From: cflatter@nrao.edu (Chris Flatters)
Newsgroups: sci.astro
Subject: Re: The Hole Story
Date: 16 Dec 92 18:47:41 GMT
Reply-To: cflatter@nrao.edu
Organization: NRAO

In article GCG@well.sf.ca.us, metares@well.sf.ca.us (Tom Van Flandern) writes:
>     The confusion is not yours alone.  Actually, it is SR, not GR, which
>says that no information can travel faster than light.  Then when GR is
>taught, the point about gravity acting without detectable delay is glossed
>over, leaving students in a state of disbelief when they learn about it later
>in their careers.

There is no confusion.  In GR gravitational effects propagate at the
speed of light.  If you don't believe me check out the use of retarded
potentials to determine the effects of gravity on page 83 (equation
101) of Einstein's monograph "The Meaning of Relativity".

Also: if gravitational effects propagate instantaneously there would be
no wave solution for Einstein's equations.

Also (if I remember the GR courses I took many years ago correctly): the
Kerr metric for a rotating mass is derived using retarded potentials.

>     First, here's what is true.  Light propagates through the solar system
>at lightspeed, taking minutes to hours to reach the planets.  When light from
>the Sun applies a force, for example, the Poynting-Robertson effect, that
>force seems to come from the Sun's retarded position, as one logically
>expects.  As a direct consequence, dust in the inner solar system slowly
>spirals into the Sun, since delayed forces are non-central forces and always
>change the angular momentum of an orbit.
>
>     Gravity, by contrast, always appears to act from the true, instantaneous
>position of the bodies involved.  It never appears to associate with retarded
>positions.  And the Sun's gravity does not change the angular momentum of the
>planets.  By direct observation, the directions of the Sun's arriving photons
>at the Earth and the direction of its gravitational force on the Earth are
>not parallel, since one comes from the retarded position and the other from
>the true position.

A few pages from equation 101 in Einstein's monograph we find the following:

	"The previous developments are valid however rapidly the masses
	whose which generate the field may move relatively to our 
	chosen system of quasi-Galilean co-ordinates.  But in astronomy
	we have to do with masses whose velocities, relatively to the
	co-ordinate system employed, are always small compared with
	the velocity of light, that is, small compared to 1, with our
	choice of the unit of time.  We therefore get an approximation
	which is sufficient for nearly all practical purposes if in
	(101) we replace the retarded potential by the ordinary (non-
	retarded potential, and if, for the masses which generate the
	field, we put

	dx1/ds = dx2/ds = dx3/ds = 0, dx4/ds = ... = sqrt(-1)	(103)"

				Op cit, p85

>     This can be verified by pure computation in a computer.  If we insert
>lighttime delay into either Newtonian or GR equations of motion of the
>planets, they quickly spiral out of their known orbits.  Gravity acts without
>detectable delay.

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.

	Chris Flatters
	cflatter@nrao.edu
Newsgroups: sci.astro