Evidence for Variable Speed of Gravity in Coordinate Spacetime

[Thinkor]

Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space.

The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?

 

[Simon Bridge]

The answer is "no" ... I don't think there has been any definitive experiment done yet that measures any speed for gravity, never mind observing the speed of gravity for a distant location.
Searching "speed of gravity" in google scholar will show you a lot of discussion.

 

[zoki85]

"Speed of gravity" sounds like nonsensical statement. For example, perhaps one can talk about speed of propagation of gravitational waves to flat spacetime, not about speed of gravity. Similarly, you can't talk about "speed of magnetism", but you can talk of speed of propagation of EM waves in vacuum.

 

[PeterDonis]

Speed of gravity" sounds like nonsensical statement.

It isn't, but it does take some care in defining what it means, physically. See below.

you can't talk about "speed of magnetism"

Sure you can. In fact, it's easier than talking about the speed of gravity, because unlike gravity, you can shield something from magnetism, or turn magnetism on and off.

For example, suppose I have an electromagnet that is turned off. I turn it on at some spacetime event O. The only events that will see any effects from the electromagnet are in the future light cone of O, because magnetism propagates at the speed of light. For example, if I have a metal object 1 meter away from the electromagnet, it will take 3.3 nanoseconds for it to respond to the magnetic field of the electromagnet.

(You might want to say that what the metal object is responding to is really an expanding EM wave created when the electromagnet turns on, so what we're actually measuring is the speed of EM wave propagation, but that's a matter of words, not physics. EM wave propagation and propagation of magnetism are not two different things; they're two different ways of describing, with words, the same physics.)

Measuring the speed of gravity, in principle, works the same way: you make some change in the source of gravity at some event O, and verify that the only events that see any effects of the change are in the future light cone of O, indicating that gravity propagates at the speed of light. In practice, however, there are two issues with doing this. First, there's no way to shield something from gravity, or turn it on and off; I can't just create a source of gravity where there was none before, like I can with the electromagnet by turning on the current, because the source of gravity is stress-energy, and stress-energy obeys local conservation laws that make it impossible to create or destroy it. So I have to be a lot more subtle in how I set up an experiment to look for changes in the source of gravity and watch how their effects propagate.

The second issue has to do with the light cones. As above, the light cones determine how gravity propagates; but gravity itself, in turn, determines the light cones! So in order to determine at which events I would expect to see the effects of some change in the source of gravity at some event O, I can't just assume that the light cones stay the same. It seems like I have to know how gravity changes the light cones, which requires me to know how gravity propagates, which requires me to know the light cones... Obviously this is a circle that can't be closed. The only way around it is to find a self-consistent solution from the start, by solving the Einstein Field Equation, and then look within that solution to see whether the effects of the source of gravity at any event O are only seen in events within the future light cone of O, as the light cones are determined by the solution. This is, in fact, what we find theoretically; but, as above, it's hard to set up an experiment to actually measure it.

 

[Nugatory]

Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space.

Be careful with that phrase "coordinate spacetime" - there's no such thing. Spacetime exists the same way that the surface of a sheet of paper exists before we draw coordinate axes on it, and we can draw the axes any way we want without changing the two-dimensional Euclidean geometry of the sheet of paper.

 

[pervect]

There are a few authors who claim (in published papers) to have measured "the speed of gravity", such as Fomalont and Kopeikin, also van Flandern. These claims are widely dismissed, so I will link to the rebuttal papers rather than the original claims. See for instance Steve Carlip, "Abereration and the speed of gravity", http://arxiv.org/abs/gr-qc/9909087, and Clifford Will's comments to the press in http://www.aps.org/publications/apsnews/200306/gravity.cfm.

A method of measuring the speed of gravity that most would find convincing would be to measure the propagation speed of a gravitational wave. This would be the same method we use to measure the speed of light, we measure the speed of the wave. However, current efforts to detect gravitational waves as of this date have been negative. It goes almost without saying that we need to detect gravitational waves before we can measure their speed, but I suppose I should state that explicitly.

 

[Thinkor]

Thanks for the comments, especially about google scholar, where I found the Carlip paper which cleared things up about Van Flandern's bad estimate of the speed of gravity.

Apparently, at present, the speed of gravity just doesn't matter in application.

No wonder Newton's theory works so well!