Has
the
Speed
of Gravity
Been
Measured?

In
2002, Sergei Kopeikin suggested that measurement of the
deflection
of light from a quasar by the planet Jupiter could be
used to measure
the speed of the gravitational interaction.
He argued that,
since Jupiter
is moving relative to the
solar system, and
since gravity propagates with
a finite
speed, the
gravitational field experienced by the light ray should
be
affected by gravity's speed, since the field experienced here
now
depends
on the location of the source a short time
earlier,
depending on how fast
gravity propagates.
According to his
calculations, there should be a small
correction to the
normal general relativistic formula for the
deflection,
which depends on the velocity of Jupiter and on the
velocity of
gravity
(technically, it's an extra term in the
``Shapiro''
delay in arrival of
waves at a radio
telescope). On
September 8, 2002, Jupiter passed almost
in
front of a
quasar, and, in collaboration with Ed Fomalont of the
National
Radio Astronomy Observatory, precise measurements were made
of the
Shapiro
delay, with picosecond timing accuracy.
Kopeikin and
Fomalont argued that
the results were in
accord with the
prediction of GR for this tiny effect,
with
a precision of
about 20 per cent. This would be an interesting new
confirmation of GR, albeit at modest accuracy.
The
question
is:
Does this tell us
anything about the speed
of
propagation
of
gravity?
The
consensus
among
relativists
is
NO!

Papers by Kopeikin
claiming
this
tests the speed
of gravity
 Testing the relativistic
effect of the propagation of gravity by very long baseline interferometry,
S. Kopeikin, Astrophys. J. 556 (2001) L1L5 (grqc/0105060)
 General relativistic
model for experimental measurement of the speed of propagation of gravity
by VLBI, S. Kopeikin and E. Fomalont, Proceedings of the 6th European
VLBI Network Symposium, Ros, E., Porcas, R.W., Zensus, J.A. (eds.),
June 25th  28th, 2002, Bonn, Germany, p. 49 (grqc/0206022)
 The PostNewtonian Treatment
of the VLBI Experiment on September 8, 2002, S. Kopeikin, Phys.
Lett. A312 (2003) 147 (grqc/0212121)
 The Measurement of the
Light Deflection from Jupiter: Experimental Results, E. B. Fomalont,
S. M. Kopeikin, Astrophys. J. 598 (2003) 704 (astroph/0302294)
 The Measurement of the
Light Deflection from Jupiter: Theoretical Interpretation, S. Kopeikin,
(astroph/0302462)
 Speed of Gravity in
General Relativity and Theoretical Interpretation of the Jovian Deflection
Experiment, S. Kopeikin, Class. Quantum Gravit. 21 (2004) 3251
(grqc/0310059)
 On the Speed of Gravity
and Relativistic v/c Corrections to the Shapiro Time Delay, S.
Kopeikin and E. B. Fomalont, Phys. Lett. A 355 (2006), 163 (online
version) (grqc/0310065)
 Aberration and the Speed
of Gravity in the Jovian Deflection Experiment, S. Kopeikin and
E. B. Fomalont, Foundations of Phys. DOI: 10.1007/s1070100690597
(2006) (online
version) (astroph/0311063)
 Comments on "On
the speed of gravity and the Jupiter/Quasar measurement" by S.
Samuel, S. Kopeikin, Int. J. Mod. Phys. D 15 (2006), 273 (online
version)(grqc/0501001)
 Gravitomagnetism and
the Speed of Gravity, S. Kopeikin, Int. J. Mod. Phys. D 15 (2006),
305 (grqc/0507001)
 Comment on 'Modeldependence
of Shapiro time delay and the "speed of gravity/speed of light"
controversy', S. Kopeikin, Class. Quantum Gravit. 22 (2005) 5181
(grqc/0510048)
 Gravitomagnetism and
the Aberration of Gravity in the Gravitational LightRay Deflection
Experiments, S. Kopeikin and E. B. Fomalont (grqc/0510077)
 Note on the relationship
between the speed of light and gravity in the bimetric theory of gravity,
S. Kopeikin (grqc/0512168
 Radio interferometric
tests of general relativity, E. B. Fomalont and S. Kopeikin, Proc.
IAU Symposium No. 248, eds Jin et al. (2007), p 383.

Papers by
authors claiming the measurement
is NOT sensitive to the
speed of gravity
 The
Lightcone Effect on the Shapiro Time Delay, H. Asada,
Astrophys. J. 574 (2002) L69
(astroph/0206266)
 Propagation Speed of Gravity and the Relativistic Time
Delay,
C. M. Will, Astrophys. J. 590 (2003) 683
(astroph/0301145)
 On the Speed of Gravity and the v/c Corrections to the Shapiro
Time Delay, S. Samuel, Phys. Rev. Lett. 90 (2003)
231101
(astroph/0304006)
 The speed of gravity has not been measured from time
delays,
J. Faber
(astroph/0303346)
 Comments on "Measuring
the Gravity Speed
by VLBI",
H. Asada,Proc. of "Physical
Cosmology", the XVth Rencontres
de Blois, 1520 June
2003
(astroph/0308343)
 ModelDependence of Shapiro
Time Delay and the "Speed of
Gravity/Speed of Light" Controversy, S. Carlip,
Class.Quantum
Gravit. 21 (2004) 3803(grqc/0403060)
 Speed of gravity and gravitomagnetism,
J.F.
PascualSánchez,
Int.J.Mod.Phys. D 13 (2004) 2345
(grqc/0405123)
 On the Speed of Gravity and the Jupiter/Quasar
Measurement,
S. Samuuel, Int. J. Mod. Phys. D 13
(2004) 1753 (astroph/0412401)

Other
papers commenting on the effect
 Aberration by gravitational
lenses in motion, S. Frittelli, MNRAS 344, L85 (2003) (astroph/0311189)
 Microarcsecond light
bending by Jupiter, M. T. Crosta and F. Mignard, Class. Quantum.Gravit.
23 (2006) 4853 (astroph/0512359)
 Gravitational bending of light by planetary multipoles and its
measurement with microarcsecond astronomical interferometers,
S. Kopeikin and V. Makarov, Phys. Rev. D 75 (2007), 062002 (astroph/0611358)

The idea seems natural. What's wrong with
it?
 In all calculations of
the effects of finite propagation speed (electrodynamics,
gravitational waves), for slowly moving sources, the first nontrivial
effects appear at order (v/c)^2, NOT at first order (v/c),
which is
what Kopeikin claimed
 If you're
working to only the first order in v/c, then all that counts
is the uniform motion of the planet, Jupiter (its acceleration about
the sun contributes a higherorder, unmeasurably small
effect). But
if that is the case, then the principle of
relativity says you can view
things from the rest frame of
Jupiter. But in this frame, Jupiter's
gravitational field
is static, and the speed of propagation of gravity
is
irrelevant.
 A detailed calculation of the effect was
done by Clifford Will (here),
in
a model of gravity in which the speed of gravity can be different
from that of light, and showed explicitly that, at first order in
(v/c),
the effect depends on the speed of light,
not the speed of
gravity, in line with intuition.
 Stuart Samuel (here)
has
also argued that the experiment was not even sensitive to the general
relativistic (v/c) correction, if one interprets the
formulae properly.
How can we
really measure the speed of propagation of
gravity?
 If we could
measure the effects on the Shapiro delay to order (v/c)^2,
then we could test the speed of gravity. But these effects would be
at the thousandths of a picosecond level, hopelessly small.
 The real way to measure the speed of
gravity is to detect and study gravitational waves. By
comparing the
arrival of a gravitationalwave signal with
that of an electromagnetic
signal from an astrophysical
source, one could compare the speed of
gravity to that of
light to parts in 10^(17).

Opinions expressed on this page are
those of
Clifford Will, and should not be construed as representing
official policy of Washington
University or its Physics
Department, or of any other entity or organization.

