## The Speed of Light and General Relativity

Although physics has long assumed that the speed of light is a fundamental constant and also forms a “universal speed limit”, Sergei Kopeiken (University of Missouri) and Ed Fomolont (National Radio Astronomy Observatory, or NRAO) have announced that they have measured the “speed of gravity” and found that it is possibly 1.06 times faster than the speed of light!

It has long been assumed that as gravity can be used to carry information (in the form of gravity waves), then the laws of relativity require that gravity waves must also travel no faster than light. As early as 1676, the finite speed of light has been an experimental fact in observational astronomy, following Roemer’s observation of the eclipses of the moons of Jupiter. Roemer found that as Jupiter moved further from the Earth, his predictions of when Jupiter’s moons would cross its face became less and less accurate. However, as he continued to observe, he was able to discount the idea that his predictions were simply wrong, as on its approach to the earth, the events once again approached his predicted times. In a stroke of genius, Roemer attributed this discrepancy to the finite speed of light, and he even published an estimate of that speed, approximately two thirds the currently accepted value (due to the inaccurate estimates of the size of Earth and Jupiter’s orbits, not faults in his calculations).

In an unwitting homage to Roemer, the motion of Jupiter now seems to have allowed measurement of the speed gravity propagates. Now, in the theory of relativity, masses cause a curvature of space-time, and gravity is simply the manifestation of particles moving in straight lines across this curved space. This is like a plane flying over a hilly landscape. Although the plane moves in a line, the shadow it casts on the ground moves left and right, forward and backwards, faster and slower than the plane itself across the ground.

You can think of space like a sheet of rubber (only this sheet of rubber is many, many orders of magnitude stiffer than steel). When a mass is placed on the sheet, it forms a “well”. Then, when a beam of light goes past the mass, like a rolling ball on the sheet, it is deflected – even though it has no mass! This bending was first observed for stars very close to the sun (during an eclipse) early last century – one of the most telling justification of general relativity. This light passing on either side of a heavy object is bent inwards, so the light passing close enough to an object that is heavy enough will be bent around so that the two beams meet. Just like light passing through a glass lens, these converging rays form an image (well, not just like a spherical lens – the shape of the gravitational potential usually leads to images that are blurred or stretched). Other beams, defected by lighter masses, or at larger angles are bent sos that it appears the original object is at a greater angle (you might have seen the “Einstein Rings” in the Hubble deep field images – these rings are caused by gravitational lensing of distant galaxies by closer ones).

## Has the Speed of Gravity Been Measured?

These effects, and other astronomical observations, make it easy to observe the strength of gravity. However, they leave open the question of the speed of gravity. When an object moves, obviously the curvature of spacetime has to alter to reflect its new position. The question is, does the effect of the movement propagate out at a speed faster than, slower than or equal to the speed of light? It is this speed that we refer to when we talk about the “speed of gravity.” Unfortunately, in order to observe any propagation effects, we need an object that creates a measurable curvature of space, but is moving at a speed high enough that it is possible to see any lag in the response of the continuum. Even though Jupiter is not heavy enough to have formed a star, it is heavy enough to slightly lens objects it passes in front of. Moreover, due to its proximity to the Earth, its angular speed is much higher than any high mass object outside out solar system we can observe with any precision.

In fact, as Jupiter swept by a Quasar (a source of intense radio beams, thought to be the super massive black holes at the center of galaxies) known as quasar J0842 + 1835 around September 8, 2002, the radio waves it emitted were bent by Jupiter’s gravity, making the apparent position of the quasar trace a small loop over the course of a few days. Using the Very Long Baseline Array ( a series of ten radio antennas spread across the United States and its territories from St. Croix, the Virgin Islands, to Mauna Kea, Hawaii with an angular resolution of 10 microarcseconds , Kopeiken and Fomolont were able to image this very small loop and track it.

Now, if the effect of Jupiter’s motion propagated at less than infinite speed, the position of the image on the loop would be determined by the position of Jupiter at a slightly earlier time. In fact, Kopeiken and Fomolont found that the loop was slightly displaced from the “infinite speed” loop – a clear indication of the finite speed of gravity. However, this was not the most surprising conclusion. Using the value of this displacement, they arrived at an estimate of the propagation speed of gravity effects equal to 1.06c!

That’s 6% faster than light!

Can this possibly be correct? Only if relativity as we know it is wrong, perhaps in a drastic way. However, all is not lost for Einstein’s mathematical masterpiece – the stated uncertainty in this value of the speed of gravity is an enormous 20% - so the true speed of gravity could be exactly c, or even 0.86c with almost the same likelihood of getting this result. A speed of 1.06c is still the result most compatible with these particular observations, but in the face of the overwhelming evidence in favor of the almost perfect correctness of relativity, I feel we need to see a significant decrease in the uncertainty of this value before its far reaching implications can be accepted.

Moreover, a number of physicists have already published their counter arguments that, accuracy questions aside, this experiment was simply a measurement of the speed of light.