us, metares@well.sf.ca.us (Tom Van Flandern) writes:
>and cflatter@nrao.edu (Chris Flatters) replied:
>> There is almost certainly something wrong with this calculation.  It sounds
>> as if the motions of the planets are being calculated in a different
>> reference frame from the motion of the Sun.
>
>     No, the center-of-mass frame is used for all.  And there is nothing
>wrong with these calculations.  I'm not referring to some result of mine, but
>to what every dynamicist knows to be the case.  Their calculations agree with
>observations to 8-9 significant figures.  Not many fields get that kind of
>accuracy.  Yet there are no delay terms, direct or indirect, hidden or
>cancelled.  Retarded potentials are not used, not because they are
>negligible, but because their effects are large and in conflict with
>observations.

[and later]

>     I'm sorry, Chris, but none of the sentences in this paragraph describing
>your impressions of how the universe ought to work is consistent with
>observation or experiment.  Consider:  Aberration for the Earth is 10^-4
>radians, reflecting the fact that the Earth's velocity is 10^-4 that of
>light.  By no stretch of the imagination is 20 arc seconds on the sky a
>negligible amount.  If the Earth's velocity were nearly equal to c, the
>apparent Sun would be well out in front of the Earth, and clearly trying to
>accelerate it.  Since it is 10^-4 of c, the Sun's force vector can be
>decomposed into two components: a central force toward the focus of the
>Earth's elliptical orbit from a mass nearly equal to the Sun's, and a
>tangential force along the Earth's orbit of strength 10^-4 that of the Sun's
>radial force.  The tangential force is always present, and always trying to
>accelerate the Earth in all parts of its orbit.  The absence of such an
>acceleration tells us that aberration for gravity is less than 10^-10 of what
>it is for light.  Either nothing propagates from the Sun, or it propagates
>faster than light by a factor of 10^10.  Try to set up your integration with
>retarded potentials (as thousands have done before you) and see for yourself.

This as attempt to have things both ways.  If you are doing calculations in
the Sun's rest frame then you need to calculate the gravitational forces in
that frame: the motion of the Earth in this reference frame makes no difference
to the Sun's gravitational field.

>     In the light of the preceding, let's reexamine Einstein's argument.  His
>eqn. 101 is based, as he says, on an electrodynamics analogy.  But MTW in
>Chapter 7 show at great lengths all the efforts that have been made to make
>retarded potentials work, without success.

No they don't.  Chapter 7 of Misner, Thorne and Wheeler shows that a consistent
theory of gravitation can not be developed without introducing curved space.

>
>     Here is Eddington's argument that calculations with retarded positions
>cannot help but alter the angular momentum of the system (i.e., cause the
>orbits to spiral) [Eddington, S. A., "Space, Time & Gravitation", Cambridge
>University Press, Cambridge & New York (1920; reprinted 1987).  See p. 94.]:
>
>     "If the Sun attracts Jupiter towards its present position S, and Jupiter
>attracts the Sun towards its present position J, the two forces are in the
>same line and balance.  But if the Sun attracts Jupiter toward its previous
>position S', and Jupiter attracts the Sun towards its previous position J',
>when the force of attraction started out to cross the gulf, then the two
>forces give a couple.  This couple will tend to increase the angular momentum
>of the system, and, acting cumulatively, will soon cause an appreciable
>change of period, disagreeing with observations if the speed is at all
>comparable with that of light."

I can't check the context of this quotation since Eddington's book is 
checked out of the library here but I believe that this is also an
argument against flat space-time.

Remember: the general theory of relativity attributes the effects of gravity
to the curvature of space and time in the neighbourhood of a mass.  If the
gravitational field is weak and the a particle is moving slowly through
it then Newton's law of gravitation is recovered with the gravitational
potential being determined by the single component g_{00} of the metric
tensor (where the 0 subscript denotes time).  If these approximations
do not hold you must use the full metric tensor to determine the equations
of motion.

Tom appears to be using the Newtonian approximation to derive a force on
a planet and then transforming the force as a vector to the comoving frame
of the planet.  This is not a valid methodology in Einstein's theory.  Tom is
basically repeating a demonstration that a consistent theory of gravitation
can not be developed in flat space-time.  GR holds that space-time is not
flat.

	Chris Flatters
	cflatter@nrao.edu
Xref: sparky sci.astro:13047 sci.physics:20931