From: ecc_jim@ecc.tased.edu.au
Newsgroups: alt.folklore.science
Subject: Re: Speed of gravity
Date: 2 Oct 92 12:18:31 +1000

> 
> Pardon my skepticism.  You wouldn't happen to have a copy of that
> availible, would you?
> 
No problem. Here it is:


     [The following article is reprinted here by its author from the June
issue of the Meta Research Bulletin.]
     The question is often asked, "At what speed does the force of gravity
propagate?"  To answer this question properly, one must  first define terms
to insure that the question is well-formed.
     The quick answer one invariably hears to the above question is "at (or
near) the speed of light".  But this answer is incorrect.   This false but
widespread impression exists because there is a hypothetical phenomenon
called "gravity waves" which, if they  exist, are expected to propagate at
or near the speed of light.  But gravity waves are not a factor in the
question as posed; and may  not exist at all.  Let us examine why. Gravity
waves.  The most popular interpretation of gravity in General Relativity
(GR) is that it is a curvature of spacetime.  The  Earth accelerates toward
the Sun because the spacetime near the Earth's orbit is curved in such a way
that it "slopes" toward the  Sun.  There are no gravity waves in an ordinary
gravitational field.  Theoretically, gravity waves are a sort of "ripple" in 
spacetime caused by the rapid acceleration of mass, as in a supernova
explosion.  Something must happen to disturb the static  gravitational field
in order to produce gravity waves.  If we neglect the masses of the planets,
the Sun would emit no gravitational  waves whatever; yet it obviously still
exerts a gravitational pull on the Earth.
     The predicted existence of gravity waves is not a part of GR, and is
based on a supposed analogy between gravity and  electromagnetism (EM) which
is suspect.  Both gravity and EM give rise to an inverse square force, but
there the similarity ends.   EM forces are both attractive and repulsive,
gravity is attractive only.  A body's own charge affects its motion in EM,
but its own  mass does not affect its own acceleration in gravity.  There is
no Equivalence Principle in EM, and no analog of magnetism for  gravity.  EM
forces between two bodies act with lighttime delay, while gravity acts with
no detectable delay.  (More on this  below.)  And the relative strengths of
the two forces differ by 40 orders of magnitude.
     This faulty analogy is also the main reason for suspecting that gravity
waves travel at or near the speed of light.  And their  predicted strength,
if they did exist, depends upon the resistance of spacetime to deformation,
which is an unknown parameter  about which assumptions must be made. 
Indeed, belief in the existence of gravity waves would be ill-founded but
for an  experiment involving a binary pulsar, which is said to provide
indirect evidence for the existence of gravity waves.  When the  motion of
the two stars was modelled with a gravity wave theory predicting orbital
acceleration, the fit between theory and  observations was good enough to
infer the existence of the predicted acceleration to about the 1% level
(Taylor & Weisberg,  1989 ApJ, v. 345, pp. 434-450) .  The authors claimed
this as evidence for the existence of gravity waves.  But it has since been 
pointed out (Damour, 1992 Class.Quant.Grav. v. 9, pp. 55-59) that their fit
to observations is equally good without any gravity  waves in the model,
since the apparent small acceleration is then fully compensated by other
parameters in the solution.  So this  case does not, after all, support the
existence of the phenomenon of gravity waves. Gravity has no aberration. 
Whether they exist or not, gravity waves play no role in answering the
question posed at the  beginning of this article.  To answer that we must
consider the static gravitational field which has no waves.  Let us again 
examine the orbit of a massless Earth around the Sun. It takes 8.3 minutes
for the Sun's photons to traverse the distance between  it and the Earth. 
During that interval, the Sun appears to move relative to the stars by an
angle of 20 arc seconds  a large and  easily measurable amount.  This is
called aberration, and is caused by the Earth's motion relative to the Sun,
and the finite speed  of the photons.  Since the Earth moves at 30 km/s =
10^-4 of the speed of light, the visible disc of the Sun appears displaced
on  the sky toward the direction of motion by 10^-4 radians or 20 arc
seconds relative to its instantaneous, true position.  This is just  like
the effect a moving train has on the direction of a vertically-falling rain. 
The faster the train moves relative to the speed of  the raindrops, the
greater will be the angle relative to the vertical at which the rain streaks
across the train's windows.
     As all this pertains to gravity, it is important to note that gravity
has no aberration.  The direction of acceleration of the Earth  at each
instant does not parallel the direction of the arriving photons from the
Sun. Instead, the Earth's acceleration is toward the  true, instantaneous
position of the Sun, to the full accuracy of the best observations we can
make.  So whatever gives rise to the  acceleration which the Earth
experiences, or to the curvature of spacetime near the Earth's orbit, it
cannot simply be the  absorption of some hypothetical "gravitons" traveling
out from the Sun at the speed of light; for if it were, gravity would suffer 
aberration, and the Earth's acceleration would be toward the Sun's apparent
disc, and its direction would be anti-parallel to the  arriving photons.
     We know this result, that gravity has no aberration, in two ways:
through computations and observations.  We can calculate  the motion of the
Earth in the gravitational field of the Sun by a process called numerical
integration.  If we permit any delay at  all comparable to that of light in
the action of the Sun on the Earth, a torque is introduced which quickly
accelerates the Earth out  of orbit.  It is easy to visualize why this must
be so.  Let the Sun be so massive that the circular orbital velocity of the
Earth is  close to the speed of light.  Then the apparent disc of the Sun is
always well out ahead of the Earth in the direction of its motion  (just as
vertically-falling rain would appear to streak almost horizontally if the
train moves fast enough).  But if the Earth  accelerated toward that
apparent Sun rather than the true one (as it would if force-carrying agents
propagated outward at  approximately the speed of light), the Earth would
always be gaining velocity from the Sun's forward pull until it accelerated
out  of orbit.
     It is not difficult to measure the direction of the Earth's
acceleration observationally as well; for example, by determining the 
direction of the radius of curvature of its orbit.  Moving beyond these
simple experiments, which do show that the Earth's  acceleration is toward
the true Sun, I designed a tougher experiment and analyzed the observations
myself.  The Moon's orbit  around the Earth is approximately an ellipse. 
But the gravitational perturbations of the Sun are so strong on the Moon's
orbit that  it is distorted from an ellipse by an appreciable amount.  I
undertook an analysis of timings of occultations of stars at the Moon's 
limb to solve for many parameters, including corrections to the Moon's
orbit.  In one such analysis I eliminated the effects of  other
perturbations such as the planets, leaving only the Moon's elliptical motion
plus the Sun's perturbations.  I then posed the  following question for the
analysis: in what direction does the body perturbing the Moon's orbit from
elliptical lie?  I expected  the analysis to give one of two answers: either
toward the direction of the Sun's apparent disc, or toward its true,
instantaneous  position.  The actual solution gave the latter answer to
within about one arc second, with an uncertainty of about one arc second.  
If gravity were caused by the absorption of gravitons propagating outward
from the Sun, they had to be moving at least 20 times  faster than light to
reduce the lag angle from 20 arc seconds to only one arc second or less.
Gravity acts without detectable delay.  So curved spacetime could not be the
result of something propagating out from the Sun at  the speed of light or
less in a straightforward, classical sense.  But there were other
possibilities: the Earth might sense the  linearly-extrapolated position of
the Sun instead of either its apparent or its true position; or spacetime
might not respond  instantly to changes in the acceleration of the Sun due
to a sort of viscosity of spacetime.  Either of these possibilities might 
create the illusion that the Sun's gravity acted faster than light.  In the
first case, I expected that the Earth must somehow sense  the linear motion
of the Sun during the light transit time, and therefore accelerate toward
the linearly-extrapolated position of the  Sun, which would be close to the
Sun's true position.  In the second case, I expected that close, massive
binary star systems  which constantly accelerate with respect to their
center of mass would show the effects of any viscosity of spacetime.  But 
numerical integrations showed that either case still introduced far too much
angular momentum to agree with observations.  The  only way to secure such
agreement appeared to be the avoidance of torques, which required nearly
instantaneous interactions  between bodies.  So I turned to the equations of
GR for an answer to the question of the speed of propagation.
     The field equations of GR are for a single mass.  That mass is assumed
to generate a static field (e.g. curved spacetime) at a  distance.  Then all
particles encountering that distant field are assumed to react to it
instantly, as if the curved spacetime were  "cemented" in place and no
longer required continual regeneration by the central mass.  But the
equations simply assume that the  effective direction of the local field in
the vicinity of a particle is toward the true, instantaneous position of the
central mass, and  is unaffected (to first order) by the particle's orbital
velocity (see, e.g., Misner, Thorne & Wheeler, 1973 "Gravitation", chapters 
7, 18 & 39, and especially equation 39.64).  When it comes to two or more
massive bodies, the field equations are silent about  how to combine their
effects on spacetime at a distant point.  The issue is one of whether the
effects combine instantly, or with  delays, presumably approximating
lighttime delays.  When GR is used in numerical integrations to determine
the motions of, say,  the planets in the solar system, all mutual
interactions are assumed to occur instantaneously for the very good reason
that it is the  only known way to get computed motions which agree with the
observations.
     So what is the answer to our motivating question?  At what speed does
the force of gravity propagate?  We are reduced to  offering a pragmatic
answer.  Certainly no experiment has detected any propagating aspect of the
ordinary gravitational field  moving near the velocity of light.  It is
equally clear that the gravitational accelerations of bodies are directed
toward the true,  instantaneous positions of the source masses to extremely
high precision, even when the source mass undergoes rapid  gravitational
acceleration.  At first glance this appears to be an action occurring faster
than light.  However relativists argue that,  since each body simply follows
a geodesic path through curved spacetime, and since that path can be
computed indefinitely far  into the past and future, no information is
transmitted faster than light; so there are no violations of Special
Relativity (SR) on  this account.
     The best answer we can presently offer is that gravitational
interactions occur without detectable delay.  Explanations offered  for that
experimental fact are inevitably arguable.   Tom Van Flandern / Washington,
DC / metares@well.sf.ca.us
     Meta Research was founded to foster research into ideas not otherwise
supported because they conflict with mainstream  theories in Astronomy.