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Speed of gravity

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The speed of gravity is the speed at which changes in the location of an object propagate to all other objects in the universe.

Theoretical predictions

When Newton proposed his original mechanics, he had point particles exerting forces at each other instantaneously over great distances. Many people, including him, were bothered by this. The introduction of a gravitational field provides a medium of sorts for broadcasting that information, but changes in positions of objects still instantly affects the field infinitely far away; that is to say, the speed of gravity is infinite, according to this theory.

In general relativity, the currently accepted theory, the gravitational field is equated with the curvature of space-time, and propagations (including gravity waves) can be shown, according to this theory, to travel at the speed of light, usually written as c. According to Einsteinian relativity, a higher speed would violate causality.

Experimental measurement

In January 2003, Ed Fomalont and Sergei Kopeikin made an indirect experimental measurement of the speed of gravity, by observing the transit of Jupiter across the line-of-sight of a bright radio source. The speed of gravity, according to this experiment, was 0.95c +/- 0.25c, which is consistent with the theoretical prediction of the speed of gravity as being precisely c.


Tom Van Flandern's non-standard theory of gravity

Tom Van Flandern argues that the pre-Einstein formulation of gravity as a force of nature rather than as a pure geometric effect of curved space-time is correct and believes that the speed of gravity can't be appreciably less than the speed of light, since that could be detected by changes in the angular momentum of the planets. He claims that while faster-than-light force propagation speeds do violate Einstein special relativity (SR), they are in accord with Lorentzian relativity, which has never been experimentally distinguished from special relativity.

A summary of the problem with Van Flandern's theory follows. Consider the earth revolving around the sun. It takes eight minutes for light to travel from the sun to the earth. Van Flandern asserts that if you simulate a gravitational system in which the force of gravity is pointed in the direction of where the objects were eight minutes ago, you end up with an unstable system, and asserts that in order to create a stable system the forces have to point in the direction of where the objects are at the current time.

Where Van Flandern disagrees with mainstream opinion is the assertion that that proves that gravity must propagate instantaneously. This is not the case. Most scientists believe that his mistake is to think of the forces being transmitted rather than the potentials.

Imagine the sun being stationary, and the gravitational potentials moving away from the sun at the speed of light. The potentials would be concentric circles. Now imagine the sun starting to move. The lines of equal potentials will begin to bunch up in front of the sun and start to expand behind the sun. Now imagine the earth in front of the sun, and ask yourself what direction the force of gravity will be pointed at. The force of gravity will point down the slope of the potentials and will be pointed at where the sun is at the moment, not where the sun was in the past. However, causality is not violated. If the sun suddenly shifted direction, there would be a delay before this change affects the forces and the potentials affect the earth. (I wish I could draw some pictures.)

Note that the same thing happens with electromagnetic forces.

The scientific consensus considers Tom Van Flandern's theory to be crankish, and that Van Flandern simply fails to understand the argument against his theory. This consensus opinion should be contrasted with other non-standard gravitational theories such as Modified Newtonian Dynamics. Although the latter theory is considered wrong by most physicists, it is widely believed that proponents of the latter theory are at least "playing the game" in that they seriously responding to their critics, changing their theories to match criticisms, and that some of the disagreements with the standard model of gravity involve the results of observations which have not been made yet.

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