The Speed of Gravity: Einstein Was Right!
(Released July 2003)
by Salvatore Vittorio
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Gravitational force, or gravity, is the mutual attraction between all masses in the universe. Most scientists assume that gravity travels at the speed of light, which is actually the propagation speed of electromagnetic waves (such as light) in a vacuum. The speed of light is a physical constant equal to exactly 299,792.458 kilometers per second (km/s), or about 186,471 miles per second. The assumption that gravity also travels at this speed is implicit in Einstein's general theory of relativity, formulated in 1915, which recognizes the universal character of the propagation speed of light and the consequent dependence of space, time, and other mechanical measurements on the motion of the observer performing the measurements. Although this is still our best working theory of space-time, the concept that gravity travels at the speed of light is an assumption, and, until recently, has never been tested.
The assumed speed of gravity remained untested and unchallenged for so long because most physicists thought that gravity shows its speed only in the propagation of gravitational waves through space, and since no one has even detected gravitational waves, measuring how fast they travel was not possible.
Sir Isaac Newton thought that the speed of gravity was instantaneous, and Einstein assumed it traveled at the speed of light. Although scientists believe that Einstein was right, for nearly a century no one had been able to directly measure gravity's speed. However, on September 8, 2002, an international team of scientists did just that, using an experiment conceived by Sergei Kopeikin, professor of physics and astronomy at the University of Missouri-Columbia.1
A Reworking of General Relativity and a Breakthrough
Professor Kopeikin realized that Einstein's theory could be reformulated in a way that made gravity analogous to electromagnetic radiation. Physicists have known for more than a century that a uniformly moving charge generates a constant electric and magnetic field whose strength depends on the magnitude of the charge, its velocity, and the speed of light. The relationship is expressed in what are known to every physicist as Maxwell's equations. In short, this means that it is possible to calculate the speed of light from measurements of the electric and magnetic field of a moving charge, without having to detect electromagnetic waves directly. In the same way, Kopeikin's reworking of general relativity expresses the gravitational field produced by a moving body in terms of the mass of the body, its velocity, and the speed of gravity. This information could be used to work out the speed of gravity. Obtaining this information, though, is not easy. One obvious approach is to use "gravitational lensing". This is the apparent (but not actual) shift in position of a distant celestial object that occurs when its light is deflected on the way to Earth as the rays pass through the gravitational field of a massive body. If that body is moving, measurement of the lensing effect should give us the information we require.
However, there are problems. Although physicists have known for some time how a stationary body or one moving at a uniform speed lenses light, the equations that describe the deflection of light around a rotating orbiting body looked totally intractable. In 1999 Kopeikin, who was then at the University of Jena in Germany, made a crucial breakthrough. To the surprise of physicists worldwide, he came up with an exact solution to these equations.2
September 8, 2002: A Close Encounter with Jupiter
Despite Kopeikin's breakthrough, what is also needed is knowledge of the exact mass and orbit of the body that is lensing the light. Although the sky is full of stars and dark clusters that move in front of other light sources and deflect the light from them, we do not know the mass and velocity of most of these "cosmic lenses" nearly well enough. One body for which we do have this information is the planet Jupiter. Thanks to fly-bys by the Pioneer, Voyager, and Galileo spacecraft, we know the planet's mass and orbital velocity (velocity around the Sun) with unparalleled precision. So, to find the speed of gravity, all we need is an occasion where Jupiter moves in front of a good strong light source, lensing the rays on their way to Earth.
In 2000 Kopeikin compared the orbit of Jupiter for the next 30 years with catalogs of suitable astronomical radio sources (i.e., sources of extraterrestrial radio radiation). A close encounter of Jupiter with a radio source is a rare event, happening only about once every decade. Fortunately, a close passage of Jupiter to the strong radio quasar J0842+1835 was due on September 8, 2002. Kopeikin then enlisted the help of Ed Fomalont, a scientist at the National Radio Astronomy Observatory (NRAO) in Charlottesville, Virginia. Some 20 years earlier (circa 1976), Fomalont was part of a team that had been taking accurate measurement of the bending of radio waves as the waves passed near the Sun. The lensing effect that they planned to measure would cause the apparent position of the quasar J0842+1835 to shift slightly. The best available measurement method for this is to observe the quasar using an array of radio telescopes spaced as far apart as possible, due to the fact that radio waves travel at the speed of light. Therefore from the time it takes the distant body's radio signals to reach each telescope one could work out its position in the sky. Put simply, if one telescope receives a signal before the other, the quasar must be closer to the telescope at which the signal arrives first.3
The Very Long Baseline Array (VLBA) and Potential Problems
In order to make their measurements as accurate as possible, Kopeikin and Fomalont arranged to take measurements on the largest array to which they could get access. The plan was to use the worlds most powerful intercontinental array of radio telescopes, the Very Long Baseline Array (VLBA) run by the U.S. National Radio Astronomy Observatory (NRAO). The VLBA is made up of a series of ten radio telescopes, each one 25 meters in diameter, stretching from Saint Croix in the U.S. Virgin Islands in the east to Mauna Kea, Hawaii, in the west. To that they added the 100-meter radio telescope from the Max Planck Institute in Effelsberg, Germany, giving an array that extended over 10,000 kilometers with which to measure the apparent change in the quasar's position and thus to determine the speed of gravity. This would be able to pin down the position of a quasar to an accuracy of 10 microarcseconds, or about 5 billionths of the diameter of the full Moon. That is a resolution three times as high as anyone had previously achieved, yet it is the bare minimum needed to be able to tell whether Jupiter's gravity reaches Earth instantaneously, traveling at infinite speed, or takes a finite amount of time for the journey.
Although this experiment was possible in principle, in practice it could go wrong in numerous ways. Tiny changes in the locations of the telescopes, due to continental drift and variations in the Earth's rotation rate, could affect the measurements. Even more seriously, the weather above each telescope could ruin the measurements entirely. As the wind moves clouds over the various telescopes, the radio source can appear to jitter, masking the much smaller effect from Jupiter's gravity.
The key to dealing with these uncertainties was to find sources near J0842+1835 that would not be lensed by Jupiter on September 8 but were close enough in the sky to be subject to similar atmospheric conditions. With fast-alternating observations of several radio sources, the difference in positions could be measured much more accurately than the position of each source alone. In the end two quasars were chosen to use as reference sources on the day of the experiment.
Five observing days were available on the array of telescopes, each lasting 10 hours. The crucial day was, of course, September 8, 2002 when the closest passage of Jupiter to J0842+1835 occurred at 16:30 Greenwich Meridian Time (GMT), but that alone would not have been enough. Quasars are caused by outbursts of energy from a black hole in the center of a galaxy, and this phenomenon can vary over time. So, additional observations were made on days when the effect of Jupiter's gravitational field on J0842+1835 would be negligible. These observations were also made in order to check that the sources were not jittering in a way that might confound the measurements.
Perhaps the most serious worry concerned what was happening on Jupiter itself, namely, in its large and variable magnetosphere. This is a plasma of fast-moving electrons from the solar wind that become trapped by the Jovian magnetic field. The fear was that the quasar radio waves passing near the planet's surface on September 8 could be warped by the magnetosphere. Kopeikin and Fomalont were worried that if the magnetosphere were very active, this effect would be as large as the gravitational bending they were looking for. Instead of overcoming this problem by observing at two different frequencies simultaneously, which would have added complexity to the experiment and decreased its overall accuracy, Kopeikin and Fomalont decided instead to trust that the Jovian weather would be good for the observations.4
The Answer
As it turned out, the Jovian weather cooperated, and everything did go well, until the big day itself. On September 8, the telescope at Saint Croix malfunctioned because of serious tape recording problems. Fortunately, it turned out that the data from other telescopes could compensate for the loss. Although Kopeikin and Fomalont also had to discard about 15 percent of their data because of bad weather on Earth, this still left enough data to carry out the analysis. They compared the position of J0842+1835 on September 8, 2002, with its average position on the off-Jupiter days. Plugging this into Kopeikin's formula for the gravitational field of the moving Jupiter gave them the answer they were looking for. Kopeikin and Fomalont became the first two people to quantitatively measure the speed of gravity, one of the fundamental constants of nature. They found that gravity does move at the same speed as light. Their actual figure was 1.06 times the speed of light, but there was an error of plus or minus 0.21. The results were then announced at the 2002 American Astronomical Society annual meeting in Seattle, Washington.5
The result rules out the possibility that gravity travels instantaneously, as Newton imagined. If it did, a minutely different shift in the position of the quasar would have been visible on the night of September 8. This vindicates Einstein's instinct when formulating his general theory of relativity, which was to assume that the speed of gravity was equal to the speed of light.6
Conclusion
The future may see new theoretical efforts to unify fundamental forces in physics with gravity that take the speed of gravity into account. Over the next decade Russia, Japan, and the U.S. may succeed in extending the largest radio telescope arrays beyond the diameter of the Earth by putting large radio telescopes in orbit. Scientists hope that this will confirm and greatly increase the accuracy of the result obtained by Kopeikin and Fomalont.7