53 Does gravity travel at the speed of light?
Description
This article is from the Astronomy FAQ, by Joseph Lazio (jlazio@patriot.net) with numerous contributions by others.
53 Does gravity travel at the speed of light?
By Steve Carlip <carlip@dirac.ucdavis.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu>
Geoffrey A Landis <Geoffrey.Landis@sff.net>
To begin with, the speed of gravity has not been measured directly in
the laboratory---the gravitational interaction is too weak, and such
an experiment is beyond present technological capabilities. The
"speed of gravity" must therefore be deduced from astronomical
observations, and the answer depends on what model of gravity one uses
to describe those observations.
In the simple Newtonian model, gravity propagates instantaneously: the
force exerted by a massive object points directly toward that object's
present position. For example, even though the Sun is 500 light
seconds from the Earth, Newtonian gravity describes a force on Earth
directed towards the Sun's position "now," not its position 500
seconds ago. Putting a "light travel delay" (technically called
"retardation") into Newtonian gravity would make orbits unstable,
leading to predictions that clearly contradict Solar System
observations.
In general relativity, on the other hand, gravity propagates at the
speed of light; that is, the motion of a massive object creates a
distortion in the curvature of spacetime that moves outward at light
speed. This might seem to contradict the Solar System observations
described above, but remember that general relativity is conceptually
very different from Newtonian gravity, so a direct comparison is not
so simple. Strictly speaking, gravity is not a "force" in general
relativity, and a description in terms of speed and direction can be
tricky. For weak fields, though, one can describe the theory in a
sort of Newtonian language. In that case, one finds that the "force"
in GR is not quite central---it does not point directly towards the
source of the gravitational field---and that it depends on velocity as
well as position. The net result is that the effect of propagation
delay is almost exactly cancelled, and general relativity very nearly
reproduces the Newtonian result.
This cancellation may seem less strange if one notes that a similar
effect occurs in electromagnetism. If a charged particle is moving at
a constant velocity, it exerts a force that points toward its present
position, not its retarded position, even though electromagnetic
interactions certainly move at the speed of light. Here, as in
general relativity, subtleties in the nature of the interaction
"conspire" to disguise the effect of propagation delay. It should be
emphasized that in both electromagnetism and general relativity, this
effect is not put in _ad hoc_ but comes out of the equations. Also,
the cancellation is nearly exact only for *constant* velocities. If a
charged particle or a gravitating mass suddenly accelerates, the
*change* in the electric or gravitational field propagates outward at
the speed of light.
Since this point can be confusing, it's worth exploring a little
further, in a slightly more technical manner. Consider two
bodies---call them A and B---held in orbit by either electrical or
gravitational attraction. As long as the force on A points directly
towards B and vice versa, a stable orbit is possible. If the force on
A points instead towards the retarded (propagation-time-delayed)
position of B, on the other hand, the effect is to add a new component
of force in the direction of A's motion, causing instability of the
orbit. This instability, in turn, leads to a change in the mechanical
angular momentum of the A-B system. But *total* angular momentum is
conserved, so this change can only occur if some of the angular
momentum of the A-B system is carried away by electromagnetic or
gravitational radiation.
Now, in electrodynamics, a charge moving at a constant velocity does
not radiate. (Technically, the lowest order radiation is dipole
radiation, which depends on the acceleration.) So to the extent that
that A's motion can be approximated as motion at a constant velocity,
A cannot lose angular momentum. For the theory to be consistent,
there *must* therefore be compensating terms that partially cancel the
instability of the orbit caused by retardation. This is exactly what
happens; a calculation shows that the force on A points not towards
B's retarded position, but towards B's "linearly extrapolated"
retarded position. Similarly, in general relativity, a mass moving at
a constant acceleration does not radiate (the lowest order radiation
is quadrupole), so for consistency, an even more complete cancellation
of the effect of retardation must occur. This is exactly what one
finds when one solves the equations of motion in general relativity.
While current observations do not yet provide a direct
model-independent measurement of the speed of gravity, a test within
the framework of general relativity can be made by observing the
binary pulsar PSR 1913+16. The orbit of this binary system is
gradually decaying, and this behavior is attributed to the loss of
energy due to escaping gravitational radiation. But in any field
theory, radiation is intimately related to the finite velocity of
field propagation, and the orbital changes due to gravitational
radiation can equivalently be viewed as damping caused by the finite
propagation speed. (In the discussion above, this damping represents
a failure of the "retardation" and "non-central, velocity-dependent"
effects to completely cancel.)
The rate of this damping can be computed, and one finds that it
depends sensitively on the speed of gravity. The fact that
gravitational damping is measured at all is a strong indication that
the propagation speed of gravity is not infinite. If the
calculational framework of general relativity is accepted, the damping
can be used to calculate the speed, and the actual measurement
confirms that the speed of gravity is equal to the speed of light to
within 1%. (Measurements of at least one other binary pulsar system,
PSR B1534+12, confirm this result, although so far with less
precision.)
Are there future prospects for a direct measurement of the speed of
gravity? One possibility would involve detection of gravitational
waves from a supernova. The detection of gravitational radiation in
the same time frame as a neutrino burst, followed by a later visual
identification of a supernova, would be considered strong experimental
evidence for the speed of gravity being equal to the speed of light.
However, unless a very nearby supernova occurs soon, it will be some
time before gravitational wave detectors are expected to be sensitive
enough to perform such a test.
References:
There seems to be no nontechnical reference on this subject. For a
technical reference, see
T. Damour, in _Three Hundred Years of Gravitation_, S.W. Hawking and
W. Israel, editors (Cambridge Univ. Press, 1987)
For a good reference to the electromagnetic case, see
R.P. Feynman, R.B. Leighton, and M. Sands, _The Feynman Lectures on
Physics_, chapter II-21 (Addison-Wesley, 1989)
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