First speed of gravity measurement revealed

The speed of gravity has been measured for the first time. The landmark experiment shows that it travels at the speed of light, meaning that Einstein's general theory of relativity has passed another test with flying colours.

Ed Fomalont of the National Radio Astronomy Observatory in Charlottesville, Virginia, and Sergei Kopeikin of the University of Missouri in Columbia made the measurement, with the help of the planet Jupiter.

"We became the first two people to know the speed of gravity, one of the fundamental constants of nature," the scientists say, in an article in New Scientist print edition. One important consequence of the result is that it places constraints on theories of "brane worlds", which suggest the Universe has more spatial dimensions than the familiar three.

John Baez, a physicist from the University of California at Riverside, comments: "Einstein wins yet again." He adds that any other result would have come as a shock.

You can read Fomalont and Kopeikin's account of their unique experiment in an exclusive, full-length feature in the next issue of New Scientist print edition, on sale from 9 January.

Isaac Newton thought the influence of gravity was instantaneous, but Einstein assumed it travelled at the speed of light and built this into his 1915 general theory of relativity.

Light-speed gravity means that if the Sun suddenly disappeared from the centre of the Solar System, the Earth would remain in orbit for about 8.3 minutes - the time it takes light to travel from the Sun to the Earth. Then, suddenly feeling no gravity, Earth would shoot off into space in a straight line.

But the assumption of light-speed gravity has come under pressure from brane world theories, which suggest there are extra spatial dimensions rolled up very small. Gravity could take a short cut through these extra dimensions and so appear to travel faster than the speed of light - without violating the equations of general relativity.

But how can you measure the speed of gravity? One way would be to detect gravitational waves, little ripples in space-time that propagate out from accelerating masses. But no one has yet managed to do this.

Measuring the speed of gravity

Kopeikin found another way. He reworked the equations of general relativity to express the gravitational field of a moving body in terms of its mass, velocity and the speed of gravity. If you could measure the gravitational field of Jupiter, while knowing its mass and velocity, you could work out the speed of gravity.

The opportunity to do this arose in September 2002, when Jupiter passed in front of a quasar that emits bright radio waves. Fomalont and Kopeikin combined observations from a series of radio telescopes across the Earth to measure the apparent change in the quasar's position as the gravitational field of Jupiter bent the passing radio waves.

From that they worked out that gravity does move at the same speed as light. Their actual figure was 0.95 times light speed, but with a large error margin of plus or minus 0.25.

Their result, announced on Tuesday at a meeting of the American Astronomical Society meeting in Seattle, should help narrow down the possible number of extra dimensions and their sizes.

But experts say the indirect evidence that gravity propagates at the speed of light was already overwhelming. "It would be revolutionary if gravity were measured not to propagate at the speed of light - we were virtually certain that it must," says Lawrence Krauss of Case Western Reserve University in Cleveland, Ohio.

So what was the measured speed of gravity in those experiments? Got the data handy?

Fomalont and Kopeikin never did measure the speed of gravity. They measured the speed of gravitational waves. Also, Kopeikin altered equations in order to get the answer he wanted. See below, especially the notes after publication appended at the end:

Kopeikin's experiment

Kopeikin's latest paper on the internet, giving the basis for his findings announced at the AAS meeting, contains some egregious errors. The following claims appear therein: "… a moving gravitating body deflects light not instantaneously but with retardation caused by the finite speed of gravity propagating from the body to the light ray. … We calculated this correction for Jupiter by making use of the post-Minkowskian approximation based on the retarded Lienard-Wiechert solutions of the Einstein equations. … Speed of gravity cg must enter the left side of the Einstein equations (2) … This will lead to the wave operator depending explicitly on the speed of gravity cg."

None of these statements is correct even in GR, provided only that "the speed of gravity" retains its classical meaning for the past two centuries of force propagation speed. The Einstein equations require the potential field of all bodies to act from the body's instantaneous direction, not its retarded direction, because they set propagation delay for the gradient to zero. But Kopeikin adopts the Sun acting from its instantaneous position and Jupiter acting from its retarded position, which is inconsistent. In fact, although the Sun moves 1000 times more slowly than Jupiter, it is 1000 times more massive, making any hypothetical retardation effects comparably important. The Lienard-Wiechert equations consider retardation in mutual distance, but not in direction – the latter being a much larger effect of propagation delay. And the parameter on the left side of the Einstein equations is c2, and therefore has nothing to do with the speed of gravity, as we noted above. This does not prevent Kopeikin from calling it "cg" and solving for this parameter as if it were the speed of gravity, which is what he has done.

            Sadly, Kopeikin here ignores both the existence of a long-standing controversy about the speed of gravity (defined as the propagation speed of gravitational force) [5] and the aforementioned arguments raised against his original interpretation by others. Kopeikin used the notion that this experiment might determine "the speed of gravity" to aggrandize the experiment, and perhaps also to justify funding for doing it. Yet the cg parameter measured is more closely related to the speed of light per se than anything else.

To clarify, it is well known to physicists that electromagnetic signals (whether light passing the Sun or quasar radio signals passing Jupiter) are not bent or slowed by the force of gravity, but by passage through a gravitational potential field. A potential field slows the rates at which clocks tick, produces gravitational redshift, bends light, and retards radar and radio signals. Gravitational force, by contrast, has no such effects even in fields as strong as 1019 g, where g = acceleration of gravity at Earth's surface [[9]]. Gravitational force simply produces the 3-space (Newtonian) acceleration of bodies. Kopeikin has not cleanly separated potential-change propagation effects from force propagation effects, despite an attempt to do so in his latest paper that was absent from the original paper.

Kopeikin makes another claim in his new paper: "The spectrum of plausible values of cg ranges from cg = c in general relativity to cg = infinity as advocated by Van Flandern (1998)." This is also false. Van Flandern has long maintained in USENET discussions and on the Meta Research web site [2] that Kopeikin's cg parameter is essentially equal to the speed of light. So this statement by Kopeikin is again an attempt to falsely claim that his experiment bears on the subject of the speed of propagation of gravitational force, which it does not.

            However, the misrepresentation in this new paper and announcement is more serious than mixing speed-of-light and speed-of-gravity parameters. Kopeikin's new paper has modified the equations to be used in determining the speed of gravity in a fundamental way. His own formalism now rules out the possibility of cg = infinity or cg >> c in his results even before the experiment is performed. Here is why. Kopeikin now defines a new time tau = (c/cg) t to replace the coordinate time t in the Einstein equation. However, because (c/cg) is obviously forced to become very small or zero for large or infinite cg, the role of the time coordinate is diminished or suppressed altogether by this substitution, which effectively eliminates many relativistic effects already verified in other experiments. So even if the speed of "gravitational waves" had been much faster than the speed of light, Kopeikin's experiment is incapable of showing that with his present method of analysis. More than that, Kopeikin has violated scientific protocol by changing the equations to be used for the analysis after the results are in, thereby presumably avoiding the embarrassment of having to announce an unexpected result. We were also unable to verify one of his key references in the December 30 paper, "E. Fomalont & S. Kopeikin (2002)" which says simply "submitted to Science". But as of January 6, Science magazine has no record of such a submission.

            The basic point here about the physical meaning of the speed of gravitational force as it appears in relativity theory has been brought to Kopeikin's attention by at least two authors of published technical papers, yet is still being ignored. Now Kopeikin has altered the analysis equations after the results were in. This raises serious questions about whether Kopeikin has maintained his scientific objectivity after using the promise of a measurement of the speed of gravity to justify funding for his experiment. Almost certainly, his erroneous announcement has damaged scientific inquiry into an important and worthy matter, the speed of propagation of gravitational force.

The speed of gravity is the subject of a recent definitive paper concluding that the real physical parameter vg must be much greater than c [[10]]. Because this paper is the third in this series to appear in mainstream journals, because both its authors are senior and widely published, because this paper was rigorously peer-reviewed (as appropriate for controversial subject matter), and because it addresses every objection raised by anyone over the past decade in a way that was satisfactory to neutral parties, including the journal editors, there is no scientifically valid excuse for ignoring or riding roughshod over these results by creating the false impression that Kopeikin's experiment supercedes these already published findings. Moreover, because the viewpoint that the speed of gravity vg must be >> c is in good standing by the aforementioned criteria, there is no good reason why Kopeikin should refuse to debate this matter in a suitable forum. He is hereby challenged to do so.

          Note added 2003/01/10: Noted relativist C. Will has now joined those who agree that Kopeikin's result measured only the speed of light and not the speed of gravity [[11]].

Note added 2003/01/18: C. Will's objections are detailed; and Peter van Nieuwenhuizen, a physicist at Stony Brook University in New York, calls the interpretation of the results by Fomalont and Kopeikin "complete nonsense" [[12]].

          Note added 2003/02/09: Retired physicist K. Nordtvedt, instrumental in proposing a key test of relativity theory, is quoted in Nature magazine of 16 January (p. 198): "The experiment is wonderful, but it has nothing to do with the speed of gravity."

          Note added 2003/03/20: J.A. Faber, Northwestern U. has calculated the expected experimental results using an infinite speed of gravity and found no difference [[13]]. He also concludes that only the speed of light, not the speed of gravity, was measured.

          Note added 2003/05/26: Clifford Will made a presentation to the American Physical Society explaining why Kopeikin and Fomalont's interpretation is incorrect [[14]].

          Note added 2003/06/22: C.M. Will argues that the Jupiter-passing-quasar experiment is not sensitive to the speed of propagation of gravity [[15]]. In a related paper, S. Samuel at Lawrence Berkeley National Laboratory makes a similar argument, and concludes that Kopeikin measured the speed of light, not gravity [[16]].

Note added 2003/08/04: Stuart Samuel showed that the real effects of the speed of gravity were at least 100 times too small to have been measured in the Kopeikin experiment [[17]].

          Note added 2004/01/14: The Kopeikin-Fomalont paper on the experimental results, previously rejected, is restyled as a measurement of the deflection of a light signal by Jupiter and published [[18]].

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