Back in 2003 there was a Staff Report about the speed of gravity- whether gravity propagates at the speed of light or if it’s effectively instantaneous:
Over the years there have been several threads re-asking the question:
I recently came across this article, which imho is the best explanation for how gravity traveling at the speed of light doesn’t contradict orbital mechanics. The whole article is worth a read but I’ll quote the pertinent part below:
It’s (almost certainly) based on this paper by Steve Carlip this paper, but it’s not an amazing summary of that paper.
The basic summary is that in the weak-field limit of general relativity, when writing the gravitational “force” on a test particle as a function of its velocity and the retarded position of the source, the lower order terms will point the force in the direction of the extrapolated instantaneous position of the source. This is analogous to the Coulomb force in electromagnetism.
This bears emphasis. It has nothing to do with General Relativity. The same thing holds true for the orbits of electrons around protons in which the gravitational force is negligible.
So far as I know, since Einstein’s theory of special relativity, there has never been any serious doubt that gravity was not instantaneous, even though planetary orbits can be calculated as if it were, for the reason discussed above. Instantaneous gravity would immediately lead to a contradiction with special relativity.
And to further pile on, sending anything, information included, faster than light is the same thing as sending it back in time, which pretty immediately leads to paradoxes. As far as we can tell reality is logically consistent.
Eh, there’s a very narrow window of scientific knowledge and ability where one will be aware of this apparent problem, while also not being aware of the solution. I don’t see it as being worth worrying about.
To these add:
I think overall you just need to be aware of what you’re talking about when using the ambiguous term “the speed of gravity”. If you read Steve Carlip’s paper he notes that even in the electric field terms dependent on instantaneous position appear if you choose the Coloumb gauge. Of course though you would expect the speed of propagation of a force to be a bit more fundamental than being merely dependent on gauge choice.
So even in electromagnetism there are some ambiguities that must be dealt with to find a robust and general definition for the speed of propagation of the field. In general relativity though there is an additional ambiguity that the field is in fact the metric describing the spacetime geometry. This ambiguity unfortunately can never be completely overcome to get a completely unambiguous and completely general definition of the speed of propagation of gravity in general relativity.
Steve Carlip in creating a context to discuss the “speed of gravity” uses the weak-field approximation and it is worth noting their is a bit of circularity going on here. The aim of the weak-field approximation is to decompose the metric into a background spacetime and field which are invariant under (a restricted class of) global Lorentz transformations and global Lorentz symmetry of such a field will lead you to a propagation speed of c in short order. I.e. the propagation speed of gravity as c in this case can be seen as an artifact of the weak-field approximation rather than a general property of general relativity. However the circularity is also justified in creating a context in which the speed of propagation of gravity makes sense.
Just to clarify my last post a little as it may be too inaccessible:
When you are talking about the “speed of gravity” you need to be aware of exactly what you mean by that otherwise there is a lot of room for confusion. What we’re really interested here is the propagation speed, which is the speed that information travels in the gravitational field. Even in electromagnetism, where there is an unambiguous propagation speed (i.e. the speed of light, c), there’s a few pitfalls which you could fall into which will lead you to identify the wrong speed as the propagation speed.
In general relativity gravity is described by the curvature of spacetime and this brings a complication into finding the propagation speed of gravity you can’t ever fully get round. To understand what this complication is we need to think about what curvature is. Taking a very simple example of a curved space: a sphere; we might ask how could someone on that sphere detect that the space is curved. One simple way would be to draw a triangle on the sphere, as the angles of a triangle on a spherical surface add up to greater than 180 degrees. However one thing to note is that as the lengths of the sides of the spherical triangle go to zero, the sum of the angles goes to 180 degrees. What does this tell us? That curvature isn’t the property of any single point on the sphere. What implications does this have for the gravitational field? For an electric field it makes sense to say the electric field at point A is much stronger than at point B, however for curvature (i.e. the gravitational field) it doesn’t have any meaning to talk about one point being more curved than another. The reason this makes the speed of propagation of gravity hard to define is that the information transmitted by the gravitational field exists over a fuzzily-defined volume which brings in an element of ambiguity to the definition which can never be got rid of.
The usual way of defining the speed of gravity is to use the weak-field approximation. The weak-field approximation is just a way of taking the gravitational field of GR and making it much more like the electromagnetic field by divorcing it from the curvature of spacetime. This will work as long as the gravity is weak and the relative speeds are much less than c. However the intrinsic aims of the weak-field approximation automatically lead to a speed of propagation of gravity of c, so using the weak-field approximation to find out the speed of propagation of gravity is a little circular. The saving grace though is that the weak-field approximation specifically works when gravitational fields look very much like they obey the laws of Newton, which is largely the world we live in.