# “Speed” of Gravity and Speed of Light

Some threads here touching speed of gravity made me think about that. This lead to some questions.

• The speed of gravity was not measured until today (at least there are no undebated papers to that effect).

• It seems common knowledge/belief among physicists that the speed of gravity is the same as the speed of light.

And this is my question: Is that speed of light = speed of gravity a result of GR or is that fed into the theory? Or is there some evidence from other sources than GR for this? Does the same speed imply some deep-lying relation between gravity and electromagnetism?

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Note that Newtonian gravity moves at infinite speed. – Carl Brannen Mar 17 '11 at 0:45
duplicate? physics.stackexchange.com/q/5456 – endolith Nov 18 '11 at 5:15

## 4 Answers

The special theory of relativity is really enough to see that gravitational signals have to propagate by the speed $c$ which we call "speed of light" because the light is the most commonly understood entity that is moving by this maximum speed. Special relativity is OK to describe infinitesimal deformations of spacetime.

All other massless particles also have to propagate by the same speed $c$ because this speed $c$ is needed to enhance the vanishing rest mass to a finite total relativistic energy. And gravitons are inevitably massless because they don't pick any preferred reference frame - or, alternatively, because gravity is a long-range force. Massive particles could only induce short-range forces (similar to the weak nuclear force caused by W,Z bosons).

Any particle - e.g. neutrino - whose energy is much greater than the rest mass is moving nearly by the speed of light, too. The same thing would hold for massless scalar particles such as the "moduli" (their quanta) if they existed. It's an elementary consequence of the formulae of special relativity. The speed of light is the maximum speed that the information and material objects may pick, by causality, and it's also the typical speed that massless (exactly) and light (approximately) particles actually choose.

So the answer to your last question is No, the appearance of the same speed $c$ doesn't imply any additional dynamical relationship between electromagnetism and gravity - it's a direct and elementary consequence of the special theory of relativity - and its kinematics - that was fully understood in 1905. The importance of the speed $c$ in the scheme of things - because of special relativity - is so high that adult physicists use units in which $c=1$ and they are never ever surprised when $c$ plays an important role - it's exactly the same degree of "surprise" as if the number $1$ appears somewhere in maths.

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You could, theoretically, have a theory of gravity where the graviton is massive, and then gravity would propagate with $v<c$. That gravitational signals propagate with $c$ is most certainly a result derived from GR (and most competing theories of gravity, admittedly). – Jerry Schirmer Mar 16 '11 at 23:55
Dear @JerrySchirmer, if the "graviton" were massive, then the force wouldn't decrease as $1/r^2$ but approximately exponentially and it wouldn't be long-range. Consequently, it would never be called "gravity" because it wouldn't produce a detectable force from the planets. Gravity means that it is a long-range force linked to the spacetime geometry, as we know from Einstein, and such a graviton has to be massless. – Luboš Motl Aug 30 '13 at 9:55
We may also use the word "gravity" in a generalized way - surely for massive KK modes of higher-dimensional gravity and perhaps for speculative theories with massive spin-2 particles - but it is not "the" gravity. – Luboš Motl Aug 30 '13 at 9:56
"adult physicists"? You mean there are child physicists too? – Lawrence I. Siden Dec 26 '15 at 2:32
Yes, that's what I meant. The phrase came from an undergraduate instructor of ours, in this very context of sensible units. The idea is that schoolkids are taught to be very careful about using SI units and nothing else, and so on, and this is the teacher-led "disciplined" attitude that most physicists know even when they're high school students. But in the college,they should get adult and be in charge of the conventions they adopt. They should understand why they adopt a convention and whether and how they may avoid it. As adults, they can drink alcohol and start to use more conveneitn units – Luboš Motl Dec 27 '15 at 8:38

I think the main argument would be causality. If gravitational disturbances traveled faster than light, presumably you could use them to convey information backwards in time. Although now that I think about it, that argument is based on special relativity. I can't think of a reason it wouldn't carry over to GR, but I don't know whether anyone has explicitly checked.

You can derive from GR the fact that gravitational waves (disturbances in the weak-field approximation) propagate at speed $c$.

I'm not aware that any experimental measurements have been done, since gravity is a weak force and is difficult to measure. Building a "gravity telescope" is a lot more complicated than a regular telescope, although there are plans in place, e.g. LISA, which might be able to detect gravitational waves for the first time, if it gets funded and built.

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Sorry to bring this up again...maybe a new question should be asked? Could you possibly elaborate on the derivation of the speed of propagation of gravitational waves directly from the field equations? I have been thinking about this lately and can't figure a way to show this – TylerHG Mar 7 '15 at 21:01
@TylerHG that would definitely be a matter for a new question. But I'm fairly sure the derivation is available elsewhere on the internet, and definitely in some GR textbooks. So you should check the resources you have available before asking about it. – David Z Mar 8 '15 at 6:27
If gravitational disturbances traveled faster than light etc : if it was true, metric would be changed and then causality would stay protected. This change would introduce conceptual difficulties and the usage of 2 speed limits but not any kind of acausality – igael Jan 22 at 11:44

Yes, there is another derivation: String Theory. The action and its QFT implies the existence of not only tachyons (which would move faster than $c$), but two massless particles of spin $1$ and $2$ ... the spin-1 particle is the photon, and the spin-2 particle is the graviton (both must necessarily travel at speed $c$ because of their mass).

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Is that speed of light = speed of gravity a result of GR or is that fed into the theory?

"speed of light = speed of gravity" is fed into the theory of GR.

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Again an unexplained minus. All the time I get minuses from the same individual for unknown reasons. – Energizer777 Nov 15 '15 at 21:21
While (if I remember correctly) I have not voted on any of your posts, I'll try to say this as nicely as possible: Low-quality answers get downvotes from many different people. Interpret that as you will. – HDE 226868 Nov 15 '15 at 22:56
All the time I get minuses from the same individual for unknown reasons. Given that there's thousands of registered users capable of downvoting, what makes you think it's the same one? – Kyle Kanos Nov 15 '15 at 23:29
This is not a low quality answer. It is exactly the right answer for the question of the OP. Albert Einstein elaborated his theory (GR) in such a way that the speed of light and speed of gravity are the same. The coincidence is not a spectacular result like the tunnel effect which was unsuspected and surfaced from Schrodinger's equation after the relation had been discovered. – Energizer777 Nov 16 '15 at 1:23

## protected by Qmechanic♦Nov 16 '14 at 15:36

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