# Speed of Gravity: a final explanation **URL:** \ **Category:** Factual Questions\ **Created:** [March 19, 2015, 2:54pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383 "2015-03-19T14:54:16Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [March 19, 2015, 2:54pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/1 "2015-03-19T14:54:16Z")
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: > **[What is the speed of gravity?](https://www.straightdope.com/21343230/what-is-the-speed-of-gravity)** > > A STAFF REPORT FROM THE STRAIGHT DOPE SCIENCE ADVISORY BOARD Over the years there have been several threads re-asking the question: > **[The Speed of Gravity](https://boards.straightdope.com/sdmb/showthread.php?t=8916)** > > I don’t mean 32 ft./sec/sec. I mean, does the “pull” of gravity travel at C? Example: A super-massive star suddenly appears 930 million miles away from Earth in the opposite direction from Ol’ Sol. Do we turn right immediately or wait an hour or so? > **[Light, Gravity, and speed limits.](https://boards.straightdope.com/sdmb/showthread.php?t=75707)** > > I came across this site a few days ago, and it got me to thinking. In Relativity, gravity is a bend in the space time fabric of the universe caused by mass. It was also predicted by Einstien that it propogates at the speed of light. Correct? Well,... > **[Yet Another Speed of Light question: Gravity](https://boards.straightdope.com/sdmb/showthread.php?t=31905)** > > Physics question in two parts: (1) What is the propagation speed of gravitational force? I’m no physicist, but it seems to me that if Gravitational energy moved only at light speed, orbits would not be possible because planets, moons, etc would be... > **[Meaning of the "speed of gravity"](https://boards.straightdope.com/sdmb/showthread.php?t=134186)** > > Interesting scientific discussion about measuring gravity. "Meaning of the “speed of gravity” > **[The Speed of Gravity=Light?](https://boards.straightdope.com/sdmb/showthread.php?t=155190)** > > Ok, so my question isn’t actually about whether or not the speed of gravity is equal to that of light, however, after being given a link from BBC News about the speed of gravity being proven as equal to the speed of light I got a little confused.... > **[Another "speed of gravity" question.](https://boards.straightdope.com/sdmb/showthread.php?t=262369)** > > I’ve read a couple of interesting threads here on the speed of gravity, but can’t for thr life of me remember what that speed is. Gettin’ old, I guess, but I seem to remember a comparison to light speed. Anyway; What limits the speed of a mass in... > **[What is the speed of gravity?](https://boards.straightdope.com/sdmb/showthread.php?t=368375)** > > According to this article http://news.bbc.co.uk/1/hi/sci/tech/4923396.stm scientists expect soon to be able to see the first evidence of gravitational waves. The article states that these waves would travel at the speed of light. Since light... > **[A question about the speed of gravity and black holes](https://boards.straightdope.com/sdmb/showthread.php?t=579430)** > > Or, why do black holes have accretion disks? The obvious answer is gravity. But wait! We have experimental knowledge that gravity propagates at the speed of light. And a black hole has so high a gravity that nothing, not even light, can escape. So... I recently came across [this article, which imho is the best explanation](https://medium.com/starts-with-a-bang/what-is-the-speed-of-gravity-8ada2eb08430) 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: > [@](#): > > Want to know something that’s kind of messed up? If that was the only thing that was different from Newtonian gravity, Einstein’s theory would be wrong. The predictions that we’d get for planetary orbits, based on where objects like the Sun and the other planets were 8+ minutes ago (or whatever the light-travel time for the planet in question was) are different enough from even observations a century ago that General Relativity would have been determined to be false right away. This effect on its own demanded that, if Newton’s theory was right, the speed of gravity be at least 20 billion times faster than the speed of light! > > But there is another piece to the puzzle. > > The Earth, since it’s also moving, kind of “rides” over the ripples traveling through space, so that it comes down in a different spot from where it was lifted up. It looks like we have two effects going on: each object’s velocity affects how it experiences gravity, and so do the changes that occur in gravitational fields. What’s amazing is that the changes in the gravitational field felt by a finite speed of gravity and the effects of velocity-dependent interactions cancel almost exactly! The inexactness of the cancellation is what allows us to determine, observationally, if Newton’s “infinite speed of gravity” model or Einstein’s “speed of gravity = speed of light” model matches with our Universe. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [March 20, 2015, 12:39am UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/2 "2015-03-20T00:39:29Z")
It’s (almost certainly) based on this paper by Steve Carlip [this paper](http://arxiv.org/abs/gr-qc/9909087), 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. ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [March 20, 2015, 1:07am UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/3 "2015-03-20T01:07:47Z")
> [@Asympotically\_fat](#): > > 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. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [March 20, 2015, 12:48pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/4 "2015-03-20T12:48:56Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 20, 2015, 2:05pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/5 "2015-03-20T14:05:44Z")
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. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [March 20, 2015, 2:13pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/6 "2015-03-20T14:13:19Z")
> [@Lumpy](#): > > 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: > [What is the speed of gravity? - The Straight Dope](http://www.straightdope.com/columns/read/2095/what-is-the-speed-of-gravity) > > Over the years there have been several threads re-asking the question: > [The Speed of Gravity - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=8916) > [Light, Gravity, and speed limits. - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=75707) > [Yet Another Speed of Light question: Gravity - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=31905) > [Meaning of the "speed of gravity" - Miscellaneous and Personal Stuff I Must Share - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=134186) > [The Speed of Gravity=Light? - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=155190) > [Another "speed of gravity" question. - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=262369) > [What is the speed of gravity? - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=368375) > [A question about the speed of gravity and black holes - Factual Questions - Straight Dope Message Board](http://boards.straightdope.com/sdmb/showthread.php?t=579430)… To these add: > **[The Sun vanishes. Earth keeps orbiting just fine for 8 min 20 sec](https://boards.straightdope.com/sdmb/showthread.php?t=720509)** > > See subject. This is true, right? Hard to understand. The fact that the Sun could be gone but we wouldn’t see/know it for a while seems much easier to understand. Self-evident, really. But gravity is information, too. I just had a brainstorm, in... ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [March 21, 2015, 4:26pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/7 "2015-03-21T16:26:17Z")
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. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [March 21, 2015, 9:59pm UTC](https://boards.straightdope.com/t/speed-of-gravity-a-final-explanation/715383/8 "2015-03-21T21:59:19Z")
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](http://mathworld.wolfram.com/SphericalTriangle.html). 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.