Subject: IUFO: The Speed of Gravity Faster than the Speed of Light



                THE SPEED OF GRAVITY - WHAT THE EXPERIMENTS SAY

      The Speed of Gravity Faster than the Speed of Light Tom Van Flandern
                             tomvf@metaresearch.org

          Meta Research, Univ. of Maryland Physics, Army Research Lab
               6327 Western Ave., NW / Washington, DC 20015-2456
                               (metaresearch.org)

                                  [cover.gif]
                       Boris Starosta / metaresearch.org


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      Abstract

      Standard experimental techniques exist to determine the
      propagation speed of forces. When we apply these techniques
      to gravity, they all yield propagation speeds too great to
      measure, substantially faster than lightspeed. This is
      because gravity, in contrast to light, has no detectable
      aberration or propagation delay for its action, even for
      cases (such as binary pulsars) where sources of gravity
      accelerate significantly during the light time from source to
      target By contrast, the finite propagation speed of light
      causes radiation pressure forces to have a non-radial
      component causing orbits to decay (the "Poynting-Robertson
      effect"); but gravity has no counterpart force proportional
      to v/c to first order. General relativity (GR) explains these
      features by suggesting that gravitation (unlike
      electromagnetic forces) is a pure geometric effect of curved
      space-time, not a force of nature that propagates.
      Gravitational radiation, which surely does propagate at
      lightspeed but is a fifth order effect in v/c, is too small
      to play a role in explaining this difference in behavior
      between gravity and ordinary forces of nature. Problems with
      the causality principle also exist for GR in this connection,
      such as explaining how the external fields between binary
      black holes manage to continually update without benefit of
      communication with the masses hidden behind event horizons.
      These causality problems would be solved without any change
      to the mathematical formalism of GR, but only to its
      interpretation, if gravity is once again taken to be a
      propagating force of nature in flat spacetime with the
      propagation speed indicated by observational evidence and
      experiments: not less than 2 x 1010 c. Such a change of
      perspective requires no change in the assumed character of
      gravitational radiation or its lightspeed propagation.
      Although faster-than-light force propagation speeds do
      violate Einstein special relativity (SR), they are in accord
      with Lorentzian relativity, which has never been
      experimentally distinguished from SR-at least, not if favor
      of SR. Indeed, far from upsetting much of current physics,
      the main changes induced by this new perspective are
      beneficial to areas where physics has been struggling, such
      as explaining experimental evidence for non-locality in
      quantum physics, the dark matter issue in cosmology, and the
      possible unification of forces. Recognition of a
      faster-than-lightspeed propagation of gravity, as indicated
      by all existing experimental evidence, may be the key to
      taking conventional physics to the next plateau.

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                                  Introduction

The most amazing thing I was taught as a graduate student of celestial
mechanics at Yale in the 1960s was that all gravitational interactions
between bodies in all dynamical systems had to be taken as instantaneous.
This seemed unacceptable on two counts. In the first place, it seemed to
be a form of "action at a distance". Perhaps no one has so elegantly
expressed the objection to such a concept better than Sir Isaac Newton:
"That one body may act upon another at a distance through a vacuum,
without the mediation of any thing else, by and through which their
action and force may be conveyed from one to the other, is to me so great
an absurdity, that I believe no man who has in philosophical matters a
competent faculty of thinking, can ever fall into it." (See Hoffman,
1983.) But mediation requires propagation, and finite bodies should be
incapable of propagate at infinite speeds since that would require
infinite energy. So instantaneous gravity seemed to have an element of
magic to it.

The second objection was that we had all been taught that Einstein's
special relativity (SR), an experimentally well established theory,
proved that nothing could propagate in forward time at a speed greater
than that of light in a vacuum. Indeed, as astronomers we were taught to
calculate orbits using instantaneous forces; then extract the position of
some body along its orbit at a time of interest, and calculate where that
position would appear as seen from Earth by allowing for the finite
propagation speed of light from there to here. It seemed incongruous to
allow for the finite speed of light from the body to the Earth, but to
take the effect of Earth's gravity on that same body as propagating from
here to there instantaneously. Yet that was the required procedure to get
the correct answers.

These objections were certainly not new when I raised them. They have
been raised and answered thousands of times in dozens of different ways
over the years since general relativity (GR) was set forth in 1916. Even
today in discussions of gravity in USENET newsgroups on the Internet, the
most frequently asked question and debated topic is "What is the speed of
gravity?" It is only heard less often in the classroom because many
teachers and most textbooks head off the question by hastily assuring
students that gravitational waves propagate at the speed of light,
leaving the firm impression, whether intended or not, that the question
of gravity's propagation speed has already been answered.

Yet, anyone with a computer and orbit computation or numerical
integration software can verify the consequences of introducing a delay
into gravitational interactions. The effect on computed orbits is usually
disastrous because conservation of angular momentum is destroyed.
Expressed less technically by Sir Arthur Eddington, this means: "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." (Eddington, 1920, p.94) See
Figure 1.

                                   [fig1.gif]

Indeed, it is widely accepted, even if less widely known, that the speed
of gravity in Newton's Universal Law is unconditionally infinite. (e.g.,
Misner et al., 1973, p.177) This is usually not mentioned in proximity to
the statement that GR reduces to Newtonian gravity in the low-velocity,
weak-field limit because of the obvious question it begs about how that
can be true if the propagation speed in one model is the speed of light,
and in the other model it is infinite.

The same dilemma comes up in many guises: Why do photons from the Sun
travel in directions that are not parallel to the direction of Earth's
gravitational acceleration toward the Sun?

Why do total eclipses of the Sun by the Moon reach maximum eclipse about
40 seconds before the Sun and Moon's gravitational forces align? How do
binary pulsars anticipate each other's future position, velocity, and
acceleration faster than the light time between them would allow? How can
black holes have gravity when nothing can get out because escape speed is
greater than the speed of light?

Herein we will examine the experimental evidence bearing on the issue of
the speed of propagation of gravity. By gravity, we mean the
gravitational "force" from some source body. By force, we mean that which
gives rise to the acceleration of target bodies through space. [Note:
Orbiting bodies do accelerate through space even if gravity is geometry
and not a true force. For example, one spacecraft following another in
the same orbit can stretch a tether between the two. The taut tether then
describes a straight line, and the path of both spacecraft will be curved
with respect to it.] We will examine the explanations offered by GR for
these phenomena. And we will confront the dilemma that remains when we
are through: whether to give up our existing interpretation of GR, or the
principle of causality.

                      Propagation Delay versus Aberration

To understand how propagation speeds of phenomena are normally measured,
it will be useful to discuss propagation or transit delay and aberration,
and the distinction between them. The points in this section are
illustrated in Figure 2.

                                   [fig2.gif]

In the top half of the figure, we consider the view from the source. A
fixed source body on the left (for example, the Sun) sends a projectile
(the arrow, which could also be a photon) toward a moving target (for
example, the Earth). Infinitely far to the right are shown a bright
(large, aberration 5-pointed) star and a faint (small, 4-pointed) star,
present to define directions in space. Because of transit delay, in order
to hit the target, the source body must send the projectile when it is
seen in the direction of the faint star, but send it toward the direction
of the bright star, leading speed to the radial projectile speed. For
small angles, this ratio equals the lead angle in radians.

In the bottom half of the figure, we consider the view from the target,
which will consider itself at rest and the source moving. By the
principle of relativity, this view is just as valid since no experiment
can determine which of two bodies in uniform, linear relative motion is
"really moving" and which is not. The projectile will be seen to approach
from the retarded position of the source, which is the spatial direction
headed toward the faint star. The angle between the true and retarded
positions of the source, which equals the angle between the two stars, is
called "aberration". It will readily be recognized as the same angle
defined in the first view due to transit delay.

Indeed, that is generally true: The initial and final positions of the
target as viewed from the source differ by the motion of the target
during the transit delay of the projectile. The same difference between
initial and final positions of the source as viewed from the target is
called the angle of aberration. Expressed in angular form, both are
equal, and are manifestations of the finite propagation speed of the
projectile as viewed from different frames. So the most basic way to
measure the speed of propagation of any entity, whether particle or wave
or dual entity or neither, is to measure transit delay, or equivalently,
the angle of aberration.

                        Fact: Gravity Has No Aberration

1. The effect of aberration on orbits is not seen

As viewed from the Earth's frame, light from the Sun has aberration.
Light requires about 8.3 minutes to arrive from the Sun, during which
time the Sun seems to move through an angle of 20 arc seconds. The
arriving sunlight shows us where the Sun was 8.3 minutes ago. The true,
instantaneous position of the Sun is about 20 arcs seconds east of its
visible position, and we will see the Sun in its true present position
about 8.3 minutes into the future. In the same way, star positions are
displaced from their average position by up to 20 arcs seconds, depending
on the relative direction of the Earth's motion around the Sun. This
well-known phenomenon is classical aberration, and was discovered by the
astronomer Bradley in 1728.

Orbit computations must use true, instantaneous positions of all masses
when computing accelerations due to gravity for the reason given by
Eddington. When orbits are complete, the visible position of any mass can
be computed by allowing for the delay of light traveling from that mass
to Earth. This difference between true and apparent positions of bodies
is not merely an optical illusion, but is a physical difference due to
transit delay that can alter an observer's momentum. For example, small
bodies such as dust particles in circular orbit around the Sun experience
a mostly radial force due to the radiation pressure of sunlight. But
because of the finite speed of light, a portion of that radial force acts
in a transverse direction, like a drag, slowing the orbital speed of the
dust particles and causing them to eventually spiral into the Sun. This
phenomenon is known as the Poynting-Robertson effect.

If gravity were a simple force that propagated outward from the Sun at
the speed of light, as radiation pressure does, its mostly radial effect
would also have a small transverse component because of the motion of the
target. Analogous to the Poynting-Robertson effect, the magnitude of that
tangential force acting on the Earth would be 0.0001 of the Sun's radial
force, which is the ratio of the Earth's orbital speed (30 km/s) to the
speed of this hypothetical force of gravity moving at light-speed
(300,000 km/s). It would act continuously, but would tend to speed the
Earth up rather than slow it down because gravity is attractive and
radiation pressure is repulsive. Nonetheless, the net effect of such a
force would be to double the Earth's distance from the Sun in 1200 years.
There can be no doubt from astronomical observations that no such force
is acting. The computation using the instantaneous positions of Sun and
Earth is the correct one. The computation using retarded positions is in
conflict with observations. From the absence of such an effect, Laplace
set a lower limit to the speed of propagation of classical gravity of
about 108 C, where C is the speed of light. (Laplace, 1825, pp.642-645 of
translation)

[eq1.gif]

We will use this formula later to set limits on [nu.gif]

2. 

Gravity
 and light do not act in parallel directions
And here for
Possible new properties of gravity

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